The fracturing of a hip prosthesis stem at its neck, in the absence of a trauma, is an extremely rare but serious adverse event. The patient in our case was young, active, and tall, thereby putting high mechanical loads on the prosthesis. Radiographs of the initial procedure and blood and synovium analysis showed no abnormalities. Analysis of the stem revealed niobium-rich precipitates, that is, alloy artifacts, at the introducer stud hole. The mechanically vulnerable location of the introducer stud hole, combined with alloy artifacts at that location and high mechanical stress, ultimately led to failure of the prosthesis. As younger and heavier patients will demand hip arthroplasty in the future, simple stem design adaptations should be considered to prevent stem fractures at the introducer stud hole. Total hip arthroplasty (THA) is one of the most commonly performed procedures in orthopedic surgery and is one of the most successful major surgeries of modern medicine . The Exein vivo because of failure of the metal alloy. A recent study of 80 retrieved fractured Exeter prostheses in the period 1991-2008 showed that this type of fracture is very rare, with a minimum reported failure rate of 1 in 10.000 stems (0.01%) [Although very unlikely, a femoral stem can fracture  (0.01%)  or estimWhenever an implant fails, it is common practice that the manufacturer retrieves the implant for further analyses . As suchIn this case report, we set out to synthesize all the available and obtainable information on a recent patient case that suffered from an Exeter stem fracture that initiated at the introducer hole. The unique “perfect storm” that, in this case, ultimately led to failure of the Exeter femoral prosthesis provides important implications for future stem designs and surgical considerations.A healthy and active 44-year-old male patient  presented at our emergency department with pain in the left groin or hip. A sudden “crack” had occurred during a low-speed pivoting movement while working as a kitchen chef and left him unable to bear weight. Exactly 6 years earlier, the patient had been treated for a 4-week-old fracture of the left hip with hybrid THA ; the stem was cemented at that time because of the superior survival of cemented stems after femoral neck fractures [in situ stem fragment appeared well-fixed without signs of loosening or infection. The proximal neck fragment and taper were well-engaged with the femoral head. The acetabular component had an intact rim with no signs of neck impingement, no local display of metallosis, and no evidence of eccentric wear of the polyethylene liner. The stem was removed without damaging the intact cement mantle. In brief, a hole was drilled  are shown in An overview of the blood metal ion concentrations over time is shown in Histopathology of the obtained capsule tissue  shows deA:at the stem away from the fractured surface;B:surface perpendicular to the initiated crack near the stud hole;C:surface perpendicular to the stud hole.Cross-sections of the implant were processed at the Eindhoven University of Technology using successive grinding and polishing of the surfaces to obtain a high-quality surface finish as required for orientation imaging microscopy. Samples were taken from 3 different locations :A:at theCross-section B revealed white spots under the scanning electron microscope which appeared to be niobium (Nb)-rich phases on higher magnification . Energy Orientation imaging microscopy was used at cross-section B to analyze the grain structure and orientation, allowing to visualize the microstructure of the base material (austenite). The average grain size was ~5 microns. The global microstructure was visualized using electron backscatter diffraction imaging , wherebyThe fracture plane and the microstructure of the material in the fracture plane were initially assessed using stereomicroscopy. The fracture plane mainly consisted of a smooth surface with striations and beach marks, which are characteristic for fatigue failure. The residual crack surface was rough and dimpled, which is the surface where the prosthesis ultimately failed under loading. As the 2 stem parts were in frictional contact with each other, surface damage in the form of abrasions emerged .Figure 9The introducer stud hole was further analyzed using secondary electron and backscattered electron analyses. The presence of multiple smaller cracks near the stud hole and near or at the Nb-rich precipitates was identified .Figure 1This case report is not the first to describe a fracture that initiated at the introducer hole of an Exeter stem . Nor is The patient in this case report is not a typical senior with low physical demand. Instead, it is a young, tall, heavy, and active male. Not coincidentally, this seems to be the category at risk for a fracture of the femoral prosthesis itself, particularly at the neck .Perhaps the odds of the combined presence of unfavorable patient and implant determinants in a single patient are generally very low. However, the consequence of implant failure on individual level, such as the risk of impaired clinical outcomes and infection after revision surgery, could give rise to high morbidity and even mortality and is therefore unacceptable ,19. More1)high stress due to an undersized prosthesis,2)cantilever bending resulting from good distal fixation in the presence of an inadequate proximal mantle, and3)varus orientation of the stem.According to Jazrawi et al., there are 3 surgical factors that can result in failure of a cemented stem :1)high sIn this case, the prosthesis was neither undersized nor was it placed in varus. Inadequate medial support combined with a well-fixed distal portion of the stem mostly results in a body fracture , which mIn addition to the aforementioned surgical factors, Swarts et al. suggest that fretting corrosion or wear can also contribute to the implant failure . We founIt has been suggested that the cause of neck fractures lies in the use of large heads with augmented offsets, in combination with overweight patients . HoweverNonetheless, as more Exeter stems are placed in obese patients with a variety of offset, stem, and head sizes, surgeons must be aware of the risk of stem fracture. Wherever possible, the largest stem that will fit the femur with correct size offset should be used, and heads with larger necks should be avoided .In present case, we performed a cement-in-cement revision, which implied the implantation of an undersized stem. Indeed, in light of the acquired knowledge outlined previously and in previous reports , one couOverall, the material reveals a rather homogeneous microstructure. The heterogeneities that stand out are the Nb-rich phases. Niobium is typically used in austenitic stainless steels as a stabilizing element. The higher C content entails a risk for the formation of Cr carbides, which tend to deplete the austenitic matrix from C along the grain boundaries, possibly resulting in corrosion . The Nb has a stabilizing role by preventing the formation of Cr carbides. The addition of Nb to stainless steels is known to induce the precipitation of Nb carbonitrides, in different sizes and shapes . The eneFrom the experimental analysis, there are indications that the interfaces of the precipitates are rather weakly bonded. This also means that the precipitates are easily “broken out,” for example, during mechanical processing treatments. Voids were also observed at and near the precipitates.The fractography revealed the presence of multiple smaller cracks near the stud hole and near or at the Nb-rich precipitates. The present study indicates that the manufacturing of the stud hole may well have induced these cracks, or at least initiated them. As the stem was removed by means of a separately drilled hole in the stem, the introducer hole remained untouched. We therefore postulate that cracks in the introducer stud hole were formed during the manufacturing of the prosthesis. Most likely, the Nb-rich precipitates (CrNbN zeta phase) are abrasively removed upon machining the stud hole, leaving behind regions of stress concentrations and tiny microcracks. These likely serve as initiators for fatigue cracking.Beach marks and fatigue striations clearly indicate a fatigue failure mode . A hole Moreover, the Exeter stem design consists of a lever-arm geometry. From a pure mechanical perspective, it is, therefore, remarkable that the relatively large introducer hole is manufactured at its current location where, provided that the stem is adequately cemented in the femur shaft, the bending moment is large. From a mechanical perspective, it would be relatively easy to propose a solution that does not entail such undesirable stress concentrations. For instance, future stem designs could reduce the normal stress due to the bending moment at the introducer hole by placing it more lateral, that is, at the wider part of the stem, such as with the small 30-mm cemented Exeter . AnotherBlood metal ion concentration levels were elevated when the patient presented with the failed prosthesis. However, the observed levels were all lower than the highest values found in well-functioning Exeter prostheses after 1 year of follow-up . MoreoveThe histologic patterns of joint endoprosthesis particle disease would consist of the accumulation of macrophages and multinuclear giant cells in the neosynovium. Although abrasion particles differ in quality, quantity, and size subject to the materials and the intensity of the mechanical stress involved, most wear particles are not diagnosed by light microscopy examination becaue of their small size . As the Failure of the metal alloy of a hip prosthesis is an extremely rare but serious adverse event. In this case, the combination of high mechanical stress and an alloy artifact at a mechanically vulnerable location provided the “perfect storm” which ultimately led to the cascade of crack initiation, metal fatigue, and implant fracture. Although rare, this was not the first case and, most certainly, will not be the last. Simple design adaptations could and should prevent the current fracture from happening in the future, especially since younger and heavier patients will demand hip arthroplasty in the future.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.The author(s) confirm that informed consent has been obtained from the involved patient(s) or if appropriate from the parent, guardian, power of attorney of the involved patient(s); and, they have given approval for this information to be published in this case report (series).


