Knowledge about body motion kinematics and underlying muscle contraction dynamics usually derives from electromyographic (EMG) recordings. However, acquisition of such signals in snakes is challenging because electrodes either attached to or implanted beneath the skin may unintentionally be removed by force or friction caused from undulatory motion, thus severely impeding chronic EMG recordings. Here, we present a reliable method for stable subdermal implantation of up to eight bipolar electrodes above the target muscles. The mechanical stability of the inserted electrodes and the overnight coverage of the snake body with a “sleeping bag” ensured the recording of reliable and robust chronic EMG activity. The utility of the technique was verified by daily acquisition of high signal-to-noise activity from all target sites over four consecutive days during stimulus-evoked postural reactions in Amazon tree boas and Western diamondback rattlesnakes. The successful demonstration of the chronic recording suggests that this technique can improve acute experiments by enabling the collection of larger data sets from single individuals. Acquisition of long-term chronic EMG data is well-established in many animal species ranging from fish  with respect to relative body position  or type of muscle activation (tonic vs. phasic) is the major goal, a high spatial resolution would be desirable but is not essential to obtain the respective information. To overcome the technical limitations of sEMG recordings in snakes and to allow for chronic multi-site muscle activity analyses, we have developed a new technique for collecting multi-channel EMG data from multiple body segments during the execution of a natural snake behavior. Our technique resembles the use of patch electrodes, with the skin providing electric insulation from one side, while electric activity is recorded from the surface of large epaxial muscles with bipolar electrodes. This recording technique avoids surgical exposure of the muscle or the use of barbed electrodes and is thus less invasive. This technique permits stable EMG recordings with a high signal-to-noise ratio. Both, individual spikes and local muscle group dynamics, normally associated with sEMG data, were robustly and consistently acquired in two species of snakes. Furthermore, this technique is suitable for the recording of high-quality data over several days and can thus be employed for chronic recording of EMG data in snakes.Corallus hortulanus) and two semi-adult Western diamondback rattlesnakes   were used. In addition, four carcasses of Amazon tree boas were used to establish the electrode implantation prior to the actual animal experiments. Snakes were bred at the Chair of Zoology  and maintained on a 12 h:12 h light:dark regime, 22–33°C temperature range, and a diet of pre-killed rodents with water ad libitum. Permission for the experiments was granted by the respective governmental institution for animal welfare .In this study, five semi-adults  Amazon tree boas  were used, which consisted of a miniaturized connector (7.4 × 4.4 × 1.8 mm), pre-wired with 18 cables . Each cable was electrically shielded with an individually colored layer of biologically compatible PTFE coating and was thus protected from producing a short-circuit with other wires. The total weight of the wires including the connector was 2.8 g which equals 1.6–3.5% of the snakes' bodyweight and was thus easily supported even by the smallest snakes employed for the study. The cables were used in pairs, such that the cut ends formed a bipolar EMG electrode . Using aIn order to secure the EMG electrodes in a close and constant relative position to each other, cables were affixed to each other using a small drop of cyanoacrylate glue . To prevThe steps for producing an electrode were as follows: the position of the sphere on the cable was visually marked while aligning the two cables. At the same time a small drop of glue was applied to both cables at the marked position. Both cables' relative length was ensured to remain invariant relative to each other, as this would have caused problems with cable management during the experiments. After application, while the small drop of glue hung from both cables in a half-spherical form, a pinch of sodium bicarbonate was sprinkled from above onto the glue to facilitate solidification and drying. This caused the downwards hanging glue to be pulled upwards into a half-spherical form, due to the combination of surface tension and instantaneous fixation. Rotation of the cable and repetition of the procedure ensured a small but strong hold that was spherical in form . Care waPrior to the electrode implantation, snakes were placed in an induction chamber and pre-anesthetized with 2 ml isoflurane . As soon as the tail-pinch reflex ceased, snakes were intubated with a cat catheter (diameter: 1.2 mm) connected to an isoflurane vaporizer . The isoflurane concentration provided by the vaporizer was set to 2.0–2.5%, to ensure adequate surgical anesthesia throughout the entire duration of the implantation process. Additionally, Carprofen  was administered  for analgesic treatment 1 h before the start of the implantation and once thereafter every following day throughout the entire period of EMG recordings.semispinalis-spinalis (SSP) muscles. If necessary, precise electrode positions could be determined by dissection or X-ray imaging.Before electrode implantation, all surgical tools, needles and wires were sterilized through submersion in a disinfectant  for at least 5 min. For the electrode implantation, the sharp end of the needle was used to penetrate the skin of the snake at predetermined positions at the side of the body and was subdermally guided over a distance of 4.5 cm . Great cIn order to prevent cable removal, a suture  binding skin and cables was placed at the side of the glue sphere opposite to the cable's entry hole to tightly hold the two cables in place . We usedFollowing implantation, the isoflurane concentration was set to 0%, which caused complete recovery of the snakes from the anesthesia within a few minutes. During the experimental procedure each snake was regularly and systematically monitored. There was no alteration of the health of the snakes nor any obvious inflammatory signs at the site of the implanted electrodes. It was important that during the recovery period and prior to the experimental trials on successive days the snake's movements remained restricted to prevent the occurrence of forces onto the implanted cables. This measure assisted in preventing accidental removal of cables and consequential damage of the skin. In chronic experiments that lasted for several days, snakes were kept overnight in quarantine cages. A particular challenge during the overnight rest was the prevention of the cables from becoming entangled in cage enrichments, e.g., branches. A major advancement for the performance of chronic measurements across several days was therefore the reliable and faithful affixation of recording electrodes and cables at all times. This was particularly challenging at night in the home cage when the animals were essentially unobserved. Instrumental for successfully maintaining all electrodes in place and functionally intact was the use of an individually adjusted “snake sleeping bag,” which prevented impairment and deterioration of electrode placements and thus ensured the continuity of the recording condition over the experimental period of up to 4 days . The maxCorallus hortulanus) employed in our study, the use of such a bag was highly beneficial as these snakes generally use their prehensile tail to wrap around objects, as well as around their own body. The “sleeping bag” was constructed from a stretchy jersey fabric. Critical for the stable positioning of the bag was the extension of the snake out of the fastened shut bag on both sides  was used to provoke compensatory postural reactions driven by stereotypic muscle activity for the assessment of EMG quality. Accordingly, the snake was placed on a branch that was positioned in the vertical rotation center of the turntable. The turntable had a dimension of 30 × 30 cm and was driven by a brushless DC motor . A MATLAB script  was used to control turntable movements. The standard stimulus consisted of a sinusoidal rotation in the horizontal plane with a positional excursion of ±60° and a frequency of 0.1 Hz (period of 10 s). A spatially invariable infrared stimulus  was presented in front of the snakes to attract the attention of this infrared-sensitive species. Since the snakes focused on the position of the IR-Emitter, the head remained relatively stable in space during turntable rotation. This was achieved by the snakes through an activation of compensatory movements of the head/body involving the most rostral body loops. Thus, turntable motion caused the snake to decrease or increase the diameter of its S-shaped body loops, which resulted in a relatively stereotyped motor behavior, ideally suited to assess the quality of the EMG recordings. To reconstruct the change in body shape, a video camera  was mounted above the turntable and was temporally synchronized with the EMG recording device.N = 4) was chosen for the evaluation of the electrode performance across successive recordings days. Accordingly, the data on the strikes recorded at the first day after electrode implantation was compared with those recorded 4 days after implantation. To differentiate data that consisted mostly of noise from data with actual strong EMG activity, the first second of each recording without stimulation or movement was selected and referred to as “noise”  in front of the animals at a distance of 10–20 cm was used to attract their attention and to elicit aggressive targeted strikes. The video camera (see above), mounted above the turntable and synchronized with the EMG recordings, was used to capture the strikes for offline analysis. To determine when strike activity started in the EMG signal a measure of 1.5 standard deviations above the mean of the total signal capture was used. This metric alone has many false positive correlations. To mitigate these aspects, a sliding window of 35 ms was used. The start of EMG activity of the strike was only marked once all timesteps in the window were above threshold. Furthermore, the search for the strike start was started 250 ms prior to the time of visual strike start. The data set obtained during the strike behavior of Amazon Tress Boas  using an animal decapitator .The success of simultaneous EMG recordings from eight bipolar electrodes along the snake body was initially demonstrated by data sets of muscle activity recorded from two different Amazon tree boas 1 day after electrode implantation –4. When Likewise, EMG data, collected from a given animal at two separate days (day 1 and day 4 after the implantation) were used to evaluate the temporal consistency of the recordings during the experimental period . RecordeN = 5) and 71 strikes of the Western diamondback rattlesnake (N = 2) were recorded. In contrast to the slow compensatory postural reactions provoked by a turntable rotation, the EMG activity during snake strikes was considerably shorter with the maximum activity at the time when the actual strike was launched  at which for a given recording position, EMG activity was encountered earlier than the corresponding activity on the other side was signified as fast activation side  and the However, a noticeable difference emerged when the distribution of fast-side activation and slow-side activation was compared between the strikes of the Amazon tree boa and the Western diamondback rattlesnake. In the data obtained from the Amazon tree boa, there was hardly any correlation between the fast-side activation and the slow-side activation . In contFollowing stable subdermal implantation of up to eight bipolar electrodes directly above epaxial target muscles, robust EMG activity with high signal-to-noise ratio