The field of smart health monitoring, intelligent fault detection and diagnosis is expanding dramatically in order to maintain successful operation in many engineering applications. Considering possible fault scenarios that can occur in a system, indicating the type of fault in a sensor is one of the most important and challenging problems in the area of intelligent sensor fault diagnostics. Within this frame of reference, we extended the physics-informed transfer learning framework, first presented previously for a fault cause assignment, to the level of sensor fault diagnostics for a range of different fault scenarios. Hence, the framework is utilized to perform intelligent sensor fault diagnostics for the first time. The underlying dynamics of the reference system are extracted using a completely data-driven methodology and dynamic mode decomposition with control (DMDc) in order to generate time-frequency illustrations of each sample with continuous wavelet transform (CWT). Then, sensor fault diagnostics for bias, drift over time, sine disturbance and increased noise sensor fault scenarios are achieved using the idea of transfer learning with a pre-trained image classification algorithm. The classification results yields a good performance on sensor fault diagnostics with  The demand and utilization of fault diagnosis and health monitoring tools are increasing dramatically over the last decade. A variety of applications in this context evolved into recognized instruments in many areas of engineering to preserve a successful operation in a variety of applications. As one of the key components in complex applications, sensors are open to introduce many different faults into the system due to their nature and working environment . The maiThere are a variety of applications in the literature focused on the sensor fault diagnosis framework. A general methodology for fault diagnosis with the emphasis on the isolation of multiple sensor faults is presented in . A comprAs they became standardized in many engineering operations, data-driven techniques are utilized in the fault diagnosis context in a variety of different applications, such as aircraft engines , inductiThe fundamental motivation of using a data-driven approach is to eliminate the requirement of a system model or prior information regarding underlying system dynamics. However, handling this high-volume system data can also be considered as one of the challenges in fault diagnosis frameworks . With thGoogLeNet [In this paper, a systematic methodology is applied to achieve sensor fault diagnosis using a purely data-driven dimensionality reduction technique, DMDc and idea of transfer learning. With the aid of these, our proposed methodology overcomes the requirement of prior system knowledge and the burden of handling a high-volume of data with a from-scratch training process. Over the last decade, the fault diagnosis and health monitoring framework became one of the most critical aspects of complex systems. However, identifying the exact fault in a sensor using only the system measurements is still a critical process in the literature with a growing research impact . This proogLeNet  is used The structure of the paper is presented as follows: The overall methodology and general framework of the sensor fault diagnosis with physics-informed transfer learning is presented in this section. The general structure of the methodology is first introduced in  and the An example case study is introduced in order to investigate sensor fault diagnosis on a generalized process control example. Five scenarios for the injected fault types are defined as nominal, bias, drift over time, sine disturbance and increased noise. Normalized sample sensor fault scenarios are illustrated in A generalized reference control system is given in r and the sensor feedback One of the key limitations in the framework of the fault diagnosis is the fact that the system measurements are restricted to only the reference The use of data-driven techniques in many engineering applications is dramatically increased over the last few decades. As a completely data-driven method, the dynamic mode decomposition (DMD) is utilized in various contexts to acquire linear reduced-order models of any dynamic system with input–output data. DMD does not require any previous knowledge on underlying physics between the input and output data. Only the revealed input and output measurements from the system are used in order to extract spatial temporal modes and patterns in the data ,37.Then, the DMD framework is extended for systems that include actuation, such as many different control applications. The dynamic mode decomposition with control (DMDc) includes system measurements together with the applied control signal in order to extract the governing dynamics of the system ,37. Thenr and sensor feedback X′ can be considered as the time-shifted copy of X. X consists of columns X′ consists of columns r signal is also reconstructed as a tall matrix consisting of snapshot columns asThe mathematical roots of the DMDc framework start with the signals obtained from the system, namely the reference input and sensor measurements. Once the reference case study is considered, the reference Approximately linear dynamics of the system can be written in terms of tall data matrices defined above as:k represents each singular value sorted hierarchically.By the very nature of the DMDc methodology, the extracted linear reduced-order dynamics of the system can be considered as on (SVD) . To demoBy using the shape of the total energy contribution graph, the truncation level is determined. As the slope of the total energy contribution graph is decreasing dramatically after In order to utilize the underlying physics of the corresponding system extracted using a completely data-driven method, DMDc, the dynamic modes of the first two dominant contributors are transformed into images of time-frequency representations. To perform the transformation of DMDc modes into images, there are many different time-frequency representations or illustrations, such as the Short-Time Fourier Transform (STFT)  and WignThe image set generated with the CWT can be considered as the input layer of the image classification models. To perform a sensor fault diagnosis, a deep convolutional neural network (DCNN) image classification structure is constructed. In this context, the images generated using DMDc modes represent the physics information to be utilized in the classification process. One of the key points in the implementation of the image classification with DCNN is the initiation of the model. Although different applications in deep learning implementations increases the performance dramatically, training a DCNN image classification model from scratch is still a computationally heavy task. Hence, one of the most commonly utilized and efficient ideas is to implement a transfer learning concept. In this context, previously trained DCNN models are used to improve the training performance and decrease the computational time.AlexNet introduced in [ResNet) presented in [GoogLeNet model is used [GoogLeNet performs better in terms of accuracy even if it has less parameters, and the most successful learning methodology is transfer learning [GoogLeNet DCNN model, primary layers shall be constructed as basic filters for a universal feature detection such as colors or edges within the corresponding image. The earliest GoogLeNet model is trained for the image classification of 1000 different labels [Different alternative image classification algorithms in the ImageNet Large-Scale Visual Recognition Challenge (ILSVRC) are investigated, such as duced in  and the ented in . In the  is used , as it a is used . Furtherlearning . In the t labels . With tht labels ,44. The GoogLeNet model consists of a 224 × 224 × 3 RGB image. The data set, including 1500 samples of five different scenarios, is separated in order to obtain three different data sets, namely, the training, validation and test. These data sets consist of 1200, 150 and 150 images, respectively, with random selection. The training data set consisting of 1200 samples is utilized in order to perform training operations. Then, the validation data set consisting of 150 samples is utilized once in each 10 epochs to check the validation accuracy during training operations. Then, the test data set consisting of 150 samples is utilized to check the test accuracy after the training process. Finally, the training process is completed for the transfer learning of the DCNN model using the Stochastic Gradient Descent with Momentum algorithm along with the DCNN model training parameters given in As stated in the time-frequency representation process, the input layer of the gputimeit.The training process is conducted on a laptop computer with an Intel Core i7-8750H CPU processor running at 2.20 GHz using 16 GB of RAM and GeForce GTX 1050 with Windows 11 and MATLAB r2021b. The gradient magnitude is utilized to track and terminate the training procedure. Within these configurations, the average training time for a sample set is 25 min using the MATLAB function The fault diagnosis accuracy is defined as the classification accuracy of the DCNN model for each data set corresponding to the train, validation and test data sets. Then, in order to visually inspect the classification accuracy of the DCNN model for each data set, we employed confusion matrices, which can be defined as a two-dimensional matrix with dimensions of true target classes and model output classes. In this configuration, the diagonal terms correspond to true classifications, where off-diagonal terms can be considered as misclassified samples. Confusion matrices are introduced for the training data set in As it can be extracted from the confusion matrices, the overall accuracy of the methodology is limited by the case of the slow drift fault in the sensor reading. Other fault scenarios are successfully diagnosed for all training, validation and test data sets. However, misclassifications are high on the slow drift fault and nominal scenario cases. This property shows that the proposed methodology is successful for bias, noise and sine fault scenarios, but the diagnosis capability between the nominal and drift fault scenario is limited. The classification accuracy levels are presented in From To further examine the effect of the DCNN model, the activation areas on the original time-frequency representation images of data spatial temporal DMDc modes are utilized. A sample scenario for the sensor bias fault with activated areas by the convolutional layer are presented in In order to demonstrate the effectiveness of an activation on top of the original time-frequency representation of a sample scenario, the strongest activation channel is presented in To demonstrate the effectiveness of the framework, a target system is