Nowadays, location awareness becomes the key to numerous Internet of Things (IoT) applications. Among the various methods for indoor localisation, received signal strength indicator (RSSI)-based fingerprinting attracts massive attention. However, the RSSI fingerprinting method is susceptible to lower accuracies because of the disturbance triggered by various factors from the indoors that influence the link quality of radio signals. Localisation using body-mounted wearable devices introduces an additional source of error when calculating the RSSI, leading to the deterioration of localisation performance. The broad aim of this study is to mitigate the user’s body shadowing effect on RSSI to improve localisation accuracy. Firstly, this study examines the effect of the user’s body on RSSI. Then, an angle estimation method is proposed by leveraging the concept of landmark. For precise identification of landmarks, an inertial measurement unit (IMU)-aided decision tree-based motion mode classifier is implemented. After that, a compensation model is proposed to correct the RSSI. Finally, the unknown location is estimated using the nearest neighbour method. Results demonstrated that the proposed system can significantly improve the localisation accuracy, where a median localisation accuracy of 1.46 m is achieved after compensating the body effect, which is 2.68 m before the compensation using the classical K-nearest neighbour method. Moreover, the proposed system noticeably outperformed others when comparing its performance with two other related works. The median accuracy is further improved to 0.74 m by applying a proposed weighted K-nearest neighbour algorithm. Knowledge about location information becomes the key to numerous location-based services (LBS) in various application domains including healthcare and safety, search and rescue, assisted living, robotics, shopping and museum assistance, context awareness and social networking, advertising, and marketing . One of Typically, an indoor localisation system utilises an infrastructure inside a building with a set of devices wirelessly connected to locate an unknown target carrying devices compatible with that network. Various technologies are used so far for indoor localisation including Bluetooth low energy (BLE), radio frequency identification (RFID), ultra-wideband (UWB), ultrasound, wireless local area network (WLAN), and wireless sensor network (WSN) . Among tRecently, WSN has become an attractive research area, especially for various monitoring applications, due to its real-time and accurate response, coverage, and simple infrastructure. With the continuous advancement and miniaturisation of sensing, as well as communication technologies, wearable devices are becoming an essential component for daily living. WSNs using wearable sensor devices are emerging for many IoT applications. Acquiring information about the location of a user is one of the key features of wearable devices, which becomes one of the major issues for WSN due to the presence of a massive number of wearable sensor nodes in modern IoT applications. The estimation of the orientation angle between a user and an RN in real time.The derivation of a BSE compensation model that can mitigate the user’s body effects for every single orientation angle scenario instead of some discrete orientation angles.The adaptation of the orientation angle estimation and BSE mitigation methods in real-life indoor localisation applications.One of the major limitations of RSSI-based indoor localisation is the erroneous determination of RSSI. The main reasons for this are the abovementioned complex nature of indoor environments and the non-line-of-sight (NLOS) situations triggered by the signal blockage between a sender and a receiver. In the case of wearable devices, the user’s body can introduce the NLOS scenario that leads to an additional effect on the resulted RSSI. The human body encompasses around 70% of water that can absorb part of the radio signal . MoreoveKnowledge of the indoor area, i.e., the spatial information, may be an assistive tool that can be leveraged to improve the indoor localisation accuracy without paying extra cost for setup. Landmark, i.e., the sensory landmark, is one such piece of spatial information that is distributed naturally to a floor plan and can be helpful to enhance localisation accuracy ,6. SpeciAn in-depth analysis of the behaviour of XBee RSSI is performed to investigate its effect on the user’s body.A unique method is proposed to estimate the orientation angle between a user and the RNs.A new model is proposed that can compensate the user’s BSE on XBee RSSI for every possible orientation angle.A landmark-assisted weight calculation method is used to implement the WK-NN algorithm to improve the localisation accuracy.Experiments were conducted in a real indoor scenario by applying the proposed method and model for real-time application.The aim of this study is to compensate the user’s BSE on RSSI to improve the RSSI fingerprinting-based indoor localisation performance with a chest-mounted wearable device in a WSN setting. The proposed fingerprinting system composed the offline and online phases similar to the traditional fingerprint methods. However, the online phase performs several additional tasks to mitigate human body shadowing errors. To compensate the RSSIs of a query fingerprint with proper values, the angle between the wearable device and the RNs is estimated considering the user’s orientation. The concept of landmark graph along with arctangent function is utilised for angle estimation. To identify a landmark, an IMU-aided decision tree-based motion mode detection classifier is implemented. Then, a human body shadowing compensation model is proposed to correct the RSSIs of the query fingerprint. Finally, both the classical k-nearest neighbour (K-NN) and weighted k-nearest neighbour (WK-NN) algorithms are employed to calculate the location of the unknown target. The main contributions of this research are as follows:The remainder of the paper is organised as follows: Until now, there are numerous studies that investigate the effects of the human body shadowing on wireless signal transmission to characterise and model the wireless channel and antenna radiation by focusing on various aspects of body-centric radio frequency-based communication. Moreover, human BSEs have been analysed and modelled for a variety of applications, including people counting ,8, fall In the literature, researchers utilised several wireless technologies; this study only focuses on the systems that exploited RSSI as their measurement approach and/or fingerprinting as their localisation method. An RFID-based system is presented in , where tFrom Institute of Electrical and Electronic Engineers (IEEE) 802.11 family of standards, the impact of the human body on RSSI-based ranging measurements for cooperative localisation is presented in . The autFrom Zigbee-based indoor localisation solutions, a body-worn device is used in , where tRecently, Deng et al. reported an IMU-aided system to compensate body shadowing error for BLE-based indoor positioning . The effIn this study, the user’s orientation is estimated by applying a unique approach using a BSE compensation model that is proposed to mitigate the user’s body shadowing error in real time to improve indoor localisation accuracy.Several experiments were performed to investigate the effects of the user’s body on radio signal RSS values. This section describes the experiments and provides observations from the experiments. The experiments were conducted in two different indoor environments with a similar type of setup. The details of the hardware modules used for the experiments are discussed in As can be observed from To further understand the reason for the results obtained above, When the body is placed with an angle of In wards Q4 f, the reAlthough the traditional way of creating a radio map is to partition the area of interest into grids of uniform size followed by the radio fingerprint data collection along a straight path within those grids, this type of manual collection of fingerprint incurs the radio map with RSSIs which have human body shadowing error with them. To exclude this error from the collected RSSI, this study utilised a self-directed car to collect radio fingerprints for radio map. The details of the car, along with its working principle, can be found in our previous work . The carAs shown in The basic concept of landmarks and landmark graph are adopted from previous studies ,6. Here,Although there are various types of landmarks used for indoor localisation in previous works, this study only considers two types of landmarks: door landmarks and turning landmarks, which are useful for localisation in a 2D indoor environment.Door landmarks are the sensory markers in the indoor floor plan where the state of motion modes of a subject experience a distinct change in signal patterns. In this work, accelerometer readings are utilised to perceive the door landmarks that can present a specific signal pattern. The usual change pattern in motion modes when accessing a doorway is “walking→static→walking”, which is exploited to infer the door landmark.  follows :(5)LdooTurning landmarks are the sensory markers in the indoor map where the motion modes provide distinct signal patterns. In this study, data from both the gyroscope and accelerometer combinedly provide a specific motion pattern such as “walking→turning→walking”, corresponding to the direction of turning. A landmark graph is a directed graph where the landmarks act as nodes and the path segment between two adjacent landmarks acts as edges. Let The understanding and detection of motion mode are helpful to implement IMU-assisted indoor localisation. There are different kinds of motions experienced by an IMU which mainly depend on the placement of the sensor on a user’s body. Usually, motion models used by the researchers are specific to the position of IMU installation on the body, e.g., foot-mounted , handhelStatic motion: this type of motion mode includes all the circumstances when a subject is static. A subject will be deemed to be in static mode when his/her spatial position does not change throughout a considered time window. This mode also considers the states as static when a subject obtains slight motion that is not significant enough to infer it as typical locomotion, for example, if a subject moves slightly by stepping on the same spot while opening a door. To detect a landmark correctly, this type of movement must be identified as static.Striding motion: this type of motion mode involves the continuous and smooth motion states that contain periodicity and similarity characteristics for a particular time period in their feature set attributes. It includes the motions that change a subject’s spatial position, e.g., plain walking, walking on stairs, or running.Turning motion: this refers to the motion states when a subject takes a turn while standing or walking, e.g., performing left or right turning.Intermittent motion: this type of motion mode refers to the cases that