Compared to time-consuming and unreliable manual analysis, intelligent fault diagnosis techniques using deep learning models can improve the accuracy of intelligent fault diagnosis with their multi-layer nonlinear mapping capabilities. This paper proposes a model to perform fault diagnosis and classification by using a time series of vibration sensor data as the input. The model encodes the raw vibration signal into a two-dimensional image and performs feature extraction and classification by a deep convolutional neural network or improved capsule network. A fault diagnosis technique based on the Gramian Angular Field (GAF), the Markov Transition Field (MTF), and the Capsule Network is proposed. Experiments conducted on a bearing failure dataset from Case Western Reserve University investigated the impact of two coding methods and different network structures on the diagnosis accuracy. The results show that the GAF technique retains more complete fault characteristics, while the MTF technique contains a small number of fault characteristics but more dynamic characteristics. Therefore, the proposed method incorporates GAF images and MTF images as a dual-channel image input to the capsule network, enabling the network to obtain a more complete fault signature. Multiple sets of experiments were conducted on the bearing fault dataset at Case Western Reserve University, and the Capsule Network in the proposed model has an advantage over other convolutional neural networks and performs well in the comparison of fault diagnosis methods proposed by other researchers. In modern industry, machines are a key part of the production process. Failures of these machines can cause significant economic losses and sometimes pose a threat to the people who use them. In fact, more than 50% of mechanical defects are related to bearing failures ,2. ThereTraditional fault diagnosis techniques usually fail when analyzing complex faults without further fault information. The intelligent diagnosis theory based on machine learning has recently become the core of research and application ,7. The iIn recent years, CNNs have also been used in fault diagnosis, due to their adaptive feature extraction capabilities. Convolutional neural networks or CNNs were first proposed by LeCun . After tThe above study demonstrates convolutional neural networks are a feasible solution to the fault diagnosis problem. CNNs are able to guarantee diagnostic efficiency without the experience of professionals and have a certain anti-noise ability in noisy environments. However, the input images of these schemes are derived from simple steps, allowing the performance of the entire scheme to be focused on the CNN model. However, CNNs have unavoidable drawbacks in fault diagnosis classification due to their inherent defect of translation invariance. After pointing out this question, Hinton proposed a solution—the Capsule Network . TherefoIn this paper, a new fault diagnosis method named GAFMTF-CapsNet is proposed. The original vibration signal is first encoded and converted into a two-dimensional grayscale image using GAF and MTF, and then the encoded image is input into a CNN or capsule network for training. During the experiment, we found that the GAF-encoded image preserves more complete static information, and the MTF-encoded image preserves the dynamic information of the original vibration signal. Therefore, the principle of GAFMTF-CapsNet is that the images obtained by these two conversion methods are fed as two channels into a Capsule Network with a small convolution kernel, so that this model can extract the static and dynamic characteristics of the original vibration signal with fault features. The excellent experimental performance of the model on the bearing dataset was investigated at Case Western Reserve University. The remainder of this paper is organized as follows: With the rapid development of computer vision technology, the idea of using computer vision techniques to classify raw vibration signals has been inspired. The key is the conversion method to encode the vibration signal into a two-dimensional image (or array) acceptable to computer vision, and the process is required to reveal the features and patterns of the original vibration signal as much as possible.The first transformation method is the Gramian Angular Field (GAF). The encoding of the time series into images by means of GAF polar coordinate-based matrices is able to maintain the correlation between the one-dimensional signal and the time series in Gramian matrices, where each element is actually the value of the trigonometric function of the angle . The oriAnother transformation method is the Markov Transition Field (MTF). The Markov transition field is a framework for encoding dynamic transition statistics, representing Markov transition probabilities sequentially to preserve information in the time domain . For a gIn order to incorporate the temporal information into squashing” as shown in Equation (7):Capsule networks were proposed by Hinton in 2017 . The uni(1)The prediction vector (2)Update the vector (3)The input capsule (4)Update (5)Return the final output vector after Since the capsule is a vector unit different from the neuronal scalar, the iterative update algorithm of the convolutional neural network will no longer be applicable. For the vector update, the capsule network uses the dynamic routing algorithm, which updates the weight parameter Although the capsule network has an excellent feature extraction ability, it generates too many parameters at the input of large-size images, which greatly reduces the speed of network training. In order to reduce the number of parameters in the capsule network, improve the speed of the network, and ensure that not too much information is lost, a small-sized convolutional layer is constructed before the capsule layer to compress the image size and increase the depth to ensure the integrity of the input image information.Because vectors in capsules are different from scalars, we use the length of the vector to represent the probability of positive correlation, so the model marginal loss function in this paper is the loss function, and each digital capsule Splitting. The original vibration signal is divided into appropriate signal segments to make it suitable for later encoding transformation. We will experiment to determine the appropriate signal split length.Encoding transformation. By the above transformation method, every segment is converted into a one-channel or two-channel image. The entire original vibration signal is converted into a large number of feature images. In this step, three transformation methods are considered feasible. There is GAF for the one-channel image, MTF for the one-channel image, and GAF and MTF for the two-channel image. We will compare the diagnostic accuracy of these methods in the experiment.Images datasets. The feature images are classified according to the fault type of the original vibration signal to form the image dataset.Network model. The image dataset is fed into the configured neural network model for training and testing. The image dataset will be fed into the conventional convolutional neural network and the proposed improved capsule network. We compare and summarize the advantages of the proposed network in the following experiments.The proposed fault diagnosis method has four main steps:The whole fault diagnosis process is shown in Our experiments were conducted using the Case Western Reserve University bearing dataset, which covers experimental drive-side bearing data sampled at 12 kHz and 48 kHz and 12 kHz fan-side bearing data. The experimental equipment included a 1.5 kw motor, a torque sensor/translator, and a power test meter . The expThe simulation tests are conducted by a personal computer with CPU (Intel(R) Core i7-10750H @ 2.60GHz) and GPU (NVIDIA GeForce RTX2070super 8G).In the first experiment, we put GAF images into a capsule network or convolutional neural network model. First, we processed the raw vibration signal to make it easy to convert it into a GAF image. If you take a segment of the signal of length The convolutional neural network was chosen to use the VGG16 network. The VGG16 network is a deep network model developed in 2014 by the Computer Vision Group at the University of Oxford together with researchers at Google DeepMind . The netThen, we input the encoded GADF and GASF images into VGG16 and CapsNet, respectively, for training. The experimental results are shown in When the size is 64, it is obvious that it is difficult to guarantee that an image contains complete information about the fault features. Images sized 128 have the best performance, and larger images contain more information but cause the network parameters to increase and make the training time of the network much longer.Except for the case of incomplete information at size 64, the experiments on images of other sizes show that GADF has higher accuracy than GASF.In the comparison between VGG and CapsNet, CapsNet performs better than VGG in most cases, but there is no significant advantage.The experiment was summarized into the following three conclusions:The second experiment uses MTF images input into the CapsNet and VGG16 networks. First, the original vibration signal is converted into an MTF image. The size of the MTF image is not fixed and is determined by both the length of the input signal and the size of the fuzzy kernel. The MTF technique embodies the dynamic characteristics of the original vibration, so the largest possible size of the signal is converted into an MTF image. However, too large an MTF input size can reduce the number of available training images or make the training set data too repetitive to extract fault features. Moreover, too large a fuzzy kernel size can reduce the MTF to the size we need, but this also causes information loss. For these two reasons, MTFs are required to have smaller fuzzy kernels and appropriate input vibration signal lengths.However, in the actual experiments, we found that the experiments hardly showed satisfactory results regardless of the input length of the MTF images. In It is concluded from Experiment 1 and Experiment 2 that the network model can extract different fault features from GAF images and MTF images, and that GAF retains much of the static information and MTF retains more dynamic information. Therefore, we consider a network model that makes it possible to extract fault features in GAF and MTF for the diagnosis and classification of faults separately. In addition, since the signal segmentation length that makes GAF work best is not the same as the signal segmentation length that makes MTF work best, we need to unify the two coded images by compromising one to the other.In this experiment, we want to let the deep learning model extract more complete fault features, so the model can extract fault features in both GAF images and MTF images. We encode the same vibration signal with both GAF and MTF, and the two images (arrays) after encoding are used as the two input channels of CapsNet. In this process, we need to change the CapsNet structure so that it takes a two-channel image as input. In addition, the size at which the GAF image appears best is different from the MTF image. We had to compromise the size of the MTF image based on the optimal size of the GAF image. We selected a size of 128 × 128 for this two-channel image. So, we need to split each signal in the fault dataset into vibration signals with lengths of 128. The processed images are divided into four 4-category datasets and four 10-category datasets, which are presented in The converted image dataset is input into CapsNet for training, and the structure of CapsNet for 10-category and 4-category scenarios is shown in These eight datasets were trained on CapsNet and commonly used convolutional neural networks and compared. We experimented five times with cross-validation and averaged the test set accuracies of the five trials to produce In the figure, the eight confusion matrices correspond to the training results of eight datasets on CapsNet: ABCD is four-category datasets, where “NO” means no fault, “OF” means outer fault, “RF” means roller fault, and “IF” means inner fault. EFGH is 10-category datasets, where “NO, OF, RF, and IF” represent the fault location, and the number after the location is the degree of fault. We can see the failure diagnosis through the eight confusion matrices in Sometimes the number of datasets does not necessarily mean the network is adequately trained. The datasets of the previous experiments were in a ratio of 8:2 for the training set and the test set. We re-trained with dataset D and dataset H to explore the performance with a smaller training dataset. In this experiment, we re-divided dataset D and dataset H. CapsNet was retrained inputting the new dataset, which had ratios of 6:4, 7:3, 8:2, and 9:1 for the training set with the test set. We performed multiple trials to reduce errors by cross-validation. The average accuracy is shown in We find that for a four-category dataset, reducing the training set does not lead to a significant decrease in accuracy. Even 60% of the training set is enough for CapsNet to extract fault features. For the 10-category dataset, 70% of the training set can still obtain good diagnostic accuracy. Fewer training episodes would not allow CapsNet to extract enough fault features and thus the accuracy would be significantly reduced.Through the results, it seems that CapsNet has higher accuracy than other convolutional neural networks. However, there is no significant advantage of GAFMTF-CapsNet in terms of accuracy when compared with the methods for fault diagnosis in other studies, which are presented in Although the proposed method is not the best, the GAF and MTF transformations are proved to be feasible for fault feature extraction of bearings.The GAF technique retains sufficient bearing failure characteristics. Neural networks more easily extract fault features and perform classification and diagnosis by GAF images. For the capsule network and VGG network, the original vibration signal cut into 128 and converted into a 128 × 128 GAF image has a better performance compared to other cut lengths. GAF-CapsNet has, at most, 99.17% accuracy in training 128 × 128 GAF images.For different sizes of signal cuts and output image sizes, MTF is only less than 80% accurate in CapsNet and VGG. The MTF technique loses a large number of fault characteristics, but also retains some of them. MTF retains more dynamic features and less static information than the GAF technique.The four-category dataset and the 10-category dataset have an average accuracy of 99.8% and 99.5% on GAFMTF-CapsNet. Using GAF and MTF images as two-channel inputs in the neural network allows the network to be trained to obtain both the static information by GAF and dynamic information by MTF for the vibration signal. For this signal processing method (GAFMTF), CapsNet has 1–2% higher diagnostic accuracy than VGG16 and ResNet-50, and 5–10% higher accuracy than LeNet-5.In this paper, the application of GAF and MTF techniques in bearing fault diagnosis is studied and a feasible fault diagnosis method (GAFMTF-CapsNet) is proposed. In the experiment, we obtained the following conclusions:Compared with other fault diagnosis methods based on deep learning, the proposed GAFMTF-CapsNet has higher diagnostic accuracy. In addition, the proposed method does not require any a priori knowledge, so it can be applied more widely. However, the use of GAFMTF-CapsNet requires the advance acquisition of the operating signals of the same bearing in the fault condition. Moreover, the raw vibration signal may be inaccurate. These issues will be investigated later to further improve the method.