defined as a velocity control in a real-time application, as shown in GoogLeNet, is implemented in order to perform transfer learning. By using the transfer learning methodology, the training effort is decreased dramatically while preserving the fault diagnosis accuracy. A reference case study with the FOPTD model is utilized in order to provide a benchmark sensor fault diagnosis application. An effective sensor fault diagnosis accuracy is achieved for all training, validation and test sets by the implementation of a systematic framework. Different plant parameters are implemented in order to perform robustness of the framework. High accuracy for the sensor fault diagnosis problem is demonstrated for bias, noise and sine fault scenarios. The confusion matrices presented within the results demonstrated that the diagnosis capability of the methodology can be improved for the drift fault scenario. Finally, a real-time application of the velocity control target system is utilized in order to demonstrate that the proposed methodology is valid for real sensor applications. There are no limitations on extending the proposed methodology for a range of different fault scenarios and even different fault severeness degrees. Once the corresponding labeled historical input–output data streams are available for a system, the methodology can offer a systematic way to perform fault diagnosis. Future work for the proposed methodology can be considered as an extension of the physics-informed transfer learning-based fault diagnosis framework into more complex real-world applications with labelled experimental data. A systematic framework is presented in order to achieve sensor fault diagnosis using only the sensor measurements and reference input signals. The physics-informed transfer learning framework, first proposed in  for the


Thrombosis seriously threatens human cardiovascular health and the safe operation of medical devices. The Food and Drug Administration’s (FDA) benchmark nozzle model was designed to include the typical structure of medical devices. However, the thrombosis in the FDA nozzle has yet not been investigated. The objective of this study is to predict the thrombus formation process in the idealized medical device by coupling computational fluid dynamics and a macroscopic hemodynamic-based thrombus model. We developed the hemodynamic-based thrombus model by considering the effect of platelet consumption. The thrombus model was quantitatively validated by referring to the latest thrombosis experiment, which was performed in a backward-facing step with human blood flow. The same setup was applied in the FDA nozzle to simulate the thrombus formation process. The thrombus shaped like a ring was firstly observed in the FDA benchmark nozzle. Subsequently, the accuracy of the shear-stress transport turbulence model was confirmed in different turbulent flow conditions. Five scenarios with different Reynolds numbers were carried out. We found that turbulence could change the shape of centrosymmetric thrombus to axisymmetric and high Reynolds number blood flow would delay or even prevent thrombosis. Overall, the present study reports the thrombosis process in the FDA benchmark nozzle using the numerical simulation method, and the primary findings may shed light on the effect of turbulence on thrombosis. Cardiovascular disease has become the number one threat to human life in the world . Thrombuin vitro thrombosis experiments using bovine blood in a backward-facing step (BFS) model and macroscopic data on thrombus were obtained with magnetic resonance imaging (MRI) technology. Subsequently, they developed a computational thrombosis model and correctly reproduced the location of device-induced thrombosis including the result of the above experiment  methodologies, the U.S. Food and Drug Administration (FDA) developed a benchmark nozzle model with a conical shape in diameter at one end of the throat and a sudden expansion at the other end. Particle image velocimetry and laser Doppler velocimetry have been used to measure the transitional and turbulent blood flow in the FDA nozzle . BesidesThe specific objective of this study is to investigate the thrombosis mechanism in the FDA benchmark nozzle. We first validated the predictive capacity of the hemodynamics-based thrombus model using the latest BFS experimental data. Subsequently, the thrombosis in the FDA nozzle was predicted under the same conditions as the BFS experiment. Finally, the effect of turbulence on thrombosis was explored. This is the first study to report the thrombus formation process in the FDA benchmark nozzle and the findings may make an important contribution to the field of device-induced thrombosis.RT) of blood flow, resting  and activated platelets (RP and AP), and coagulant (C) were coupled with Navier-Stokes equations to produce the physiological environment for thrombus formation, which could be depicted by the concentration of bound platelets (BP). It should be emphasized that the shear strain rate (SSR) is a crucial parameter in this thrombosis model. C and BP. The dark red arrow line denotes the consumption of platelets during thrombosis. The critical governing equations and our contribution are given below:The present study is based on a previous hemodynamics-based thrombosis model , which wRT) of blood flow could capture the regions of stagnancy and flow recirculation. High RT means a long stay of platelets and the corresponding convection-diffusion-reaction transport equation is as follows  is applied to simplify the complex coagulation cascade and the corresponding transport equation is diffusion-dominated:C is specified on the low SSR wall to activate the thrombosis model:BP and time-averaged SSR, respectively. BP is formed in regions with a high value of RT, AP, and C. It should be noted that the governing equation of BP only has one source term:C and AP] is the normalized form of AP to its initial value (AP0). BP and RTt, respectively.The coagulant =2QComputational Details) . For turbulent flow, the shear-stress transport turbulence model (SST) was used to predict the blood flow field, which was validated by experimental data (Details) . An autoDetails) .+ < 1). All the simulations were performed on ANSYS-CFX . Sensitivity analyses were carried out and the differences in velocity and SSR between the chosen meshes and finer meshes were less than 1%.Both the BFS and FDA nozzle were meshed by using ANSYS-ICEM 16.1 . The two blood flow domains had more than two and six million hexahedron elements, respectively. We placed ten grid nodes inside the near-wall boundary layer and the first layer near the wall was set to 20 Thrombosis in the BFS experiment was predicted by the hemodynamics-based thrombus model . The locThe relationship between the axial length of the thrombus and simulation time is also investigated in 3). The final thrombus is shaped like a ring.The same setup of the BSF experiment was applied to the FDA nozzle. The comparison of axial velocity along the centerline between simulation and experiment  is shownThe relationship between the thrombus volume and simulation time is revealed in The thrombus formation has placed enormous strain on the human cardiovascular system and medical devices. Both blood properties and the flowing geometric environment have contributed to the thrombus issues. Prediction of the thrombosis process can play a key role in mitigating the risk of blood clots in humans and devices. The present study was designed to simulate the thrombus formation in the FDA benchmark nozzle by coupling the computational hemodynamics and thrombosis model.Platelets are one of the important components of the thrombus and the thrombi would stop growing when the platelets are depleted. We propose a positive proportional relationship between the thrombus volume and platelets number based on the thrombosis experiment. In the present hemodynamics-based thrombosis model, platelet consumption is considered by using a simplified method.Thrombus model validation is indispensable before application. In the present study, the SST model was applied to simulate the turbulent blood flow and the performance of this model was confirmed by the previous interlaboratory results . AdditioWe found that the turbulence has remarkable effects on the thrombus shape and simulation time, while the role of laminar flow is negligible. As the Reynolds number increases, the final thrombus shape changes from centrosymmetric to axisymmetric due to the presence of turbulence. Besides, the rate of thrombosis is significantly reduced and eventually stops when the Reynolds number is 6,500. This result may be explained by the fact that the low-SSR region to initiate coagulant disappeared. This phenomenon has two implications for us in avoiding thrombosis in medical devices. On the one hand, the low-wall shear stress region should be eliminated to reduce the thrombosis in the medical devices, and on the other hand, it should be noted that hemolysis would occur when the Reynolds number is high, and a balance between thrombosis and hemolysis can be sought by controlling turbulent flow.C is applied to simplify the complex coagulation cascade in this hemodynamics-based thrombus model. However, the simulation strategy may reduce the accuracy to some extent. Finally, we adopted the SST model to simulate the turbulent blood flow. This model may neglect the complex fluctuating turbulent patterns, which have been reported in previous DNS/LES studies of the FDA nozzle (This paper firstly reports the thrombus formation process in the FDA benchmark nozzle. However, the major limitation should be clarified. The thrombosis model was validated based on the BFS experiment, we adopted the same model and setup to predict the thrombus formation process in the FDA nozzle, while there is a lack of experimental measurement data to support our primary findings. Besides, the coagulation cascade involves a lot of biochemical species, such as thrombin, fibrin, and fibrinogen . ConsideA nozzle . High-leThis study firstly investigates the thrombosis process in the FDA benchmark nozzle by coupling the CFD method with the macro-scale thrombus model. We considered the effect of platelet consumption and the hemodynamic-based thrombus model was validated by referring to the latest experimental data. The annular thrombus was observed in the FDA nozzle. Besides, the accuracy of the SST model was confirmed in different turbulent flow conditions. We found that turbulence could change the shape of centrosymmetric thrombus to axisymmetric and high Reynolds number blood flow would delay or even prevent thrombosis, which confirms the opposing relationship between thrombosis and hemolysis. In conclusion, the thrombosis process in the FDA nozzle was predicted using the numerical simulation method and the effect of turbulence on the thrombosis was preliminary revealed.