was reliably recorded from all sites. The overnight coverage of the snake body ensured a position-invariant arrangement of all electrodes throughout the recording period, without loss or deterioration of the signals. The recording of comparable EMG waveforms across consecutive daily sessions confirmed the suitability of multiple subdermally implanted electrodes for the chronic acquisition of large sets of myogenic activity during natural motor behaviors in snakes. The robust recording of EMGs in rattlesnakes demonstrated the suitability of this method also for snakes with a different body shape.Electromyography recordings from different individuals with comparable body formation and curvatures revealed similar activity patterns in response to turntable stimulation, suggesting 1) the presence of comparable task-dependent muscle activation patterns and/or 2) the recording of similar groups of muscle fibers. This indicates that the established method represents a suitable technique to reliably record and compare the contraction dynamics and temporal pattern of multiple equivalent groups of axial muscles across individual snakes. However, snakes assumed slightly different body configurations, when placed on the positioning branch during repetitive recording sessions. Thus, the recorded EMGs naturally showed variations across individuals and subsequent days of data collection related to the specific body loop formation.The different body loop formation is also relevant for the interpretation of the fast aggressive strike of snakes. Since in our EMG data no clear fixed sequential activation of consecutive body positions became apparent, it is unlikely that the snake strike is activated by a fixed motor pattern. This would require that the snakes repetitively strike from identical positions with generalized loop formations. However, from our experience, especially with rattlesnakes, strikes can be initiated from any position independent from the actual loop formation. Thus, we hypothesize that the activation order is rather related to the distance that each loop adds to the strike, with larger loops being activated before smaller ones. This might also explain the difference, between fast-side and slow-side activation in both the Amazon tree boa and the Western diamondback rattlesnake. The comparison of the coordination of the slow- and fast-sides of the strikes provides information about how the first (fast-side) activity is being counteracted by the delayed (slow-side) activity of the other side. First activation of the outside of a loop pushes the snake into a more linearly aligned position. If that would not be counteracted by an opposing force, the snake would be unable to maintain this linear position and this particular section of the body would go past the midline to form a new loop at the opposite side of the body. Thus, the delay of the slow-side activation would depend on the actual loop size. This indicates that it takes more time for the body to straighten a big loop in comparison to a small loop. Therefore, counteraction by slow-side activity would be delayed when a big loop has to be straightened during a strike. Thus, the difference between the Amazon tree boa and the Western diamondback rattlesnake might be explained by the loop size before launching a strike. Smaller loops cause a slow-side activation with a shorter delay and therefore result in a stronger correlation between fast-side and slow-side activation. However, a more detailed study design that includes high-speed video acquisition from multiple cameras for a detailed analysis of loop formation would be necessary to confirm this hypothesis considering the actual strike model (gate vs. tractor tread) as described by Kardong and Bels . This woNonetheless, independent of all activity details, the overall robustness of the recordings suggests that chronic compound EMG recordings of axial muscles for at least up to 4 days in snakes are possible and allow reliable acquisition of myogenic potentials of similar sets of muscle fibers at particular body positions in both employed species of snakes. It must be pointed out, however, that recordings of sEMGs, either using surface electrodes .GJ, HS, PS, and TK: conceptualization. GJ and TK: methodology, investigation, writing—original draft, and visualization. GJ: validation and data curation. GJ, HS, HL, PS, and TK: formal analysis and writing—review editing. PS, TK, and HL: resources. HS, HL, PS, and TK: supervision. TK: project administration. HS, PS, and TK: funding acquisition. All authors contributed to the article and approved the submitted version.This research was funded by a grant from the Bernstein Center for Computational Neuroscience (BCCN) Munich (Project B-T7) to PS, TK, and HS as well as by additional intramural funding from the Biomimetics Center at TUM to TK.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The network meta-analysis, through direct and indirect comparison between the different autoclave cycles , revealed that treatment involving 15 autoclave cycles produced the most robust results in terms of having the greatest effects in terms of altered cutting efficiency with a probability of 57.7% and a SUCRA (surface under the cumulative ranking) of 80%. The alterations in the effects on cutting efficiency appear to be triggered after five cycles of sterilization by heat (autoclave). In conclusion, the meta-analysis of the data indicates that the autoclave sterilization protocol must not be repeated more than five times to preserve cutting efficiency. Within the limitations of this review, we can therefore establish that sterilization by autoclaving alone results in steel and NiTi instruments becoming less efficient in cutting after five cycles, as measured by a reduction in cutting efficiency.Sterilization processes guarantee the sterility of dental instruments but can negatively affect instrument features by altering their physical and mechanical properties. The endodontic instrumentation can undergo a series of alterations, ranging from corrosion to variation in the cutting angle and then changes in the torsional properties and torsional fatigue resistance. This systematic literature review and meta-analysis aims to investigate alterations to the cutting efficiency of endodontic instruments that are induced by procedures for their disinfection and sterilization. Methodologies adopted for this investigation follow the PRISMA  guidelines. The following were used as search terms on PubMed and Scopus: “endodontic sterilization”, “endodontic autoclave”, “cyclic fatigue”, “torsional”, “cutting efficiency”, “sterilization”, “surface characteristics”, and “corrosion”. At the end of the selection process, 36 articles were identified, and seven of them are included in this systematic review. The results of a meta-analysis conducted for the use of 10 autoclaving cycles shows a standardized mean difference (SMD) of 0.80 with a  The sterilization of endodontic instruments represents an important process for proceeding with the reuse of endodontic instruments. Sterilization has the purpose of breaking down and eliminating all microorganisms, viruses, and spores and preventing cross-infections .The sterilization process includes several phases: pre-sterilization, drying, packaging, heat sterilization, and storage of the sterile material .Pre-sterilization consists in the disinfection, decontamination, and cleaning of the dental instruments. This phase involves disinfection either by immersion of the instruments with decontaminating and disinfecting liquids or by washing with vanish disinfectors. The purpose of decontamination is to achieve a reduction in the microbial load, while cleansing aims to remove organic and inorganic residues from endodontic instruments  .The subsequent phases involve the rinsing, drying, and packaging of instruments followed by heat sterilization (autoclave at 134 °C at 2 bar) to eliminate spores. The last phase is storage of the instruments  , revealing a significant association between autoclaving and reduction in cutting depth.The meta-analysis was conducted by applying random-effects models given the high rate of heterogeneity  . After tI2 = 72% .The meta-analysis compared the data of the studies concerning only two different groups (instruments that have undergone 10 cycles of autoclaving and instruments have not undergone sterilization processes). We performed the network meta-analysis in order to compare different sterilization treatments by autoclaving  using indirect and direct comparisons of the various treatment protocols. Data included in the network meta-analysis were related to the principle of similarity since the methodology adopted is similar in each study making them therefore comparable. The network plot shown in 2 (2) = 0.88, p = 0.645. The general consistency test reports a ChiSince the inconsistency was absent in both global and local tests, the incoherence hypothesis was accepted.For the analysis of the effect size, we proceeded through the representation by forest plot .p-value displayed in the lower left part of the graph is congruent with the results of the global test on inconsistency, which confirms that the coherence is accepted.It should be noted that the The values of heterogeneity between individual studies within a treatment are confirmed. In addition, based on the similarity between the aggregate effect size of each treatment in the comparison set (blue color) and the aggregate overall effect size (red color), it can be confirmed that the consistency model is supported.Having assessed the comparative effectiveness of the treatments through the previous steps, we ranked the treatments to identify superiority. We then evaluated the treatment interventions that show the highest treatment effect . As showThe disinfection and sterilization procedures of the endodontic instruments can vary depending on the material, whether they are single-use or reusable  .P. lentimorbus), even in the presence of instruments supplied as sterile by the manufacturing industries. The presence of these microorganisms underlines how important it is to decontaminate the instruments before use, which do not, however, require sterilization by heat that may alter their physical, mechanical, and surface properties  and a The meta-analysis network directly and indirectly compared the various treatments . The network meta-analysis highlights how the treatment that determines the greatest effect of reducing cutting efficiency is the 15 autoclave cycles, with a probability of 57% overall with a SUCRA equal to 80%.The limitations of this meta-analysis are the small number of included studies that present a low risk of bias due to the different types of endodontic instruments investigated and the frequently varying methods for determining cutting efficiency.We can establish that steam sterilization provides the best instrument sterility but will still negatively influence the cutting efficiency.Our analysis of the scientific literature shows that there are various effects induced by the application of sterilization processes results in various effects on the physical and mechanical properties of endodontic instruments, some favorable and others unfavorable. Among the negative effects, the reduction in cutting capacity, that seems to emerge after five autoclave cycles , is fundamental, but not all studies reported similar data. Given the heterogeneity of the adopted measurement methods and the lack of in vitro studies, it is difficult to perform a meta-analysis of the data in the absence of bias between studies.The effects on reduction in cutting efficiency are reflected in the majority of the results of the studies included in the systematic review. A reduction in the cutting efficiency can lead to an endodontist exerting greater pressure on the instrument in order to maintain constant cutting capacity, which would lead to a greater risk of instrument fracture due to torsional stress.