generate irregular motion states without having the periodicity and continuity properties. It includes all the motion states that a subject performs while remain standing and does not contribute to the change in his/her spatial position, for example, bending or shaking the subject’s body while standing on the same spot.The purpose of a typical classification system is to allocate an input pattern automatically to a known set of items based on some decision rules. As shown in As proposed by , this woThere are two main parts to compensate the effect of user’s body shadowing on RSSI calculation: angle estimation and compensation model.Because of the geometrical structures of the indoor environment, the movement of people indoors usually tends to be in the same direction at least for a few seconds, e.g., in the case of a corridor, a user can walk in two directions. As the usual direction of a chest-mounted wearable device is the same as the movement direction of a user, this behaviour, along with the concept of landmark graph, RNs location information, and indoor environmental geometrical constrain, can be exploited to calculate the angle between the chest-mounted wearable tag and the RNs. To calculate the angle between a user and an RN, the two-argument arctangent function (atan2) is used, which can estimate the angle in the Euclidean plane between the positive x-axis and a line connecting to a point, as shown in In this study, the path segment where the user is walking during the angle estimation is considered as the line corresponding to the x-axis. Thus, the angle is calculated between the moving path and the line connecting the current location of the user and the location of the RN b, as folTo compensate the effects of the user’s body on signal RSSI value, a compensation model is proposed in this study. This model can intensify the signal RSSI values that are being interrupted by the user’s body. Thus, the proposed model for correcting the raw RSSI is as follows, which considers the angle between the user’s body and the RN: However, as observed from To estimate the values of Irrespective of the utilised features, a fingerprinting-based localisation problem is mainly a pattern matching problem. During the online phase, a target sends a query fingerprint from an unknown location that needs to be matched with the fingerprints stored in the radio map. It is very unlikely that a radio map will contain a fingerprint with an exact match. Thus, the traditional way is to find Let posed in , the weiIn this study, the coarse location of an unknown target is estimated first to calculate the spatial distance between the RPs and a target location. The coarse location of the target is computed by leveraging the landmark graph and using the same technique proposed in This section presents the evaluation of the proposed models through quantitative experimental results.The experiments were carried out using two customised sensor boards designed by our group. To collect the RSSI fingerprint, the XBee wireless technology-based XBee S1 802.15.4 module was used as the radio in the first sensor board, as shown in Several experiments were carried out for collecting an adequate amount of data with ground truth labels to train and test the designed motion mode classifier. Data from four adults  of different heights and weights were collected to evaluate the performance of the proposed classifier. The data collections were conducted in an open field, and each participant was equipped with a chest-mounted IMU device. The participants were requested to walk approximately 500 m of distance while performing several activities. The experiments were performed using a predefined protocol that consisted of six activities including static, walking, turning right, turning left, opening a door, bending, and random movement. As the data were collected from an open field, the participants were asked to simulate the door-opening activity. To complete one run of the defined protocol, a participant required four minutes, and each participant repeated the protocol three times. Thus, enough data was collected for training and testing of the classifier. https://x-io.co.uk/ngimu/ (accessed on 10 February 2021), was utilised. Pressing the power button of the device while powered on will send a message to the receiver with timestamped information for the button-pressing event. During the experiment, the participants were asked to press the button of the NGIMU each time they began an activity. Thus, by annotating the exact number and sequence of performed activities and mapping this information with the timestamped button event’s data, the ground truth labelling was performed. For precise evaluation of the classifier, the data recorded during the transition of two activities were removed manually.To facilitate the labelling of ground truth, another IMU device, named NGIMU  for a motion class is the ratio of correctly positive-labelled motion modes for that class to the total number of motion modes that actually belong to that class. The specificity for a motion class is the ratio of correctly negative-labelled motion modes for that class to the total number of motion modes that do not belong to that class. F-measure is the harmonic average of precision and sensitivity. These metrics are defined as follows:As can be seen from the confusion matrix, the classifier can detect the correct motion mode in more than 95% of cases, irrespective of the type of motion class performed by a participant. The highest accuracy of 99.5% was attained by the classifier for the static motion mode. As reported, 2 and 3 segments out of 928 segments for static type motions were misclassified as striding motion and intermittent motion, respectively. The main reason behind this confusion is because of the simulated door opening activities performed by the participants, which are actually considered as static activities; however, this type of activity sometimes may generate high energy and variance in the signal which can satisfy the decision thresholds, leading to misclassification.The lowest accuracy of 95.4% was achieved for detecting the intermittent motion mode by the classifier. This is because intermittent motions are more likely to be confused as other types of motions. As reported in the confusion matrix, among the total 696 segments for intermittent motions, 17 were detected as striding motion. One possible reason for this confusion may be the consecutive occurrence of a similar type of movement several times , which can produce periodicity and lead to that misclassification. However, during the landmark identification phase, it is very unlikely that such intermittent movement will occur in a pattern that can satisfy the landmark rules. Thus, the defined rules for landmark identification can mitigate the impact of this type of misclassification. Moreover, 17 segments out of 1020 for the striding motion mode were misclassified as intermittent motion, causing the accuracy for that class to be 96.8%.As presented in The proposed BSE compensation model was evaluated firstly using the same experimental data as shown in As the human body shape is uneven, the amount of RSSI depletion, while facing the different body parts, by the signal will be different. The intensification parameter To validate the efficiency of the proposed model, RSSI data were also collected using the same experimental setup, except the wearable device was placed on the back of a user. The impacts of the parameter To evaluate the performance of the proposed localisation system, experiments were performed in an office building. The experiment building was Building 72 at the Clayton campus of Monash University, which comprises three floors. The experiment was carried out on the second floor, with a total area of about 1475 To evaluate the system performance, 40 key points were set along the experimented path, which served as the ground truth for comparison. During the experiment, the participant was asked to stop a little at each key point for the purpose of recording the markers. Let This study reports the mean error, median error, standard deviation, 25th, 75th, and 90th percentile errors, and a cumulative distribution function (CDF) plot to analyse the localisation performance of the proposed system.The localisation performance of the proposed system was compared with two other studies that proposed different models for angle estimation and BSE compensation, including the work presented in , referreThe details of the positioning performance are presented in The superiority of the proposed system is further increased by applying the WK-NN algorithm when comparing a query fingerprint with the radio map. The performance is improved by including the spatial prominence of the neighbouring RPs in terms of weight factor. This study describes solutions for improving the accuracy of wearable sensor-based fingerprinting indoor localisation by mitigating the user’s BSE on RSSI. An in-depth analysis of RSSI for different orientations of the user’s body was performed, and a body shadowing compensation model is proposed. To calculate the orientation angle between a wearable device and an RN, an IMU-aided motion mode detection technique was implemented by fusing the spatial knowledge from the indoor floor plan. The decision tree-based classifier yields an outstanding performance for motion mode detection that, in turn, accurately identifies the landmark to produce high precision for the estimation of the user’s orientation angle. Results demonstrated that the implemented classifier achieves an overall accuracy of 97.31% for detecting a motion mode correctly, which eventually helps to compensate the errors caused by the user’s body. To validate the proposed body shadowing compensation model, both the classical K-NN and the WK-NN methods were implemented with a unique weighting technique. For selecting the K nearest neighbours in the case of the WK-NN method, the spatial prominence of the neighbouring RPs was applied as the weights, which were calculated by using a unique landmark-assisted distance measurement method. Finally, the localisation performance of the proposed system was compared with two other recent studies that proposed different models for angle estimation and BSE compensation. The experimental results show a mean and median accuracy of 1.62 m and 1.46 m for the classical K-NN method, which is further improved to 1.01 m and 0.74 m, respectively, using the WK-NN method. Overall, the proposed BSE compensation model along with the landmark-assisted WK-NN method can realise sub-metre median localisation accuracy that noticeably outperforms the considered related studies. Although the proposed methods are intended for RSSI fingerprinting localisation, these can be adopted in other RSSI-based indoor localisation applications with body-mounted wearable devices. The main limitation of the proposed system is the dependency of the orientation angle estimation phase on the previously estimated location. Future work will include the implementation of the proposed system in multistorey buildings by addressing this issue.