Non-union rate after tibial fractures remains high. Apart from largely uncontrollable biologic, injury, and patient-specific factors, the mechanical fracture environment is a key determinant of healing. Our aim was to establish a patient-specific simulation workflow to determine the mechanical fracture environment and allow for an estimation of its healing potential. In a referred patient with failed nail-osteosynthesis after tibial-shaft fracture exchange nailing was performed. Post-operative CT-scans were used to construct a three-dimensional model of the treatment situation in an image processing and computer-aided design system. Resulting forces, computed in a simulation-driven workflow based on patient monitoring and motion capturing were used to simulate the mechanical fracture environment before and after exchange nailing. Implant stresses for the initial and revision situation, as well as interfragmentary movement, resulting hydrostatic, and octahedral shear strain were calculated and compared to the clinical course. The simulation model was able to adequately predict hardware stresses in the initial situation where mechanical implant failure occurred. Furthermore, hydrostatic and octahedral shear strain of the revision situation were calculated to be within published healing boundaries—accordingly the fracture healed uneventfully. Our workflow is able to determine the mechanical environment of a fracture fixation, calculate implant stresses, interfragmentary movement, and the resulting strain. Critical mechanical boundary conditions for fracture healing can be determined in relation to individual loading parameters. Based on this individualized treatment recommendations during the early post-operative phase in lower leg fractures are possible in order to prevent implant failure and non-union development. Despite current clinical advances diaphyseal tibial fractures are associated with delayed- and non-union rates of over 10% . The devThe aim of this study was, thus, to establish a simulation workflow based on clinical imaging data to (1) determine the pre- and post-treatment mechanical fracture environment in a tibial fracture revision case, (2) simulate the associated volumetric strain and octahedral shear strain resulting from patient weight-bearing, and (3) provide a clinical proof-of-concept over the treatment course.A 55-year old, female patient  was treated for an open distal tibial shaft fracture  with debThe simulation workflow is divided into three main steps: (1) the geometric model generation based on clinical imaging, (2) the computation of individual biomechanical parameters from patient monitoring, and (3) the performance of the final finite element (FE) simulations and follow-up mechanical data analysis.The basis of the geometric model creation is established on an image processing chain of various algorithmic steps in a semi-automated sequence. The starting point is the dicom image stack of the patient's post-operative CT scan combined with a six-rod bone density calibration phantom . The images were segmented into different masks  with an adaptive threshold procedure with respect to the calibration phantom, supplemented by a morphological close filter with isotropic values and a mask smoothing with a recursive Gaussian filter with anisotropic values. Afterwards, for each segmented mask an island removal, a cavity fill and a fill gaps with a priority order procedure was performed resulting in a high segmentation quality without detectable problems. In addition, the orthopedic trauma surgeons manually controlled the segmentation results of the fracture gap and if necessary corrected them. All image processing steps as well as the generation of the FE meshes were performed in the image processing and model generation software ScanIP . After segmentation was completed, a high-resolution adaptive FE mesh was created from the individual masks. Since all simulations were performed with the FE analysis and computer-aided engineering software suite Abaqus , quadratic tetrahedral FE of type C3D10 with straight lines were chosen. The material parameter assignment for the masks of the intramedullary nailing, the corresponding screws and the fracture gap were chosen as homogeneous materials with standard properties from literature. The Young's modulus for the nail and the screws was set to 108,000 MPa and the Poisson ratio was set to 0.37 . For theFor the bone mask, material properties with respect to the calibration phantom were defined, in order to derive an empirical elasticity-bone density relationship. For this purpose, a histogram analysis of the individual segmented rods was performed in a first step. Then, by means of a linear regression, a mapping of the Hounsfield units (HU) to the hydroxy apatite values from the calibration phantom was defined. This mapping provides the basis for the gray-scale-dependent definition of the material parameters representing local bone properties , 20. Herwith a fixed Poisson ratio of ν = 0.30. The ash density relation corresponding to the equivalent mineral density is in accordance with Les et al. . All matThe second step in our simulation workflow consists of monitoring the patient during normal forward gait by means of the full body motion capturing system Xsens MVN Awinda . The MVN Awinda system uses 17 wireless sensors, which are fitted on the body with adjustable straps and a specific T-shirt. The T-shirt is used to attach the sensors on the shoulder , one sensor on the sternum and one sensor on the pelvis. Tapes are used to attach the sensors to the biomechanically relevant segments: on the upper arms, on the forearms, on the thighs, on the lower legs and on the feet. Finally, two sensors are attached to both hands with special gloves and one sensor is fixed to the head with a headband. To obtain a simulation model of the failed treatment case of which only conventional radiographs but no CT data existed, a CT scan of an identical intramedullary nail was achieved. This CT scan was segmented in ScanIP and transferred to a computer aided design (CAD) file in stereolithography (stl) format using a mask to surface operation. The surface model was imported into the CT image stack after the exchange of the intramedullary nails. Along with a visual inspection by the treating trauma surgeons the surface model of the first treatment was aligned with the distal end of the new treatment and followed proximally. The positioning at the knee was performed according to the radiographs and the new treatment. Subsequently, the additional screw used in the first failed treatment compared to the new one was also integrated into the model based on the radiographs and the positional locations present in the associated intramedullary nail. In addition, all other screws were also adjusted corresponding to their type and positioning in the model. Then, the same workflow was applied to create the geometric model and associated material parameters, which is described in detail above. The further clinical course of our patient after the exchange nailing procedure was uneventful with undisturbed soft tissue healing and mobilization with full weight-bearing. At the final follow-up at 18 months the patient was walking free, without aids and back to her self-reported activity and pain level as before the initial fracture event. The radiographic controls showed a healed fracture situation with an mRUST score of 15 .The boundary conditions derived from the musculoskeletal simulations based on the patient's motion capturing data were applied on the knee in the computational model, while on the side of the foot fixed Dirichlet boundary conditions were defined. In this study, we focus on the mechanobiological approach based on the mechanical stimulus, as addressed in the works of Claes and Heigele  and ShefEstimating a tibial fracture healing potential based on readily available clinical information remains a challenge, especially immediately after the initial treatment. To identify the risk factors associated with delayed healing several clinical studies have been performed that have shown the overall influence of three general parameters: patient condition, fracture/implant type and morphology and soft tissue integrity/damage , 30, 31.post-hoc simulation results of the failed implant situation in our patient, where the highest amount of hardware strain was seen in the area, where the implant ultimately failed. As the initial fixation failed in a valgus direction, we also chose to perform a fibular plate osteosynthesis as part of the revision. However, the importance of fibula fixation in rather distal tibial fractures has not been clearly defined and biomechanical as well as clinical studies point toward a limited influence on torsional rigidity and maintenance of the resulting stability of the construct in a clinical context  for the publication of any potentially identifiable images or data included in this article.TP, BB, MO, and MR conceptualized the study, supervised its conduct (investigation), and prepared the manuscript. TP, BB, MO, and SD secured funding. BB, MO, and TP were involved in the clinical treatment and decision process. AB and JG provided and prepared the clinical imaging for further simulation (resources and investigation). KW, AA, MR, and SD performed the movement analysis and simulation . All authors contributed to the manuscript and approved the final version.This study was funded by the Werner Siemens Stiftung.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Monitoring instrumentation plays a major role in the study of natural phenomena and analysis for risk prevention purposes, especially when facing the management of critical events. Within the geotechnical field, data collection has traditionally been performed with a manual approach characterized by time-expensive on-site investigations and monitoring devices activated by an operator. Due to these reasons, innovative instruments have been developed in recent years in order to provide a complete and more efficient system thanks to technological improvements. This paper aims to illustrate the advantages deriving from the application of a monitoring approach, named Internet of natural hazards, relying on the Internet of things principles applied to monitoring technologies. One of the main features of the system is the ability of automatic tools to acquire and elaborate data independently, which has led to the development of dedicated software and web-based visualization platforms for faster, more efficient and accessible data management. Additionally, automatic procedures play a key role in the implementation of early warning systems with a near-real-time approach, providing a valuable tool to the decision-makers and authorities responsible for emergency management. Moreover, the possibility of recording a large number of different parameters and physical quantities with high sampling frequency allows to perform meaningful statistical analyses and identify cause–effect relationships. A series of examples deriving from different case studies are reported in this paper in order to present the practical implications of the IoNH approach application to geotechnical monitoring. Nowadays, monitoring systems play a key role in the study and description of natural phenomena, together with the analyses for what