This paper proposes an action recognition algorithm based on the capsule network and Kalman filter called “Reading Pictures Instead of Looking” (RPIL). This method resolves the convolutional neural network’s over sensitivity to rotation and scaling and increases the interpretability of the model as per the spatial coordinates in graphics. The capsule network is first used to obtain the components of the target human body. The detected parts and their attribute parameters  are then analyzed by Bert. A Kalman filter analyzes the predicted capsules and filters out any misinformation to prevent the action recognition results from being affected by incorrectly predicted capsules. The parameters between neuron layers are evaluated, then the structure is pruned into a dendritic network to enhance the computational efficiency of the algorithm. This minimizes the dependence of in-depth learning on the random features extracted by the CNN without sacrificing the model’s accuracy. The association between hidden layers of the neural network is also explained. With a 90% observation rate, the OAD dataset test precision is 83.3%, the ChaLearn Gesture dataset test precision is 72.2%, and the G3D dataset test precision is 86.5%. The RPILNet also satisfies real-time operation requirements (>30 fps). Machine vision has been widely used in the imaging field, particularly as artificial intelligence grows increasingly advanced. Action recognition, a notable research direction related to machine vision, includes the detection, recognition, and analysis of targets in image sequences. It is widely used in human–computer interactions, such as medical rehabilitation, dancing instruction, and traffic supervision. Its efficacy is impacted, however, by issues with target diversity and background complexity.There are two main methods of traditional action recognition. The first is based on template matching for geometric calculation, which is operated mainly by artificial and high-dimensional modeling for comparison among various parts of the human body in static images to find their spatial correspondence. The second is graph structure based; these techniques have relatively low complexity but are sensitive to noise and other factors which drive down their accuracy. In 2012, Alex’s convolutional neural network (CNN) dominated the ImageNet competition , and a set z that represents the capsule’s features.The part capsule is formed by a six-dimensional pose The part capsule’s parameters are predicted as:mth template is predicted as:The color of the Affine transforms are applied to the image templates:Mixing probabilities are computed as:Additionally, then the image likelihood is calculated as:After training, the parameters of the network are evaluated and unnecessary parameters are deleted. This allows the model to work at a rapid speed. For example, posture analysis of the forearm only requires observation of the elbow and wrist joints, while the surrender action only requires focus on the upper body or arms. The whole network can be optimized by regularization and batch standardization, but the structure does not need to be adjusted.S is evaluated as per its contribution to the high-level capsule, not for a certain neuron:i,j,nZ(ib) is the contribution of the combination of the ith low-level capsule to the nth feature of the jth high-level capsule. All features are scored by this method. The average score is taken as the contribution of current low-level capsules to current advanced capsules; the capsules are sorted according to the score. When the top low-level capsules sum more than 85%, the remaining capsules are discarded. The remaining low-level capsules are then used as the basis for judging the activation of the current high-level capsule. As shown in The score The evaluation model allows for clarification of the relationship between high-level capsules and low-level capsules, which minimizes the influence of unnecessary low-level capsules on the process of combining high-level capsules. After retraining, the network realizes that, when some low-level capsules are activated and meet certain conditions, high-level capsules can be combined and activated to determine their characteristics.Experimental results show that the performance of the tree network structure satisfies practical application requirements with relatively quick calculation speed.Action recognition can be carried out on a single frame image, but the features of the sequence are not used. In a video, the target’s action is continuous. We believe the use of Kalman filtering can constrain the predicted coordinates. It prevents any erroneous prediction at a certain moment from creating uncertainty in the result of the entire sequence.In this study, we used a median filter to denoise the coordinate information of the first 30 frames, then used the filtered result as the initial point to build a Kalman filter to predict the motion range of the joint point at the next moment. The prediction results of the Kalman filter were used as the reference range; the predicted coordinates within the range could then be regarded as the correct points. Any incorrect prediction of the coordinates of the joint points in the current frame were used to check the detection results. As shown in kx and kx−1 denote the object’s coordinate of the current and last moment, respectively. u is the optional control input, which is generally ignored in actual use. kw−1 is Gaussian noise that is generated in the prediction process.The state equation of Kalman filter system is as follows:kv is the observation noise obeying a Gaussian distribution. The time update equation of the Kalman filter is:The observation equation is as follows:In our model, a Kalman filter checks the predicted points and curve fitting shows the movement trajectory of a part in the video. The part capsule already contains the position information of the human body, so it does not predict the position of the human object in the image. However, we can use a constellation capsule to obtain the location of the body and the size of positioning frame through transfer learning.Finally, the capsules processed via Kalman filter are taken as an input and analyzed by the transformer to deduce the posture represented by the video.We tested the proposed method on the OAD dataset , ChaLear(1)SSNet , a netwo(2)FSNet , which u(3)FSNet-MultiNet , an upgrAll of these architectures use multi-layer structured skeletons for comparison. In order to make a more objective comparison, we used a similar concept for further comparative experiments.(4)ST-LSTM , which h(5)JCR-RNN , a varia(6)Attention Net , where aThe prediction accuracy of the observation ratio p%, as reported here, represents the average prediction accuracy in the observation interval of the action instance. As shown in The OAD dataset was collected using Kinect V2 in a quotidian living environment. Ten movement training sessions were conducted by different subjects. The long video sequences in this dataset correspond to about 700 action instances. The start and end frames of each action are marked in the dataset. Thirty long sequences were used for training and 20 long sequences for testing. The prediction results of different models on the OAD dataset are shown in The proposed RPILNet produced the best prediction results under different observation rates. When the observation rate was only 10%, RPILNet performed with accuracy of 68%, which is better than SSNet or FSNet. It also appears to be superior to JCR-RNN or ST-LSTM based on RNN/LSTM, which can handle continuous skeleton sequences. The performance differences between models can be explained as follows.In the early stages , RPILNet focuses on the executed part of the current action. The JCR-RNN and ST-LSTM in the RNN model may bring information about previous actions at this point, which interferes with the current operations. The accuracy of RPILNet can be further improved by Kalman filtering to prevent any individual errors from affecting the final results. In the later stages , the information learned in the early stages of the current action may gradually disappear in the RNN model. RPILNet, however, uses the transformer to analyze all input vectors at the same time and make them refer to each other. This retains knowledge and ensures that all outputs are based on global characteristics.The ChaLearn Gesture dataset is a large data set for analyzing body language that consists of 23 h of Kinect video, where 27 subjects perform 20 actions. This dataset is very challenging because the body movements of many action classes are very similar. Each video in the NTU RGB + D only includes one action, while each video in ChaLearn includes multiple actions. The ChaLearn Gesture dataset is better-suited for this reason to online action recognition applications. The dataset annotates the start and end frames of 11,116 action instances; 75% of videos with labels are used for training and the rest for testing. Considering the large amount of data, one frame is sampled every four frames.The experimental results are shown in The FSNet appears to be more sensitive under different scales. These results further prove that the RPILNet is effective for online applications.The G3D dataset contains 20 movements collected using Kinect cameras. There are 209 uncut long videos in the dataset. In this study, we used 104 of them for training and the rest for testing. Again, the RPILNet performed very well. Our model appears to be well-suited to the G3D dataset as well as to the network structure changes operated through the proposed evaluation process. The experimental results are shown in We conducted ablation experiments to determine the effectiveness of each part of the model. The transformer, capsule network, and both of them were eliminated in turn to run comparative experiments. The results are shown in RPILNet-with FC uses a fully connected layer to replace the transformer and capsule network, then uses the fully connected layer to analyze the features extracted by DenseFusion. RPILNet-with capsule and FC uses a fully connected layer to replace the transformer, but retains the capsule