Target-following mobile robots have gained attention in various industrial applications. This study proposes an ultra-wideband-based target localization method that provides highly accurate and robust target tracking performance for a following robot. Based on the least square approximation framework, the proposed method improves localization accuracy by compensating localization bias and high-frequency deviations component by component. Initial calibration method is proposed to measure the device-dependent localization bias, which enables a compensation of the bias error not only at the calibration points, but also at the any other points. An iterative complementary filter, which recursively produces optimal estimation for each timeframe as a weighted sum of previous and current estimation depending on the reliability of each estimation, is proposed to reduce the deviation of the localization error. The performance of the proposed method is validated using simulations and experiments. Both the magnitude and deviation of the localization error were significantly improved by up to 77 and 51%, respectively, compared with the previous method. Recently, human-following mobile robots have been introduced to ease the burden of human operators in various applications ,2,3. RobHuman-tracking methods can be classified depending on the type of sensors used to measure the location of a target person. Camera vision was generally adopted in previous studies because it provides abundant scene information with relatively low cost . HoweverA wireless-communication-based indoor positioning system (IPS) can be used to robustly measure the position of the target person regardless of surrounding obstacles. Even though the accuracy may be affected by the obstacles, the system does not lose the target. Wireless LAN (WLAN) , BluetooUWB-based IPS is composed of multiple UWB transceiver modules that are stationarily installed in the environment, called anchors, and a transceiver module installed on a moving target, called a tag. The system estimates the position of the tag using the given distances between the tag and each anchor, which are calculated using the time-of-flight of UWB communication. Previous studies describe two types of approaches to reduce positioning errors under the given errors in a distance measurement, i.e., fingerprinting and geometric approaches. In the fingerprinting approaches, machine learning techniques are used to estimate the position of the tag using empirical datasets, which consist of experimentally measured UWB transceiver signals and corresponding true locations ,19. It pA typical example of the nonparametric method is the least square (LS) approximation. In a practical situation, the LS approximation sensitively responds to non-line-of-sight (NLOS) situations and device-dependent measurement errors . The weiPrevious UWB-based positioning methods assumed that the UWB transceivers are configured as a UWB tag moves in the area enclosed by multiple (>3) UWB anchors that are stationarily installed in the environment. However, the configuration of the UWB transceivers should be modified for human tracking in the following robot. The UWB anchors should be mounted on the robot because it aims to identify the position of the tag relative to the robot instead of the environment. In this configuration, the positioning error can increase because the tag is located outside the convex hull made by the anchors . The ancThis study proposes a component-wise error correction method to increase the accuracy of UWB localization based on the in-depth analysis of UWB error characteristics. The core UWB error components are classified into two parts, i.e., bias and noise, and error corrections that fit into each component are proposed.The sensor calibration is proposed to measure and compensate the device-dependent bias errors, which consistently appear in UWB localization. By conducting the calibration only once in the initialization, it can successfully correct the consistent bias of the localization.The interactive complementary filter is proposed to alleviate the high-frequency noise of the localization. Radial and tangential components of the localization noise are significantly reduced by the proposed filter.Assuming a configuration in which the human holds a UWB transceiver (tag) and four UWB transceivers are mounted on the mobile robot, this study proposes a novel method to estimate the position of the tag relative to the mobile robot for precise and robust human tracking in the following robot. Based on the previous LS approximation framework, the proposed method improves the positioning accuracy by developing sensor calibration to manage device-dependent error characteristics, as well as the interactive complementary filter to reduce the standard deviation of positioning errors. The main contribution of this study is the novel component-wise localization error correction method that alleviate not only the bias but also the deviation in the localization error. This paper identified two main components of localization error in the LS approximation through the mathematical derivation and proposed the error correction methods that alleviate the errors component by component. As the proposed method precisely tackles each error component based on in-depth error analysis, it achieved superior localization performance compared to the methods proposed in the literature. The contributions of this paper are as follows:The following manuscript is structured as follows. In ith anchor, and ith anchor, respectively. By substituting Equation (2) can be expressed in a matrix form asBecause there exist measurement errors in ximation :(4)X˜=arith anchor. Equation (6) indicates that the absolute value of the estimation error increases proportionally to the distance between the tag and the anchors : The calibrated estimation at time k . The distance-measurement error between the UWB anchor and tag is defined by the mean and standard deviation. These values were acquired through the experiment, in which the distance-measurement data was collected for a minute at four reference points  located 1 m away from the center of the robot. The mean and standard deviation of the error used in the simulation are shown in T˜) a shows aThe performance of the proposed method for each step was analyzed through the simulation. Therefore, the final result of the proposed method  situations to the localization accuracy. We have conducted pilot experiment to identify the human effect to the localization accuracy. The experimental results reveal that the human effect was not significant, but it requires in-depth analysis and additional experiments to prove practical applicability of the proposed method. Although the magnitude and deviation of the error were reduced compared with previous methods, the error still increases as the tag position moves farther away from the anchor, as shown in In this study, we proposed a component-wise error-correction method to improve the localization accuracy of a target-following mobile robot. The localization bias and high-frequency deviation of the error were successfully alleviated through the proposed initial calibration and iterative complementary filter. The performance evaluation conducted via the simulation and experiment confirmed that the proposed method significantly improves the localization accuracy of previous methods. We believe that the proposed method can be used for the industrial application of following robots, and it contributes to easing the burden of the human operator.


Remote photoplethysmography (rPPG) is a video-based non-contact heart rate measurement technology. It is a fact that most existing rPPG methods fail to deal with the spatiotemporal features of the video, which is significant for the extraction of the rPPG signal. In this paper, we propose a 3D central difference convolutional network (CDCA-rPPGNet) to measure heart rate, with an attention mechanism to combine spatial and temporal features. First, we crop and stitch the region of interest together through facial landmarks. Next, the high-quality regions of interest are fed to CDCA-rPPGNet based on a central difference convolution, which can enhance the spatiotemporal representation and capture rich relevant time contexts by collecting time difference information. In addition, we integrate the attention module into the neural network, aiming to strengthen the ability of the neural network to extract video channels and spatial features, so as to obtain more accurate rPPG signals. In summary, the three main contributions of this paper are as follows: (1) the proposed network base on central difference convolution could better capture the subtle color changes to recover the rPPG signals; (2) the proposed ROI extraction method provides high-quality input to the network; (3) the attention module is used to strengthen the ability of the network to extract features. Extensive experiments are conducted on two public datasets—the PURE dataset and the UBFC-rPPG dataset. In terms of the experiment results, our proposed method achieves 0.46 MAE (bpm), 0.90 RMSE (bpm) and 0.99 R value of Pearson’s correlation coefficient on the PURE dataset, and 0.60 MAE (bpm), 1.38 RMSE (bpm) and 0.99 R value of Pearson’s correlation coefficient on the UBFC dataset, which proves the effectiveness of our proposed approach. Heart rate is a vital indicator of health monitoring. Heart rate measurement is essential for health management, disease diagnosis and clinical research. Traditional contact heart rate measurement methods, including electrocardiograms, require specific equipment such as ECG technology. The surface electrode is in direct contact with the patient’s body surface, which brings inconvenience and discomfort to the patient, psychologically. In addition, ECG equipment is expensive, complicated to install, inconvenient to carry, and not suitable for real-time mobile heart rate monitoring. Remote photoplethysmography (rPPG) is a non-contact method to capture the periodic changes in skin color caused by the heartbeat through sensors such as cameras. The process of the method is as follows: 1) use the camera to capture the skin area  video; 2) analyze the periodic color changes in the skin area due to the blood flow pulsation caused by the heartbeat; 3) recover the corresponding rPPG signal and measure physiological indicators. The subtle color changes of skin in the video directly reflect changes in the rPPG signals, in other words, the deep learning models can capture the temporal variation of skin color to recover the rPPG signals. Today, severely affected by the COVID-19 pandemic, traditional heart rate measurement methods have greater safety risks. Close contact may cause infection, so that the study of non-contact rPPG signals measurement has attracted more attention [ use the  analyze  recover With the continuous application of image video in the field of computer vision, AI has many applications in the field of healthcare such as HR measurement and blood pressure measurement , many noIn order to extract more accurate rPPG signals, the attention mechanism has been widely used in the rPPG signals recovery ,12. Hu e1.We design the network based on central difference convolution to obtain rich time difference information for the extraction of the rPPG signals;2.We propose a more reliable ROI extraction method. Face detection is used to extract the forehead and cheek, then we splice them as the input of the model;3.The 3D-CBAM attention mechanism is designed to direct our network to learn information more efficiently and focus on more important features;4.Experiments based on PURE  and UBFCIn summary, the flow of the existing non-contact heart rate measurement methods mainly includes three steps: ROI selection, rPPG signal extraction, and heart rate measurement. The ROI selection is the first step to obtain the rPPG signal, which directly effects the quality of the rPPG signal . There ax and y coordinates of the top-left vertex respectively. All pixels of the face, except for the non-skin regions that contain no rPPG information, contribute to the rPPG signal. Most all heart rate estimation methods require the ROI selection. If we select the face region as the input of our model, the predicted rPPG signals will be interfered by the non-skin regions such as eyes and bread. Regarding only the cheek or forehead as input will ignore the other region that contains high-quality rPPG information, which will lead to a decrease in the robustness of the signal. In order to maximize the ratio of skin region, we splice the forehead and cheek as the input of our model. Face detection is used to extract the face region, precise facial landmarks are used to define the specific coordinates of the cropped regions. We use OpenFace  to get fThe process of extracting the rPPG signal is to obtain the temporal variation of skin color. In order to extract the spatiotemporal features more effectively, Yu et al.  first apCBAM  attentioAs shown in MLP represents the multi-layer perceptron, the weights The output Diagram of spatial attention is shown in Hence, the output feature map To efficiently predict the rPPG signal, we propose an efficient network. An overview of CDCA-rPPGNet is presented in x is the predicted rPPG signals, y donates the ground truth rPPG signals, and T is the length of the rPPG signals. Our proposed network architecture is developed to recover rPPG signals with similarity in trend and to accurately estimate pulse peak time positions that match with ground truth rPPG signals. A suitable loss function needs to be designed to guide our networks. The frequently used loss functions are inappropriate for rPPG signals, since both rPPG signals  and PPG signals (from contact measurement) reflect the blood volume changes, but their exact values are not the same. We only care about the trend of signals but ignore the specific value, so Negative Pearson Correlation is used as the loss function. Pearson Correlation indicates the linear similarity between rPPG signals and PPG signals, which can guide our networks to maximize the trend similarity. It is formulated as: To train and evaluate our network efficiently, experiments based on PURE and UBFC datasets were conducted. We used three performance metrics for heart rate measurement: mean absolute error (MAE), root mean squared error (RMSE), Pearson’s correlation coefficient (R).PURE: The dataset contains ten subjects, every subject contains six different activities . It is a fact that talking and head movements will cause large light variation, which makes it difficult to recover rPPG signals. In a total of 60 videos, every video is about 1 min and all videos were recorded by the industrial camera at 30 fps with 640 × 480 pixels spatial resolution. The ground truth PPG signals were captured with a finger pulse oximeter pulox CMS50E with a sampling rate of 60 Hz.UBFC-rPPG: the dataset includes 42 videos of 42 subjects; each subject has one video, every video is about one minute. In the video recording process, in order to make the subject’s heart rate change, the subject is asked to play a game that can trigger the heart rate change. The video was recorded by Logitech C920 HD Pro at 30 fps with a spatial resolution of 640 × 480 pixels. A finger pulse oximeter CMS50E was used to capture the ground truth rPPG signals with a 60 Hz sampling rate. Since UBFC-rPPG dataset is really small, we performed data augmentation on the sample, we flipped each sample left and right, which doubles the number of samples.The examples of the two datasets are shown in At present, three performance metrics are used for heart rate measurement: mean absolute error (MAE), root mean squared error (RMSE), Pearson’s correlation coefficient (R).1.Mean absolute error (MAE)MAE is the average value of the absolute deviations of all estimated HR and the ground truth HR. It can be expressed as:2.Root square mean error (RMSE)RMSE is the average value of the standard deviations of all estimated HR and the ground truth HR. It can be calculated by the following formula:3.Pearson’s Correlation Coefficient (R)R measures the linear dependence between two signals.where N is the number of heart rate samples. x and y.For our experiments, due to the different frequencies of the ground truth rPPG signals and the video frame sampling frequency, we should normalize the rPPG signal first then subsample it to the video frame. The input of the model is the continuous ROI images We used the Adam optimizer to train our model, the batch size is eight, the learning rate is set to 0.0002, the model is trained with 30 epochs. ReLU activation is used in each convolutional layer. All network components are implemented by Pytorch framework and trained with Quadro P6000.To evaluate the effectiveness of our model for non-contact heart rate measurement, we conduct experiments on the PURE dataset and the UBFC dataset. We perform the following ablation study: (1) replace 3DCDC-T with conventional 3D convolution and remove the attention module; (2) only remove the attention module. Some traditional methods and deep learning methods are used for comparison, the result shows that the proposed method outperforms other methods.The experimental results of the PURE dataset are shown in We also evaluate the proposed method on UBFC dataset, and the results are shown in In addition, as shown in To show the results of our model more intuitively, we analyze the linear similarity of two signals via the scatter plot. As shown in We proposed a central difference convolution network with an attention mechanism to recover rPPG signals from facial video. We evaluated the proposed method on two public datasets. The experimental results indicate that our proposed method was more accurate than the previous method. The proposed method mainly included two steps: ROI selection, rPPG signals prediction using our model.First of all, the ROI selection is very important to the recovery of the rPPG signals, because the region of the face in the video is originally small, which means that the skin pixels can be used to predict rPPG signals are really scarce. If the video is compressed, the quality of the skin pixels will be worse, which will make it difficult to estimate the rPPG signals. In theory, all skin pixels of the face have an effect on the extraction of signals, but the existing methods are difficult to use skin pixels efficiently. To solve this problem, we take the two ROIs that have the largest area and the most rPPG information as the input of our model. The cheek and forehead are affected by the background environment and light to varying degrees, but they both reflect the rPPG information. Using both of them can reduce the impact of the background on our signal extraction, which makes the rPPG signals we extract more robust. At the same time, we minimize the learning difficulty of our network, which can make the network more focused on learning useful information to recover the rPPG signals.The next step is the construction of the neural network. The rPPG signals are essentially a kind of time series, the signals change with time. 3DCDC-T has the ability to better obtain the differences in time context, which is useful for the extraction of the rPPG signal, so we use 3DCDC-T to extract features. Changes in the rPPG signals are reflected from the subtle changes in the color of skin; they are relatively shallow features. Unlike video classification or action recognition, our task does not require a deep network to extract . TherefoIn conclusion, the ROI selection is as important as the signals extraction method. Two steps of our method have an impact on heart rate prediction. Our proposed method showed an MAE of 0.46 bpm in the PURE dataset by combining two stages. We also achieved an MAE of 0.60 bpm in the UBFC dataset. Although our proposed method performed well in experiments, there are still some limitations. First of all, our preprocessing process requires accurate face detection and landmarks, which will not work normally if the subject’s face is partially occluded or the subject is in motion. In addition, a deep learning based method requires a large number of training samples, which is a challenge for remote heart rate measurement. Since heart rate distribution is between 40 bpm and 150 bpm for most samples, our method fails to achieve good accuracy for predicting abnormal heart rate values. Although there are still some limitations, our proposed method has the potential to make a contribution to the practical use of assisted living, which is suitable for our measurement scenarios.Remote HR measurement plays an important role in the field of healthcare. Due to the COVID-19 pandemic, remote HR measurement may be widely used in disease diagnosis and real-time heart rate monitoring. However, the process of most existing rPPG methods is too complicated to be applied to real scenarios. In this paper, we proposed a central differential convolutional network with an attention mechanism for more robust rPPG signal measurement from facial video. The preprocessing part uses face key point detection to segment and splice the regions of interest of the face. Compared with the conventional 3D convolution, the improved 3DCDC-T can estimate the rPPG signal more accurately by enhancing the spatiotemporal representation with an abundant temporal background. The attention mechanism can guide the network to learn more critical feature channels and spatial features for the rPPG signal recovery. On the one hand, our network only includes approximately 0.66 M parameters, which means we can easily deploy the model on the mobile device and, on the other hand, experimental results on two public datasets—PURE and UBFC-rPPG—demonstrate the effectiveness of our proposed method. Our model achieves an MAE of 0.46 bpm and an MAE of 0.60 bpm on the PURE dataset and the UBFC dataset, respectively, which is superior to other current methods. In the future, we will be looking to improve the robustness of the model in low-constraint environments, such as head movements, and reduce the impact of unbalanced HR distribution.


The electrical signals triggering the heart's contraction are governed by non-linear processes that can produce complex irregular activity, especially during or preceding the onset of cardiac arrhythmias. Forecasts of cardiac voltage time series in such conditions could allow new opportunities for intervention and control but would require efficient computation of highly accurate predictions. Although machine-learning (ML) approaches hold promise for delivering such results, non-linear time-series forecasting poses significant challenges. In this manuscript, we study the performance of two recurrent neural network (RNN) approaches along with echo state networks (ESNs) from the reservoir computing (RC) paradigm in predicting cardiac voltage data in terms of accuracy, efficiency, and robustness. We show that these ML time-series prediction methods can forecast synthetic and experimental cardiac action potentials for at least 15–20 beats with a high degree of accuracy, with ESNs typically two orders of magnitude faster than RNN approaches for the same network size. Cardiac electrical signals, known as action potentials, exhibit complex non-linear dynamics, including period-doubling bifurcations in their duration   were introduced as a special class of neural networks in which the recurrent connections allow information to persist in the network. However, they suffer from vanishing and exploding gradient problems, which limit their ability to learn long-term dependencies in temporal sequences. Gated RNNs like long short-term memory networks (LSTMs) were developed to remedy such problems. These networks employ memory cells and a gating mechanism to address exactly these issues. it, ft, and ot denote the input, forget, and output gates, at time t, respectively; xt is the input vector; W and U are the weight matrices that along with biases b are adjusted during the learning process, ct is the cell state , and where Gated recurrent units (GRUs) also were introduced to avoid vanishing and exploding gradient problems and share many similarities in architecture and performance with LSTM networks. The GRU memory cell can be considered as a simplification of an LSTM cell see . Comparezt and rt are update and reset gates, respectively, and W and U and the bias vector b are adjusted, thereby enabling the update and reset gates to select which information should be kept through time and which information is irrelevant for the problem and can be forgotten.where ESNs are a simple yet successful RNN architecture in which most of the network parameters are initialized randomly and remain untrained. ht is updated according toThe reservoir state Win and W are the input weight and reservoir weight matrices, respectively; both are initialized randomly and remained untrained. We utilize an extension of the standard ESN formalism that includes a “leaky” update model, which explicitly includes a linear history term. The input signal is denoted by xt and the constant parameter α ∈  is known as the leaking rate. The output of the network is calculated by the following equation:where fout is the output layer activation function, which is chosen here as a unity function. The output weights Wout are obtained here by regularized least-square regression with Tikhonov regularization to avoid overfitting.where Since the initial success of reservoir computing techniques and ESNs, a variety of network topologies have been proposed in the literature, including clustered reservoirs and deep ESNs. The main components of the network are similar to the baseline ESN architecture except for the reservoir topology; for clustered ESNs, the randomized connections between neurons form a set of sub-reservoirs sparsely connected to each other. The network topology is schematically illustrated in u1(t), the pacing stimulus exciting the network at prescribed intervals; u2(t) = VKB(t), the knowledge-based model providing the voltage dynamics of a cardiac cell; and u3(t) = V(t), the synthetic or experimental voltage measurements. The knowledge-based model can be a much simpler  model that provides an approximation of the dynamical behavior of the system, such as the two-variable Mitchell-Schaeffer  model . Time is effectively rescaled in the Lorenz system by multiplying each of the three differential equations by a factor of 0.001. The anionic current conductance in the Noble model was set to be proportional to the z variable of the Lorenz model, thereby driving oscillations in the anionic current magnitude in concert with the Lorenz oscillations. Specifically, the conductance was set to 0 for z = 0 and to 0.2 for z = 60. This extension provides two important features of this dataset: first, the variation in cycle lengths is driven by a chaotic, rather than a random process, and second, there is no need for application of an external stimulus, as action potentials occur when the cell is quiescent and the Lorenz-driven current brings the voltage above the threshold for excitation. Therefore, in this case, only a univariate time series of voltage data is provided, with no external stimulus data. All other model parameters remain as specified in Noble  of either sex were anesthetized via cold water bath. Following anesthesia, hearts were quickly excised and immersed in Tyrode's solution . Blebbistatin, used to stop contraction without major effects on electrophysiology  pacing Cherry, ; see FigIntra- and extracellular voltages were acquired by two glass micropipettes containing 2.5 M KCl solution fastened into microelectrode holders . Ag/AgCl half cells within the microelectrode holders sent signals to be buffered by pair of DC-powered preamplifiers , which were connected together to output a differential measurement of transmembrane voltage. This transmembrane voltage was then split into two paths. One path led through a BNC breakout board  to be read by a DAQ  and written to a file at 10,000 samples/s by a computer running a custom-built MATLAB script. Transmembrane voltage was also sent through a custom-built circuit that applied a gain and offset to the signals before being read by an Arduino Due. The Arduino Due then interpreted signals on-the-fly and determined when the heart should be stimulated to enforce a user-set DI, which was communicated to a current source stimulus isolator  that stimulated the heart.Although constant-DI pacing can lead to stable and predictable APDs  and were run on the same computer equipped with a 1.4 GHz Quad-Core Intel Core i5 processor and 8 GB of RAM, operating with macOS Big Sur (Version 11.4).The optimum values of various hyperparameters required for each method were tuned through an extensive grid search, the set of values for which are given in The LSTM and GRU networks are constructed using the MATLAB Deep Learning toolbox, where the network topologies are specified by a graph of layers. To predict the action potential time series multiple steps into the future, a sequence-to-sequence regression LSTM architecture is employed that entails several main components. First, a sequential input layer is required to feed the input time series into the network. Then, an LSTM layer is used to learn the long-term dependencies between the time steps of the input sequential data. Finally, a fully connected layer connects the LSTM layer to a regression output layer to complete the design. The architecture of the GRU networks is the same as for the LSTM network except for employing a GRU layer instead of an LSTM layer. In addition to the single-layer architectures, multi-layer networks with multiple stacked gated layers are also tested in this work.The main hyperparameters to configure in gated RNNs include the number of hidden layers and hidden units, the optimizer for the training network, and the hyperparameters related to the optimization solver, such as the maximum number of epochs, learning rate, learning rate drop factor, and regularization factor. Due to the high computational costs of gated RNNs, running an exhaustive grid search on all hyperparameters is not pragmatically feasible. Therefore, based on our initial experiments, some of these hyperparameters are set while the grid search determines the optimum values of those demonstrating a more significant role in the performance of the network. Accordingly, the Adam optimizer  over time, resulting in a univariate time series. However, the input time series can be either a univariate or multivariate time series. The former occurs when the input data is assumed to be endogenous and is not driven by an external stimulus. The latter portrays cases in which cardiac cells are stimulated exogenously; in such a case, the pacing stimulus can also be introduced to the network along with the cardiac voltage signal. In this work, both scenarios are considered. Accordingly, the univariate input models are employed for forecasting the Noble dataset, where the auto-oscillatory nature of this model eliminates the requirements of applying an external stimulus. In contrast, both the FK dataset, which uses random stimulus timings, and the experimental dataset, which uses varying stimulus timings owing to the constant DIs but variable APDs, are used with multivariate time series prediction, which incorporates the pacing stimulus signal. In the case of the experimental data, the timing of applied stimuli is not directly available; thus, a pre-processing step is applied to detect the starting point of each beat in time and then a 2-ms stimulus current with a relative magnitude of 0.2 is used to generate the pacing stimulus signal. This process generates a stimulus current that is then resampled so that stimulus values are available for each resampled voltage data point. Our initial experiments demonstrate that the magnitude of the stimulus does not affect the quality of the predictions in this setup, but introducing the stimulus signal considerably improves the predictive ability in the first place.To assess prediction accuracy, we use the root mean square error (RMSE) metric:Vi and n denotes the length of the test dataset. Note that the voltage values of the Noble and experimental datasets have been linearly rescaled to be between zero and one. The FK model is already scaled so that its upstroke reaches a maximum of one; no further rescaling is performed. As discussed in section 2.3.4, in all cases, the dataset values used here are not uniformly spaced in time.where We also assess error by comparing action potential durations (APDs). We define an APD as the time interval over which the voltage during an action potential is continuously larger than the threshold value, which is selected as 0.3 for the synthetic datasets (FK and noble) and 0.35 for the experimental dataset.The FK model-derived dataset (hereafter referred to as the FK dataset), shown previously in Network size has a limited effect on overall accuracy as measured by RMSE. The lower plot in The results of using the five methods to predict action potentials in the Noble dataset shown in  using a As with the FK model, the RNN approaches consistently take longer than the ESN and clustered ESN approaches, with the hybrid ESN in between. For network sizes of at least 100 hidden units, the ESN and clustered ESN methods require about two orders of magnitude less computational time than the RNN methods. For all approaches, there is a modest increase in computational time for 100 or more hidden units as the network size increases, with the exception of the hybrid ESN, for which the computational time is approximately constant across all network sizes tested.For the experimental dataset, obtained from zebrafish paced using a constant-DI protocol and shown in As the number of neurons is changed, there is no clear effect on accuracy, except possibly for the hybrid ESN, which appears to have a slight trend toward lower RMSE with more neurons; see In this paper, we tested five different ML time series prediction methods, two based on RNNs and three based on a type of reservoir computing, to predict irregular voltage dynamics arising from random or chaotic effects for three cardiac datasets. We found that for clinically relevant intervals  for the detection of cardiac arrhythmia in embedded devices , which is independent of network size, was more expensive than the cost of the ESN itself and thus dominated the total training and prediction time.We investigated different types of dynamics, including those influenced by underlying randomness and chaos. We found the lowest RMSE values for the FK and experimental datasets and the highest RMSE values for the chaotically-driven Noble dataset. For the FK dataset, the hybrid ESN typically achieved the lowest error for all but the smallest network size, with the other ESN approaches achieving slightly less error than the LSTM and GRU methods. The Noble dataset elicited a particularly poor performance for the GRU method, with RMSE values typically three or four times larger than for the other methods; also, the hybrid ESN did not perform as well as the other ESNs. However, it is possible that use of a univariate time series in this case contributed to lower accuracy, rather than just the chaotic dynamics alone. For the experimental dataset, which likely has elements of both randomness and chaos, the hybrid ESN generally achieved the lowest error, with the other methods producing similar RMSE values. Overall, our results indicate that the ESN architecture provides better performance than LSTM and GRU approaches for the voltage forecasting task.The action potential time series used in this work were highly imbalanced. In this study, although we found the need to downsample the original data for use with testing and training, we did not perform systematic studies regarding how to optimize this task. As a general observation, starting from the initial highly imbalanced time series, by increasing the sampling spacing and reducing the number of data points, the training and testing errors were reduced. However, the information loss caused by removing data points is the obvious side effect if the spacing becomes too large. Our choice of tying the time spacing to changes in voltage ensured good resolution during rapidly changing parts of action potentials, including the upstroke, but led to a lack of points during the rest and plateau phases, contributing to apparent errors during these times of slow changes in voltage. Further studies are required to investigate various spacing and resampling strategies to propose an optimal approach.Although our results illustrate that ESNs provide the best prediction accuracy together with the lowest computational times in most cases for the methods and datasets considered, the ESN approach shows the most sensitivity to the hyperparameter and network parameter values. Our grid search results demonstrated a wide variability in the prediction performance obtained by various ESNs with very similar configurations. This motivates more study to improve the robustness of this approach. Among the three RC techniques used in this work, the hybrid ESN showed the least sensitivity to the hyperparameter values. We expect that the knowledge-based model promotes the predictive ability of the network by generating an approximate action potential, which the network perturbs to resolve the precise AP shape.Incorporating the pacing stimulus into a multivariate input setup considerably improved the prediction performance of the network over using a univariate voltage input and extended the forecasting horizon to a higher number of beats. In the absence of the stimulus information, depending on the dynamics of the system, the predictions remain accurate only for the first few beats after the training.Our study contains a number of limitations. First, we studied a limited number of datasets. It is possible that different types of dynamics  could lead to different results, and in particular experimental data from other sources could prove more difficult to predict. In addition, we did not study how much training data was needed to obtain good results. Furthermore, it remains an important open question how long the action potential predictions will remain accurate without deteriorating, although in this case we have found lower bounds.We also considered a small number of time series prediction methods. There are many variations on these methods  and CMMI-1762553 (FF) and by the National Institutes of Health grant 1R01HL143450-01 (EC and FF).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.