concerns risk prevention. This allows obtaining useful information for continuous and optimal management of infrastructures, landslides and critical events in general . The geo-The perception layer, consisting of a network of connected sensors responsible for collecting the data and transmit them to the elaboration center;-The data layer, which entails dataset storage and elaboration. This is an essential component in an IoT-based system since traditional approaches are usually unable to manage the amount of data generated by an automatic system;-The presentation layer, where monitoring outcomes are represented and made available for the end-user through dedicated mobile applications or web-based services.One of the major advancements introduced by innovative instrumentations is the possibility to overcome the so-called “manual philosophy”, thanks to the integration of Internet of things (IoT) technologies in the design process of automated monitoring systems ,5,6,7. WThis approach has found successful applications in the geotechnical monitoring field, with the integration of both traditional and innovative sensors for monitoring and early warning purposes. Some examples include the multi-device wireless monitoring of a sloped surface , as wellThe implementation of IoT-based procedures is the core component of the Internet of natural hazards (IoNH) approach . IoNH reThe ability of IoT tools to automatically acquire and elaborate monitoring data has laid the basis for the development of dedicated self-learning or machine-learning automatic software, able to analyze the dataset and apply self-check controls in order to provide a preliminary validation of raw data, excluding outliers and sensors errors. The statistical validation is possible thanks to the high sampling rate available with modern technologies . IoNH also relies on the possibility to record a large number of different parameters and physical quantities, obtaining a more accurate description of the ongoing phenomenon. This aspect permits to definition cause–effect relationships or failure predictions, sometimes only based on numerical data. Moreover, an automatic procedure would permit monitoring even rapid and impulsive events that manually operated tools would not be able to identify due to their lower sampling frequency.The management process requires the design and application of web-based representation platforms, making the monitoring results easily and quickly accessible for further analyses and interpretation . This asThis paper will focus on the features and applications of the IoNH system, which is intended to provide a new methodology to overcome the traditional approach that characterizes the geotechnical monitoring field. Particular attention will be dedicated to the different advantages resulting from the integration of these IoT-based components into automatic monitoring systems. Moreover, a series of examples taken from different case studies are reported in order to underline the methodology value in different aspects of the monitoring activity, e.g., power supply control, data elaboration procedures, cause–effect correlations, etc. Additionally, the following sections report a description of the IoNH structure and components, also exploring some details regarding the algorithms involved in the elaboration process.The IoNH approach is based on the experience acquired along 7 years of automatic geotechnical monitoring through a modular underground monitoring system (MUMS), from on-site sensors acquisition to results representation. MUMS was designed as an automatic inclinometer composed of several nodes (links) located at custom distances along a single chain, linked by an aramid fiber and a quadrupole electrical cable. The array functionality is automated, collecting multiparametric data through a remotely controlled datalogger and RS485 protocol . Since iCU queries sensors at the specified sample period and applies the first filter on the raw dataset, performing 64 readings and saving the mean value in an external SD card. Moreover, the datalogger is able to record any kind of traditional sensors featuring an analog output signal. This particularly useful feature permits the management of complex and diversified monitoring systems with a single logger, DB, software and web platform, with relevant advantages in terms of data management and visualization. The CU power supply comes from a lead battery recharged through a solar panel or, if possible, directly connected to the electrical line. Both these configurations are intended to provide a reliable power source, which is an absolute necessity for any acquisition system . MoreoveAs anticipated in previous paragraphs, one of the main features of the IoNH approach is the possibility to integrate a wide selection of different sensors. This characteristic is intended to provide a flexible and customizable system, able to adapt to different contexts according to the relevant parameters to be monitored. The most common configuration, designed to measures displacements in landslides and underground constructions, relies on microelectromechanical system (MEMS) sensors, composed of an accelerometer, a magnetometer, and a thermometer. In those cases where a higher resolution is needed , it is possible to integrate an electrolytic tilt sensor. It is worth mentioning that MEMS have a 360° measuring range, while electrolytic cells feature a full-scale value of ±25°. Additionally, the structure of MUMS-based arrays permits the exploitation of different sensor typologies in the same array, such as piezometers to detect water level variations  or high-The data transmission generally relies on 4G, 3G or GPRS lines with a UMTS router, while in some cases, it is also possible to use fiber optics leading to a local elaboration center. Raw data  are stored in a cloud DB and always available for a back analysis or subsequent elaborations by exploiting new algorithms or statistical filters. In the case of monitoring systems based on the IoNH structure, the elaboration process takes into account several variables, resulting in a quite complex and potentially expensive procedure from a computational point of view. For this reason, the system is designed to transmit raw data and calculate the results at the elaboration center or, alternatively, run on a specific elaboration center on-site.Recognition of spike noise;Coherence of gravity acceleration vector;Variability of gravity acceleration vector;Coherence of magnetic field vector;VVariability of magnetic field vector;Coherence of node temperature;Running average;Recognition of instrumental noise;Recognition of not-operating sensors.The elaboration algorithm, specifically designed for each MUMS-based application, converts electrical signals into physical units, removes spike noises and accidental errors, and calculates the final results. Self-check data controls are a fundamental aspect when dealing with the management of automated tools. In particular, MUMS devices exploit a multilevel automated control procedure implemented in the elaboration algorithm, relying on the verification of specific physical entities listed below :RecognitSpike noise (or impulse noise) is a sporadic and impulsive electrical disturb, related to sharp and sudden disorder in the signal, often related to external factors, which heavily contaminate the acquired data . The idefunction .The recognition of spike noises shows high performances if the dataset is centered . For thii;The frequency of data transmission is an important parameter because it determines the data elaboration and consequently the time period , identifies sensors with relevant malfunctions that would undermine their calibration. The variation (Equation (9)) could be related to instrumental noise that characterizes every electronic device, and it is eligible under a certain threshold  exploits a 3D MEMS and a 2D electrolytic cell , monitorMoreover, the redundancy measures provided by this approach play a major role in data analysis and validation processes . Figure As previously discussed, the management of a large number of multiparameter data with proper sampling frequencies could bring to the identification of significant cause-effects relationships, such as direct correlations between rainfalls, water levels and displacements over specific time periods. As mentioned in the previous paragraph, a trigger activation should lead to cross-check controls that analyze outcomes of related sensors. An application of this idea is displayed in Another relevant advantage of the correlation between various physical entities is to provide more information in order to avoid interpretation errors and identify the phenomenon behavior. The enhancement of connection between different devices has been one of the most influential technological improvements that emerged in recent years. Thanks to Internet connectivity, it has been possible to improve the remote interaction of various technologies, thus creating the Internet-of-things (IoT) concept. As a result of their wide applicability and the several advantages deriving from its implementation, IoT principles have been integrated into a significant number of different processes and fields. In particular, the development of new automated and innovative monitoring tools has brought to the application of IoT to the geotechnical sector, leading to the design of advanced systems with the improved connection between different components.One of the systems deriving from this new approach is the defined Internet of natural hazards (IoNH) and allows the remote collection and management of information that are fundamental for risk prevention purposes. As described in the present paper, the IoNH concept focuses on integrating IoT-based technologies to permit a constant check of instrumentation functionality, both in terms of sensor operativity and control unit conditions. Another advantage regards the possibility to control a large number of critical areas from a single control room thanks to completely automated procedures for data acquisition and elaboration. Moreover, the high sampling frequencies achievable by devices connected to the IoNH system give the possibility to perform statistical analyses to validate numerical results. Other features are the establishment of reliable cause–effect relationships related to multiparameter information, the activation of alert procedures with warning messages to the authority in charge of the direct activation of traffic lights and/or sirens. This paper presented a series of examples acquired from different case studies in order to underline the positive effects of the IoNH integration in a geotechnical monitoring system.Finally, one of the most relevant topics related to automatic monitoring and early warning systems concerns risk communication strategies and procedures. In fact, when dealing with systems that can autonomously control the closure of roads, the preliminary evacuation of landslide areas, etc., it is necessary to implement specific actions that should be followed by the authority in charge and by the population. It is fundamental to keep in mind that technology should not be intended as a substitution of human decisions and evaluations, but it represents a valid tool for the proper and timely management of potentially hazardous situations.