network so that each layer can retain the space coordinates and attributes of the capsule.Finally, RPILNet-with transformer uses the transformer to analyze the extracted features, but does not use a capsule network—an individual layer does not include capsules or their attributes.The accuracy based on the capsule network and transformer is higher than that of the method without the capsule network or transformer. Moreover, the capsule network contains the attributes of the extracted target .The accuracy of the model decreases slightly when the observation ratio is 100%. This may be attributable to interference between two adjacent actions. This experiment also shows that the RPILNet satisfies real-time operation requirements (>30 fps) under the conditions of the RTX2080S graphics card and the Kinect V2 camera.To verify the generalization ability of the model, we adjusted its structure and retrained it. We chose the action recognition model based on RGB images (no more than five years old) as the object of comparison. We compared them on the three datasets UCF101, Hollywood2, and YouTube.The experimental results are shown in We found that the proposed method achieves similar performance on UCF101 and YouTube datasets with the current latest method after adjustment. Its accuracy on the Hollywood2 dataset surpasses the other state-of-the-art methods we tested.The proposed combination of the capsule network and transformer shows favorable training effects in action recognition. The running speed of the proposed algorithm also satisfies the needs for practical application. By analyzing images, the dependence of the traditional model on the random features extracted by CNN is effectively reduced. The transformer analyzes all input features and extracts new features to improve the interpretability and operability of the network over the traditional approach without sacrificing the accuracy of the CNN. The transformer has unique advantages over the LSTM. While analyzing each element through the attention mechanism, other elements in the sequence model are used as a reference for obtaining new features. The CNN module, which is often used to process images as a tool for sequence analysis, resolves the problem that traditional RNN models are not easily parallelized.The results of this study confirm that the NLP concept can be used as a tool for analyzing images. We were able to exploit the CNN’s parallelism to preprocess an image while remedying its over-sensitivity to angle changes and noise with the transformer and capsule network. This allows the proposed model to read the content of the image rather than simply observing its pixels.


When tracking very long-range targets, wide-band radars capable of measuring targets with high precision at ranges have severe measurement nonlinearities. The existing nonlinear filtering technology, such as the extended Kalman filter and untracked Kalman filter, will have significant consistency problems and loss in tracking accuracy. A novel mid-state Kalman filter is proposed to avoid loss and preserve the filtering consistency. The observed state and its first-order state derivative are selected as the mid-state vector. The update process is transformed into the measurement space to ensure the Gaussian measurement distribution and the linearization of the measurement equation. In order to verify the filter performance in comparison, an iterative formulation of Cramér-Rao Low Bound for the nonlinear system is further derived and given in this paper. Simulation results show that the proposed method has excellent performance of high filtering accuracy and fast convergence by comparing the filter state estimation accuracy and consistency. Target tracking is a process that uses sensors to estimate the characteristics of a moving object of interest. It is widely used in unmanned aerial vehicles (UAV), military strikes, and other fields ,2. As thThe extended Kalman filter (EKF) is the most widely used nonlinear filter in practical engineering because of its simple algorithm and small computation. The EKF uses a Taylor series expansion to approximate the nonlinear system model. When the nonlinearity is severe, the filtering accuracy will be reduced or even diverged due to a high-order truncation error . TherefoDue to the complexity and uncertainty of very long-range target tracking, the Gaussian noise distribution in the measurement space will become a severe non-Gaussian distribution when it is converted into the state space in the update process. This phenomenon is often encountered in wide-band radar systems with high-range accuracy . Due to In practical engineering applications, discrete nonlinear systems are generally characterized using additive noise and the system model is expressed asThe EKF obtains linear approximation of nonlinear system by using Taylor series expansion and then uses a KF to deal with the filtering problem of nonlinear system. The EKF approximates the nonlinear functions The UKF is different from the EKF in that it directly calculates the mean and covariance of the target distribution, avoiding the approximation of nonlinear functions. The UKF uses the mean and covariance of initial distribution to generate a series of determined sigma sampling points according to Formulas (6) and (7). These sigma sampling points are propagated through nonlinear functions to get the estimated mean and covariance .(6){χ0=The corresponding weight isUnder the Gaussian assumption, the state estimation of the nonlinear KF can ultimately be equated to the calculation of multidimensional vector integral, which can be summarized in the form of a nonlinear function The KF is proposed based on the least mean square error criterion. Under the assumption that the observation noise obeys the Gaussian distribution, the KF is a constant minimum variance and linear unbiased estimate that can recursively obtain the state. In this paper, a Mid-state Kalman Filter is proposed based on the KF method. A MSKF selects the observed state and its first-order state derivative as the mid-state vector and transforms the filter update process into the measurement space. The proposed method guarantees the Gaussian distribution of the measurement and correspondingly transforms the measurement equation into a linear form.Consider a nonlinear discrete system for target tracking as shown below:In the typical two-dimensional radar target tracking, the target is assumed to be in uniform linear motion. Its state vector at time The MSKF selects In this case, the nonlinear system in Equation (10) can be transformed into the following linear system:This avoids the linearization process of the measurement function In the mid-state, The mid-state is introduced into the Kalman filter to form the tracking filter algorithm MSKF, which is suitable for dealing with nonlinear problems. The algorithm steps are given as follows.Initialization: Given the initial state estimate Prediction: Assume that the input of filter in prediction step is the filtering result State transformation: The predicted state vector According to the geometric relation and velocity decomposition in The predicted covariance (1)Obtain (2)The value of the sampling point after conversion is (3)Then the covariance The state transformation represents the target state transformation relationship under different coordinates. This module can be quickly replaced according to the actual situation without modifying the filter prediction and update module. This also improves the practical engineering applicability of the MSKF.Update: The state estimation results Extraction of state estimation: Obtain the state estimation This process is the reverse process of state transformation. Therefore, the conversion relationship from the mid-state vector At the same time, The algorithm flow of the estimator is shown in In order to better verify the performance of nonlinear filters, it is necessary to analyze and evaluate the filtering accuracy, credibility, stability, and other aspects of the filter which largely depend on reasonable evaluation metrics. In addition to the common evaluation metrics of state accuracy, such as root mean square error, this paper also deduces and gives the Cramér-Rao Low Bound iteration formula for nonlinear systems and analyzes the consistency of a filter by using a normalized error square.Root Mean Square Error (RMSE) is widely used in performance comparison and evaluation of nonlinear filtering algorithms. It is based on the estimation error set obtained by the Monte Carlo simulation to evaluate the accuracy of the algorithm , definedFor nonlinear systems, the optimal Bayesian nonlinear filter is impossible , so therLiterature ,21 proviFor the nonlinear system in Equation (1), the unbiased estimate of the state Among them,If both the system noise Defining Through the above derivation process, the CRLB provides the lower bound of the mean square error of unbiased estimation and gives the mean square error of an ideal nonlinear filter. In this paper, the RMSE curves of all filters are compared with the CRLB curves of the nonlinear model. The degree of approaching the CRLB curve reflects the accuracy and performance of the corresponding algorithm.Normalized Estimation Error Squared (NEES) gives a more accurate quantitative evaluation of the consistency of the filtering algorithm. Literature  gives a When When the wide-band radar tracks a very long-range target, a typical problem caused by the measurement nonlinearity is the “Contact Lens” problem. It is directly related to the filter update process and is the leading cause of filter inconsistency and divergence.The wide-band radar has high range accuracy and low angle accuracy when tracking very long-range targets. The uncertainty region of measurement will present a severe non-Gaussian distribution when the state in the Cartesian coordinate system is updated with nonlinear measurements from different coordinate systems. The uncertainty region presents a curved shape, similar to a banana shape in two dimensions and a contact lens shape in three dimensions. Therefore, this distribution is called the “Contact Lens” distribution and