Since it is not efficient to physically study many machine failures, models of faulty induction machines (IMs) have attracted a rising interest. These models must be accurate enough to include fault effects and must be computed with relatively low resources to reproduce different fault scenarios. Moreover, they should run in real time to develop online condition-monitoring (CM) systems. Hybrid finite element method (FEM)-analytical models have been recently proposed for fault diagnosis purposes since they keep good accuracy, which is widely accepted, and they can run in real-time simulators. However, these models still require the full simulation of the FEM model to compute the parameters of the analytical model for each faulty scenario with its corresponding computing needs. To address these drawbacks (large computing power and memory resources requirements) this paper proposes sparse identification techniques in combination with the trigonometric interpolation polynomial for the computation of IM model parameters. The proposed model keeps accuracy similar to a FEM model at a much lower computational effort, which could contribute to the development and to the testing of condition-monitoring systems. This approach has been applied to develop an IM model under static eccentricity conditions, but this may extend to other fault types. One of the most common electrical machines in industry is induction machines (IMs). These machines play an important role in the safe and efficient operation of various types of industrial applications due to their numerous strengths, such as simplicity, ruggedness and high reliability, at relatively low cost. However, they are not free from faults that may lead to unexpected failures, causing large economic losses. For this reason, reducing operation and maintenance costs as well as improving reliability have become crucial issues in their maintenance . Much haOnline CM systems and CM systems based on artificial intelligence (AI), as neural networks (ANN) , principIMs in many applications scenarios work under non-stationary conditions or even transient conditions, such as in wind farms, where the wind variability involves non-stationary working conditions. Under these conditions, traditional fast Fourier transform (FFT)-based techniques are no long effective to the fault diagnosis of the IM. Several advanced signal processing techniques have already been investigated to overcome the limitations of the conventional FFT-based techniques . NonetheIn an attempt to avoid these problems and to make diagnostic algorithms more reliable, artificial intelligence (AI) tools are used for fault diagnosis of the electrical rotating machines with the aim of detecting faults at very early stage and of reducing false alarms rates. These techniques could also be used with online CM systems, which continuously monitor the machine status. However, the development and training of these expert systems to predict the upcoming failure from IMs is a challenge presently, since it requires the obtaining of many current measurements from different types of machines and with different severity degrees of a given fault or simultaneous faults under different working conditions . These rAlternatively, the interest in accurate models of faulty IMs is increasing. Models would allow the reduction of the number of destructive tests needed to develop new diagnostic techniques and to develop and test CM based on embedded devices . They woSeveral models of faulty IMs can be found in the technical literature, which can be broadly categorized as models based on electrical circuits, models based on magnetic circuits, models based on numerical methods and hybrid models. Models based on multiple coupled circuit (MCC) comprise the stator and rotor in multiple inductive circuits, which are coupled together . ResistaAfterwards, with the aim of simplifying MCC models, d-q models were introduced. They use orthogonal components of voltage and currents by Park and Clark transforms . The samContrary to MCC approach, which is based on coupled electrical circuits, magnetic equivalent circuit (MEC) is based on detailed magnetic modeling of the machine by estimation of reluctances and permeances . These mAccurate simulations of faulty IMs requires taking into account the non-linearities of the magnetic materials as well as avoiding the simplifying hypotheses regarding the geometry and windings arrangement. Circuit-based models run fast but cannot provide comprehensive modeling as numerical methods, as those based on FEM. FEM methods use the exact magnetic and geometric characteristics of the machine to compute their magnetic field distribution, thus, accurately reproduce the IM behavior under failure conditions. However, they require a significant computational capacity and long simulation times, which can vary from minutes to weeks or even months in cases of highly asymmetrical faults such as eccentricity or rotor broken bars . The effTo overcome these drawbacks, hybrid FEM-analytical model simulations have been recently proposed in the technical literature for fault diagnosis purposes . FEM anaThe paper is structured as follows. In The behavior of an IM with m stator and n rotor phases can be defined by the following equations system ,33:(1)[Us and r are used for the stator and rotor, respectively. Where subscripts J is the inertia moment and B is the friction coefficient.On the other hand, the electromechanical torque generated by the machine, In this work, the system of Equations –9) is s is s9) iDue to the presence of the derivatives in the Expressions , 2) and and2) anThe main issue to address in this work is the accurate computation of the coupling parameters to develop a faulty IM analytical model minimizing computational effort and simulation times. These inductance or coupling parameters matrix should be calculated depending on the rotor position and saved in a Simulink 3D look up table, where the third dimension corresponds to the rotor position. This computation is performed offline using FEM, whose accuracy is widely accepted. However, this method has several drawbacks that the proposed method tries to overcome, as illustrated in the following subsections.N. After that, each rotor phase is also fed with 1A of direct current, the FEM magneto-static simulation runs again to obtain the parameters M. As a result, a three dimension coupling parameters matrix The general process to compute the coupling parameters The process just described assumes linear conditions for the computation of the coupling parameters of the faulty IM. Magnetic effects such as saturation have little effect of fault harmonics and the main objective of this work is to present an efficient method for computing the coupling parameters of an IM that reproduces accurately the effect of the static eccentricity. Hence, considering only the linear, incremental problem, the results are less computational intense and a reasonably accurate solution for fault diagnosis purposes.In this paper, a different way of addressing the computation of the inductance matrix is undertaken, presenting a new method based on FEM results but a much lower cost, while keeping good accuracy. FEM is used to compute the coupling parameters for a few specific rotor positions. Once these FEM coupling parameters are computed, they are used to build a trigonometric interpolation polynomial basis from which the coupling parameters for the other rotor positions are obtained.The proposed method is applied to an IM whose characteristics are shown in The severity of the fault is usually defined by degrees, between 0% for healthy machine (axis of rotation coincides with the axis of rotor and the axis of stator) and 100% for the maximum rotor rotation center displacement, which corresponds to the maximum displacement of the rotor rotation, 0.28 mm in the case of study.i in k in On the other hand, to exemplify the cost savings in running times, computer power and memory resources, the inductance matrix for each degree of fault severity was obtained using FEM software open source femm 4.2 running on a computer with intel processor (R) Core (TM) i5-6400 CPU@2.70 GHz and 16 GB of RAM memory. To build the FEM model, as aforementioned in the previous subsection, it is necessary to feed sequentially the stator phases i in , a rotorSpecifically in the case of static eccentricity fault, it is possible to reduce the number of simulations taking into account the symmetry of the machine. When a stator phase is fed, each rotor bar has the same flux linkage but with a specific geometry offset. According to this, the rotor positions can be reduced to a rotor bar travelling through a stator slot N=36 in  to calcuM=504 in  is requiAlternatively, ref.  apply thIn a try to address these drawbacks, this paper proposes the use of the sparse identification and trigonometric interpolation polynomial to compute the coupling parameters matrix posed in .Hence, the process will reduce computing time and memory requirements while keeping a similar accuracy to FEM with the interpolated solution using the trigonometric approximation.As the coupling parameters or inductance matrix of the IM model under a specific degree of eccentricity fault change with the rotor stepping, this paper proposes the SSL to select the rotor positions al basis . This bapolation .The bottom graph of the For the case of trigonometric interpolation polynomial, the recommendations are to select equally spaced points in the parametric space . Thus, TOn the other hand, the mutual inductance between rotor bars, due to their geometric complexity, requires a detailed explanation of their parametric space to interpolate as well as the selected points to perform FEM simulations. To reproduce accurately both the eccentricity and slot effect characteristic of Once the set FEM simulations are performed, the parametric basis is developed using the trigonometric interpolation polynomial with separated cases for odd and even number of data . For an For an even number of data 14).B in which the magnetic permeability is infinite and smooth air gap are assumed [5. Calculate the inductance matrix for the desired degree of severity of the fault using the polynomial base obtained in the step 4. It must be highlighted that contrary to analytical approaches as modified winding function approach (MWFA)-based models where the trigonometric interpolation is used to model the air gap and simplifications as radial magnetic field  assumed , in thisTo illustrate the accuracy of the proposed method, the inductance matrix for three different levels of static eccentricity  are computed and compared with those obtained with a full FEM analysis as shown in k is any positive integer, s is the slip, p is the number of pole pairs, f is the main frequency and The inductance matrix obtained using FEM, sparse identification and trigonometric polynomial interpolation, The stator current signals are acquired using the analog outputs of the HIL device, as shown in It is very common for IMs to work under transient conditions, such as the start-up transient, varying load conditions or supplying frequency changes. In these cases, the Expression  indicateUnder these conditions, traditional fast Fourier transform (FFT)-based diagnostic techniques cannot be used for fault diagnosis purposes. The current analysis of the start-up transient of the IM and time–frequency distributions as the spectrogram , can corThis approach has attracted a rising interest in the technical literature in recent years. It provides advantages such as greater accuracy, since various operating points are analyzed. On the other hand, the slip evolution is well known, from 1 to ≃0 in start-up transient conditions, which allow identification of the patterns in the fault harmonic components. Moreover, IMs such as wind turbines usually work under non-stationary working conditions, so developing diagnosis techniques and systems that can work under these conditions is reasonable. Thus, the amplitude evolution of the upper side harmonic (USH) is used to validate the proposed model in transient regime, using the start transient of the IM. The fault analysis is based on Gabor analysis of the current to capture the characteristic pattern from the start-up machine current generating an image of the trajectory of the USHst in the time–frequency plane. The procedure followed is detailed in . The metThe effect of the spaces harmonics when applied the trigonometric interpolation polynomial to build the basis to obtain the coupling parameters is analyzed as follows. The inductance matrix for a level of static eccentricity of 30.87% is computed using trigonometric interpolation and compared with the inductance matrix obtained with a full FEM analysis, as shown in As can be seen, the coupling parameters obtained with the trigonometric interpolation are essentially the same as those computed using only FEM, and therefore very similar to the results obtained using the approach considering the space harmonic content.Regarding the space harmonics, Therefore, the ideal is that the parameters computed with the proposed method have not only the same distribution along the rotor position as shown in Cross terms may even overlap with the desired harmonic signals. Thus, if the graphs of this figure are compared, it can be seen that the USH amplitude resulting using the traditional trigonometric interpolation polynomial is far from the USH amplitude obtained using FEM for the degree of severity simulated. The results obtained using the traditional trigonometric interpolation correspond to a higher degree of fault, which would imply a misdiagnosis.Attending to the results, as can be seen in To validate the proposed method, an experimental setup has been arranged with a commercial 1.1 kW, 50 Hz IM, in healthy state and with eccentricity to compare the presence of the fault harmonics to the obtained results using the hybrid model. The characteristics of the machines used are given in Secondly, to reproduce the eccentricity conditions, the hood fastening holes have been enlarged to introduce a small tolerance in the rotor axis place, as detailed in the zoom in Hybrid FEM-Analytical modeling has become a powerful tool for rotating electrical machine analysis, since it can provide very accurate modeling for various faulty IM conditions, offering insight and the needed signals for further analysis using signal processing and/or machine learning. By exploiting the benefits of this hybrid approach and advanced numeric techniques for computation, in this paper the SSL and the trigonometric interpolation polynomial are proposed to reduce the computation requirements to calculate an accurate hybrid FEM-Analytical model of a faulty IM. FEM is used to compute a reduced set of coupling parameters along the rotor positions. These FEM coupling parameters are used to build a trigonometric interpolation polynomial through which the full set of coupling parameters of the machine are computed. The proposed method has been illustrated for various degrees of static eccentricity fault, from an incipient level to more severe, to associate the amplitude of the fault harmonic components with the fault severity degree. Following the same reasoning the method could be extended to other types of faults or even to simultaneous faults since the proposed algorithm will compute the suitable coefficients to faithfully reproduce each type of fault.Coupling parameters are calculated in


Anti-welfare negatively predicted the acceptance of the restrictions regarding social distancing and those limiting civil rights and increasing safety. These associations were discussed in relation to basic needs and values which motivate persons who endorse right-wing or left-wing political views. The latent profile analysis revealed three profiles of political beliefs, which were termed “Conservative Statists,” “Liberal Laissez-fairists,” and “Conservative Laissez-fairists.” The profiles differed in terms of acceptance of the pandemic restrictions, and the patterns of these relationships were different for particular groups of restrictions.We investigated the relationships between political beliefs regarding two aspects of the right-left distinction  and the acceptance of the pandemic restrictions using variable-centred and person-centred approaches. The community sample consisted of 305 participants. Four groups of the restrictions were considered. Religious fundamentalism predicted positively the acceptance of the  It regulated the rules of social life in an explicit and stringent manner, limiting the freedom of movement and any form of activity of the citizens to the necessary minimum. It is therefore difficult to predict the end of the pandemic, all the more so since experts have warned that similar pandemics might frequently recur , CFI = 0.96, GFI = 0.97, NNFI = 0.96). The Polish and English versions of the questionnaires are provided as Supplementary material.Political beliefs of the participants were assessed with the use of the Political Beliefs Questionnaire, PBQ . The queThe relationships between the four groups of the pandemic-related restrictions F1, F2, F3, and F4) and sociodemographic variables were checked using Mann-Whitney’s and Kruskal-Wallis’s tests for categoric variables  and Pearson’s correlations for age  on the outcome variable and makes no assumption regarding the distribution of the outcome [To assess the relationships between political beliefs and the acceptance of the pandemic-related restrictions, a series of quantile regression analyses was performed. This method of estimation was chosen because the assumptions of regression analysis were not met. Quantile regression can estimate the conditional median  was performed to empirically distinguish the groups of participants who shared similar profiles of political beliefs. The LPA allows estimating categorical latent variables using a set of continuous variables. The Latent Gold statistical program (v. 5.1) was used. The LPA represents a person-centred approach and enables comparing the competing models using several goodness-of-fit indices. Thus, it is not necessary to assume c, corrected for sample size); [c and BIC indicate a better fit. Following the recommendation of Burnham and Anderson . The models with Δi>10 are considered to have no support. The ΔBIC values (Δi = BICi—BICmin) were also calculated to facilitate interpretation of the values within the context of the model, which fits the data best.We tested several models ; , 88 werenderson . However, a four-profile solution contained a profile that was composed of less than 5% of the sample (7 persons). Thus, only the two-profile solution  and three-profile (satisfactory) solution were analysed in terms of interpretability. Both models were interpretable on the grounds of political science. The two-profile solution contained two profiles that differed in terms of religious fundamentalism and xenophobia (low vs. high scores). However, they did not differ in terms of capitalism acceptance or anti-welfare (average scores). The three-profile solution  was chosen as it delivered more information about the structure of the sample. The three profiles can be readily interpreted as characteristic of two groups sharing the mix of opposing right-wing and left-wing attitudes and the one group sharing consequently right-wing  political attitudes see .H = 133.2, df = 2, p<0.001) and xenophobia . LP1 and LP3 had significantly higher scores on these dimensions than LP2. Similarly, there were significant differences in terms of economic attitudes: the acceptance of capitalism  and anti-welfare dimensions . LP1 and LP2 had significantly lower scores on the acceptance of capitalism than LP3. In the case of anti-welfare, significant differences were observed between all the profiles. LP1 had relatively the lowest scores, and LP3 presented relatively the highest scores. The profiles did not differ significantly in terms of age .The Kruskal-Wallis H test and post-hoc pairwise comparisons (with a Bonferroni correction for multiple comparisons) were done to compare the latent profiles (LP). There were significant differences between the profiles on cultural attitudes: religious fundamentalism . The post-hoc tests  or less useful (F2—restrictions associated with the limitations of labour rights and F3—restrictions limiting civil rights without a direct impact on safety) in reducing the probability of contagion. Generally, the participants endorsed the restrictions from the F1  and F4 (limiting civil rights and increasing safety) groups more than those from the remaining groups. For the F1 group of the restrictions , the variability of scores was relatively the lowest as there was a consensus among the participants that these limitations were necessary to stop the pandemic.higher acceptance was associated with more right-wing cultural beliefs. In turn, anti-welfare negatively predicted the acceptance of the remaining groups of restrictions . Therefore, higher acceptance of these groups of restrictions was associated with more left-wing political beliefs. However, as xenophobia and acceptance of capitalism were unrelated to the acceptance of restrictions, our predictions were only partially supported by the data. The analysis did not demonstrate any significant relationships between xenophobic views and acceptance of capitalism on the one hand, or any of the groups of restrictions distinguished on the other hand. This result may have several sources. First, it may be the case that neither xenophobia nor acceptance of capitalism as such contain motivational elements related to attitudes, values, or behaviours associated with centrally imposed restrictions. Secondly, in the social discourse in Poland during the pandemic, no content related to these factors appeared. There was no room for discussions related to foreign cultures or foreigners. Although there were cases of insulting foreigners and their cultures [i.e. Four median regression analyses were performed to identify whether political beliefs regarding two aspects of right-left distinction  would be significant predictors of the acceptance of each group of pandemic-related restrictions. Religious fundamentalism positively predicted the acceptance of two groups of restrictions (F2—restrictions associated with the limitations of labour rights and F3—restrictions limiting civil rights without a direct impact on safety), which means that for these groups of restrictions, res i.e. , howeverrestrictions associated with the limitation of the labour rights (F2) and those limiting civil rights without a direct impact on safety (F3). The participants with more right-wing cultural beliefs showed more positive evaluations of this type of restrictions compared to people with left-wing cultural beliefs. Both groups of restrictions consisted of the measures which were imposed  or could be imposed by the Polish state during the pandemic , but their potential impact on health and security can be viewed as controversial. These two groups of restrictions (F2 and F3) were generally less accepted by our participants than the remaining pandemic restrictions . However, our finding suggests that religious fundamentalism can be viewed as a factor potentially influencing the results of the appraisal, enhancing the approval of such kind of restrictions only if the pandemic restriction was not clearly beneficial for an individual and/or the society.In the current study, religious fundamentalism was significantly and positively associated with the acceptance of pandemic Our results are in line with a study conducted in June 2020 in the UK, in which strong authoritarian and conservative attitudes were linked to greater acceptance of the most draconian restrictions introduced to prevent the spread of the coronavirus, such as imprisonment for breach of the rules, or the obligation to use contact-tracing applications . In addiIndividuals with strong fundamentalist beliefs are characterised by a particular cognitive functioning style, making them search for available and simple solutions that provide a sense of security. In particular, such individuals tend to attribute more significance to values associated with order rather than to those promoting openness and change . Religiorestrictions regarding social distancing (F1) and those limiting civil rights and increasing safety (F4). The participants with more left-wing economic beliefs, i.e., entitling the state to intervene in the field of central regulations, evaluated more positively these groups of restrictions compared to those with more right-wing attitudes. As in the case of F2 (restrictions associated with the limitations of labour rights) and F3 (restrictions limiting civil rights without a direct impact on safety), these groups of restrictions also contained the measures which were imposed  or could be imposed during the pandemic . However, unlike the remaining restrictions, their potential impact on health and health care was straightforward. These groups of restrictions were highly accepted by the participants. Nevertheless, the participants who endorsed more anti-welfare attitudes had a tendency to evaluate these restrictions as less acceptable.Anti-welfare was associated with the Pro-welfare attitudes  can be viewed as a source of a stronger agreement with the state’s involvement. The content of such beliefs is protection of the poorest social groups by providing access to education, work, and housing. At their core is consent to social equality and the approval of countering social exclusion, which the state should strive for, according to those with strong interventionist beliefs. Consequently, for individuals sharing such beliefs, restrictions intended to save the lives of vulnerable individuals (elderly and ailing people) and unquestionably connected to that aim are more acceptable than for those with opposing views. However, our study results indicated that these effects could be limited to such interventions, which seems rational. When the pandemic restrictions were questionable, the welfare dimension was not related to the acceptance rates.The reasons for the negative direction of the link between anti-welfare and the two most legitimate groups of restrictions can also be sought in the stronger pandemic-related fears and concerns of people with liberal views compared to conservatives , 99. OurIt is worth emphasising that of the four dimensions of political beliefs that were analysed, the two which were found to be significantly associated with the acceptance levels  were precisely the ones most strongly associated with seeking a sense of security. As proven by the research, individuals with high religious fundamentalism scores are characterised by a particular manner of cognitive functioning, e.g., being more dogmatic –37 and hAccording to the results of the latent profile analysis, three groups of participants were distinguished. Each group members shared a similar profile of political beliefs in the cultural and economic domains. Cluster 1  consisted of persons with relatively high scores on both cultural dimensions and relatively low scores on both economic dimensions of political beliefs. These were therefore individuals convinced of the superiority of religion over law, believing that the order of the sacred should determine the rules of public life. At the same time, these individuals believed that Poland should be above all for Poles, protecting itself against being flooded by foreign cultures, values, and norms. However, attitudes shaped in this manner did not prevent them from having expectations in relation to the state . The state should also eliminate the differences between the richest and the poorest to achieve as much equality as possible between the citizens. The profile of this group was consistent with the results of other studies on political beliefs in Poland. It reflected a characteristic trend of the co-occurrence of right-wing cultural beliefs with left-wing economic beliefs –74, 76.Cluster 2  included individuals with the lowest levels of fundamentalism and xenophobia and average scores on the anti-welfare scale  as well as an average level of acceptance of capitalism (around the grand median). These were therefore individuals who opposed the domination of traditional values, including religious ones. In their opinion, Poland should be a secular country, open to other cultures, and its borders should be open to foreigners. At the same time, their attitudes towards the market were more right-wing compared to the first group. They were significantly more opposed to state interventionism in the sphere of functioning of the citizens—they had a lower acceptance of the state orders regulating social and economic life. The Liberal Laissez-fairist profile can be described as the opposite of the Conservative Statist profile, but it is worth emphasising that the differences between them were more pronounced in the area of cultural beliefs than in that of economic views.Cluster 3 (N = 55 “Conservative Laissez-fairists”) brought together individuals with a similar cultural belief profile to those forming Cluster 1, but the groups differed in their attitudes towards the market. Conservative Laissez-fairists more strongly accepted capitalism and anti-welfare compared to Conservative Statists and Liberal Laissez-fairists. These were therefore the individuals with consistent right-wing views in terms of cultural and economic beliefs.restrictions associated with the limitations of labour rights.The results of the latent profile analysis seem accurately reflect the structure of political beliefs in contemporary Polish society as they are congruent with a number of past research results , 73, 76.restrictions regarding social distancing was similar in Conservative Statists and Liberal Laissez-fairists and significantly lower in Conservative Laissez-fairists. Conservative Statists and Liberal Laissez-fairists differed significantly in their scores on the cultural dimension of political beliefs. However, their scores were similar on the economic beliefs dimension. This suggests that social security would be a significant value for both groups of respondents, including the expectation that the state should also provide health security to its citizens. Perhaps that is why acceptance of the basic restrictions to protect health was relatively higher in these two groups.The acceptance of the restrictions limiting civil rights and increasing safety was higher in Conservative Statists than in the remaining groups of participants. However, these differences lost significance after controlling for multiple tests. The lower acceptance of this group of restrictions may be related to the higher level of anti-interventionist and capitalist attitudes in Liberal Laissez-fairists and Conservative Laissez-fairists groups. It is therefore possible that the differences can be mainly related to the differences in the level of the economic dimension of political attitudes.The acceptance of the restrictions limiting civil rights without a direct impact on safety was relatively highest in Conservative Statists and significantly higher in Conservative Statists compared to Liberal Laissez-fairists. The result confirmed the relatively stronger tendency of Conservative Statists to follow the restrictions imposed by the state, even when it was difficult to achieve the goals . Of note, due to its position on both dimensions of political attitudes, this group seems to be the largest in size in Poland. This allowed us to pose an interesting question: to what extent will Conservative Statists consent to restrictions and rules imposed by the state in the name of maintaining or regaining a sense of security?The acceptance of the Although Liberal Laissez-fairists also appeared to be motivated by a desire to regain or maintain a sense of security, they seemed to differentiate their degree of approval of restrictions more strongly depending on how they viewed a particular restriction. This group appeared to judge the restrictions more rationally, which makes it possible to assume that their behaviour would follow the guidelines which they would believe to be effective, but they would resist in an ambiguous situation. Communication from the political decision-makers might be significant in terms of convincing them of the effectiveness of the proposed solutions. This conclusion also prompts a search for other variables linked to the assessment made by this group.Conservative Laissez-fairists showed a tendency to less favourable evaluations of the pandemic restrictions, even if their usefulness was difficult to question. This sub-group of participants (approximately one-sixth of the sample) can be characterized by a consistent set of right-wing political beliefs. Thus, the participants who shared this profile of political beliefs, which is not common in Poland , 77, canOverall, the findings of the current study correspond to other research results showing the specificity of the Polish political scene with respect to the right-left distinction. Although our study distinguished the groups of supporters of right-wing and left-wing values in terms of cultural beliefs, we did not observe such a clear differentiation in terms of economic beliefs. This result reflects the fact that in Poland we are dealing with a left based on worldview—focusing on freedoms and rights of minorities and opposing religious regulations in public life  , 108. ThWeight is given to the results obtained by the socio-political and cultural contexts of the process of formation of political beliefs and socio-political attitudes of Poles. In the former area, the relationships between the central government and the Catholic Church, defining the specific social expectations towards these two entities, are not without significance. In the latter case, the influence of the Catholic Church on social attitudes of the citizens is interesting. The activity of the hierarchs is certainly not unimportant for these attitudes, as it affects nearly every area of the functioning of Polish citizens, and this is clearly condoned by the central government. As it has already been pointed out, the formation of a civil society opposing communist rule in Poland was strongly linked with the activity of the Catholic Church. Consequently, national identity formed in a strong relationship with Catholic identity, which nowadays has not only a religious, but above all a cultural quality to it.The current study has some limitations. Firstly, the study had a cross-sectional design, thus causal conclusions could not be drawn, and the results should be interpreted with caution. According to Spector ( p. 133),The results of the current study provided evidence on the relationships between political beliefs, placing people on the right-left political dimension and the approval for the pandemic restrictions and recommendations. Cultural and economic types of political beliefs showed opposite relationships with the acceptance levels. Religious fundamentalism  positively predicted the acceptance of the restrictions, whose potential impact on health and security was rather controversial. In turn, pro-welfare attitudes  positively predicted the acceptance of these groups of restrictions, whose potential impact on health and health care was rather straightforward.The obtained three profiles of political beliefs termed Conservative Statists, Liberal Laissez-fairists, and Conservative Laissez-fairists seem adequately reflect the political division of the Polish society. Generally, Conservative Statists tended to accept the pandemic restrictions more than the remaining groups no matter whether the restrictions seemed rational and effective against the pandemic. Liberal Laissez-fairists seemed to differentiate the degree of approval depending on the specificity and the potential efficiency of the restriction. Conservative Laissez-fairists, who shared cultural and economic right-wing political beliefs, were distinguished by a more critical attitude towards the most widespread pandemic measures. Based on political beliefs, it can be speculated that only Conservative Statists and Liberal Laissez-fairists could be sensitive to arguments promoting pandemic measures, particularly when these arguments were related to security need.The effectiveness of the measures adopted to combat the pandemic is of primary importance, which warrants further research on the factors that have significance for their effect –118. HowS1 File(DOCX)Click here for additional data file.