We present a noise estimation and subtraction algorithm capable of increasing the sensitivity of heterodyne laser interferometers by one order of magnitude. The heterodyne interferometer is specially designed for dynamic measurements of a test mass in the application of sub-Hz inertial sensing. A noise floor of  In the past decades, displacement measuring interferometry (DMI) has extended its application to gravitational wave (GW) detection, including free-falling test mass measurements in space-based gravitational wave detection as the Laser Interferometer Space Antenna (LISA) and its technology demonstrator, LISA Pathfinder ,2,3,4,5,Efforts have been made to identify noise sources in heterodyne interferometry ,22,23,24In this article, we present a noise identification and mitigation algorithm that can be applied to general heterodyne interferometers. We have tested this in a compact laboratory benchtop interferometer. In M. This noise term M and M and d is calculated byThe phases ps (PLL)  or discrps (PLL) . By takiWe built a benchtop prototype with commercial optical components and mechanical mounting parts, as shown in The benchtop system is tested in the vacuum chamber with a pressure of To evaluate the noise floor of the interferometer, we utilized a single static mirror instead of using individual fixed, reference, and test mirrors. The preliminary test demonstrated that the benchtop compact interferometer reduces the interferometer noise floor by rejecting common-mode pathlength noises, thus enhancing the sensitivity level by three orders of magnitude. The residual noise sources in the differential measurement are investigated in this section to determine their contribution to the overall noise floor. The interferometer performance is further improved by combining a linear fit method ,27,28 wiThe noise investigation of the LISA Pathfinder interferometer demonstrated that the electromagnetic coupling of the radio-frequency (RF) signals between two AOFS drivers, generates sidebands that imprint on the optical signals ,13. FiguBased on the analysis presented in references ,13, the Equation  can be rM. Therefore, the magnitude of the laser frequency noise is determined by the axial distance between the reference mirror The traceability of interferometric measurements is dependent on the accurate knowledge of the laser source frequency. Therefore, fluctuations of the laser frequency in an interferometer with unequal armlengths directly impact the interferometer phase following the equationThe DIFO is a heterodyne interferometer with an intentionally designed unequal arm length using a 2-meter fiber in one interferometer arm. The laser frequency fluctuation then gets amplified when coupled into the DIFO phase readout Equation .We perform a linear fit of the band-passed phase, Equation , it is iEquation , the lasTemperature fluctuations lead to OPD variations due to changes in the refractive index of the air, and thermo-elastic distortions of the optical elements and mounts. Temperature fluctuations usually limit the sensitivity of an interferometer in the frequency regime below 1 mHz ,21. EffoIn contrast to the two noise sources introduced above, thermal fluctuation effects are recorded with a delay in the optical readout. In other words, the group phase between the temperature measurement and the actual effect on the differential interferometer must be considered in the analysis. Therefore, when analyzing temperature fluctuations, a spectral analysis method  is adoptBefore applying the spectral analysis method, we first evaluate the correlation between the displacement and the temperature measurement by calculating the coherence between them. In this spectral analysis method, the transfer function between the temperature and the differential measurement is estimated by the equationThe photodetector (PD) technical noise determines the minimum noise floor that an interferometric system can achieve, aside from fundamental limits such as shot noise. In a PD system, typical noise sources include dark current noise from the photodiode, shot noise originating from potential barriers, Johnson noise from thermal fluctuation in the resistor of the sensor circuits, and capacitive noise from the photodiode and circuit . While oual to 1 .Assuming a small displacement that can be modeled as By applying trignometric identities and Bessel expansion to Equation Equation  can be sTherefore, the time average of the irradiance and the time-averaged incoherent square sum of the irradiance on the photodetector ared, is converted by the relation B is the detector bandwidth, G is the transimpedance gain and is usually specified by the manufacturer. Assuming the interferometer has a visibility of V, the SNR when PD noises are present can be expressed asThe actual displacement to be measured, For the benchtop system, the RMS of output voltage square without detecting signal is Equation , the minWe investigated three common noise sources for heterodyne interferometry, including non-linear OPD noise, laser frequency noise, and temperature noise. The correction method for each noise source is identified, and the overall post-processing correction algorithm is described in the flow chart in According to this correction algorithm, This post-processing noise correction algorithm provides an effective alternative to improve the sensitivity of heterodyne interferometers without implementing active stabilizations and can achieve high sensitivity over long-term measurements. Moreover, the application of the post-processing algorithm allows us to maintain an overall compact system footprint, and minimal complexity to the control system. The proposed interferometer and noise correction algorithm achieve a performance that is comparable to a few other techniques in GW applications, and has its own relative advantages, such as low hardware complexity and simple interferometer layout.In addition to the benchtop system we built in the laboratory, this noise correction algorithm can be applied to general heterodyne interferometers ,9. FurthWe have presented a noise identification and noise correction algorithm that applies to general heterodyne interferometry. A compact heterodyne interferometer has been developed and tested to determine its performance, when applying this algorithm to its measurement results. We have developed a mitigation strategy for typical noise sources that are present in heterodyne interferometers such as non-linear OPD noise, laser frequency noise, and temperature fluctuations. The contribution from each noise source is estimated and subtracted from the main phase measurement. After correction, the noise floor is reduced by an order of magnitude to a level of approximately There are a few modifications to be made in the future to further improve the interferometer performance over the bandwidth above 1 mHz. On the operation environment side, the natural frequency of the pendulum platform can be reduced below 100 mHz to provide noise attenuation to a broader frequency band. To mitigate the non-linear OPD noise, better management of the crosstalk between RF signals can be implemented, such as building electromagnetic shield for each individual AOFS RF amplifier to reduce the amplitude of the sideband interference. On the instrument side, the interferometer design can be optimized to minimize the common-path noise term, Equation , in the


Micro-surface texturing of elastomeric seals is a validated method to improve the friction and wear characteristics of the seals. In this study, the injection process of high-viscosity elastomeric materials in moulds with wall microprotusions is evaluated. To this end, a novel CFD methodology is developed and implemented in OpenFOAM to address rubber flow behaviour at both microscale and macroscale. The first approach allows analyzing the flow perturbation induced by a particular surface texture and generate results to calculate an equivalent wall shear stress that is introduced into the macroscale case through reduced order modelling. The methodology is applied to simulate rubber injection in textured moulds in an academic case (straight pipe) and a real case . In both cases, it is shown that textured walls do not increase the injection pressure and therefore the manufacturing process is not adversely affected. In industry, environmentally friendly processes are presently a must for a greener future. Within the broad industry concept, elastomers are one of the most versatile engineering materials and one of their main engineering applications is in the production of dynamic seals. Although they are generally regarded as high volume, low cost components, elastomeric dynamic sealing elements are a critical part of rotating and sliding devices in diverse industries such as manufacturing, automotive, aerospace, energy, power generation and construction since they must prevent any kind of leakage between the domains they separate, enduring millions of cycles under often harsh operational conditions. While they have a very important function, the problem with seals is that friction generates heat, accelerates wear and causes premature damage and leakage, shortening the seals lifetime, as well as increasing the energy consumption of the systems ,2. AccorRecent innovative approaches aim at producing high performance seals with no addition of new raw material and with a cost-effective and easy-to-integrate mass production approach of textured elastomeric seals . SurfaceComputer-aided engineering (CAE) simulation technologies based on computational fluid dynamics (CFD) are extensively used by injection moulders to predict and optimise the mould design and operational conditions for the injection process, because trial and error analysis based on industrial pilot lines would be unaffordable in terms of both time and costs. Likewise, numerical tools can be used to virtually evaluate the material response without the physical use of the real material and without compromising the mould manufacturing and the available time for production. Additionally, CFD studies provide an efficient tool to predict, and hence avoid re-designing the mould before it is actually made, distinct problems that may appear when the mould is under operation such weld lines, sink marks or air trapped inside the mould, among others. Therefore, it is possible to minimize mistakes and costs before the mould production. In this regard, numerous computational studies of injection processes can be found in the literature ,5,6. NevThe increasing demand of micro-components has motivated many CFD studies in the literature that are focused on micro injection moulding ,13,14,15Within this background, the promising technology of micro-surface texturing of elastomeric seals for friction reduction motivates the current paper whose goal is to assess the behaviour of the injected material over the mould wall protrusions, in order to see how the moulded material will conform to the mould texture. In this research, a novel numerical methodology implemented on open source software is developed to analyze the injection process of elastomers in micro-textured moulds considering effects at both the micro and the macro scales. The microscale approach pursues the knowledge generation regarding the flow perturbations induced by the presence of mould wall protrusions in the range of tens of microns. In contrast, the macro-scale approach is aimed at the CFD simulation of the injection in rubber moulds. To link the results from both approaches, the microscale results are used to generate a reduced order model (ROM), which is introduced in the macroscale simulation as a boundary law in the textured walls. The outcome from this investigation will definitely contribute to increasing the knowledge of the industrial sector, which is strongly interested in building a greener future by improving the efficiency of the manufacturing processes of high-performance components.This section consists of three main subsections. First, The governing equations of the rubber flow, during rubber injection moulding, are presented in this section. The physics involved in this process are, namely: (i) multiphase flow with interface tracking; (ii) mass conservation; (iii) momentum conservation; (iv) curing; and (v) heat transfer.Mass conservation equation of the primary phase:h phases .To ensure