this kind of nonlinear problem is called the CL problem . Figure Bar-shalom uses a parametric expression to describe the uncertainty region ribution :(36)β=rδThe EKF needs to linearize the measurement equation in Equation (10). Assume Carrying out the matrix multiplication operation of Formula (37), we can getFor high-resolution wide-band radar, Thus,From the above formula,Therefore, the following formula can be obtained:Assuming that The above formula shows that when the target is far away from the radar, the estimation error may exceed the distance measurement error The UKF is a numerical method to calculate the statistical characteristics of random variables after nonlinear transformation. Its essence is to use multiple deterministic sampling points to approximate the Gaussian probability density function. However, in the CL problem, the probability distribution of measurement in the Cartesian coordinate system obviously cannot be approximated simply by Gaussian distribution, so the filtering accuracy of the UKF is poor. MSKF uses The following two very long-range target tracking scenarios are designed for different radar performances:(1)(2)The experiment uses 100 Monte Carlo simulations, the initial target position is The state component estimation RMSE and theoretical performance lower bound CRLB is given in A typical nonlinear CL problem occurs when high-resolution wide-band radar tracks very long-range targets. To solve this problem, a novel mid-state Kalman filter is proposed in this paper. The MSKF uses the observed state and its first state derivative as the mid-state vector to transform the update process of the filter into the measurement space and rederives the update equation of the Kalman filter. The state transition module can be replaced according to the actual situation without modifying the filter prediction and update module. This improves the practical engineering applicability of the MSKF. When the CL problem occurs, the MSKF has the characteristics of high state estimation accuracy and fast filter convergence compared with other filters. This will significantly help the wide-band radar system to form the target trajectory quickly and accurately.


Damage in concrete structures initiates as the growth of diffuse microcracks that is followed by damage localisation and eventually leads to structural failure. Weak changes such as diffuse microcracking processes are failure precursors. Identification and characterisation of these failure precursors at an early stage of concrete degradation and application of suitable precautionary measures will considerably reduce the costs of repair and maintenance. To this end, a reduced order multiscale model for simulating microcracking-induced damage in concrete at the mesoscale level is proposed. The model simulates the propagation of microcracks in concrete using a two-scale computational methodology. First, a realistic concrete specimen that explicitly resolves the coarse aggregates in a mortar matrix was generated at the mesoscale. Microcrack growth in the mortar matrix is modelled using a synthesis of continuum micromechanics and fracture mechanics. Model order reduction of the two-scale model is achieved using a clustering technique. Model predictions are calibrated and validated using uniaxial compression tests performed in the laboratory.  Concrete is a heterogeneous, multiphase material with a disordered material structure across multiple length scales. At the mesoscopic scale  across multiple length scales using multi-level homogenisation schemes . Inevitably, the range of length scales that can be considered using computational mesoscale models is limited. Thus, for concrete, given the wide range of length scales involved, micromechanics-based multiscale modeling, in conjunction with model-order reduction techniques such as proper orthogonal decomposition ,50,51, dThe aim of the paper is to model the load induced distributed microcracking phenomenon in concrete by means of a multiscale reduced order modelling approach. To this end, we have developed a multiscale model, characterised by the combination of continuum micromechanics and fracture mechanics on the microcrack level and a direct computational resolution of the mesoscale of concrete to describe load induced microcrack evolution. We demonstrate the predictive capability of the model by validations with experimental measurements.The remainder of the paper is organised as follows: In In order to support and validate the proposed model, three cubes (a = 10 cm) made of concrete and mortar serve as test specimens. We used ordinary Portland cement with a water-to-cement ratio of 0.45 for both types of specimens, crushed aggregates with an AB16 grading curve  and a ceThe volume fractions of aggregates and air pores, along with their spatial distribution, are key parameters for characterising the mesostructure of concrete specimens and serve as input data for the generation of synthetic concrete mesostructure models. For the test specimens, an optimised aggregate composition was computed using the Generalised Reduced Gradient Method  by minimA more refined quantification procedure of the quartzitic aggregates was also carried out to extract the statistical data required for the generation of synthetic concrete mesostructures. The resulting absolute volume fraction of each concrete constituent is listed in The proposed multiscale model also requires data regarding the mechanical properties of the material composition. Thus, a series of tests were performed to determine the properties of mortar, quartzitic aggregates and concrete of standard AB16. The testing machine is a Walter+Bai AG DB 3000/300 kN with a digital controller, Digicon 2000 . In order to design the testing procedure, we used the materials testing software “Proteus”. The material parameters of interest include the Young’s modulus, Poisson’s ratio, and the compressive strength. These parameters are summarised for each constituent in p-value of 5% . Moreover, it involves mechanisms that interact across multiple length scales i.e., the loading is applied at the macroscopic scale, the coarse aggregates serve as stress concentrations at the mesoscopic scale and the microcracks initiate and start growing at the microscopic scale. In order to bridge these scales, a multiscale model that takes into account the most essential physics contributing to the damage evolution in concrete is required.In this paper, a reduced order model for scale-bridging modelling of damage evolution in concrete is formulated. In summary, this modelling approach entails separate model descriptions at different scales as well as the coupling relations between the scales. The interaction among scales is realised through homogenisation and localisation procedures. In the homogenisation process, information at lower scales is transferred to the higher scale through physically consistent averaged quantities . Localisation  is a downscaling procedure that relates strain or stress measures across the scales.See l is considered, which is consisting of a mortar solid matrix and microcracks as inclusions. Microcracks represent the initial defects in the mortar and their evolution accounts for the fracture and damage mechanism at this length scale.In order to model distributed microcracking in the mortar material, we adopt the multiscale concrete model proposed in . The moda, and half microcrack opening c. The volume fraction of each microcrack family is evaluated as crack density parameterThree microcrack families, embedded in an "intact" mortar matrix material and oriented in three mutually orthogonal planes aligned with the major axes, are considered as inclusions. The geometry of these microcracks is idealised as penny-shape (oblate ellipsoid) with aspect ratio  used in ,30).When concrete is subjected to loading, the growth of microcracks is idealised in the model as an extension of microcrack radius. Microcracks may grow only if they satisfy the criterion:art of E . The homEquation  involvesk, the microcrack radius increment is computed asAt iteration With After a converged microcrack radius is computed, the reduced effective stiffness tensor corresponding to the current microcrack configuration is updated. It should be noted that each microcrack family is allowed to grow independently, and, therefore, depending on the direction of microcrack growth, an anisotropy of the homogenised stiffness is induced.In order to verify the proposed microcracking model, we simulate a uniaxial tension and uniaxial compression loading on a mortar REV. The investigated mortar REV consists of fine aggregates (sand) with a volume fraction of 35% embedded in a cement matrix. The material stiffness for the cement matrix and the aggregates are 21.6 GPa (taken from ) and 84.0.2 . The mod0.2 .A summary of input and calibrated parameters as well as the numerical results can be found in z-direction in this particular numerical example) and a slight reduction in the stiffness in the transversal directions. The volume fraction of microcracks belonging to family 1 grows with increasing loads while the volume fraction of the other (two families) remains constant.In this numerical experiment, the micro-cracked mortar REV is assumed to contain an initial microcrack volume fraction of 11.79% with aspect ratio 17. As a consequence of introducing initial microcracks, the mortar REV stiffness reduces to When subjected to uniaxial compression, microcrack families 2 and 3 grow due to the effect of the Poisson ratio. This leads to a dramatic reduction of material stiffnesses in the transversal directions, while At the mesoscopic scale, concrete is idealised numerically in terms of a two-phase composite occupying a given volume  authors  that all authors ) is alsoThe stress and strain fields  follows :(8)Γ^0=1equationε(x)+∫ΩMΓFor the iterative solution, strain-based convergence criterionOffline stage Pre-computation of a reduced-order dataset characterising the behaviour of a given REV by decomposing the entire domain of the high fidelity REV into a set of sub-domains (often denoted as clusters) and computing the so-called interaction tensors