For the state estimation problem of a multi-source localization nonlinear system with unknown and bounded noise, a distributed sequential ellipsoidal intersection fusion estimation algorithm based on the dual set-membership filtering method is proposed to ensure the reliability of the localization system. First, noise with unknown and bounded characteristics is modeled by using bounded ellipsoidal regions. At the same time, local estimators are designed at the sensor link nodes to filter out the noise interference in the localization system. The local estimator is designed using the dual set-membership filtering algorithm. It uses the dual principle to find the minimizing ellipsoid that can contain the nonlinear function by solving the optimization problem with semi-infinite constraints, and a first-order conditional gradient algorithm is used to solve the optimization problem with a low computational complexity. Meanwhile, the communication confusion among multiple sensors causes the problem of unknown correlation. The obtained estimates of local filters are fused at the fusion center by designing a distributed sequential ellipsoid intersection fusion estimation algorithm to obtain more accurate fusion localization results with lower computational cost. Finally, the stability and reliability of the proposed distributed fusion algorithm are verified by designing a simulation example of a multi-source nonlinear system. Multi-source data fusion is widely used as a hot research problem in vehicle localization ,2, autonCurrently, the existing methods for multi-sensor data fusion estimation are divided into centralized fusion and distributed fusion. The advantage of centralized fusion is that it can provide optimal fusion information. However, it can lead to inaccurate fusion information because the multi-source system may fail and damage individual sensors in actual operation. However, the distributed fusion strategy solves this problem. It processes multiple sensor measurement processes in parallel, which can well isolate the faulty sensors . The disFor multi-source localization systems, a common model of localization systems is the idealized linear system. However, in the actual positioning process, the input and output of the system can be disproportionate due to many factors that are not under control in the system . In ordeAn existing filtering method for UAD noise disturbances in the system is the set-membership filtering (SMF) strategy . As the Minkowski sum fusion strategies. They use a joint fusion approach to improve the reliable performance of the system. An intersection method to find the maximized global estimated ellipsoid is proposed [For the problem of data fusion in multi-sensor distributed systems, the existing fusion techniques are proposed , which pproposed . For theproposed . This meproposed . As thisproposed . In ordeproposed . It is bproposed , the EI proposed .This paper studies the data fusion problem for a multi-source localization nonlinear system with UAD noise interference. In order to obtain a flexible and accurate localization system, we use a distributed fusion strategy for the design of the multi-source localization system. To describe the system noise in the localization process more realistically, we use a bounded ellipsoidal region to model the design of the UAD system noise. Meanwhile, we describe the process of linearizing the nonlinear function in terms of solving a semi-infinite constrained optimization problem based on the dual principle. The local estimator is designed at the sensor link nodes. It is based on the idea of combining the set-membership principle with the dual principle to design a DSM filter to filter out the interference of system noise. A first-order conditional gradient algorithm is used to reduce the computational complexity of solving the filtering process. Finally, we resolve the problem of unknown correlation arising from the communication chaos between multiple source sensors. A distributed sequential ellipsoidal intersection (DSEI) fusion estimation algorithm is designed to fuse the obtained local filtering estimates at the fusion center. The architecture diagram of the DSEI fusion positioning system is shown in For the verification of the target tracking performance of a positioning system, the accuracy of the positioning results is one of the primary conditions to be considered. The common positioning system model is an idealized linear system. The actual situation of the positioning system is more realistically considered in the target tracking process. This paper adopts a nonlinear system to describe the state space model of the target positioning system. It provides a guarantee for obtaining more realistic and reliable positioning results . The staFor the actual localization process, we cannot describe the statistical characteristics of the noise accurately. If an idealized model with an exact distribution is used to model the noise, the accuracy of the localization results may be reduced . In ordeith sensor at the kth moment. The measurement function In order to obtain more accurate positioning results, this paper designs a high-precision positioning system using multiple sensors. The measurement model of the sensors in the positioning system is as follows:As the system noise is modeled with an UAD ellipsoidal region, we assume that the initial target state For filtering methods of nonlinear systems, the extended filtering technique is often used. It is based on the principle that the nonlinear function is linearized by Taylor expansion . The TayAs the system noise characteristics are UAD, the set-membership filtering strategy is given primary consideration . It encoxko,uko) .Based on the above analysis, we urgently need to find a new set-membership filter to eliminate the interference with UAD noise in the nonlinear system, to lay a solid foundation for obtaining a high-accuracy localization result.In this section, for the presence of UAD noise disturbances in a multi-source localization nonlinear system, a DSM local filter is proposed to effectively filter out the system noise disturbances. First, we assume that the ellipsoidal region Due to the existence of the characteristics of nonlinear systems, the region rregular . If the Based on the above analysis, we find a minimal ellipsoid that can contain a nonlinear function. The solution of the minimax ellipsoid is often handled using optimization techniques. As the target state values are not unique, the set lems. In , it propHowever, we use the dual approach to solve the semi-infinite programming problem that arises in the process of finding the minimizing ellipsoid. First, we compute the target state values through continuously differentiable nonlinear functions, which is obtained as an irregular compact ensemble xk∈εi,k} . Our goaOur goal is to obtain the optimal solution of the semi-infinite programming problem. We use the dual principle to convert the problem of solving the minimizing ellipsoid into the corresponding maximizing optimization problem.As the measure of the constraint in the optimization problem can be described in the form of a discrete metric , we can We convert the semi-infinite constrained problem of solving the minimum ellipsoid into a semi-positive definite planning problem with discrete constraints. A first-order conditional gradient algorithm is proposed for solving the semi-positive definite optimization problem . This ist method . TherefoWe use the first-order conditional gradient algorithm to solve the semi-positive definite optimization problem. First, let the objective function Substituting (12) into the optimization problem (11), it is obtained thatWhen Immediately afterward, the minimum ellipsoid Using the information about the minimum ellipsoid Based on the above analysis of the transformation of nonlinear functions, we transform the measurement transfer function in the system. First, we describe the target state values using the information in the measurement equation (Equation (3)).Finally, based on the first-order conditional gradient algorithm principle, we can obtain the optimal solution to the semi-infinite constrained problem. By substituting the optimal solution into Equation (17), the result of the linearized measurement equation is obtained as follows:In this way, we convert the nonlinear system into a linear system.Due to the interference of UAD noise in the system, this paper uses the DSM principle for the design of the local filter. The DSM filtering method is to find a minimum estimated ellipsoid to contain the possible range of target states. Therefore, we discuss the prediction step and update step based on the information of the minimizing ellipsoid Minkowski sum of the ellipsoid Minkowski sum, we can determine the range of However, the target state llipsoid . TherefoAs the minimum ellipsoid containing .Similarly, for the design of the state update step, we determine the update ellipsoid Based on the above analysis, we have completed the design of a local filter. It filters out the UAD noise disturbances present in the multi-source nonlinear system by the DSM filtering method. The proposed filtering method reduces the computational cost of the localization system to a certain extent.For a multi-source localization system, in order to effectively deal with unexpected situations that affect the measurement results such as the failure or malfunction of a sensor, a distributed system is used to improve the reliability and flexibility of the multi-source positioning system. Multiple sensors form a distributed positioning network to communicate through a wireless sensor network. These sensors can be placed at any position of the vehicle to ensure the flexibility of the system and the reliability of the measurement results . HoweverThe unknown correlation means that the mutual correlation covariance  unknown . For the unknown : the fus unknown . This me unknown . The CI However, as the CI fusion process discards the analysis of unknown correlations, the CI fusion method needs to provide a large range of fusion results. It leads to the absence of qualifying conditions in the optimization problem. If the CI method is used for the design of distributed fusion estimators. It leads to the problem of conservative estimation of the localization results, which reduces the accuracy of the localization results of the multi-source localization system . In ordeFor dealing with the problem of unknown correlations, a new fusion method is proposed: the ellipsoidal intersection (EI) fusion method . It is bIn order to verify the superior performance of the EI fusion method, we compare the differences of the two fusion methods by a numerical example . SupposeBased on the described analysis, for the design of a distributed fusion estimator, it is a proper choice to use the EI fusion approach for the fusion estimator of the multi-source localization system . TherefoAlgorithm 1 summarizes the designed DSEI fusion estimation. The ellipsoidal center of the DSEI fusion estimation result is Algorithm 1. DSEI Fusion Estimator.Input: Estimated ellipsoids Output: Initialization.1:Set 2:Calculate the mean 3:Calculate the fusion estimation of ellipsoid 4:Repeat steps 2 to 3 for the next sampleTo verify whether the designed DSEI fusion estimator satisfies the consistency property, we perform consistency analysis on the designed fusion estimator. Based on the analysis of the fusion process of the previous numerical example, we can conclude that the shape matrix of the fusion result is smaller than the shape matrix of each local estimate . That isThen, the iteration-based property analysis yields the results of the fusion of the first three local estimators as follows:The collation gives:L sensors are used to observe the system for the multi-source localization system, L local estimation results are obtained. The DSEI fusion estimator performs the EI fusion process L − 1 times.As a total of In summary, our designed the DSEI fusion estimator outperforms the individual local estimators and provides a great guarantee for accurate localization results of the multi-source localization system.X-Y axis plane. To demonstrate the reliability of the designed DSEI fusion estimator based on the DSM filtering method, we consider a multi-source nonlinear localization system to validate the localization results of intelligent vehicles. The state-space model of the multi-source nonlinear localization system is shown as follows:The center of the initial target tracking state ellipsoid is The position information By solving the inverse of the measurement equation as required in (9), the following results are obtained:The shape matrices of the ellipsoid containing the process noise X-axis and Y-axis directions, respectively. The results show that our designed DSEI fusion estimator using DSM filtering has good tracking performance. Meanwhile, to verify the superior performance of the fusion estimator, we compare the errors of the DSM filter estimation results and the fusion estimation results by comparing them. The results of the error analysis are shown in Based on the designed simulation example, we verify the tracking performance of the proposed DSEI fusion estimator with DSM filtering for the target’s state. The target tracking performance results are shown in In order to visualize the performance of the designed distributed fusion estimation, we compare the traces of the shape matrix of each estimation result. The comparison of the traces of the shape rectangles of each part of the ellipsoid is shown in Meanwhile, in the simulation experiments, we analyze the computational cost of the proposed DSEI fusion algorithm. A comparison of the computational time cost of the DSCI fusion method and the DSEI fusion method during operation is shown in This paper addressed the reliability problem of target tracking for multi-source localization nonlinear systems. In order to obtain a flexible and accurate localization system, we proposed a fusion estimation method for multi-source localization nonlinear systems based on the fusion estimation of DSEI with the DSM filtering method. First, for the nonlinear systems with UAD noise characteristics, we used a dual method based on the first-order conditional gradient to solve the minimized ellipsoid containing the nonlinear function. Then, the information of the minimized ellipsoid was used to convert the nonlinear system into a linear system. Meanwhile, we used the principle of set-membership filtering to design a DSM local filter at the link nodes in the sensor network to filter out noise interference. To solve the situation that the correlation information is unknown due to the communication confusion between sensors, we designed a DSEI fusion estimation algorithm. It described the unknown correlation information between local estimates with explicit expressions. It performed sequential fusion at the fusion center. This method can obtain more accurate fusion results at a lower computational cost. The performance analysis demonstrated that the proposed fusion estimator can obtain estimation results with high accuracy and low computational complexity. In future research, we can apply the proposed method of DSEI fusion estimation based on the DSM filtering method to other practical applications such as smart grids.