continuity, the secondary phase volume fraction must satisfy:Expanding Equation , dividinAssuming linear equations of state:Replacing  and 6)  6) into For convenience, the term Equation :8)∂α1∂tEquation  into the∂α1∂tEquaFor numerical reasons, an artificial term is added to the left-hand side of Equation  to counts region ,23.The differential form of the mass conservation equation may be written as the sum of the mass conservation equations of the two phases (from Equation ) as:11)Equation  into EquEquation The momentum-conservation equation is, in differential and vector form:given by :(14)fv→=∂(ρv→)∂t+)fv→=ρg→fs→=σκ∇α1itten as:τ→→=μ[∇v→p) is replaced by the modified pressure  thus reThis variable change is advantageous for the specification of the pressure at the boundaries of the space domain. Additionally, this treatment enables efficient numerical treatment of the steep density jump at the interface by including the term n, B, In Equation , the rubcure see ; n, τ*, T is the temperature; t represents the time; and the parameters Rubber cure kinetics is here described according to the n-th order reaction kinetics , used to calculate the curing behavior of a thermoset material, given by:T is the temperature and Some materials, such is the case of rubber, undergo an induction period befores curing starts to take place. The length of this induction period is given by:To take into account the induction period, Equation  is modife is the specific internal energy, The equation of the total energy Rubber is a highly viscous non-compressible fluid, where viscous dissipation effects might be of significance: Equation  can thusBy definition: Equation  leads toIn Equation  the specA novel approach is here presented to include the microscale wall texture effects on the macroscopic filling model. It consists of developing a new wall law that accounts for the wall texture effects and enables the use of smooth walls geometries for the macroscale filling simulation of textured moulds.T), wall see . Please In order to be able to model the effective viscosity at the wall, according to Equation , it is iique see .rubberFoam, has been developed to solve the comprehensive mathematical model described in compressibleInterFoam for two compressible, non-isothermal immiscible fluids using a VOF (volume of fluid) phase-fraction-based interface capturing approach [A new OpenFOAM solver, called approach .rubberFoam stands thus for an evolved version of the compressibleInterFoam, being the major modifications aimed at accounting for the particular non-Newtonian behaviour of rubbers (Equation (The Equation ) and theEquation ). A new mixture), where the thermo-physical properties of the main-phase (of a new type rhoThermoNonNewtonian) are not only dependent on the operating pressure and temperature, but also on the velocity field (U) and an auxiliary scalar field (omega); whereas the properties of the secondary-phase (of standard type rhoThermo) remain only dependent on the operating pressure and temperature.A new mixture class is created (rhoThermoNonNewtonian) to describe the full thermo-physical behaviour of rubbers, including the effects of the strain rate  by means of a reduced order model (ROM), aimed at describing the behaviour of a complex system using simple mathematical expressions without losing relevant information.The effective viscosity wall law described in N not necessarily independent variables into the product of N one-dimensional functions. Each of these N one-dimensional functions takes one argument only, so that the number of one-dimensional functions is the same as the number of the system’s variables. This can be written as follows:M is the order of approximation of the ROM and An in-house developed ROM-generation algorithm based on Canonical Polyadic Decomposition (CPD) of tensors ,29 is usT, where T τwalconstant folder of the OpenFOAM case. The rubberFoam solver reads it and calculates the viscous stress tensor at each time-step and for each face of the textured wall boundaries , given the resulting T at the corresponding cell near the wall face.The output of the ROM is a text file  on ever−1 up to 750 s−1 shear rate, the resulting data are used to fit the parameters of the “Reactive Viscosity Model” , 30 μm in height (h) and 100 μm spacing, as is illustrated in To implement the effective wall viscosity on the macroscopic-scale simulation as described in The representative volume considered in this study, sketched in A set of eight cases is run according to the conditions specified in A summary of the boundary conditions used to simulate the representative volume near the wall, assuming periodic flow, is shown in As an example, T). The results are shown in The simulation results are further post-processed so that the viscous shear stress on the textured wall , (ii) pipe diameter (D) and (iii) filling flow rate (rubberFoam: (1) with textured walls; and (2) with smooth walls, henceforth named textured and smooth respectively. The results are shown in In order to study the effect of the textured wall on the inlet pressure , the cases reported in L, D and From A deeper analysis of the results plotted in D = 0.1 mm) is of the same order of magnitude than the pipe size (D = 0.7 mm) the methodology might be inappropriate.It is worth mentioning that case 4 is the only case where no difference is found between textured and smooth cases. It stands for the case with smaller diameter and the result could thus be affected by the meshing restrictions imposed by the methodology. For this particular case, where the texture size : (i) the distance between the wall and the center of the cell near the wall is kept between the corresponding limits of application of the texture wall law (rubberFoam of two cases: (1) standard mould where all walls are smooth; and (2) textured mould, where the internal face is textured according to the pattern shown in wallTexture. Thus, the only difference between smooth and textured cases is that the internal ring wall is called wall and wallTexture respectively.This numerical study consists of the simulation using the The results of the numerical simulation of the mould filling process are illustrated in The evolution of the inlet pressure as the rubber filling proceeds is plotted in In this numerical study the influence of the wall texture of the rubber injection moulds on the operating injection pressure is assessed. A priori, one might expect higher pressure drops in textured walls due to the increase of effective area and a higher resistance to flow induced by the dimples . However, the results of this study show that this effect can be counterbalanced by the non-Newtonian behaviour of the rubber, whose viscosity decreases near the textured wall due to the larger shear stress induced by the texture, illustrated in The results of the rubber filling of a textured straight pipe, reported in In The numerical analysis presented in this paper focuses on a particular texture described in rubberFoam was developed to calculate the rubber flow during rubber injection on textured moulds, where the effective viscosity at the wall corresponding to the textured surface is introduced by means of a reduced order model. The solver is then tested in both an academic case  and an industrial case . At any case, the textured walls do not induce any negative effect on the manufacturing process, as the injection pressure remains equal or even decreases around 2% with respect to the reference case . This behaviour is due to the non-Newtonian nature of the rubber, as the viscosity near the wall decreases due to the higher shear rates induced by the wall texture. The results of this study support the current trend towards mould walls texturization to improve the pieces mechanical properties, without compromising (or even enhancing) the manufacturing process or production costs.A novel numerical methodology for the assessment of the micro-textured wall effects on rubber injection moulding is presented in this paper. The methodology is fully based on two open-sources tools: (a) OpenFOAM, a standard open-source CFD platform ; and (b)


Landslide is a very common and destructive geo-hazard, and displacement monitoring of it is integral for risk assessment and engineering prevention. Given the shortcomings of current landslide displacement monitor technologies, a new three-dimensional underground displacement monitoring technology is proposed based on the double mutual inductance voltage contour method. The underground displacement measuring device mainly consists of an information processing unit and sensing array, connected by power and RS-485 communication lines. An underground displacement measurement model to convert the double mutual inductance voltages and the inter-axis angle into the relative displacement between adjacent sensing units is established based on the interval-interpolation and contour-modeling. Under the control of the information processing unit, the relative displacement between any two adjacent sensing units can be calculated through the underground displacement measurement model, so as to obtain the total displacement from underground depth to surface, and the measurement data can be further sent to the Internet of things cloud platform through the 4G module; thus the remote real-time monitoring of underground displacement three-dimensional measurement for the rock and soil mass from underground depth to the surface is realized. The measurement model is verified by building an experimental platform to simulate the underground displacement of rock and soil mass. The experimental results show that for each measuring unit, when the horizontal displacement and vertical displacement are within the measurement range of 0–50 mm, the maximum measurement error will not exceed 1 mm, which can meet the accuracy requirements of underground displacement monitoring of landslide. Landslide hazard is the most common geological hazard in nature and causes billions of dollars of damage every year worldwide. China is one of the countries most seriously affected by landslide hazards in the world . AccordiThere are several components of landslide monitoring, including displacement, strain, hydrology, precipitation, ground temperature, and other environmental factors . Among tTotal station, interferometric synthetic aperture radar (InSAR), global navigation satellite system (GNSS), and depth camera are widely used in surface displacement monitoring ,11,12,13The above techniques can measure local and regional displacement at the surface, but surface displacement is often hysteretic and susceptible to topographic and environmental factors. By comparison, underground displacements can more accurately analyze the internal deformation characteristics of rock and soil mass, understand the landslide’s real evolution, and obtain the local deformation of the entire landslide body. Therefore, under-ground displacement monitoring is more effective than surface displacement monitoring in predicting the trend of landslides .Borehole inclinometer ,22, timeIn general, although the above underground displacement monitoring methods can monitor the underground displacement of landslides, they all have their shortcomings in one way or another. They have a standard limitation: unable to watch the three-dimensional changes of underground displacement. However, only the three-dimensional changes of underground displacement can truly characterize the movement trend in the rock and soil mass to achieve the purpose of early warning and forecasting. In order to solve the limitations of the existing underground displacement monitoring technology, we designed an integrated underground displacement three-dimensional measuring sensor based on double mutual inductance voltage contour method, applied the Internet of Things technology to this system, and finally realized a highly automated and high-precision remote monitoring system of three-dimensional measurement of underground displacement. It solves the limitations of the current underground displacement measurement technology and has great research significance and practical value.The three-dimensional measurement system of underground displacement based on the double mutual inductance voltage contour method is mainly composed of a measuring device and remote monitoring platform; between them, data are transmitted through