Online stage Actual computation of the response of the REV for various loading conditions using the reduced-order dataset obtained from the offline stage.An explicit multiscale approach without using proper model reduction would result in an explosion of the number of unknowns, especially in the case of complex three-dimensional microstructures. To accelerate material analysis and design, one looks for a strategic way to reduce the computational complexity of the model, both in terms of computation time and data storage requirement. In our work, the clustering technique proposed by  is adoptIn the offline stage, the k-means clustering procedure was employed for grouping voxels that deform in a similar fashion. The algorithm requires a collection of data characterising the behaviour of all voxels under various loading conditions. To this end, fine-scale simulations of six orthogonal unit loading conditions were performed on the concrete REV and the corresponding strain fields are recorded, as suggested in . In our The metric used to group the voxels is the localisation tensor denoted as As a result, the k-means clustering algorithm groups the voxels into one cluster based on the similarity of their localisation tensors. Full details regarding the construction of found in .Next, for the sake of clarity, but without going into too much detail, we shall provide the basic formulation of the interaction tensor The equilibrium stress and strain for each cluster  on a simple microstructure.The convergence behaviour with respect to the number of clusters on a simplified concrete microstructure.In this section, numerical analyses are conducted to investigate the performance of the proposed reduced order multiscale model. The central interests of this study are:z-direction.Two numerical samples were considered in the analysis. From these microstructures, we generated the corresponding reduced-order microstructures with an increasing number of clusters, as illustrated in To investigate the convergence behaviour of the ROS with respect to the DNS for increasing loading strains, we used the following macrostress-based error criterionBoth DNS and reduced-order simulations (ROSs) were carried out for simulations of the simplified mesoscale structure shown in in comparison with DNS, the ROSs capture the overall response in the elastic regime (up to a strain level of 0.03%) well. In this range, an error of only 0.03–0.08% is observed , right.The ROSs generally tend to overestimate the computed effective stress as compared to the DNS.When microcracking starts in the nonlinear regime, the error increases with increasing loading strain . At the As the number of clusters is increased, the reduced order simulation converges to the result of the high fidelity simulation.Thus, we can conclude that, for a simple mesostructure, a good convergence can be achieved with the proposed ROS. Even a clustered mesostructure with a small number of clusters can capture the effective behaviour of the composite well. It should be noted that the solution of the uniaxial compression loading on this simplified mesoscale structure using DNS requires computation of a total of In the second numerical analysis, a concrete-like mesostructural model as shown in Five reduced order models with number of mortar clusters Simulations with a higher number of clusters entered the inelastic stage earlier and failed earlier as well. Subsequently, the maximum compressive stress reduces with increasing cluster count.A maximum 3.07% of error with respect to the reference result . Finally, a simulation of the mesoscale model subjected to uniaxial compression is performed on a synthetic concrete sample, and the model predictions are compared with experimental data (online stage).In this section, a reduced ordered multiscale simulation of a concrete specimen subjected to uniaxial compression is performed. The modelling strategy consists of the following four steps. First, a virtual concrete mesostructure is generated according to the measured aggregate size distribution of concrete (standard AB16). Second, the material properties of the material constituents are specified. The third step is the determination of the localisation tensors for each voxel in the mesostructure for the k-means based domain decomposition procedure  thetion see  right, aThis choice of the cluster configuration results in the computation of z-direction to zero. The strain increment is prescribed as With the preparations accomplished in the offline stage, simulation on the reduced mesostructure subjected to uniaxial compression can be performed. The uniaxial load condition is simulated by restricting the macroscopic strain component rinciple , is restrinciple ,73,74. HI, respectively.The macroscopic stress tensor at load level x and y-directions, respectively, and To examine the evolution of the stiffness degradation due to microcracking, the effective secant stiffnesses in three orthogonal directions were recorded for all clusters at each load step. To show the effect of microcracking on the transversal stiffness degradation of each cluster, we introduce the damage parameter From the stress–strain curve  and lateral (x) directions. As seen in x- and y-directions) of all clusters decrease at a much faster rate in comparison with the longitudinal one due to the growth of microcracks, whose orientation is parallel to the major stress axis. Moreover, a closer inspection into the spatial distribution of damage in the mortar matrix reveals that microcracking takes place predominantly in the immediate vicinity of the aggregates, caused by the stress concentration in these regions of the mesoscale structure. In addition, these degradation mechanisms revealed by the multiscale reduced order model is in agreement with experiment observations [rvations .Recording the microcrack volume fraction provides information on the damage evolution in the clusters as well as in the complete mesostructure of the virtual concrete specimen. Once microcracking initiates, the model is also able to predict an increase of the apparent Poisson’s ratio, defined as the ratio between the transversal and axial strain,. It showAs already discussed above, the choice of the homogenisation scheme for the mortar matrix material at the microscale may have a strong influence on the predicted response of concrete at the macroscopic scale. As can be seen in To replicate a more brittle behaviour of the mortar matrix, we now investigate using the Interaction Direct Derivative homogenisation scheme  (IDD) ina, half thickness c and crack density i are the double cell radius i. The superscript D denotes quantities belonging to the distribution  of the microcracks. When the geometry of the distribution is identical to that of the microcracks, the prediction of the IDD and Mori–Tanaka schemes is identical. Assuming zero stiffness for the three crack families yieldsThe distribution of the microcracks is determined by the shape of a “double cell” surrounding a microcrack see . The shamulation  for estii.When the external load reaches a critical value, pre-existing microcracks start propagating. As the microcrack distribution in the IDD model is governed by the double cell that encloses the microcrack, we assume that this double cell evolves to accommodate the microcrack. Eventually, the microcrack distribution flattens and follows the penny shape of microcracks. The concept of an evolving microcrack distribution was suggested by various analyses, such as ,79,80. ITo control the growth of double cell A calibration procedure was undertaken to obtain parameters for the double cell i.e., the microcrack distribution, which are able to realistically replicate the response of a mortar sample subjected to uniaxial compression. According to this calibration procedure, the initial aspect ratio The modified IDD scheme has also been applied to simulations of the virtual concrete sample subjected to uniaxial compression, which has been investigated before in The stress–strain diagram obtained from this modified micromechanics-reduced order meso-scale model for concrete is shown in It was observed that the Mori–Tanaka scheme, which has been used in the initial model design at the micro-level, overestimates the compressive strength of concrete.In order to improve the model predictions, the Mori–Tanaka scheme governing microcracking at the microscale has been replaced by an improved interaction direct derivative scheme . This moAfter calibration of the additional distribution-related parameters, model predictions of the improved model for the uniaxial compression test have substantially improved, with a deviation of only 3.2%.The proposed model has been proven to be capable of simulating anisotropic microcrack evolution, leading to anisotropic stiffness degradation on the macroscopic level. In addition, the evolution of the Poisson’s ratio during loading could be predicted.In this work, a reduced order multiscale model for computational simulations of distributed microcracking in concrete on the mesoscale has been presented. Within the mortar matrix, a continuum micromechanics model takes into account pre-existing microcracks, which may propagate according to the Griffith criterion. This continuum micromechanics model in conjunction with a fracture energy model for crack propagation was incorporated into a computational mesoscale model of concrete. At this scale, a numerical model is proposed, which realistically resolves the coarse aggregates and its size distribution. To reduce the computational costs for high resolution multiscale simulations, a k-means based model reduction technique  has beenDue to the multiscale nature of the proposed model, it can be used to simulate a wide variety of concrete compositions by simply altering the predominantly physically measurable microscale and mesoscale parameters governing the topology and material properties of the required concrete composition. Thus, the proposed modelling framework can be the basis of a Virtual Material Testing Environment and can collaboratively aid in the development of concrete with a better performance.From a structural health monitoring view point, the outcome of the model can serve as a high-fidelity input for an ultrasonic-wave propagation numerical investigation of damaged concrete . Nevertheless, the model should also be extended to account for the interfacial transition zone (ITZ). This will enable the investigation of the effect of ITZ on the overall behavior of concrete. Lastly, two potential practical applications are also outlined:


Condition monitoring is an indispensable element related to the operation of rotating machinery. In this article, the monitoring system for the parallel gearbox was proposed. The novelty detection approach is used to develop the condition assessment support system, which requires data collection for a healthy structure. The measured signals were processed to extract quantitative indicators sensitive to the type of damage occurring in this type of structure. The indicator’s values were used for the development of four different novelty detection algorithms. Presented novelty detection models operate on three principles: feature space distance, probability distribution, and input reconstruction. One of the distance-based models is adaptive, adjusting to new data flowing in the form of a stream. The authors test the developed algorithms on experimental and simulation data with a similar distribution, using the training set consisting mainly of samples generated by the simulator. Presented in the article results demonstrate the effectiveness of the trained models on both data sets. Condition monitoring (CM) maintains an essential role in all industrial areas where rotating machinery is applied. Implemented a monitoring strategy allows for cost-efficient maintenance and avoidance of catastrophic failures. In most monitoring systems, assessment of the condition involves vibration signatures’ acquisition. The following actions include extraction of damage-sensitive features and data processing to determine the machine state. More detailed information related to the CM can be provided in references ,2,3.There are three major approaches to solve this problem. In the first one, the condition assessment requires only data acquired for an unknown state and a comparison of selected features with proper norms. No information on the previous condition of a particular machine is needed. The described approach is very general and easy to implement. In general, such a system is not sensitive in detecting minor faults that do not cause significant alteration of signal features. However, recent developed real-time algorithms based on eigen perturbation techniques have indicated fault identification of the order 1–5% in real-time. Moreover, studies have also demonstrated the effectiveness of perturbation schemes in a non-stationary time-varying environment with numerical, experimental, and practical applications .The second approach requires a database of signals, including examples acquired on similar machines in healthy and damaged conditions. The obtained data collection allows for designing and training a classifier model for small faults prediction. Unfortunately, such an approach is rarely feasible due to the costly acquisition of signals representing multiple instances of various faults. In work , the autThe last approach is a combination of these two. It is based on acquiring signals for one particular machine under monitoring over a long period of its operation. Such a database contains reference patterns for upcoming signals of an unknown state. Any significant alteration from the reference, detected in new data, serves as an indicator of failure. If a single signal feature is used to this end, the approach is called trend analysis. It mostly relies on visual representations, which are sometimes costly to acquire over data transmission systems. For such cases, real-time methods perform analysis online and alleviate data transmission from site to lab, thereby reducing cost. Kalman Filter techniques and eigen perturbation approaches have found extensive applications in this regard . The anaThe article  defines Various approaches related to the designation of the normal subspace boundaries were developed. Some of the methods are based on the approximation of unknown probabilistic density function (pdf) by known density functions. The most widely used function is Gaussian distribution which was applied inter alia in works ,11,12,13ND models found applications in condition monitoring for maintanace of rotating machinery. In articles ,23,24,25The task of ND in condition monitoring will have a vital role in the following years and still does not have a reliable solution. Despite the many implementations presented in the previous chapter, the industrial standard for condition monitoring is dominated by determining the structural condition based on analyzing the frequency spectrum content and comparing the values of the calculated indices with the norms ,30. ThisTo answer the problem, the article is devoted to verifying and comparing the efficiency of four different ND methods in condition monitoring for a parallel gearbox. Authors implement a data-distribution-based (DDB) method, the nearest neighbor (NN), the online novelty and drift detection algorithm (OLINDDA), and a model-based ensemble of classifiers. The article is a continuation of the analysis presented in , where tThis paper covers the described problem by introducing different types of damage with variable severity into acquired signals. The algorithms process them sequentially, which mimics the signal processing in condition monitoring and allows the introduction of OLINDDA, developed for ND in data streams . AnotherThe remainder of the paper is organized as follows: The first section describes methods used for detection of novelty in this work, the next two sections provide an evaluation based on simulation and experimental data, including their description, signal processing, feature extraction, and results discussion. Finally, the last section summarizes and concludes the article.In this approach, for each data feature, the probability distribution is estimated. The simplest and most commonly applied solution is the assumption of a normal distribution of measured data. The values of the average d between these pairs of points are used in threshold calculation. The threshold is set as The Nearest-neighbor (NN) model is based on the unlabeled point’s calculated distances to all points considered during training. If the minimal calculated distance is smaller than the threshold value, then the unlabeled point belongs to the normal class. Otherwise, it is considered a novelty. The threshold value is derived from the calculation of average The construction of the considered model is very intuitive. However, it requires significant computational effort due to comparison with each database point. Like all distance-based NN methods, it is also sensitive to low data density in feature space and scales poorly to high-dimensional feature spaces.The Online Novelty and Drift Detection Algorithm (OLINDDA) is a two-stage algorithm dedicated to detecting new and modifying previously learned concepts from unlabeled samples. The learned concepts are stored in clusters that are represented as hyperspheres with centroid and radius. The idea of OLINDDA is presented in The training process is divided into two separate stages. In the initial phase called offline presented in The representativeness is defined as the number of samples belonging to cluster ribed in .Cluster that fulfills density criteria and is far from normal data is classified as novelty,Cluster that fulfills density criteria and is close to normal data is classified as normal-extended,Cluster that not fulfill density criteria is classified as noise,In the second phase called online presented in The decision of new clusters membership depends on its centroid’s distance from the centroids of normal clusters. The algorithm applies those points to construct bounding volume. If the centroid of the unlabeled cluster is within the bounding volume, then it is considered normal-extended.The most common bounding volume is hypersphere, with the center in the centroid of the normal clusters centroids and the radius as the maximum distance between the centroid and normal clusters centroids. However, the hypersphere assumption imposes a constraint of the same distance on every feature dimension. This increases the misclassification of novelty data. Therefore, in this article, the authors applied a convex hull as abounding.The auto-associative neural network (AANN) is a multilayer perceptron (MLP) trained for reproducing input values at its output. The network architecture employs bottleneck to prevent duplicate entries and force generalization: one hidden layer is designed to contain fewer neurons than the input layer. Example of AANN architecture is presented in During operation, the unlabeled sample is reconstructed by the AANN model. The error between the sample and its reconstruction is calculated and compared to the threshold value. If the error is smaller than the threshold value, the sample is considered normal. Otherwise, it is labeled as a novelty. The threshold value is described by The training process of AANN is non-deterministic. Therefore, each network, trained on the same training set, gives different normal regions, as presented in An ensemble is a set of models whose outputs are combined. The obtained set tends to have a smaller estimation error than the individual models. The ideal ensemble members should be diverse, meaning that their errors should be uncorrelated and accurate, meaning that they provide good-enough classification on their own . The mosThis basic approach can be further extended using the overproduce-and-choose method , in whicThe ensemble construction schematic is presented in The simulated data are generated from an object representing a drivetrain, which includes a driving shaft associated with referential speed, a one-stage parallel gearbox, a power take-off shaft, and a rolling element bearing (REB). The gearbox is a speed reduction with 23 teeth on the driving shaft gear and 67 teeth on the power take-off shaft gear. The total transmission ratio is 23/67 = 0.34328. The simulated object operates at three nominal speeds of 3000, 4200, and 6000 rpm with a typical minor speed fluctuation of around 12 rpm.The simulated data represent eight modes of object structural failures. The list of existing modes is presented in The simulated model consists of two elements—a synthetic model of vibration signal and a synthetic model of development of particular fault of rotary machinery. Depending on the simulated fault mode, consecutive vibration signals are modified differently. Each vibration signal is constructed as a phenomenological-behavioral model with generalized angular deterministic (GAD)  shaft coDuring years of research related to condition monitoring (CM), many signal processing and feature extraction algorithms have been proposed. From the fundamental calculation of filtered raw signal root mean square (RMS) to more sophisticated as spectral kurtosis. The detailed description of the various algorithms are described in works ,30,43.The choice of signal processing methods for simulation data was based on contextual knowledge. Much of the damage manifests itself in the presence of additional harmonics at specific frequencies. Therefore, spectral analysis was introduced, and the signal was resampled into the order domain based on the phase marker information.The imbalance is manifested by an increase in the fundamental harmonic amplitude, directly related to the rotational velocity. The raw signal from the generator is supposed to imitate the acceleration waveform. Therefore, to obtain the velocity signal, one must perform the numerical integration operation.The last applied processing algorithm was time-synchronous analysis, often used to detect gear failure in Vibro-diagnostics. The detailed list of signal processing algorithms and extracted features is gathered in Unidimensional distribution-based (UDDB) model,Nearest-neighbor (NN) model,The Online Novelty and Drift Detection Algorithm (OLINDDA) based model,Auto-associative neural networks (AANNs) ensemble,After extracting the features described in the The ND models were trained on features extracted for the first mode of failure see , which rThe fourth model consisting ensemble composed of 15 AANNs was trained, using the Oveproduce-and-Choose method, in the following manner. For the development of the ensemble, 100 networks were trained on previously split sets. After this process, 15 networks with the best score on the testing set  were selected for ensemble construction.The models were trained on a computer containing an Intel Core i7-8750H CPU with 16 GB of RAM. The development times for each model are included in All trained models were evaluated on simulated vibrational data, which contained failure modes from 2 to 8 (5) for three rotational velocities. Since the results for each rotational speed were similar, the article presents those selected for 3000 rpm. The features in each failure mode were processed sequentially from the 1st to 150th signal as a data stream from a CM system.In order to present different types of faults, in this subsection only outcome of mode 2, 3, 4 and 6 analysis for one shaft velocity will be discussed see . The resThe four subfigures in each figure  reveal sequence of novelty prediction (novelty) and novelty reference (novelty reference) in comparison to the failure development functions (FDFs). In the juxtaposition of the novelty waveforms from these figures, the deviation of models from most samples in the immediate vicinity is present. When such fluctuations occur for an undamaged machine, it indicates false alarms, which generate additional costs.The rest subfigures in each figure  contain confusion matrix values in form of bar graphs. All points are divided into 4 groups: True Negatives (TN), False Negatives (FN), True Positives (TP), and False Positives (FP). The values representing the efficiency and false positives percentages for each of the modes are presented in The novelty reference was obtained from FDFs. For FDFs values corresponding to the normal state, the novelty reference is equal 0. For values significantly different from the normal range, the novelty reference is set to 1. For signals in between, the function takes the value 0.5 and, it is not accounted for confusion matrix results. The novelty reference was unknown for the ND algorithms.The discussion will begin from Mode 2-Imbalance. The results of sequence novelty evaluation are presented in Another of the analyzed failures is mode 3-Gearbox, which simulated the generalized gear failure. The waveforms showing the development of damage for 3000 rpm are presented in The last type of analyzed failure concerns rolling elements bearings (REB), simulated in mode 4. The waveforms containing the development of damage for 3000 rpm are presented in An explanation of the NN and UBBD improvement is related to the last waveform in The important observation concerning all models is their high sensitivity for detecting this type of damage. Compared to gearbox failure f or imbaThe last results presented in An important aspect regarding the implementation of the algorithms is their computational complexity. Experiments have been conducted on an AMC Vibro VibStand 2 test bench. VibStand 2 test bench configuration is similar to the simulation data generator presented in Data acquisition was performed with AMC Vibro VibMonitor. As sampling frequency and acquisition time was selected, for each signal, respectively, the following values: 25 kHz and 10 s. Data were gathered with the PCB 333B30 piezoelectric accelerometer mounted on the bearing, similar to the data generator presented in Due to the similar structure of the data used during the simulation studies, it was decided to utilize the same signal processing algorithms. The reasons behind their application are described in detail in this The presented functions have a similar shape to those obtained for simulation signals in Because of the low number of normal data samples (only 10 representing the intact state), the training dataset was built by adding to simulation data the experimental samples. The combined samples were divided into a ratio of 70% of training and 30% of testing data. The selected samples concerning previously selected measurement data are presented in Models were trained on the same computer. The development times for each model are included in The retrained models were tested on extracted features from collected data series. The results are presented in The novelty reference was obtained by built from fault index before the analyses and was unknown for the ND methods. For fault index values corresponding to the normal state, the novelty reference is equal 0. For values significantly different from the normal range, the novelty reference is set to 1. For signals in between, the function takes the value 0.5 and, it is not accounted for confusion matrix results.Considering the number of false positives (FP), OLINDDA and Ensemble perform the best. The worst prediction is obtained for the UDDB model. The explanation is related to model architecture, where a few additional points do not affect the distribution parameters. Other methods have no such limitations and therefore produce improved results.Regarding the overall miss-classification rate, the best performance in detecting inbalance was obtained by the Ensemble method. The combination of responses from different models improved the resultant novelty prediction.In this paper, four different ND methods for CM were implemented. The tests were performed on simulation and experimental vibration signals. The algorithms’ inputs consisted of a vector of features calculated from signals by three different signal processing algorithms. Since the simulation signals had a similar distribution of frequency components to experimental signals, they were introduced to the overall training data.The data included in the article contained three types of damage: unbalance, gear meshing problem, and bearing failure. All the algorithms scored the lowest in detecting gear damage. This fact is a consequence of the lowest increase in the values of the features. At a low damage severity, sample values did not differ from those obtained for the normal condition.Worth considering are the results obtained for the shaft unbalance in the drive chain. As described in the paper, the results revealed that all algorithms performed equally well with the simulation and experimental data. It justifies the use of data generators for model preparation. Especially since collecting data from a damaged object is problematic and can cause permanent damage.The paper also compares the presented models by relating them to the problems encountered in CM. The serious problem is false alarms reported for an undamaged machine. In this category, the best models were NN and Ensemble, which obtained the lowest number of false positives (FPs). Considering the number of effectiveness, NN reached better results. The ensemble model was associated with a relatively high proportion of false-negative (FNs) samples. The calculation costs criterion favors the NN model.The OLINDDA detector results are ambiguous. The mentioned detector obtained the lowest number of misclassifications on experimental data  and false negatives (FNs). However, regarding the simulation data results, a different view of the OLINDDA detector emerges. Simultaneously, it is the most effective for one type of failure and the worst for another. The algorithm is additionally the most computationally expensive of those discussed in the article.The worst performance from tested ND models presented a UDDB detector. Considering all the presented results, the mentioned model reported the highest rate of false alarms. Regarding ND capabilities, the model is mediocre in comparison to others. On the other hand, the computational cost for this model is the lowest, which enables implementation in embedded systems with low computing power. The presentation of UBBD in the article is a reference for other multidimensional algorithms which still have not a well-established place in industrial practice.