Third molar extractions are one of the most commonly performed dental procedures. It is associated with numerous complications, of which mandibular angle fracture is a rare but distressing complication. These can occur as intraoperative and postoperative (late) events. Iatrogenic fractures involving the angle of the mandible represent a unique challenge for management owing to their complex biomechanics and various anatomical factors. Intraoperative fractures occur due to various reasons, which include the position of the tooth, depth of impaction, extent of odontectomy performed, and injudicious use of dental elevators. This exhibited report describes a case of iatrogenic mandibular angle fracture (IFM) during excision of an impacted third molar in a 30-year-old female. Additionally, it discusses the various reasons and preventive strategies to avoid such complications. The face is one of the most often injured areas of the body. It accounts for 23%-97% of facial fractures . SurgicaThe mandibular angle is one of the inherently vulnerable regions prone to fracture owing to complex biomechanics and anatomical characteristics. It is estimated that the existence of an impacted third molar decreases the cross-sectional area of bone and leads to a twofold to fourfold increase in fractures of the mandibular angle . MandibuA systemically healthy 30-year-old countryside female visited our outpatient section of the department with a chief complaint of pain and swelling over the lower right side of her face with an inability to open her mouth and chew for four days. The patient had a history of a traumatic surgical procedure to extract her lower right impacted third molar under local anesthesia elsewhere.On examination, the face was grossly asymmetrical due to diffuse swelling present over the lower right region of the face extending anteroposteriorly distal to the corner of the lip to the posterior border of the ramus of the mandible and supero-inferiorly from the level of the corner of the mouth to 2 cm beyond the lower border of the mandible. The overlying skin was the same color as the adjacent skin, afebrile on touch, and tender on palpation. Detailed palpation could not be performed as the swelling was tender, and restricted mouth opening did not permit intraoral examination. The occlusion was bilaterally stable, and at rest, no abnormality was detected.An orthopantomogram (OPG) was done, which demonstrated extracted second and third molar socket through which a thin radiolucent line was seen running obliquely from the alveolar crest of the extraction site to the angle of the mandible, indicating a fracture Figure . A compuUpon resolution of the edema, the fracture was treated with open reduction and two-point fixation, one superior border plating using miniplates via a transoral approach, and lateral border plating using a trans-buccal approach with titanium plates and screws Figure . PostopeIntraoperative iatrogenic mandibular angle fractures occurring as a sequela of dental extraction are a rare but serious complication arising as an abrupt or late event. Late mandibular fractures tend to occur more frequently compared to immediate fractures . The etiIntraoperative jaw fractures are a direct result of an application of excessive force and injudicious use of instrumentation. There seems to be a general agreement among authors of the reported cases regarding the age of occurrence and gender of subjects sustaining iatrogenic mandibular fractures. Concerning age and gender, reduction of the elasticity of bone, narrowing of the periodontal ligament space, ankylosis of tooth, and greater masticatory force can be considered plausible attributing factors . In the Before dental extractions, the total volume of the mandible that is being occupied by the impacted tooth is also an essential element in assessing the risk. To avoid IFM, the tooth/jawbone ratio should be evaluated using an orthopantomogram, cone beam computed tomography (CBCT), or CT scan. Wagner et al. reported this ratio to be 62% , whereasAnother reason for IFM could be the presence of former bony pathologies such as cysts and tumors, recurrent pericoronitis, and periodontal disease, all commonly occurring lesions in the mandibular angle region. Due to the reasons mentioned above, the mandible becomes weakened, which further predisposes to fracture. An incorrect surgical technique or injudicious use of elevators or forceps is also a consideration for the incidence of iatrogenic fracture of the mandible, which should be avoided by taking necessary precautions. The risk of fracture is even higher among more inexperienced surgeons.The management strategies for mandibular angle fractures are diverse and range from no treatment, soft diet, and intermaxillary fixation to open reduction and internal fixation. Treatment options are dictated by the characteristics of a fracture and the surgeon’s preference . In the IFM is a rare condition and can be easily avoided. Besides various causes, the incidence of IFM is relatively low. A detailed preoperative evaluation of the impacted teeth and bone adjacent to the sectioning of the tooth and minimal removal of bone during trans-alveolar extraction are a few techniques that can be employed to avoid IFM. The presence of a third molar increases the incidence of mandibular angle fracture. Although IFM is rare, whenever it occurs is very much distressing to the patients. Thorough knowledge of anatomy, judicious use of elevators and forceps, and sectioning of the tooth as and when required should be implemented practically to avoid IFM.


Micro-electromechanical-systems (MEMS) based sensors are used for monitoring the state of machines in condition-based maintenance tasks. This approach is applied at tram depots for the purpose of identifying faulty wheels on trams in order to eliminate defective trams at the entry or dispatch gates. The application of MEMS-based sensors for the detection of wheel faults is the focus of this study. A method for processing of the collected sensor data is developed. It is based on assessing the energy of vibrations at different frequency bands. Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) is used for obtaining a description of the sensor data. The task of finding the energy threshold for detecting faulty wheels, frequency band and parameters of MODWPT which most distinctly distinguish the wheels is the goal of the method. The weighted difference (DW) between the extreme values of energy in a frequency band for normal and faulty wheels is proposed as the measure of the ability to distinguish the wheels. The search for the solution is formulated as a discrete optimisation problem of maximising this measure. Both the simulation and experimental results indicate that faulty wheels have greater vibration energy than normal wheels. The properties of this approach are discussed and evaluated. Potential factors that determine the success of tram transport are the durability, reliability, and safety of tram wheel-sets ,2,3. TheUnlike trains, city trams ride on very sharp curves, turnouts, rail joints, and high-traffic intersections, allowing them to efficiently utilize the space available in the city. The operation of a tramway in such a dynamic environment causes the most significant operational problems, such as the wear of wheels and rail irregularities when a tram passes . In addiDue to these dynamic operational conditions, tram wheels are subjected to cyclic impact forces resulting in various defects that impair their rotational smoothness. Wheel flatness, wear, eccentricity, discrete defects, roughness, spalling, and shelling are among the most significant categories of defects . Wheel-fWheel-rail maintenance workers and managers strive to identify problems with wheels to avoid costly system-wide repairs. The wheel-assembly’s state should be monitored and maintained effectively before huge damage can occur. Early wheel-fault detection is required to ensure tram safety and stability. Therefore, fault detection and condition-based maintenance (CBM) are a profitable strategy for railway assets. This strategy can assist in ensuring increased protection and serviceability by identifying component problems as early as possible .CBM can extend component lifetimes by minimizing downtime and enables operators to optimize any replaceable component in a particular operational condition by altering the dependency on scheduled maintenance and ensuring a unique component repair schedule . Tram-whCurrently, there are two broad categories of wheel-fault detection methods. These are wayside and on-board detection techniques. The deployment of either wayside or on-board detection depends on type of the resource we are going to diagnose and types of rail transport. On-board detection approaches are methods employed on the train to detect the nature of the fixed assets, such as switches and rail conditions, whereas the wayside-mounted detection approaches are applied to study the health condition of the moving components on the train such as wheels, axles, and bearing elements ,11. On-bThe wayside detection of wheel faults is based on measuring the effects of wheel–rail interaction during the vehicle’s passage by placing a sensor unit at a single point. This method is inexpensive, and it overcomes the drawback of on-board detection techniques. The changes of acting forces, accelerations, or deflections are measured using strain gauges, accelerometer sensors, temperature sensors, mechanical sensors, and vibration- and noise-based sensors. These diagnostic devices have digital outputs, and the continuous time signals collected are digitised and treated as discrete-time-series signals.2 [These discrete-time-series signals are mostly processed using techniques in time, frequency, and joint time–frequency domains to reveal the conditions of the wheels. The frequency bandwidth changes of such signals fall within a few kHz. This limited range of changes opens the field for the application of MEMS-based sensors. Commonly available MEMS devices can sample accelerations up to few thousand times a second. The ranges of sensed acceleration values exceed hundreds of m/s2 ,13,14. FThe application of MEMS-based sensors for the detection of wheel faults is the focus of this study. To achieve the objective of the study, we have developed a method for identifying defective wheels that detects faults within a frequency band limit. This identifies faulty wheels and suggests maintenance and replacement.The remaining parts of the paper are organized as follows. Wheel-fault diagnostics have been the subject of extensive study over the past three decades, and numerous techniques have been developed. For instance, Bosso et al.  proposedPolygonised railway wheel detection based on the numerical time-frequency analysis of axle-box acceleration is suggested by Song et al. . The autTurabimana et al.  designedChen et al.  introducMadejski and Gola  presenteGao et al. , proposeNumerous time-frequency analysis techniques have been employed to diagnose wheel faults, including short-time Fourier transforms (STFTs), wavelet transform (WT), the Hilbert Huang transform (HHT), and empirical mode decomposition (EMD). In , NowakowIn , KomorskYue Jianhai et al.  used conZhang et al.  establisLi et al.  proposedYe et al.  proposedThe reported methods for detecting wheel faults are based on mature technologies for measuring accelerations. It is crucial to detect wheel faults under variable conditions with strong interference that corrupts the fault-signal characteristics. The collected data are processed using a number of frequency-analysis techniques. These approaches successfully detect faults but can be difficult or costly for field implementation. MEMS-based sensors and MODWPT are proposed for evaluating the energy of vibration in different frequency bands. The value of vibration energy in characteristic frequency bands describes the condition of the wheels.Demonstration of the capability of using MEMS vibration sensors with limited frequency bandwidth for detecting tram-wheel faults.Development of a tram-wheel fault-detection method using MODWPT for processing MEMS sensor data.Substantiation of the idea that vibration-energy differences in characteristic frequency bands are adequate for distinguishing faulty and normal tram wheels.The contributions of this paper are:In this study, a method for processing the collected sensor data is developed. It is based on assessing the energy of vibrations in different frequency bands. Maximal overlap discrete wavelet transform (MODWT) is used for obtaining a description of the sensor data. The properties of this approach are discussed and evaluated.Trams, in comparison to trains, are much lighter vehicles and this strengthens the idea of using MEMS-based sensors for the detection of wheel faults. The measurement properties of these sensors limit the detection capability.The research problem, expressed as a question, is as follows: Is it possible to detect tram-wheel faults using MEMS-based sensors?The implementation of such a detection method can become a routine maintenance task at tram depots. It can be applied for monitoring the conditions of incoming and outgoing trams. This implies that the vehicles travel at low speeds and in consequence their wheels interact with rails with much lower dynamic forces. The problem of collecting sensor data may be highly hindered by the condition of rail tracks at the depot.The solution of this problem requires the development of a method for extracting sensor-data features disrupted by several obscuring factors. Wheel impacts at rail joints, loose sleepers, and damaged rails are the most significant sources of interference. Such interference sources can be modelled using random processes with changing parameters. The random nature of the interference demands a careful approach to the extraction task in order to avoid the erroneous interpretation of sensor data. The analysis of the variation in energies of the sensor data is proposed as the basis for the method of wheel-fault detection and wavelet transform is a promising tool for sensor-data feature extraction. Wavelet transforms have proven useful for the analysis of sensor-data samples. The transform coefficients are wavelet and scaling, at different levels of decomposition, which represent properties of the samples related to time and changes of value . The disMaximal overlap discrete wavelet transform (MODWT) overcomes the lack of translation-invariance; it is invariant to circular shifting of the data samples. Maximal overlap discrete wavelet packet transform is developed on the basis of MODWT and includes the decompositions of the wavelet coefficients. MODWPT is an energy-conserving transform, that is, the sum of the total energies of the MODWPT coefficients is equivalent to the energy of the signal .The following research hypothesis is proposed as the basis of the study: vibration energy, calculated using MODWPT coefficients, in determined bands of frequencies, enable the detection of wheel faults.lh and lg [lh and lg to obtain the first-level coefficients j are extended by adding The set of N sensor samples l and gl . The lowi, j) are given by [The MODWPT coefficients at node (given by :(1)Wi,j,n is the frequency band number at the decomposition level i. There are 2i−1 frequency bands at each decomposition level; ‘mod’ means modulus after division.The energy of the collected sensor data is calculated as:i:Expressed using MODWPT coefficients at decomposition level sf of the sensor determines the frequency ranges of the bands i:This is the sum of energies in frequency bands of the sensor samples. The sample rate sf is set to 1 kHz. The sensor registers vibrations in the rail caused by the rolling tram wheels—There are energy peaks in the bands 150–230 and 400–460 Hz. The superimposed graphs of normal and faulty wheels show common behaviour. Further analysis is required to extract frequency bands, which differentiate the vibrations caused by the movement of the wheels.The important optimization criterion is the complexity of calculations as the signals from MEMS sensors are usually processed using microcontrollers. The criterion is additionally constrained by the requirements of efficient maintenance practices and parameters of the available MEMS vibration sensors. The description properties of the MODWPT coefficients are determined by the wavelet type and the level of decomposition. Daubechies wavelets, Coiflets, and Symlets are candidates for use. The level of decomposition defines the frequency resolution of the analysis.The task of finding the energy frequency band and parameters of MODWPT which most distinctly distinguish the wheels is the goal of the study. This can be formulated by a discrete optimization problem as the variables are discrete. The weighted difference .wavelet types: w = {Db, coif, sym};number of samples processed: N = {2000, 3000, …, 9000};number of decomposition levels: number of combined frequency bands: k = {0, …, N/2};starting number of the frequency band: n = {0, …, N}.It is subject to constraints:The solution defines the parameters of calculating the MODWPT using a set of samples from a MEMS-based acceleration sensor. The mid value between The threshold for detecting faulty tram wheels is:The energy of samples in the frequency band above the threshold  and classification of the wheel condition using the threshold (3).The proposed detection method consists of the following steps: The resultant detection threshold To limit the scope of the search for the solution, the ranges of possible values of the DW variables are restricted. The DW value changes are analysed to determine the directions for controlling this process. Crucial for the resolution of the frequency analysis, apart from the sampling rate, is the length of the sequence of MEMS-sensor samples and thus the maximal decomposition level. Preliminary measurements show that most of the signal energy is gathered in two narrow frequency bands. The highest frequency of the bands does not exceed 450 Hz which indicates that the chosen 1 kHz sampling rate is sufficient to obtain information on the wheel state. i = 9. In this case, using MODWPT, the frequency bands are described using single coefficients which can be sensitive to signal disruptions. In order to diminish the influence of possible interference, the set of samples is extended to 4096, ensuring 8 coefficients for the description of the frequency bands. The set of 4096 samples is collected in about 4 seconds which is acceptable for performing wheel diagnosis in real time. Extending the set of samples may be inadvisable because the speed of moving tram is variable, and a larger set may include the impact data. Additionally, the idea of combining the vibration energy of neighbouring frequency bands is abandoned. The first step reduces the number of variables of the DW function to: w—wavelet type, i—the level of decomposition, n—starting number of the frequency band. The starting number of the frequency band indicates the range of frequencies of the band. This enables a graphical analysis of the DW behaviour.In the first step, for limiting the search for the solution, the frequency resolution is restricted to 1 Hz. This value is common for describing vibration properties of objects. This assumption determines the minimal number of samples DW values for Daubechies wavelets and Symlets are similar, which is consistent with the results presented in . CoifletDW values obtained for the lower (less than 6th) levels of decomposition are insignificant and the variation in vibration energy is very minimal for the three wavelet families presented in In the final step, for limiting the search for the solution, the decomposition level is set to 7, although the 9th level gives the highest values. The 7th level of decomposition gives wider frequency bands; in this case, the width is about 4 Hz. Wider frequency bands give a more robust approximation of wheel-fault properties. Coiflets are chosen as the MODWPT calculation basis.L of the wavelets filters—improves the DW value but at the cost of computational complexity. The highest value of the DW function is obtained for the coif4 and coif5 at the 7th level of decomposition—Increasing the number of wavelet vanishing moments—length The value of the threshold for detecting faulty wheels is sensitive to the state of the rail tracks at the depot. Badly maintained rail joints or damaged sleepers generate very large vibration signals during tram movement which can deteriorate the operation of the MEMS acceleration sensors. This results in distorted values of calculated energy in the frequency bands not corresponding to the wheel states.Field tests of the method were performed in the tram depot of the company Tramwaje Śląskie which provides tram services for the Upper Silesia Region in Poland. The depot maintains over 130 trams. There are several rail tracks at the depot which are used for organising the movement of trams on the premises. The chosen rail track for the tests is about 150 m long. A prototype of the vibration sensor is designed using a three-axis MEMS accelerometer. The measurement ranges are +/−4 g, +/−8 g, and +/−16 g. The accelerometer is AEC-Q100 qualified, it is suitable for work in harsh environments. The prototype is self-powered and capable of registering acceleration values for several weeks. In the course of a number of tests the optimal measurement range was determined. This range +/−8 g enables the registration of impacts at rail joints without “overloading” the sensor and gives large signal values during wheel rolling. Several registration sessions were carried out with trams with wheel-sets in different technical conditions. Representative data sets for “normal” and “faulty” wheels were obtained and these are the basis for the substantiation of the idea that vibration energy is adequate for distinguishing tram wheels. y axis values represent lateral movements of the rail, whereas z axis represents the horizontal. The samples of acceleration in the y and z axis do not map the vibrations in a consistent way. These phenomena may be a consequence of the condition of the rails at the depot. The x axis data are chosen for determining the detection threshold for classification of the tram wheels.The MEMS sensor is placed in the enclosure of the prototype in such a way that the MODWPT is applied to the collected data. Coiflet with five vanishing moments and the 7th level of decomposition are used as parameters of the transform. Temperature is the factor which mostly changes the measured acceleration values as the device is factory calibrated. The sensor datasheet notes a maximal zero-g level change of +/−5 mg/°C and sensitivity change due to temperature typically +/−0.01%/°C. In all, the measurement errors do not exceed single percent values for yearly temperature changes.Faulty-wheel detection tests using the threshold prove that the threshold value is robust to variation in tram speed in the range of 2–7 m/s which covers the range of speeds of maneuvering trams in the tram depot. The calculation of the MODWPT coefficients for the 7th level of decomposition and coif5 wavelet does not impose excessive requirements on the computation resources. An embedded system incorporating the MEMS sensor and an advanced microcontroller can handle the stream of samples and calculate their energy.The tested prototype is mounted on one rail and detects faults of wheels which roll on this rail. A complete system requires a sensor at each rail. Additionally, a collected history of sensor data assigned to trams will help maintenance works in the depot.Detection of tram-wheel faults can be done successfully using commonly available MEMS-based acceleration sensors with at least a 1 kHz sampling rate. The amplitudes of registered accelerations fall within the measuring capabilities of such sensors. It is important to adapt the parameters of the detection method to the conditions of the measuring site and update them with changes. MODWPT was successfully used for the calculation of the vibration energy of the samples and does not require large computation resources. The tests were carried out for trams with flat wheels. The method is sensitive to different sizes of flat spots. Future studies are proposed to determine the capability of the method to assess the size of the spots and to detect other types of wheel damage. As the tram depot where the tests were conducted maintains a large fleet of trams in different technical conditions, it will be the basis for collecting vibration data. The range of wheel irregularities of such a fleet can be regarded as representative for carrying out studies. The analysis of vibration energy content in different frequency bands has proven successful for detecting wheel irregularities. The different types of irregularities are manifested by changes of vibration energy in specific frequency bands. The highest vibration frequencies, at low vehicle movement speeds, do not surpass the frequency bandwidths of commonly available MEMS sensors.This approach may be supplemented by machine learning techniques. Machine learning, especially methods using convolutional neural networks, for classification require careful design. The design needs an extensive database for training and validation. Properly trained can be significantly more robust to changing conditions in the tram depot. This property is much desired by the management of the depot. The machine learning approach will be another goal of future studies.


The frequency-hopping spread spectrum (FHSS) technique is widely used in secure communications. In this technique, the signal carrier frequency hops over a large band. The conventional non-compressed receiver must sample the signal at high rates to catch the entire frequency-hopping range, which is unfeasible for wide frequency-hopping ranges. In this paper, we propose an efficient adaptive compressed method to measure and detect the FHSS signals non-cooperatively. In contrast to the literature, the FHSS signal-detection method proposed in this paper is achieved directly with compressed sampling rates. The measurement kernels (the non-zero coefficients in the measurement matrix) are designed adaptively, using continuously updated knowledge from the compressed measurement. More importantly, in contrast to the iterative optimizations of the measurement matrices in the literature, the deep neural networks are trained once using task-specific information optimization and repeatedly implemented for measurement kernel design, enabling efficient adaptive detection of the FHSS signals. Simulations show that the proposed method provides stably low missing detection rates, compared to the compressed detection with random measurement kernels and the recently proposed method. Meanwhile, the measurement design in the proposed method is shown to provide improved efficiency, compared to the commonly used recursive method. In both military and civilian secure communications, the spread spectrum (SS) techniques have been widely used . In thesThe non-cooperative detection of the FHSS signal is the first step of the entire signal interception procedure . AlthougIn 2006, the theory of compressed sensing (CS) was rendered ,31. The To efficiently extract the key features from the signals, fast signal feature extraction methods were studied over decades. Although methods such as principal component analysis, linear component analysis, independent component analysis, supporting vector machine, etc. were studied in various scenarios, the logics that can be represented within such methods were constrained. In the 1970s, artificial neural networks (ANNs) were proposed to model the logics between the input data and their features or processed results. The ANN was originally rendered to solve the signal classification problem. The model optimizations were done using the training procedure. In recent decades, with the development of the parallel computing and the graphic processing unit (GPU) techniques, the deep neural networks (DNNs) are enabled and is now adopted in various areas in signal processing, such as parameter estimations , audio a(1)The FHSS signal-detection method proposed in this paper is achieved directly from the low-rate sampling results without the reconstruction of the original signal.(2)The quantitative Shannon information is analyzed based on the posterior information of the channel output and is used in the measurement kernel design for the following measurements, which ensures improvement in the FHSS signal-detection accuracy.(3)More importantly, with an effective combination of the TSI optimization theory and the DNNs in this paper, the inefficiency in the existing information-based method of the compressed measurement matrix design is solved. In particular, in contrast to the iterative optimizations of the measurement matrices in the literature, the DNNs are trained once based on the TSI optimization and are repeatedly implemented to detect the FHSS signals in an efficient manner. Thus, the practical online adaptivity of the FHSS measurement and detection can be achieved with the method proposed in this paper. From the signal processing aspect, the adaptivity in the FHSS signal processing based on the DNNs is also achieved.In this paper, we propose an efficient and adaptive method to detect the FHSS signals non-cooperatively. The adaptivity of this method is achieved with the fusion of the posterior knowledge enhancement algorithm and the DNNs. The posterior knowledge is gained with the gradually increased task-specific information (TSI)  in the dThe remainder of this paper is organized as follows: In h is the modulation index of the FHSS signal. rth symbol content in the hopping period. The function In this paper, we propose a method to measure and detect the FHSS signals compressively, adaptively and efficiently. The proposed method was verified through simulations, where the Gauss binary frequency shift keying FHSS signal of the Bluetooth standard  were useAs specified in the Bluetooth standard, the carrier frequency of the signal randomly hops among 79 channels from 2.402 to 2.480 GHz, with 1 MHz bandwidth for each channel. The symbol period takes the value of 1 In this paper, the proposed adaptive measurements and detection of the FHSS signals are done compressively and non-cooperatively using the framework described in In B. Then, using the framework in The compressed measurement using the framework described in Based on the compressed measurements, the detection decision is made from the two following hypotheses:In this paper, the signal detection is conducted based on the energy of the measurement data, and the measurement matrix is designed adaptively based on the gradually obtained measurement data. The principles of the proposed methods are detailed in the following sections.M.According to the noise folding theory , as the T, the theoretical false positive rate  is:The signal detection is conducted by energy thresholding. More specifically, given a positive threshold kth  an an14) anTheoretically, the signal detection with a measurement matrix from the recursive optimization in Equation  can acquThe structure of the DNNs in the proposed method is shown in mth   T for thCR = 10, it took 5.36 days. To train the DNN for the adaptive measurement kernel design at CR = 20, it took 6.61 days. The SNR is defined as the ratio between the signal power and the noise power. As specified above, the number of Nyquist samples during the measurement procedure were The simulated curves of missing detection rates versus the signal-to-noise ratio (SNR) are shown in From the two figures, we observe that at any CR and certain false-alarm rate , the missing rates  from all the four methods in comparison decrease with increased SNRs. Non-compressed detection achieves the lowest missing rate for most cases. The partial DFT-based compressed detection method can obtain good detection performance at median SNR values. However, for higher SNR cases, the missing detection rates can be even significantly higher than the conventional compressed detection with random measurement kernels. The adaptive compressed detection method, although obtaining higher missing rates than the non-compressed detection method and obtaining higher missing rates than the partial DFT-based compressed detection method at some median SNR values, outperforms the compressed method with random measurement kernels for low and median SNR values at any CR. This improvement in terms of missing rate can even be around an order at some SNRs. For high SNR values (above To have a deeper insight into the procedure of the adaptive measurements in the proposed method, we performed a further analysis on the power spectra of the designed measurement kernels. A larger value of the measurement kernel power spectrum value within the true subband that the FHSS signal falls in indicates a higher SNR resulted in the measurement data. In turn, higher detection accuracy would be expected. As a representative, In In addition to the simulations on the detection accuracy and the measurement kernel components above, we also conducted simulations to compare the time costs of the proposed adaptive detection method using the DNNs and that using recursive measurement kernel optimization method discussed in From In this paper, a knowledge-enhanced compressed measurement method was proposed for adaptive and non-cooperative detection of the FHSS signals using the DNNs. In contrast to the conventional non-compressed receiver, which was unfeasible for wide frequency-hopping bandwidths, the proposed method in this paper conducted the FHSS signal detection with compressed sampling rates. The measurement kernels were designed adaptively based on the continuously updated knowledge from the compressed measurement. Moreover, in contrast to the iterative measurement kernel optimizations, the DNNs was trained once off-line based on the TSI optimization, and implemented repeatedly online to adaptively design the measurement kernels, enabling efficient FHSS signal detection. Simulation results showed that the proposed adaptive compressed detection method achieved stably low missing detection rates, compared to the compressed detection system with random measurement kernels and the recently proposed work. In addition, through the simulations, we also showed that the efficiency of the proposed adaptive FHSS detection method with the implementation of the DNNs was proved to be significantly higher than that using the recursive measurement kernel optimization methods. Thus, the measurement kernel design procedure improved its efficiency significantly, and became much more practical for the online adaptive measurements and detection of FHSS signals.


Active fault detection has an important significance for seismic disaster prevention and mitigation in urban areas. The high-density station arrays have the potential to provide a microtremor survey solution for shallow seismic investigations. However, the resolution limitation of the nodal seismometer and small-scale lateral velocity being inhomogeneous hinder their application in near-surface active fault exploration. Distributed acoustic sensing (DAS) has been developed rapidly in the past few years; it takes an optical fiber as the sensing medium and signal transmission medium, which can continuously detect vibration over long distances with high spatial resolution and low cost. This paper tried to address the issue of near-surface active fault exploration by using DAS. We selected a normal fault in the southern Datong basin, a graben basin in the Shanxi rift system in north China, to carry out the research. Microtremor surveys across the possible range of the active fault were conducted using DAS and nodal seismometers, so as to obtain a shallow shear wave velocity model. Meanwhile, we applied a Brillouin optical time domain reflectometer (BOTDR) and distributed temperature sensing (DTS) to monitor the real-time fluctuation of ground temperature and strain. Our results show that the resolution of the deep structures of the fault via the microtremor survey based on DAS is lower than that via the seismic reflection; whereas, their fault location is consistent, and the near-surface structure of the fault can be traced in the DAS results. In addition, both the BOTDR and DTS results indicate an apparent consistent change in ground temperature and strain across the fault determined by the DAS result, and the combination of surface monitoring and underground exploration will help to accurately avoid active faults and seismic potential assessment in urban areas. Large earthquakes occurring in urban areas often bring about catastrophic events and cause enormous casualties and huge economic losses in many seismically active regions . For exaDAS is a newly developed optical fiber sensing technology that uses the coherent Rayleigh backscattering of a low-noise laser in a common single-mode sensing fiber to continuously detect the vibration variation of an external physical field over a long distance ,13. To dIn this paper, we conduct a near-surface active fault detection experiment based on microtremor surveys using DAS in the southern suburb of Datong basin, north China. According to our seismic reflection profiles and existing geological surveys, we chose a test site and deployed optic cables to test the application of the distributed optical fiber sensing in the exploration of active faults. To verify the authenticity and validity of DAS data, we also deployed short-period three-component seismometer lines. First, we describe the major tectonic features of the test site based on previous studies. Second, we compared the microtremor data recorded by DAS arrays and three-component nodal seismometers and applied multichannel analysis of surface waves (MASW)  to identThe Datong basin is a graben in the northern part of the Shanxi rift system that is characterized by a series of basin boundary normal faults and several large earthquakes with a magnitude larger than 7 in history . No largFault F4 is the boundary normal fault of the sub-basin and dips NW; the seismic profile shown in Therefore, we selected the area where fault FP4-3 is located as the test site , we used the three-component microtremor data recorded by the nodal seismometers to calculate the H/V spectral ratio curves. This method is generally used to provide prior information for subsequent microtremor survey data processing , and we We take two sets of parameters to calculate the frequency phase velocity spectra: the length of receiving array and each time segment are 350 m, 20 s a,b, and On this basis, MASW and the damped least-squares method were used to extract the fundamental-mode Rayleigh wave phase-velocity dispersion curves and 1-D S-wave velocity profile, respectively . We usedBased on this, we have carried out precise processing on the shallow area (red box area) within the range of station 424 m to 664 m b,e. The According to the location of the shallow active fault obtained from the detection results shown in We conducted a microtremor survey numerical simulation experiment based on two-dimensional viscous acoustic equations to study this characteristic. According to the microtremor survey results, we constructed the two-dimensional normal fault model shown in The existing research results show that the loose sediments, vegetation and other overburdens above the buried faults have high humidity, high porosity and high water content, which makes the thermal inertia of those overburdens greater than that of the bedrock. The high thermal inertia means that the fault zone will form a low temperature area compared with the bedrock, which is shown as a negative anomaly zone on the thermal infrared image . At the In this paper, we investigated the applicability of imaging near-surface active fault zones with distributed acoustic sensing. The use of high spatial resolution DAS data to improve the imaging accuracy of microtremor surveys and long-term monitoring of ground temperature and strain measurements to constrain the underground detection results is expected. The experimental results suggest that in the near-surface active faults exploration, the microtremor survey results-based DAS data are similar to those obtained from conventional nodal seismometers. Affected by the directional sensitivity and DAS system noise, the SNR of the low-frequency surface wave signal received by DAS is weaker than that of the nodal seismometers. However, because the DAS signal is mainly sensitive to the elongation and compression along the direction of fibers, which is conducive to the reception of high-frequency surface waves, especially high-order surface waves, this allows us to obtain shallow active fault information with higher resolution. At the same time, the research results of this paper show that dense geometries are conducive to improving the imaging accuracy of microtremor seismic surveys; DAS can realize high density spatial sampling at a low cost, which is conducive to the exploration of near-surface active faults in a large range. How this advantage can be used to improve the accuracy of shallow active fault tomography is worthy of further exploration in the future.Secondly, comparing the results of active fault exploration by DAS and the long-term monitoring results of ground temperature and strain by BOTDR and DTS, it is not difficult to find that the location of the largest change in ground temperature and strain is in agreement with the location of the near-surface active faults obtained from the inversion results of microtremor sources. This shows that in practical exploration, we can comprehensively use the high-spatial resolution ground temperature and strain data recorded by BOTDR and DTS, as well as the underground formation information detected by DAS to estimate the location of near-surface active faults, so as to reduce the influence of human interference and lack of prior information on the detection results, and improve the reliability of the detection results.Another feature to note is the CC profile. Abukrat et al.  showed t


In this paper, a field study is carried out to monitor the natural frequencies of Malahide viaduct bridge which is located in the north of Dublin. The bridge includes a series of simply supported spans, two of which collapsed in 2009 and were replaced. The replaced spans are stiffer than most of the others and these differences resulted in higher natural frequencies. An indirect bridge monitoring approach is employed in which acceleration responses from an instrumented train are used to estimate the natural frequencies of each span of the viaduct showing the locations of the two replaced spans with higher stiffness. For the indirect approach, an Ensemble Empirical Mode Decomposition (EEMD)-based Hilbert Huang Transform (HHT) technique is employed to identify the natural frequency of each span. This is carried out by analysing the Instantaneous Frequencies (IFs) from the calculated intrinsic mode functions. The average of the IFs calculated using 41 runs of the instrumented train (with varying carriage mass and speed for each run) are used to estimate the natural frequencies. To assess the feasibility of the indirect approach, a bespoke set of direct measurements was taken using accelerometers attached successively on each span of the viaduct. The free and forced vibrations from each span are used to estimate the first natural frequencies. The frequencies obtained from drive-by measurements are compared to those from direct measurements which confirms the effectiveness of indirect approaches. In addition, the instantaneous amplitudes of the drive-by signals are used to indicate the location of the stiffer spans. Finally, the accuracy and robustness of the indirect approaches for monitoring of multi span bridges are discussed. Bridges are arguably the most critical structures in transportation infrastructure. They require monitoring to detect local and global damage caused by several reasons such as bridge strike, fatigue, loading and scour ,2,3,4,5.Bridge dynamic responses to ambient, forced, or free vibrations, are often used for bridge damage detection ,5,13,14.Indirect or drive-by techniques have recently gained interest among Structure Health Monitoring (SHM) researchers because of the ease with which dynamic responses can be measured ,30,31,32For signals in the time or frequency domain, several signal processing techniques have been proposed for the extraction of features from the acceleration responses. These include short-term Fourier transform , waveletIn this paper, an improved HHT (using EEMD) is applied to the acceleration measurements from an instrumented train to estimate the natural frequencies of the Malahide Railway Viaduct in Ireland, which consists of 12 simply supported spans. To the best knowledge of the authors, this is the first time that a drive-by technique is employed to estimate the fundamental frequency of each span of a multi span viaduct bridge in field. To validate the drive-by technique, a direct test is also carried out to find the true natural frequency of each span. This bridge experienced a collapse of two spans and one pier foundation in 2009 due to scour. These spans were replaced with stiffer elements ,51 whichn(t) signal is introduced in the original acceleration signal x(t). Each iteration (i) is given by Equation (1). The added noise provides a uniformly distributed reference frequency and IMFs associated with a series of random and uncorrelated noise signals.In the EMD process, the acceleration signal is decomposed into multiple IMFs, which are oscillatory functions with varying energy amplitude and frequency . The EEMix(t), decomposition is carried out repeatedly and the ensemble means of the IMFs are the final results. The level of added noise and the number of iterations can affect the final IMFs from EEMD. Hence, finding their optimum values for each case is important for the accuracy of the results [Using the noisy version of the signal,  results ,52. With results  use the rC(t)) with varying frequency and amplitude using EMD or EEMD, and (2) application of the HT (given in Equation (2)) to the measured IMFs to calculate the instantaneous frequencies (IFs) [H(rC(t)) represents the HT of the rth IMF and can be defined as:t represents time and P represents the Cauchy principal value of the singular integral. The HT results can be grouped for each IMF to form an analytic signal a(t) as a complex function:j is imaginary unit, rth IMF, respectively. By differentiating the phase functions with respect to time, the IFs can be calculated [The HHT is a two-step process consisting of: (1) decomposition of a signal into multiple IMFs (es (IFs) . H(Cr(t)lculated . A HilbeIn this paper, EEMD based HHT is used to estimate the natural frequencies of a multiple span bridge using train accelerations. In the drive-by signal, mode mixing creates a challenge for researchers to estimate the natural bridge frequencies . For thaThe Malahide Viaduct is a 12-span bridge, constructed in 1844 over the Broadmeadow Estuary, Dublin, Ireland . It contTo provide a baseline to compare with the drive-by measurements, the natural frequencies of each span of the viaduct are measured directly by installing accelerometers on the bridge. Five triaxial wireless MEMS accelerometers  of the free and forced vibration data. For each span, the forced and free vibrations after three passing trains were used to estimate the first natural frequency. An example of the vibration signals measured at five locations of span 8 (one of the existing/old spans with longer length) and their FFTs following a train crossing, are shown in A five-carriage train is instrumented using multiple accelerometers and a Global Positioning System installed at the first bogie of the leading carriage . The layThe train speed varied significantly between runs in the range, 85–120 km/h . A samplAn EEMD-based HHT is applied to the drive-by acceleration signals (recorded from the instrumented train). To test the approach, a raw acceleration signal is decomposed into IMFs using the EEMD technique. The amplitude of the added noise and the number of iterations are determined using recommendations from the literature ,50,52, aIMFs 5, 6 and 7 along with their FFTs and IFs are illustrated in In this paper, EEMD-based HHT is used to identify the IFs from indirect acceleration measurements. As seen in As reported in , the ampThis paper presents a field investigation of direct and indirect/drive-by bridge health monitoring approaches for a multiple span viaduct. Two spans of the viaduct were replaced by stiffer beams in 2009 after they collapsed due to foundation scour. Acceleration responses, extracted from an instrumented train are used in this paper to (i) estimate the first natural frequencies of each span of the viaduct bridge, and (ii) detect the stiffness changes present in 2 out of 12 spans of the viaduct. Direct measurements with sensors installed on the bridge, are used to validate the results. The frequencies were estimated from the indirect measurements using the EEMD-based HHT technique. The HHT is a recent technique for indirect health monitoring. The EEMD instead of EMD is used to overcome the issue of mode mixing. This technique is used to extract natural frequencies of the spans with the help of IFs from the calculated IMFs. The HT energies are seen to be strongly affected by replacing (negatively damaging) the two spans. The EEMD approach can be employed with drive-by measurements to detect the fundamental frequency of each span of a multiple span bridge. However, some preliminary information about the bridge frequencies or their ranges is required for effective application of the proposed approach.The natural frequencies estimated from indirect measurements are reasonably close to the direct measurements and both measurements follow the same pattern of frequency changes in the internal spans of equal length.The results from forced vibrations (compared to free vibrations) are closer to the ones obtained from drive-by approach which is due to the added-mass effect of the crossing train.The proposed approach shows reasonable results when is used for comparing the frequencies of the spans with same length, while it becomes more challenging for shorter spans.The energy of the frequencies are seen to decrease in the two replaced spans. Therefore, it can be used as a damage indicator for loss of global stiffness in future studies.A summary of the results is as follows:


This study discusses a nonlinear electrical impedance tomography (EIT) technique under different analysis conditions to propose its optimal implementation parameters. The forward problem for calculating electric potential is defined by the complete electrode model. The inverse problem for reconstructing the target electrical conductivity profile is presented based on a partial-differential-equation-constrained optimization approach. The electrical conductivity profile is iteratively updated by solving the Karush–Kuhn–Tucker optimality conditions and using the conjugate gradient method with an inexact line search. Various analysis conditions such as regularization scheme, number of electrodes, current input patterns, and electrode arrangement were set differently, and the corresponding results were compared. It was found from this study that the proposed EIT method yielded appropriate inversion results with various parameter settings, and the optimal implementation parameters of the EIT method are presented. This study is expected to expand the utility and applicability of EIT for the non-destructive evaluation of structures. Electrical impedance tomography (EIT) is a non-destructive evaluation method through which the electrical properties of part of a structure are determined using measured data from surface electrodes. This method is highly applicable in medical imaging, industrial process monitoring, and geotechnical site characterization because of its ease of use in field experimentation, economic feasibility, and superior ability to penetrate the target. For example, the EIT method coupled with convolutional neural networks has been explored for reconstructing human organ boundaries , and EITEIT has many advantages; however, it requires improvements in its mathematical modeling, numerical analysis, and implementation techniques to increase the accuracy of solutions and to broaden its application scope to further extensive fields. Previous studies on EIT suggest that the quality of the inverse tomographic images obtained using measured electric potentials is sensitive to electrode arrangement and current input patterns ,14,15,16Examples of current input patterns commonly used in EIT include the adjacent drive pattern , oppositBased on the previous developments, this study proposes several implementation parameters and analysis conditions for EIT, such as the number of electrodes, current input pattern, and electrode arrangement. The proposed parameters and analysis conditions are applied to the EIT procedure described in a recent study ,20. The The remainder of this paper is organized as follows: In The CEM is a mathematical model for resolving the electrostatic forward problem for electric potential. It considers current loss that occurs when the current flows to a low-impedance material through an electrode and the voltage drop due to the contact impedance between the structural surface and electrode ,23. TherThe CEM for calculating the electric potential due to the current input can be expressed as a boundary value problem, as follows: follows :(7)∫Ωσ∇uIntroducing finite element approximations to the electric potential found in ,20.The forward CEM solution is validated by comparing it to the solution obtained by ANSYS Mechanical APDL. The inverse medium problem for reconstructing the electrical conductivity profile of a structure using measured electric potential data at surface electrodes can be presented as the following PDE-constrained optimization problem:The objective functional In this study, Tikhonov (TN)  and totaFor TV regularization, The Lagrange multiplier method was used to convert the PDE-constrained optimization problem written in Equation (8) into an unconstrained optimization problem. The objective functional The state equation and the corresponding boundary conditions can be obtained from the stationarity requirement that the first variation of the Lagrangian with respect to adjoint variables The adjoint equation and the corresponding boundary conditions can be obtained from the stationarity requirement that the first variation of the Lagrangian with respect to state variables  follows ,20:(12)∇Equation (12) is the governing equation for the adjoint variable  problem .The control equation and the corresponding boundary conditions can be obtained from the stationarity requirement that the first variation of the Lagrangian with respect to the control variable  follows ,20:(16)−In deriving Equation (16), the TN regularization scheme was used. If the TV scheme were used instead, Equation (16) could be replaced bygrangian ,28,29. TThe first and second optimality conditions are satisfied by solving the state and adjoint problems, respectively. Because only the true profile of Assume the initial electrical conductivity profile of a structure to be investigated, then calculate the electric potential Calculate the adjoint solutions Using the state and adjoint solutions, calculate the gradient of the Lagrangian with respect to the control variable In Equation (20), the TN regularization scheme was used. If the TV scheme were assumed, then the Lagrangian gradient for Update the electrical conductivity at each node using a line search method. Equations (17) and (18) are not precisely enforced in updating the electrical conductivity at boundaries since they are complicated to implement. Instead, one can enforce that the normal derivative of The search direction for the optimal solution of the control variable Thereafter, the electrical conductivity vector The choice of regularization factor n scheme ,31,32 waIf the TV regularization scheme were used,The first term of Equation (24), Therefore, Consider a square domain with a side length of This study compares the inversion results according to the change in various implementation parameters using a response misfit and a relative The relative For evaluating the regularization effect on the EIT, the TN and TV regularization schemes are explored in the inversion for a three-layer heterogeneous medium. nditions . ExampleAs mentioned in For demonstrating the effectiveness of the regularization factor continuation scheme, the inversion tried fixed regularization factors in the same setting. In this study, three different analysis conditions were explored to derive optimal parameters for performing the EIT in heterogeneous media. The conditions considered are the number of electrodes, spatial current input pattern, and electrode arrangement. The number of electrodes is expected to significantly affect the inversion result because it impacts the electric potential field and the amount of measured potential data. In this work, 8, 20, 40, and 80 electrodes are tested for inversion, as shown in Uniform and cosine input patterns are investigated as the current input pattern for inversion. The uniform pattern is the same as that used in In Equation (34), This study investigated optimal implementation parameters for a nonlinear EIT technique using the CEM. The EIT method is based on PDE-constrained optimization, which reconstructs the electrical conductivity profile by solving the KKT conditions iteratively. By applying various analysis conditions, the optimal set of parameters that minimize relative The layered profile was reconstructed more clearly when using the TV regularization scheme than TN, especially at the interface of layers. The inversion result was improved when using the regularization factor continuation scheme rather than the fixed method.A higher number of electrodes did not necessarily improve the inversion results. In addition, the TN regularization scheme produced relevant results when the number of electrodes was small.The layered profiles were successfully reconstructed for all the presented current patterns. The relative In the case of arranging electrodes on all sides of the square domain, the inversion result was improved compared to the case of arranging them only on two sides.The relative This study is expected to expand the applicability of the nonlinear EIT method for the non-destructive evaluation of civil structures such as damage inspection, strength inspection of concrete under curing, fiber content inspection of fiber-reinforced concrete, etc.