wireless communication technology. As shown in Equivalent to the host of the measuring device, the information processing unit is responsible for sending measurement signals to the slaves at different addresses, processing the received data through the underground displacement measurement model, and finally sending the measurement data to the Internet of things cloud platform through the 4G communication module.The sensing array is composed of multiple sensing units. Any of the sensing units is equivalent to a slave of the measuring device and responsible for receiving the measurement signals sent by the information processing unit and performing the corresponding operations. In practical engineering application, the information processing unit works at the surface of the rock and soil mass to be measured, the sensing array is buried vertically into the rock and soil mass through drilling, and the displacement of the landslide is generally related to the displacement of the geodetic coordinate system ; therefoEach sensing unit in the array has an identical structure and adopts columnar axisymmetric design. The outside of the sensing unit is a PVC sleeve, which is resistant to deformation and corrosion, and the upper and lower ends of the sensing unit are sealed with glue, which can well protect the internal structure of the sensing unit from impact of underground displacement. The sleeve’s interior comprises the air-core coil, magnetic core coil, and PCB. During installation, it is necessary to ensure that the center points of the air-core coil and the magnetic core coil are on the same plumb lines. The structure of the sensing unit is shown in r and vertical displacement z of the rock and soil can be estimated by Equation (1), thus realizing the distributed three-dimensional measurement of underground displacement of the rock and soil mass from the deep underground to the surface.As shown in Our proposed integrated underground displacement sensing unit is designed on electromagnetic mutual inductance. In the previous research, our research team proposed the measurement methods of underground displacement based on single mutual inductance voltage and based on the integration of mutual inductance voltage and Hall voltage, respectively. The former can only achieve displacement measurement in one direction , which has certain limitations in practical application. The latter can realize three-dimensional measurement; however, limited by the large temperature drift of Hall sensor; the measurement results are easily affected by environmental factors, which reduces the measurement accuracy. To overcome the limitations of the above underground displacement measurement methods and improve measurement accuracy and stability of the measurement device, a double mutual inductance voltage contour method has been proposed in this paper on virtue of our previous research work.uI and uII with the same frequency and different amplitude will be generated on the air-core coil in the measurement end, and UI and UII will be obtained through the filter rectifier circuit, which is called type I mutual inductance voltage and type II mutual inductance voltage. The calculation equations of uI and uII are as follows:As an example of one measuring unit in ui is the excitation signal successively connected to the air-core coil and the magnetic core coil, LI and LII are the self-inductance coefficients of air-core coil and magnetic core coil, respectively, MI is the mutual-inductance coefficient between the air-core coil at the excitation end and the air-core coil at the measurement end, and MII is the mutual-inductance coefficient between the magnetic coil at the excitation end and the air-core coil at the measurement end. In this measurement system, the sensing units in the sensing array exit in the same environment and each sensing unit has exactly the same structure, so the double mutual inductance voltages are only related to the relative position between adjacent sensing units. By applying the principle of electromagnetic mutual inductance, the change of displacement can be converted into the change of mutual-inductance coefficient, and then into the change of mutual inductance voltage; thus the conversion from non-electric quantity to electric quantity is realized. The angle between the Z-axes of two adjacent sensing units, or inter-axial angle θ, can be expressed as follows:αA and αB are the tilt angles of the excitation end and the measuring end in the measuring unit respectively. By acquiring the data reflecting the double mutual inductance voltages changed with the relative horizontal displacement r and vertical displacement z between two adjacent sensing units at different inter-axial angle θ, the measurement model between the relative displacement to be measured and the measured double mutual inductance voltages for any two adjacent sensing units can be established, so as to characterize the change of the relative position between adjacent sensing units according to the variation of the double mutual inductance voltages.As shown in Equation (2), for each measuring unit, θ can be applied on the solution of the horizontal displacement r and vertical displacement z between adjacent sensing units; however, in the actual underground displacement, the moving direction of the sensing unit may be arbitrary and is usually related to the moving direction of rock and soil mass. In order to determine the relative displacement of the sensing units in different directions and realize the three-dimensional measurement of underground displacement, the azimuth β is used to indicate the moving direction of rock and soil mass, as shown in β, the displacement components of relative horizontal displacement r in X-direction and Y-direction can be figured out, thus realizing the distributed three-dimensional measurement of underground displacement of the rock and soil mass from deep underground to the surface. The displacement components in X-direction and Y-direction are shown in the following equations. The measurement principles of azimuth and tilt angle will be presented next.The measurement model at different inter-axial angle α and azimuth β will be briefed below.In order to realize the three-dimensional measurement of underground displacement of rock and soil mass, it is necessary not only to obtain the double mutual inductance voltages between adjacent sensing units, but also to determine the tilt angle and azimuth of each sensing unit. The tilt angle can be used to calculate the inter-axis angle between adjacent sensing units to establish the underground displacement measurement model at different inter-axis angles. And the azimuth can be used to judge the moving direction of the sensing unit, thus determining the three-dimensional position change between adjacent sensing units. By solving the above four parameters, we can clearly know the position and state of each sensing unit at a certain moment, so as to realize the three-dimensional distributed measurement of underground displacement of rock and soil mass. The measurement principle of tilt angle φ, ϕ, and ψ along the X, Y, and Z axes in real-time.For this measuring device, the attitude variation of any sensing unit in the sensing array can be regarded as a combination of three angles rotating around three rotating axes in sequence in its static state, which are called Euler angles. In order to measure the Euler angles of the sensing unit at any moment, an attitude detecting module including a three-axis magnetometer, a three-axis gyroscope, and a three-axis accelerometer is integrated into each sensing unit, thus capable of measuring the Euler angles A and the reference coordinate system is called coordinate system B. When this sensing unit rotates in any direction, coordinate system A will stand still, and coordinate system B will change along with the sensing unit. According to the rotation order of the attitude detecting module, the rotated sensing unit can be regarded as a sensing unit in the horizontal state to rotate ψ around Z-axis first, then rotate ϕ around Y-axis, and finally rotate φ around X-axis. These three rotation angles can be directly measured by the attitude detecting module, so the rotation matrix from coordinate system B to coordinate system A can be solved as follows:As shown in B coordinate system and finding the coordinates of points P and Q in the A coordinate system by multiplying the rotation matrix left, obtaining the coordinates of P and Q points in coordinate system B and finding their corresponding coordinates in coordinate system A by left-multiplying the rotation matrix as follows:Once the rotation matrix is obtained, the tilt angle and azimuth of the sensing unit can be calculated. The measurement principle of the tilt angle is shown in α of the sensing unit can be solved by Equation (9), where n1 and n2 are the normal vectors of XOY plane and POQ plane, respectively.Therefore, the measurement of the tilt angle of the sensing unit can be converted into the measurement of the inter-angle between the XOY plane and the POQ plane. In the spatial analytic set, the inter-angle between two planes is equivalent to the inter-angle of their respective normal vectors, so the tilt angle B and finding the coordinates of point C in coordinate system A by left-multiplying the rotation matrix:The measurement principle of azimuth is shown in β, which can be solved by the following formula:The inter-angle between the projection of point C in XOY plane and the X-axis is the azimuth β = 0°, which means x = rcos β = r, y = rsin β = 0.It is concluded in the previous sections that the type I and type II mutual inductance voltages are only related to the relative position of any two adjacent sensing units. Therefore, before the sensing array is buried in the rock and soil mass, it is necessary to build an experimental platform to simulate the underground displacement of rock and soil mass to obtain the relationship between the mutual inductance voltages of type I and type II and the relative displacement to be measured. As shown in In the data acquisition experiment, the initial position between adjacent sensing units is shown in UI) and type II (UII) respectively at different inter-axis angles, which are 10°, 30° and 50° from top to bottom.The data acquisition experiment can obtain the double mutual inductance voltage datasets at different inter-axis angles. r, z]. The corresponding coordinate points of these data pairs are called equivalent discrete points of mutual inductance voltage, the points of equal mutual inductance voltage are called the mutual inductance voltage equivalence discrete points, and the curve composed of multiple equivalent discrete points of mutual inductance voltages is called the mutual inductance voltage contour. By projecting the three-dimensional surface of the double mutual inductance voltages onto the two-dimensional plane, the double mutual inductance voltage contours at different inter-axis angles can be obtained. I and VCII respectively) at the inter-axis angles of 10°, 30°, and 50°, in which the horizontal axis represents the horizontal displacement and the vertical axis represents the vertical displacement.From It can be found from The data acquisition experiment is carried out on the experimental platform to obtain the double mutual inductance voltage datasets at different inter-axis angles and the double mutual inductance voltages, inter-axis angle and azimuth in the measuring unit are measured under the control of the information processing unit.Applying the interpolation theory, the dataset of double mutual inductance voltages at the current inter-axis angle between two adjacent sensing units at the current moment is obtained, and the equivalent discrete points of double mutual inductance voltages are solved according to the values of double mutual inductance voltages.Applying the equivalent discrete points of double mutual inductance voltages to construct two contours of double mutual inductance voltages. These two contours have only one intersection. The intersection coordinates, corresponding to the horizontal displacement and vertical displacement between these two adjacent sensing units, can be solved by numerical analysis method.The establishment of a three-dimensional measurement model of underground displacement based on the double mutual inductance voltage contour method mainly includes three steps:The steps for building the measurement model are described in detail in the following subsections.Data acquisition experiment for measuring units at different inter-axis angles is carried out to obtain the corresponded datasets of double mutual inductance voltages. Since increasing the number of datasets can also improve the accuracy of the linear interpolation method, so on the premise of not exceeding the memory size of the information processing unit, the variation range of the inter-axis angle in the data acquisition experiment sets as 0° to 80° and the variation spacing sets as 5°.Under the control of the information processing unit, the tilt angles of both the excitation end and the measurement end in each measuring unit are first solved through the attitude angle solving formula, and then converted into the inter-axis angle for this measuring unit. Find two datasets adjacent to this inter-axis angle, then calculate the double mutual inductance voltage datasets under the current inter-axis angle through the following formula:θ is the current inter-axis angle between these two adjacent sensing units, γ and η are the inter-axis angles of these two datasets adjacent to θ, satisfying η − γ = 5°.The underground displacement three-dimensional measurement model is established based on the double mutual inductance voltage datasets under different inter-axis angles, so the variation of inter-axis angles between adjacent sensing units is one of the important factors that change the measurement results. In the actual underground displacement, the variation of the inter-axis angles between adjacent sensing units is arbitrary and usually is accompanied by the change of underground displacement of rock and soil mass, so the double mutual inductance voltage datasets corresponding to each measuring unit will change accordingly. The purpose of improving the measurement accuracy of the system can be realized by collecting the double mutual inductance voltage datasets at any inter-axis angles and storing them in the microprocessor of the information processing unit. However, this will not only greatly increase the workload of data acquisition experiments, but also lead to work difficulties: limited by the memory capacity of the microprocessor, only a limited number of datasets can be stored. To broaden the measurement range of the underground displacement three-dimensional measurement sensor, it is required that the variation ranges of the relative displacement and inter-axis angle between adjacent sensing units are quite large, so it is virtually impossible to use a definite interpolation polynomial to depict the variation relationship between the double mutual inductance voltages and the inter-axis angle at the same position for the measuring unit. After comparison, the linear interpolation method is adopted. This method has a small amount of calculation. It only needs to carry out several groups of data acquisition experiments on each measuring unit under different inter-axis angles to build the datasets under any inter-axis angle with quite high accuracy. The main steps are as follows:The double mutual inductance voltage contour is composed of multiple equivalent voltage points. When the vertical displacement between adjacent sensing units remains unchanged, the relationship between the horizontal displacement and the mutual inductance voltage of type I and type II respectively at different inter-axis angles is shown in rij, r(i+1)j], , , m and n are the measurement ranges of horizontal displacement and vertical displacement respectively, and then the contours of mutual inductance voltage are approximately replaced by straight lines in each interval. Taking type I mutual inductance voltage as an example, when UIij < UI < UI(i+1)j, the horizontal displacement corresponding to the voltage under any vertical displacement can be obtained through Equation (13).r and vertical displacement z, respectively. By changing the vertical displacement successively, it is possible to find multiple equivalent voltage discrete points corresponding to this voltage within the whole measurement range, laying a foundation for the next curve solution.It can be observed from The double mutual inductance voltage equivalent discrete points of two adjacent sensing units at a certain position can be obtained by the mentioned linear interpolation method and piece-wise linear method. For example, when the inter-axis angle between two adjacent sensing units is 20°, and both the relative horizontal displacement and vertical displacement are 15 mm, then the measured mutual inductance voltages of type I and type II are 1.819 V and 1.328 V, respectively. The equivalent discrete points of mutual inductance voltages of type I and type II obtained by the piece-wise linear method are shown in r1, r4] and  within the intersection range near the double mutual inductance voltage contours, and can be called the intersection interval. The former interval represents the horizontal displacement of mutual inductance voltage contour of type I, and the later interval represents that of type II. The intersection of the mutual inductance voltage contours of type I and type II lies in this interval.The equivalent voltage discrete points in li(x) is the interpolation basis function with the following calculation expression:xi is the abscissa of the discrete interpolation point, and yi is the ordinate of the discrete interpolation point.In order to solve the intersecting coordinates of the double mutual inductance voltage contours, namely, the relative displacement between adjacent sensing units, the curve expressions of type I and type II mutual inductance voltage contours need to be obtained according to the discrete points of double mutual inductance voltage equivalence. The commonly used methods are the interpolation method and the curve-fitting method. Lagrange interpolation is a standard polynomial interpolation method and can calculate the curve expression passing through all discrete points according to the known discrete points. The Lagrange interpolation polynomial is as follows:In the case of r and vertical displacement z between these two adjacent sensing units:According to the double mutual inductance voltage contour equations expressed in Equation (16), the intersection coordinates can be solved. As mentioned earlier, the solved intersection coordinates correspond to the horizontal displacement φi(x) is a selected set of linearly independent functions and ai is the undetermined coefficient  and n is less than the number of discrete point sets.The least-squares fitting method is a standard curve fitting method, in which the fitting formula can be expressed as follows:Select the same intersection interval as shown in r, z] can be solved according to the double mutual inductance voltage contour equations expressed in Equation (18).Similarly, the intersection coordinates  is , , , respectively. Applying the least-squares fitting method, they are , , , respectively. And applying the interval-linear method, they are , , , respectively. (2) The max error, relative average error, or the variance of the measurement results obtained by the interval linear method are smaller than the other two methods. It indicates that the interval linear method has higher measurement accuracy and less calculation, so we finally adopt this method to solve the intersection coordinates of the double mutual inductance voltage contours.To fully evaluate the validity and accuracy of these methods, the Lagrange interpolation method, the least-squares fitting method, and the interval-linear method are used for experimental verification in the intersection interval where the inter-axis angle is 20°, and the measurement results are shown in To evaluate our proposed underground displacement three-dimensional measurement model, the validation experiments are conducted on the experimental platform described in Anti-interference ability is an important factor in measuring whether a device is reliable, and it is essential to eliminate or reduce the noise effect on the measurement system. The noise source of the device is related to its environment. Our proposed underground displacement monitoring sensor can be divided into data acquisition stage and engineering application stage according to the different application environments.In the data acquisition stage, the random errors caused by external factors mainly include two types: one is caused by the stepper motor in the experimental platform, and the other is caused by the temperature drift of the components in the hardware circuit. We take the following measures to effectively reduce the impact of noise on the device. Firstly, we choose the stepper motor with high displacement resolution, and the maximum movement error will not exceed 0.01 mm, which can be basically ignored. Secondly, we selected high-precision and low-temperature drift chips and components in the hardware circuit . We furtIn the engineering application stage, in order to ensure that the measurement system can work stably, we need to consider the influence of rock and soil geological environment on the sensing unit. The factors that trigger landslides mainly include soil porosity, soil depth, soil water content, and landslide velocity ,46,47. SFlexible structure design. One characteristic of our proposed underground displacement three-dimensional measurement device is that it has a flexible sensing array structure composed of multiple sensing units in series. Compared with the rigid structure of inclinometer pipe , the fleAutomatic measurement. When the system works, under the control of the information processing unit, it can measure the horizontal displacement, vertical displacement, inter-axis angle, and azimuth between any two adjacent sensing units from bottom to top to realize the distributed three-dimensional measurement of underground displacement of rock and soil mass from deep underground to surface.Three-dimensional measurement. Borehole inclinometer ,22, TDR High measurement accuracy. Several data acquisition experiments of type I and type II mutual inductance voltages under different inter-axis angles between adjacent sensing units are conducted, where the relationship between the measured mutual inductance voltages of type I and type II. The relative measuring displacement between any two adjacent sensing units under different inter-axis angles is investigated. A new three-dimensional measurement model of underground displacement is proposed based on the principle of interval-interpolation and contour-modeling. Through this method, the double mutual inductance voltage and the Euler angle of three axes measured at any time and position can be transformed into the horizontal displacement, vertical displacement, inter-axis angle and azimuth between any two adjacent sensing units. To fully evaluate the effectiveness and accuracy of the measurement model, a series of comparative experiments between the measured displacement and the actual displacement have been conducted on the self-designed underground displacement three-dimensional measurement experimental device. The experimental results show that the maximum errors of horizontal displacement and vertical displacement based on the proposed measurement model are less than 1 mm in the inter-axis angle range from 0° to 80°, which has higher measurement accuracy and reliability compared with other underground displacement monitoring technologies ,20 and mLandslide is widely distributed and frequently occur all over the world. It is one of the most severe geological disasters affecting human activities and the safety of life and property. To grasp the three-dimensional deformation characteristics and evolution dynamics of landslide rock and soil mass from the surface to the deep underground in real-time to predict the disaster trend and scope more timely and accurately, and to overcome the limitations of the existing underground displacement monitoring technology, a new underground displacement three-dimensional measurement method based on the principle of intersection-solving of double mutual inductance voltage contours is proposed in this paper. Compared to the currently available underground displacement measurement technology, our presented method has the following characteristics: