The application of edge computing combined with the Internet of Things (edge-IoT) has been rapidly developed. It is of great significance to develop a lightweight network for gearbox compound fault diagnosis in the edge-IoT context. The goal of this paper is to devise a novel and high-accuracy lightweight neural network based on Legendre multiwavelet transform and multi-channel convolutional neural network (LMWT-MCNN) to fast recognize various compound fault categories of gearbox. The contributions of this paper mainly lie in three aspects: The feature images are designed based on the LMWT frequency domain and they are easily implemented in the MCNN model to effectively avoid noise interference. The proposed lightweight model only consists of three convolutional layers and three pooling layers to further extract the most valuable fault features without any artificial feature extraction. In a fully connected layer, the specific fault type of rotating machinery is identified by the multi-label method. This paper provides a promising technique for rotating machinery fault diagnosis in real applications based on edge-IoT, which can largely reduce labor costs. Finally, the PHM 2009 gearbox and Paderborn University bearing compound fault datasets are used to verify the effectiveness and robustness of the proposed method. The experimental results demonstrate that the proposed lightweight network is able to reliably identify the compound fault categories with the highest accuracy under the strong noise environment compared with the existing methods. With the emergence of IoT, a large amount of innovative applications in fault diagnosis fields have been rapidly increasing . For insFor rotating machinery, gearbox is the most important power transmission component in mechanical equipment, which mainly consists of gears, shafts and bearings. Its health status directly affects whether the mechanical equipment can work normally. Due to different types of faults coupled together, non-stationarity and a large amount of noise, it is very difficult to effectively extract the most valuable fault characteristics from the raw data by using the existing methods . If the It is known that feature extraction and identification of the fault patterns are the two main steps to accomplish the fault diagnosis of rotating machinery . UsuallyAlthough the traditional fault diagnosis methods have achieved some satisfactory results, there still exist many shortcomings. In summary, firstly, the traditional methods largely rely on expert knowledge and prior knowledge to obtain high quality features. Secondly, the traditional approaches typically exhibit poor generalization ability and lack high diagnostic accuracy, as they are easily influenced by environmental factors such as the strong noise interference .In recent years, some new intelligent diagnosis methods based on deep learning have been widely used in the gearbox fault diagnosis fields , which hHowever, the diagnostic methods based on deep learning are largely dependent on hardware and high training cost, and the models often do not have strong generalization capability or anti-noise ability. It is noted that some researchers combined signal processing methods with deep learning to develop more effective fault diagnosis methods, which are more robust and have less learning cost . For exaTo summarize, the difficulties of the existing methods in gearbox compound fault diagnosis mainly lie in three aspects. First, the complexity of the compound faults with highly non-stationary and a large amount of noise usually leads to attain low diagnosis accuracy for locating the specific fault type. Second, the traditional methods largely depend on artificial feature extraction and more complicated algorithms to select the most valuable features. Third, the deep learning-based methods need more complex model architectures and extensive training to finish the compound fault diagnosis. Especially, the ability of the extraction feature based on the deep models is significantly affected by the strong noise.In view of the problems mentioned above, a novel and high accuracy fault diagnosis method, LMWT-MCNN, is proposed in this work for the gearbox compound faults. The proposed method decomposes the raw data into a few low and high frequency components using LMWT. Then, the feature images are designed based on these frequency components. Finally, the powerful feature learning ability of the MCNN model is implemented to further extract the more salient and valuable fault features from the feature images without artificial feature selection.It is noted that LMWT has more base functions and many excellent properties to match the complex fault characteristics of gearbox. Therefore, the feature images obtained by LMWT can effectively represent the discriminative fault characteristics of gearbox, and there is no redundancy and leakage due to its orthogonality. Furthermore, the amplitude of the noise in the feature images is usually smaller than that of the fault frequency components , thus thhttps://phmsociety.org/data-analysis-competition/, accessed on 21 October 2023) [https://mb.uni-paderborn.de/en/kat/main-research/datacenter/bearing-datacenter/data-sets-and-download/, accessed on 21 October 2023) [Finally, the effectiveness and robustness of the proposed method are verified by the PHM 2009 dataset from the 2009 Prognostics and Health Management Competition (er 2023)  and the er 2023) . The twoer 2023) ,41,42,43However, the experimental results obtained in this paper demonstrate that the proposed method has the great merits of the highest diagnosis accuracy and more robustness than other existing methods. In summary, the main contributions and advantages of this paper are described as follows.(1)This paper constructs two feature images based on LMWT frequency domain by using a sample data, which can effectively match the complex fault characteristics of rotating machinery.(2)This paper proposes an end-to-end compound fault diagnosis model based on edge-IoT. The proposed model not only avoids the complex artificial feature extraction, but also is a lightweight network only consisting of three convolutional layers and corresponding three pooling layers.(3)This paper provides an effective model for extracting multiple fault features in the strong noise environment and it is very suitable for the compound fault diagnosis in real applications.(4)This work conducts some comparative experiments on two datasets of rotating machinery, which verifies the effectiveness and robustness of the developed method. The corresponding recognition results indicate that the proposed model achieves the highest diagnosis accuracy and shows powerful anti-noise ability.The remainder of this paper is organized as follows: In this section, the framework of edge-IoT is first described in detail. In the second step, the concept and properties of LMW bases are introduced, and the decomposition and reconstruction of a sample are specifically described in this context. In the third step, the structure of CNN model is elaborately described. Finally, the multi-label method for gearbox compound fault diagnosis is briefly introduced.It is known that the mechanical equipment intelligent fault diagnosis mainly consists of three processing procedures: signal acquisition, feature extraction and classification diagnosis. The data acquisition stage has a significant impact on the industrial application of mechanical fault diagnosis. Traditional fault diagnosis systems are mostly based on the centralized cloud computing structure . HoweverAs shown in To summarize, the edge computing lightweight model based on IoT can process sensor data directly at the edge of the network, which not only meets the expansion needs of the computing power of terminal devices, but also solves the issue of long delay in accessing cloud data centers. Compared with the centralized cloud computing, the proposed fault diagnosis method based on edge-IoT makes data analysis, communication, control, and storage closer to the sensing point, with low delay, less energy consumption, and high accuracy performance.k denoted by p is the number of the adopted LMW bases. According to the literature [Legendre polynomials of degree terature , the Legn. Whereas a lot of characteristics of rotating machinery are salient to the high frequency components, the orthogonal complement of Furthermore, a subspace It is known that Alpert  has consIn addition, in order to intuitively understand Legendre scale bases and wavelet basis functions, let the finest resolution level From j, i.e., the approximation coefficients and detail coefficients, respectively. The integer m is the number of the data obtained by the resolution level n as follows.LMWT can be considered as a mathematical tool that converts a signal into a series of scale and wavelet coefficients, respectively. According to the multiresolution analysis theory and the basis knowledge of LMW explained in the above subsection, the decomposition procedure Correspondingly, the reconstruction Furthermore, a specific sample of the PHM 2009 dataset for case 2 is utilized to demonstrate the effectiveness and stability of LMWT. Then, the raw gearbox fault data of the sample with 4096 points for case 2 are described in Specifically, the convolution procedure of LMWT with the order of wavelet bases Step 1:The choice of finest resolution data is adopted as the raw data.Step 2:According to the decomposition Equations  and 9),,9), the Step 3:The processed data produce the correspondingly low frequency and high frequency components according to the decomposition Equations  and 9)  9) at reStep 4:The detailed frequency components are elaborately demonstrated in As illustrated in As shown in As one of the most important deep learning structure models, CNN model has been widely applied with great success to various fault recognition fields . In thisThe main structure of CNN model is a multi-layer network, which consists of one input layer, alternative convolutional layers and pooling layers, fully connected layers, and one output layer. The convolutional layers applied a number of convolutional kernels to serve as the local filters to slide over the whole input neurons at the previous layer for generating various feature maps. The convolutional operation between the input neurons and the learnable convolutional kernels can be described byPooling layers are used to decrease the number of the neurons in the network and achieve low resolution of feature maps, which usually follow the convolution layers adjacently. In CNN model, max-pooling, average-pooling, and stochastic-pooling are the common operations in pooling layers. After multi-stage convolutional layers and pooling layers, a fully connected layer is added to integrate the discriminative local information of the category; in the full connection layer, dropout technology is often used as a regularization method to restrain overfitting.Furthermore, extracted features of the convolutional layers are flattened and then inputted into the fully connected layers, which work in a similar manner as the traditional back-propagating neural network.x belongs to C is the number of the fault classes. Since the cross-entropy loss of CNN model can accelerate the updating speed of weights and convergence speed of the whole model in comparison with the squared error loss in common classification tasks, in this paper, the cross-entropy loss function is applied to diagnose the various fault categories of rotating machinery and is described asFinally, the output layer uses the classifier for data classification. In the classifier, the softmax function is adopted as the classifier to classify the normal and fault data. To be specific, the estimated probability denoted by In contrast with the traditional fully connected neural network, the CNN model is only sensitive to the local receptive field by employing sparse connections to a small scope of neurons, and applies a weight sharing strategy to decrease the number of parameters. Therefore, the CNN model can significantly decrease the computational burden of the whole network and make the network easier to train.The compound fault vibration signal possesses typical nonlinear and nonstationary properties, and the coupled fault characteristics are immersed in the strong noise. Thus, it is very difficult to effectively extract the coupled characteristics from the raw vibration signal.The proposed model in this paper locates the compound faults by the multi-label method. To be specific, the label vector of each health condition is represented by multi-hot labels with 1 at multiple indices rather than single hot label. That is, the occurrence of the corresponding fault type is recorded as 1. Subsequently, a softmax layer serves as the output layer in the proposed architecture, where the output represents the probability of each type of fault occurrence. If the position with the highest probability in the network output is the same as the position of 1 in the multi-label, the diagnosis result is regarded as the situation of correction.Finally, a cross-entropy loss function is implemented to calculate the loss value by the comparison between the output and the multi-label value for updating network parameters. This labelling method can locate the specific fault type of rotating machinery compound faults, where the specific fault type is effectively distinguished through the trained network model.In this section, the feature images obtained from the gearbox compound fault data by LMWD are first devised. Then, a two-channel CNN model based on the feature images is elaborately described. Finally, the proposed method based on edge-IoT is clearly explained. Correspondingly, their flowcharts are specifically explained in In this subsection, the LMWD frequency domain is implemented to construct two feature images by the sample of the gearbox dataset for case 2. This sample is obtained from the original signal sampled by the systematic sampling method. Compared with simple sampling, the data characteristics obtained by systematic sampling are more obvious . At the Specifically, the sample with 4096 points as shown in More precisely, the specific steps of the constructing feature images using the LMWD frequency domain are described in detail as follows.Step 1:The raw sample data are doubled and then decomposed by two Legendre scale bases and two Legendre wavelet bases at the resolution level 4. The length of each frequency component from the Step 2:For clarity, only the first LMW base is used to explain how to construct the feature image. The frequency components of different resolution levels are flattened to a feature signal with the same length as the raw sample data. Then, the feature signal is rearranged into a feature image in a matrix form with a size of In addition, to clearly explain the feature image differences between LMW bases and the traditional methods, the method of the constructing images is also applied to the raw data and the feature signal based on DWT, and the specific results are described in Finally, the two feature images obtained by LMWD are used for convolution operations in the MCNN model. Due to the various regularity and orthogonality of the LMW bases, the obtained feature images can effectively match the different fault categories of rotating machinery without loss of information. Furthermore, the feature images are easily implemented into a two-channel CNN model for effectively extracting the most valuable fault features and accurately recognizing the rotating machinery compound faults.This subsection mainly describes how to combine LMWT with MCNN model for gearbox compound fault classification, and the following flowchart of the proposed model elaborately describes the principle of this technique.According to the flowchart shown in Step 1:The vibration signals of gearbox compound faults are sampled from the data acquisition system as shown in Step 2:The vibration signals of the gearbox compound faults are divided into 600 samples according to the length of 4096 points for each sample of each fault category.Step 3:Each sample is transformed into two feature images by LMWT using two Legendre scale bases and two Legendre wavelet bases. Then, seventy-five percent of the feature images are randomly selected for the training samples and the rest twenty-five percent for the testing samples, respectively.Step 4:The lightweight structure of the proposed model consists of three convolutional layers with 3 ∗ 3 kernels, three batch normalization (BN) layers and three max pooling layers with 2 ∗ 2 kernels. First, the convolutional layers convolute the local regions with a series of filter kernels to generate new feature maps. The 3 ∗ 3 convolutional kernel is able to learn more excellent features with less computations relatively. Then, the BN layers are used to reduce the computational complexity of the network and accelerate network convergence. Finally, the max pooling layers perform down-sampling operations on the feature maps to decrease the size of the feature maps. The purpose of using max pooling is to extract the maximum value of the input feature map and remove the smaller noise frequency components.Step 5:Finally, a fully-connected layer and a multi-hot cross entropy classifier are attached on the top to accomplish the compound fault recognition of the gearbox.To summarize, each sample is decomposed into two feature images by LMWT, then the feature images are fed into the MCNN model, which addresses the lightweight combination of the LMWT and MCNN models.This subsection mainly discusses the overall workflow of the proposed method based on edge-IoT, encompassing the entire process from fault data acquisition to fault diagnosis and maintenance. The schematic diagram for this process is depicted in Step 1:The fault signals are sampled from the mechanical equipment by the sensors.Step 2:The acquisition data are decomposed by LMWT to construct the feature images on the edge node of the edge cloud.Step 3:The lightweight LMWT-MCNN model for fault diagnosis is trained on the centralized cloud by using labeled fault dataset. This involves initializing parameters and updating them using the loss computed from the model’s output. Once the loss of the model converges, the training process is complete.Step 4:Then, the feature images obtained from the testing samples are fed into the trained lightweight LMWT-MCNN model downloaded from the centralized cloud to attain the highest diagnosis accuracy.Step 5:The diagnosis results are transmitted into the centralized cloud.Step 6:The diagnosis results and their visualization are applied to the mechanical equipment maintenance.Finally, the two compound fault datasets of the rotating machinery are implemented to verify the effectiveness and robustness of the proposed model.In this section, the PHM 2009 gearbox dataset used in this work is first described in detail. Then, the developed LMWT-MCNN model is implemented to diagnose the various compound fault categories of the gearbox. Furthermore, the diagnosis accuracy obtained by the proposed model is used to compare with the CNN method based on the raw data (Raw data-CNN), CNN method based on DWT (DWT-CNN) and other existing methods. Finally, another compound fault dataset of rotating machinery provided by Paderborn University is implemented to further verify the effectiveness of the proposed model. The comparison of the experimental results shows that the proposed model achieves the highest recognition accuracy and is more stable and robust than the existing methods. In addition, all approaches described above are implemented with Python and tested on a computer with an AMD Ryzen 7 5800H CPU @ 3.20 GHz/4.40 GB RAM.In this subsection, the vibration signals of the PHM 2009 gearbox dataset are described in detail, and the corresponding six compound fault categories are shown in The PHM2009 gearbox dataset is a compound fault dataset that encompasses the majority of common gearbox faults under various load conditions. The specific fault categories contain the gear chipped tooth fault, gear broken tooth fault, bearing inner ring fault, bearing ball fault, bent shaft fault, and shaft imbalance fault. Then, the fault data acquisition procedure of the PHM 2009 dataset is explained in As shown in The fault signals are collected at 30, 35, 40, 45, and 50 Hz speed and low load. The sampling frequency is 66.7 kHz and the sampling time is 8 s. That is, for one operating speed, there are 533,312 sample points. For each speed condition, the validation experiments in this paper use 4096 sampling points as a sample. Therefore, there exist 600 samples taken for each fault type. In order to meet the actual diagnostic requirements as much as possible, 450 samples of each health condition are randomly prepared for the training samples and the remaining 150 samples are used for testing the diagnosis accuracy of the proposed method. The specific configuration parameters of the gearbox fault data processing are elaborately demonstrated in Finally, the temporal waveform of the raw data samples of the six working conditions of the gearbox are described in As illustrated in Usually, the different structures of MCNN have some impacts on the experimental results. In order to find a stable and effective LMWT-MCNN structure, the configuration parameters of MCNN should be continuously adjusted according to the diagnosis accuracy. As shown in Based on the comparison results, the structure of the proposed model is finally adopted as Model 1 because of achieving the highest compound fault diagnosis accuracy. In the forthcoming experiments, the optimizer for training the model will be set to Adam, with a learning rate of 0.01, a maximum training epoch of 120, and a Weight decay of 0.0005. Notably, the learning rate reduced by 30% every 30 training epochs. In addition, each experiment is repeated ten times to validate the generalizability of the proposed model, and the experiment results are shown in In In addition, to highlight the lightweight property of the proposed model, we compare the model with other lightweight fault diagnosis models in recent years. The comparison focuses on computational complexity and memory footprint, as displayed in The results of the comparison in Furthermore, Raw data-CNN method and the DWT-CNN method are implemented to recognize the same gearbox compound fault categories. The Precision, Recall, F-measure and Accuracy of the gearbox compound fault diagnosis results are utilized to thoroughly verify the effectiveness of the proposed method, which are described as follows.As shown in In the next experiment, the Gaussian white noise is added to the signals to test the anti-noise capability of the proposed model. Noise ratios ranging from −24 to 6 are applied to verify the performance of various fault diagnosis methods. The detailed comparison results by different methods under various noisy conditions are shown in The diagnosis results shown in To further verify the effectiveness of the proposed method, the loss curve and iteration accuracy curve are demonstrated in As demonstrated in Moreover, the t-SNE method is utilized to visualize the extracted features in two-dimensional space for different fault diagnosis methods mentioned above, which demonstrates that the proposed method has a good feature extraction ability for the gearbox compound faults. To be specific, From the visualized results of Finally, in order to further show the superiority and effectiveness of the proposed model, other popular methods are also utilized to compare with the proposed method, and the comparison results are listed in The effectiveness of the proposed model in the compound fault diagnosis of the gearbox is verified in To summarize, the above comparison results further demonstrate that the proposed model is able to effectively identify the gearbox compound health conditions.The bearing is the important part of gearbox, thus the compound fault dataset of the bearings provided by Paderborn University is utilized to verify the generalization of the proposed model. In this dataset, all fault data are derived from accelerated life testing, including both IR (Inner Ring) and OR (Outer Ring) bearing faults. These faults include point pitting faults and plastic deformation faults on the IR and OR of the bearings. The test bench equipment consists of a permanent magnet synchronous motor, a torque measurement shaft, a test module, and a synchronous servo motor utilized as a load motor, which is described in As illustrated in The upcoming experiments use fault data from six different health conditions to validate the proposed model. Similar to the PHM2009 dataset, each fault type contains 600 samples, and each sample includes 4096 data points. Then, the samples are randomly divided into the training set and the testing set. The specific fault categories and samples of dataset used in this paper are shown in To eliminate the influence of randomness and individuality, the experiment is repeated by ten trials, and the experimental results by different methods under different noise conditions are elaborately shown in As described in Finally, to effectively show the superiority of the proposed model, other popular methods such as CNN-ELM-JDM, MPDBN-WT, AMVMD-SCNN, and ASN are also utilized to compare with each other. The comparison results of the testing accuracy are listed in As demonstrated in To summarize, the highest testing accuracy is achieved by the proposed lightweight model based on LMWT and MCNN compared with the existing methods. Consequently, the proposed lightweight model provides a promising technique for the implementation of online compound fault diagnosis of rotating machinery based on edge-IoT.The effective and reliable intelligent fault diagnosis method based on edge-IoT is developed in this paper for the compound fault diagnosis of rotating machinery. Some comparative experiments are conducted on the PHM 2009 gearbox and the Paderborn University bearing compound fault datasets with different noise to verify the effectiveness and robustness of the proposed method. The experimental results show that the proposed method achieves the highest diagnosis accuracies of 98.01% and 99.57% without any noise, respectively, compared with the existing methods. Especially in the low signal-to-noise ratio environment, the proposed method still shows more effectiveness and robustness than other methods. To summarize, this paper proposes an effective lightweight network model for rotating machinery online fault diagnosis based on the edge-IoT context, which obtains the high accuracy, strong anti-noise ability, small storage, and low calculation costs to overcome the defects of large sensor data transmission, large cloud computing, and long-distance data transmission, and more. In future work, LMWT should be combined with other deep learning models to effectively rectify the compound fault types of rotating machinery with highly non-stationary, weak, and early faults.


Lower limb exoskeleton robots have shown significant research value due to their capabilities of providing assistance to wearers and improving physical motion functions. As a type of robotic technology, wearable robots are directly in contact with the wearer’s limbs during operation, necessitating a high level of human–robot collaboration to ensure safety and efficacy. Furthermore, gait prediction for the wearer, which helps to compensate for sensor delays and provide references for controller design, is crucial for improving the the human–robot collaboration capability. For gait prediction, the plantar force intrinsically reflects crucial gait patterns regardless of individual differences. To be exact, the plantar force encompasses a doubled three-axis force, which varies over time concerning the two feet, which also reflects the gait patterns indistinctly. In this paper, we developed a transformer-based neural network (TFSformer) comprising convolution and variational mode decomposition (VMD) to predict bilateral hip and knee joint angles utilizing the plantar pressure. Given the distinct information contained in the temporal and the force-space dimensions of plantar pressure, the encoder uses 1D convolution to obtain the integrated features in the two dimensions. As for the decoder, it utilizes a multi-channel attention mechanism to simultaneously focus on both dimensions and a deep multi-channel attention structure to reduce the computational and memory consumption. Furthermore, VMD is applied to networks to better distinguish the trends and changes in data. The model is trained and tested on a self-constructed dataset that consists of data from 35 volunteers. The experimental results show that FTSformer reduces the mean absolute error (MAE) up to  A lower limb exoskeleton robot is a kind of wearable robot. In rehabilitation therapy, the robot is designed for patients with lower limb motor dysfunction, providing efficient and safe assistance in their rehabilitation training ,2,3. In Gait data, encompassing physical quantities such as plantar pressure, angles and torques of the hip joint, knee joint and ankle joint, as well as biological signals like electromyography (EMG) and electroencephalography (EEG) signals, serve as the fundamental basis for human walking pattern analyses and motion intention predictions. EMG and EEG are capable of reflecting the motion intention with a low delay. However, the measurement of bioelectrical signals requires electrodes to be placed close to the skin surface, which inevitably causes discomfort to the subject. Moreover, these signals exhibit great randomness and a relatively low signal-to-noise ratio. Joint angles and torques are easy to measure using absolute encoders and joint drivers installed in robots. However, physical signals obtained by sensors often contain a certain delay and thus cause lagging control commands.The plantar pressure is one of the most important physical signals . During When comparing statistical methods ,12,13, dTime series can be visualized in the time domain, but mere time domain analyses cannot accurately capture the intrinsic patterns of change in the data due to the mix of trends, periodicity and nonlinearity. Frequency domain analysis methods, such as empirical mode decomposition (EMD)  and variWe propose a gait prediction method in terms of plantar pressure data and deep learning. The predicted joint angles are capable of compensating for the sensor delay and serving as a reference for the controller.We introduce the transformer-based model, TFSformer, which effectively integrates features from both temporal and force-space dimensions. The proposed model features a high performance in gait prediction tasks, achieving the minimum mean absolute errors of We construct a dataset containing data from 35 volunteers, providing a data foundation for network training and evaluation.In view of the above points, we develop a novel transformer-based neural network named TFSformer for the precise prediction of hip and knee joint angles utilizing plantar pressure data. There are several primary structures designed in TFSformer. (1) We construct a 1D convolution-based encoder to extract essential information in both temporal and force-space dimensions. (2) We design a multi-channel attention mechanism, inspired by the multi-head attention mechanism employed in transformers. We extend the data by one dimension and define this as the channel dimension. Then, the size of the channel dimension is incrementally increased by a 2D convolution operation, and each sublayer within the channel dimension serves as a single attention head. (3) The deep multi-channel attention structure is further constructed by adding a pooling layer between two multi-channel attention layers, which is capable of reducing the memory usage and calculation consumption while retaining important information. In addition, the original data are decomposed by VMD before being input into the decoder part of the model. Our main contributions are summarized as the following:The rest of this paper is organized as follows: Gait analyses play a pivotal role in the field of lower limb exoskeletons with two primary objectives: providing human factor references for controller design and adjusting the reference trajectory of the robot based on the wearer’s motion intention. Numerous studies have been dedicated to analyzing gait in this context to further advance the development of lower limb exoskeletons.To address the time delay problem of sensor measurements, human gait information and patterns are learned based on a Gaussian process model to predict joint angles . The preAs indicated above, deep learning has become a mainstream method in gait analyses for its superiority in handling non-linear problems. Furthermore, compared to RNNs and CNNs, transformer-based models are relatively less used in gait analyses.Sensor data are a type of time series data. Processing methods in time series issues are able to provide a reference for handling sensor data.Wang et al. applied a transformer model to predict stock markets . The resThe studies above demonstrate that the transformer structure is suitable for time series problems and features a strong flexibility, which is able to be combined with other networks. Most transformer variants retain the core characteristics, i.e., a sequence-to-sequence structure and an attention mechanism. Similarly, in this article, we construct a transformer-based network to predict the angles of hip and knee joints.This section introduces the work undertaken in relation to the construction of the dataset used in this paper firstly, then elucidates the methodologies and theoretical frameworks that underpin our proposal, providing a thorough understanding of the conceptual and methodological foundations upon which the proposed model is built.The dataset for the research consists of joint angle data and plantar pressure data associated with the process of human walking. To establish a precise and comprehensive dataset, we designed an experimental setup utilizing state-of-the-art equipment, including the high-precision Nokov 3D infrared passive optical capture system in combination with four Bertec force measurement platforms. This meticulously constructed experimental scenario allowed us to accurately capture and analyze the desired data points, ensuring a robust and reliable foundation for the research. A total of 35 healthy volunteers were recruited to participate in the gait acquisition experiments. During the data collection experiments, the subjects were instructed to maintain their hands by their sides to avoid obstructing the markers, and they walked at their self-perceived most comfortable speed and stride length, ensuring the natural pattern of the collected gait data. The reflective markers, which were captured by infrared cameras, were affixed to the hip joints, knee joints and ankle joints of subjects. For data with small portions missing, typically not exceeding five samples, cubic spline interpolation was applied to fill the data and ensure data continuity.For the data with severely missing values or excessive noise, all data were deleted to ensure the availability of reliable data.To further reduce the noise and enhance the quality of the data, a filtering operation with a cut-off frequency of 60 Hz was applied.The raw data obtained from the experimental equipment inevitably exhibit certain limitations or imperfections. Thus, the raw data were further preprocessed with the following principles to ensure the integrity and accuracy of the dataset:These procedures were rigorously implemented to ensure that the dataset obtained for this research was of the utmost quality, ensuring the integrity and accuracy of the research findings.The data collected by the motion capture device are joint coordinate data, while joint angle data are more applicable in the design of controllers. Therefore, the joint angle data were further calculated using the inverse dynamics kinematic principle. As shown in x, y and z axes, and n sampling time was used to predict the joint angles during the next k sampling time. Namely, Assume that the current moment is Equation ), where Decomposing data according to frequency domain characters is capable of distinctly distinguishing the trend, periodicity and noise that are mixed in the time domain. In the process of obtaining the decomposed components, VMD determines the frequency center and bandwidth of each component by iteratively searching for the optimal solution of the variational model, which enables us to segment the frequency domain of the signal adaptively and separates each component effectively.S into K intrinsic node functions VMD decomposes the input signal Equation : (3)minUn represents the number of iterations in the solution process. Based on the above solution formula, the decomposed modes are obtained.The constraint means that the sum of all modes is equal to the original signal. The symbol Equation ).(4)LUkEquation ).(5)U^kThe transformer adopts three foundational components: positional encoding, a multi-head attention mechanism and a feed-forward network. The three modules endow the transformer with a strong feature processing ability for sequence tasks and provide the backbone of our model.Q, K and V are obtained by a linear operation based on the same input.The attention mechanism is the core component of a transformer. Self-attention captures information about the whole segment of data and learns correlations between different parts. The self-attention mechanism used in the transformer is Scaled Dot-Product Attention. The computation equation is set as follows: In order to learn deeper and more diverse features, multi-head self-attention is applied in the transformer.The feed-forward network comprises two fully connected layers followed by an activation layer. It is defined in Equation :(8)FFN.(9)PE the linear layers map the decomposed data dimension to In this section, we present the experimental setup which is fundamental to the experimental design and methodology, including the experimental strategies, dataset partition and hyperparameter settings.CNN model: The CNN model is constructed by removing the decoder modules from the proposed TFSformer. Furthermore, the output of the CNN is structured by two linear layers.Transformer model: The transformer network for the comparison experiment is derived from the initial transformer architecture developed for a natural language processing (NLP) task in . In contCNN transformer model: The network is constructed on the basis of the transformer network above by replacing the encoder module with a convolutional operation, which is the same as the encoder structure in our proposal. This is to demonstrate the efficiency of the decoder mechanism in TFSformer.In order to verify the performance of TFSformer, we conducted two experiments: single-step prediction and multi-step prediction. To highlight the superiority of the proposed TFSformer, we made comparisons with three representative neural networks: a CNN, a transformer, and a CNN transformer. The architecture of the comparison models is detailed as follows:Experiments were conducted based on the dataset introduced in n and k mentioned in For the single-step prediction experiment, the parameters To ensure the validity of the comparison experiment, we set the same hyperparameters in all experiments. The batch size was set as 32. The initial learning rate was set to 0.0001 and the optimizer we used was AdamW. The loss we used in the training was the mean absolute error (MAE). In addition, both the mean squared error (MSE) and the MAE were set as evaluation indicators (Equation ).(11)MSThe transformer model exhibited an inferior performance in single-step prediction, while the CNN model demonstrated a weaker prediction ability compared to the other three models in multi-step prediction tasks. These results suggest that each individual approach, either a convolutional operation or an attention mechanism, has limitations. Furthermore, combining the strengths of both approaches contributes to obvious improvements in the network’s ability to capture temporal features.The phenomenon that TFSformer outperforms the CNN transformer in all tasks fully demonstrates the superiority of the multi-channel attention-based decoder mechanism in our proposal.Further conclusions are drawn as follows:In conclusion, TFSformer has a superior predictive ability, particularly for hip motion prediction, and though the TFSformer (the orange line) is capable of capturing the change in joint angles around poles well, while the errors of the CNN (the green line) and the transformer (the red line) are slightly larger.In During the interval within the gentle angle change, the prediction value of TFSformer is relatively smooth and in line with the true changing trends.Taking into account differences in gait due to physical metrics and individual habits, we took data from about one gait period from the results obtained based on the data of three subjects in the single-step prediction task to further compare and analyze the performance of different models. The basic information of the subjects is shown in According to the analysis above, the proposed model TFSformer exhibits the best comprehensive performance. Except for the transformer model in the multi-step prediction task when In this paper, we propose a transformer-based model, TFSformer, to predict bilateral hip joint and knee joint angles through the plantar pressure. Specifically, we design a 1D convolution-based encoder to learn features in different dimensions and use multi-channel attention to extract characteristics from temporal and force-space dimensions simultaneously. Furthermore, a deep multi-channel attention structure is employed to reduce the memory and computing consumption. In addition, VMD is utilized to discompose the data while retaining the original information to distinguish trends and variations in the data. Finally, to verify the performance of the proposed method, we built a gait capture platform and constructed a gait dataset with data from 35 volunteers. Based on this gait dataset, we conducted comparative experiments. Although FTSformer does not achieve the optimal performance with overwhelming superiority in all tasks, the results show that FTSformer exhibits the strongest comprehensive performance, not only predicting joint angles accurately in both multi-step prediction and single-step prediction tasks, but featuring a high robustness regardless of gait diversity. In practical applications, the proposal is capable of compensating for sensor delays and providing references for controllers, thus improving collaboration between humans and robots. In the future, we plan to further optimize the model and work on integrating the gait prediction model with controller design to further confirm its validity.


In response to the problem that it is easy to fall into local optimum when using the traditional clustering algorithm to divide the modules, this paper improves the initialisation strategy of the NSGA2 algorithm and combines it with the FCM algorithm to propose an improved NSGA2-FCM algorithm for clustering analysis. Firstly, the FBS mapping is used to model the functional structure of the product system and identify the relationship between the product functional structures. Secondly, a correlation synthesis matrix is constructed based on the relationships between the module division drivers. Finally, the improved NSGA2-FCM algorithm is applied to cluster analysis of the product to derive the best module division scheme. The algorithm avoids falling into local optima by optimising the initialisation strategy of the NSGA2 algorithm, while using the FCM algorithm to improve the accuracy of the clustering. This allows the algorithm to explore the solution space more effectively when finding the best module partitioning solution. Finally, the effectiveness of the algorithm for module classification of light industrial equipment is verified using beer fermenters as a case study. Rong et al. proposed a product-oriented approach to modular division of the supply chain, establishing a relationship matrix through functional and structural interactions between product components2. Ramachandran K et al. investigated the effect of product modularization rate on rapid product launches and found that by locating performance improvements in product modularization, an innovative combination of product architecture, pricing, and timing decisions was achieved for rapid product launches3. Wei et al. proposed a predefined set of modules based on assembly and disassembly to generate various working levels or functions for creating multiple product variants and enhancing product utility for design phase decisions through modularity segmentation4.As an effective tool for rapid product design, proper modular classification can improve design efficiency and effectively address the challenges of product quality, manufacturing cycle time, and cost. Most of the current literature on the subject identifies modules by focusing on structural and/or functional aspects, but overlooks modular classification factors. For example, foreign researchers such as Eppinger et al. have studied product modularity development techniques and introduced a matrix-based formal approach for the first time to study modular product structures, indicating correlations between component modules5. Liu Mingyuan et al. proposed a module classification method based on an improved genetic algorithm. On the premise of obtaining the component design structure matrix and module fitness function, the improved genetic algorithm of difference crossover and neighborhood variation was used to search for the best solution for module classification.Domestic scholar Jia Yanlin conducted a systematic study on modularity and proposed a general process for modular design of mechanical products, dividing the product modular design process into four parts: modular planning, modular division, module creation, and module combination. Gu Xinxin divided the work of product modularity division into two major parts: modular product platform construction and order product modular design. Zhang Haiyan et al. used the function-principle-behavior-structure design model to map the correlation between system components and applied gap statistics and self-organizing neural network methods for cluster analysis to complete the modular division of special cylindrical gear machine tools, laying the foundation for the reconfigurable research of machine toolsAlthough previous research on module partitioning has focused more on modularity theory and methods, the sensitivity to module initialization data is low, and there is a lack of exhaustive modularity drivers and metrics, while structured operations also limit other properties of module partitioning.In this paper, by improving the initialization strategy of the NSGA2 algorithm and combining it with the FCM algorithm, we propose an improved NSGA2-FCM algorithm to analyze clustering results. By changing the value of the cluster center m, we obtain different division schemes to optimize the FCM algorithm, which is not sensitive to the initialization data. This improves the situation where traditional clustering algorithms easily fall into local optima. NSGA2 has good performance in multi-objective optimization problems, while the FCM algorithm effectively performs fuzzy clustering of data samples. By combining the two, multiple optimization objectives  can be considered simultaneously, resulting in better outcomes in clustering problems. In addition, this hybrid approach retains the advantages of the NSGA2 and FCM methods, allowing the algorithm to be more robust and flexible in practical applications. Finally, by taking a beer fermenter as an example, the modular classification of its products is completed, and a modular classification scheme is derived.6.FBS mapping can be considered a design specification process in which a designer transforms a set function into a product that implements that function. The FBS model mapping turns the function into a desired behavior that carries out the function. This desired behavior is employed to select and combine structures in a process called synthesis. During synthesis, the structures generate their own real behavior, allowing the range of desired behaviors to change and the function to be redesigned through themProducts often consist of various functional modules, which are not only interconnected but also possess multiple properties and layers of characteristics within the modules themselves. The approach based on functional-behavioral structures aims to illustrate the connections between product function and structure using a hierarchical analysis of product function to behavior and behavior to structure. To accurately display the relationship between function and structure within the product and reduce the complexity of product analysis, this paper proposes the concept of system level and establishes a product decomposition model of system functional structure. This involves first breaking down the product into several smaller systems and then using the function pointing structure to determine the relationship between product function and structure. The product decomposition process is shown in Fig. NSGA2 is one of the most efficient and popular evolutionary algorithms for optimization, generating Pareto optimal solutions by analyzing the solution domain. However, the NSGA2 algorithm also suffers from design flaws in its computation, such as the inability to effectively identify pseudo-undominated solutions, low computational efficiency, and poor convergence and distribution of the solution set.7Improving the NSGA2 algorithm primarily involves enhancing the algorithm's initialization strategy, which changes the initial population distribution and improves the algorithm's initial population quality. Since randomly generated initial populations cannot guarantee the validity of the initial scheme, the algorithm may fall into local optima, negatively affecting the optimization performance of the NSGA2 algorithm. To obtain a good initial population, it is crucial for the algorithm to optimally specify an appropriate chromosome size, which is influenced by the number of required modules. Therefore, this paper proposes Eq.  for esti(1) FCM algorithm model.The FCM algorithm minimizes the objective function by calculating the attribute function of the sample points to the class center, which is a function of the degree to which an object x belongs to set A.Suppose there is a data set entclass1pt{minimaNSGA2-FCM algorithm design.In most clustering problems, multiple objective functions need to be optimized, such as separation between clusters, tightness, etc. Given these challenges, NSGA2 can achieve satisfactory results in multi-objective optimization problems. Therefore, combining NSGA2 with FCM may offer a better solution for automatically solving fuzzy clustering problems. This hybrid approach preserves the advantages of both NSGA2 and FCM methods, making the system more robust and flexible.As required by the clustering classification of the FCM algorithm, obtaining the optimal classification result for product modules necessitates that the number of modules be within a reasonable range. If the number of modules is too large, production costs will increase; if the number of modules is too small, the difficulty of product design will increase. This paper is based on a statistical study by Ericsson. The range of module classification, derived from the statistical laws studied by Ericsson et al., is shown in Eq.  below.5\This puts the module division scheme between the optimal number of where The performance of the NSGA2-FCM algorithm is influenced by several parameters, including population size, crossover probability, mutation probability, and the number of iterations. Setting these parameters appropriately is crucial for obtaining high-quality clustering results. Therefore, data testing was employed to find the most suitable parameter settings for the algorithm. In this paper, the population size was set to 50, the crossover probability to 0.8, the mutation probability to 0.05, and the number of iterations to 200.To implement the NSGA2-FCM algorithm, the operations and data structures of the two algorithms need to be intertwined. In the process, the selection, crossover, and mutation operations of the NSGA2 algorithm are applied to the membership matrix in the FCM algorithm to achieve multi-objective optimization. Specifically, we can treat the membership matrix of the FCM algorithm as the chromosomes of the NSGA2 algorithm and adjust these chromosomes through genetic operations to find the best fuzzy clustering solution.As a result, the improved NSGA2-FCM algorithm demonstrates better convergence and stability, while being capable of finding solution sets that are close enough to the optimal solution within a limited number of iterations. Furthermore, these solution sets exhibit high consistency across runs.Improvement of NSGA2-FCM algorithm flow.The flowchart of the improved NSGA2-FCM algorithm is shown in Fig. To verify the optimization performance of the improved NSGA2-FCM algorithm, its performance was compared with that of the NSGA2 and FCM algorithms alone. The experimental data was simulated and pre-processed, and the results of the comparison are presented in Fig. As illustrated in Fig. The weights of the selected modular division factors need to be determined, and the submatrices should be integrated into the corresponding composite matrix using the matrix integration method. This paper employs hierarchical analysis to ascertain the weights of individual module division factors.Optimization of the product's functional structure and component recycling are the two primary goals in the product design process. Functional structure optimization involves the modular optimization of product decomposition and the reconfiguration of components into new modules, without reducing the original product's functionality. The recovery optimization objective aims to increase the proportion of product components recovered while maintaining functional optimization. Consequently, the product functional structure objective is as crucial as the recycling objective.Module segmentation drivers are analyzed separately according to the hierarchical criteria of the module segmentation hierarchy analysis presented in Table Depending on the percentage divided, the modular division factor should satisfy the following formula:Establishment of Impact Factor C:Introducing a value of C would:The above equation assigns weight values to modularity factors according to their importance to the target.Finally, the relationships between product components are established through a correlation synthesis matrix.To satisfy later algorithmic optimisation the relevant synthesis matrix has the following properties:(1) The correlation synthesis matrix is a symmetric matrix, i.e.(2) The correlation synthesis matrix uses the correlations between components and components as matrix elements. So it does not include the component's own relationship value. However, for the simplicity of the algorithm calculation, the component-self relationship value is set to 1.The relevant combined matrix is then as in equation:The correlation matrix is actually a quantification of the interactions between the components of a product and is the basis for modular division using intelligent algorithms. The elements of the correlation matrix are obtained by superimposing the correlations of the various segmentation factors, indicating the total influence of one component on another. The module segmentation method in this paper is a module segmentation method that uses the influence of components to complete the product. The algorithm is designed to optimize the configuration of modular components according to the influence of each component on other components.In layman's terms, a beer fermenter is used to produce beer through the fermentation of grain. Its basic structure is shown in Fig. As can be seen from Fig. It is assumed that the range of beer fermenter products has been determined to be developed according to modular architecture. The specific type of architecture is uncertain, but the number of beer fermenter components is known to be determined. The production of beer fermenter component candidates and the manufacture of composite modules, as well as the decision to assemble, transport and recycle the product, are made by the producer based on the design developed by the designer.According to the differences in the functions achieved, beer fermenters are mainly divided into fermentation systems, temperature control systems, pressure control systems and power systems.(1) Fermentation system.Fermentation system refers to the process of fermenting raw materials in the beer fermenter to produce beer. It includes the tank body, the tank roof, the legs, the sampling valve and the discharge valve. The body and roof components are used to store raw materials to achieve the function of fermenting raw materials and storing semi-finished products. The sampling valve takes samples, the discharge valve discharges semi-finished products and waste when fermentation is complete, and the legs support the fermenter.(2) Temperature control system.The temperature system is the fermentation process in the fermenter. The internal temperature rises. This paper only selects the thermometer to achieve the function of displaying the internal temperature of the fermenter.(3) Pressure control system.Pressure control system is the fermentation process in which the internal pressure changes. Including pressure gauges, positive and negative pressure valves, exhaust valves, air distributors. Pressure gauge to achieve the function of pressure display, positive and negative pressure valve and exhaust valve to achieve the function of adjusting pressure, air distribution is mainly to control the internal oxygen content of fermenter components.(4) Power system.The power system provides power for fermenter mixing and cleaning. Including motor, agitator, cleaner, defoamer, shaft seal, coupling. The motor is the power source, the stirrer is to stir the raw material during the fermentation process to improve the fermentation efficiency, the cleaner is to clean the inside of the fermenter after the fermentation is completed, and the antifoamer is to eliminate the air bubbles generated during the fermentation process to improve the fermentation efficiency. The shaft seal realizes the function of sealing and the coupling plays the role of coupling.Through the above analysis of the beer fermenter, the final product breakdown model shown in Fig. (1) Establishing the relevant integrated matrix.According to the module division factors and methods proposed in this paper, the function-related sub-matrices, structure-related sub-matrices, material-related sub-matrices and recyclability-related sub-matrices between beer fermenter modules were evaluated as shown in Tables (2) Performing module classification.According to Tables For different values of the number of clusters, the module partitioning scheme is obtained as shown in Table In this paper, we propose an improved NSGA2-FCM algorithm by combining the NSGA2 initialization strategy with the FCM algorithm. The product functional and structural relationships are identified according to customer requirements and hierarchical models, and a comprehensive numerical matrix is obtained using the hierarchical analysis method for module division factors. A comparative analysis of the algorithm's performance demonstrates that the NSGA2-FCM algorithm outperforms the NSGA2 and FCM algorithms alone in terms of convergence algebra and objective function values, and is closer to the Pareto optimal solution.Using a beer fermenter as an example, a modular partitioning scheme is obtained by employing a combination of the improved NSGA2-FCM algorithm and the related integrated matrix cluster analysis. It is shown that constructing a comprehensive relationship matrix of components based on module partitioning drivers and conducting a comprehensive relationship matrix analysis using the improved NSGA2-FCM algorithm to obtain an optimized modular partitioning scheme improves the issue of the clustering algorithm tending to fall into local optima during partitioning. This approach makes the light industrial equipment module partitioning method more accurate and efficient.


Using point cloud to reconstruct the 3D model of a substation is crucial for smart grid operation. Its main objective is to swiftly capture equipment point cloud data and align each device’s model within the large and noisy point cloud scene of the substation. However, substation reconstruction needs improvement due to the low efficiency of traditional noise-resistant clustering methods and challenges in accurately classifying similar-looking electrical equipment. This paper proposes an automatic modeling framework for large-scale substation point cloud scenes. Firstly, we reduce the substation scene’s dimensionality to improve clustering efficiency and establish relationships between data dimensions using a re-clustering algorithm. Next, a neural network is developed to identify various device types within clusters, even with limited subdivisions. Finally, a model library is employed to register standard models onto the target device’s point cloud, obtaining device types and orientations. Real substation data processing demonstrates the ability to rapidly extract devices from complex and noisy point cloud scenes, effectively avoiding missegmentation issues. The automatic modeling approach achieves a precise substation calculation rate of 92.86%. In comparison to traditional CAD modeling and tilt photography methods, the 3D laser scanning modeling approach stands out as a method that places existing models into simulation scenarios using device point clouds. This method offers high accuracy and excellent scene integrity, effectively meeting various high-precision modeling demandsAt present, the modeling process relies mostly on manual processing. First, the point clouds of equipment in a point cloud scene are divided; next, the specific types of equipment are judged manually based on real-world experience; and then, the corresponding equipment model is found in the model library and manually dragged into the scene. The whole process revolves around two critical issues: (1) extracting the target equipment point clouds and (2) identifying the types of equipment represented by the point clouds.5. However, the actual effects of these two types of algorithms are affected by noise8.Many useful point cloud clustering algorithms for extracting a single target from a point cloud scene have been published. These methods are mainly divided into two categories: clustering algorithms based on distance information and clustering algorithms based on density information10. When the point cloud scene contains considerable noise, the noise will connect the target clusters, making it difficult to determine the distance threshold3.For clustering algorithms based on distance information, the clustering results depend mainly on the distance threshold set in advance. The prerequisite for obtaining a better clustering effect is that the interval of each target cluster has a fixed rule12. The radius filter is the most commonly used denoising method. It takes a point to be determined as the center, controls the size of a space by setting the radius, and analyzes the average distance from each point in the space to the center point of the space to measure the density of the space. The threshold determines whether the point is noise. This method can determine noise only through a fixed global threshold and is not suitable for changes in noise density14.Clustering algorithms based on density information can address the trouble caused by noise to a certain extent. The main principle is to judge the noise by relying on the difference between the target point cloud density and the noise point cloud density13. However, the neighborhood space is still controlled by a fixed radius15. During evaluation of the noise point cloud, part of the point cloud in a target with a complex shape may be judged as noise, and the effective point may be removed by mistake2. Density-based spatial clustering of applications with noise (DBSCAN) is an algorithm that can cluster target point clouds of any shape in noisy point cloud scenes and can be well applied to point cloud clustering tasks of complex-shaped devices18. However, the computational efficiency of DBSCAN is not high, and DBSCAN is not suitable for substation scenarios where the amount of point cloud data is as large as several hundred megabytes21.On this basis, the statistical filter adapts to discriminate noise of different density changes by determining the average distance information of the global neighborhood and obtaining the standard deviation distribution. Statistical outlier removal is a typical statistical filter24. Many types and models of power equipment can be found in substations. Establishing enough training samples for each kind of equipment is a very large project that is difficult to accomplish in a short time. Particularly for power equipment of the same category but different types, their differences are often difficult to intuitively discover. Generating training samples and establishing the corresponding neural networks for subtle differences are great challenges that require the cooperation of professionals with both electric power and artificial intelligence knowledge.Algorithms for target recognition based on neural networks have developed rapidly and can be used to identify two- or three-dimensional targets, but they depend heavily on the establishment of training samples27. The common two-dimensional image recognition algorithm can identify multiple targets at the same time and has been used to identify equipment in substations. A single-shot multibox detector (SSD) is a kind of target detection method with both speed and accuracy that is widely used in various fields of image recognition28. However, it has the disadvantage of not being robust to small targets, as the shallow feature map is not strong enough29. The basic network is changed from VGG to ResNet to improve the deeper network representation ability30. This direction is important to improve the SSD prediction capabilities. DenseNet, as a better CNN model of ResNet, offers greater improvements in SSD prediction33.The very large workload of generating training samples directly limits the mature application of 3D object recognition algorithms in substation equipment recognition35.In this article, we proposed a cross-constrained hierarchical clustering algorithm based on traditional voxel clustering that reduces the dimensionality of 3D point cloud information to 2D, which not only improves the computational efficiency but also effectively removes noise. This algorithm uses the constraint criteria to accurately determine the noise and can process point cloud scenarios of large substation sites with hundreds of megabytes of data at a time. In this cross-constrained hierarchical clustering algorithm based on traditional voxel clustering, the 3D point cloud data is reduced to N 2D point cloud projection data, and each 2D point cloud data is clustered. If point cloud clusters exist in all slices at the same horizontal position, these clusters are retained. Otherwise, clusters at that horizontal position are considered noise and removed. Then, we applied the improved SSD structure to the image recognition of power equipment and quickly identified the main equipment category in a cluster. Finally, for equipment of the same category but of different types, we use the iterative closest point (ICP) algorithm for fine registration, finely distinguish the equipment type through match point distances, obtain the world coordinates of the model in the scene, and put the model into the sceneOur automatic modeling approach is shown in Fig. According to the characteristics of the point cloud noise and vertical continuity of the equipment point cloud, we use the clustering results of different plane levels to constrain each one to identify and remove the noise point cloud. Point clouds of the same elevation interval are projected to the same plane, and the voxelization clustering algorithm is used for clustering. The clustering results of plane point clouds in different elevation intervals can be obtained, as shown in Fig. In practical applications, the size of each device in the substation are constructed in accordance with standard specifications, and the sizes of components such as bases, connecting rods, and insulator strings are also fixed. Therefore, we can fix the height intervals. We can obtain only the point cloud data with an elevation below 6 m (the elevation of the ground is 0 m) as the key point cloud data, as shown in Fig. After the noise point cloud clusters are removed by using the cross constraint, the remaining point cloud clusters need to be merged. We use the recombination algorithm to recluster the bounding boxes with a hierarchical strategy:This hierarchical clustering strategy is an extension of the voxel clustering strategy and can reduce the number of clusters. The shape of the box conforms to the distribution law of electrical equipment in the substation scene.36, that predicts the type of equipment based on point cloud images of the power equipment. In this detection framework, we extract deep features through DenseNet and then combine the target frame suggestion strategy and frame regression algorithm in the SSD algorithm to rebuild an end-to-end object recognition and detection network36. The Dense-SSD algorithm has a high accuracy rate for detecting small objects, can identify the divided power equipment and the parts around the equipment that are not part of the equipment, including pedestrians and other equipment, and reduce the adverse effects of oversegmentation on equipment recognition. The Dense-SSD model is divided into two parts: a feature extraction part and a prediction output part.We added a network for extracting deep features on the basis of SSD and built a new neural network, similar to what the Dense-SSD (DSOD) doesThe feature extraction part has a DenseNet structure, including a stem block, four dense blocks, two transition layers, and two transition w/o pooling layers.In the stem block, to reduce the information loss of the original input image, we replaced the large convolution kernel with several small convolution kernels and changed the original design . The clustering result comparisons are shown in the Figure In DBSCAN, when setting the neighborhood radius Smaller neighborhood radii lead to more points being classified as noise, resulting in a larger number of clusters. This causes the point cloud of the equipment to be segmented into multiple smaller clusters. For As the neighborhood radius increases, the number of clusters and noise points decrease, and there are fewer instances of equipment points being incorrectly segmented. However, if the neighborhood radius becomes too large, most noise points are included in equipment clusters and retained. Additionally, points belonging to different equipment may be assigned to the same cluster, leading to poor clustering results. This behavior is primarily due to the fact that when the neighborhood range is small, a significant number of non-noise points are subdivided excessively. Since the minimum point count is fixed, clustering results with smaller neighborhoods mistakenly identify many excessively subdivided equipment points as low-density noise. On the other hand, setting a larger neighborhood range disregards the distance between different equipment points, causing points that are close but do not belong to the same equipment to be grouped together, along with some low-density noise points being retained.In the comparison of clustering results for different neighborhood radii, with neighborhood radii values of 0.1 m, 0.5 m, and 1.0 m, and a minimum neighborhood point count of 30, we observed the following patterns:MinPts), with a neighborhood radius  of the matching distance given by the ICP registration is twice as different.In the substation scene, some ancillary devices will exist around the main part of the power equipment. The usual modeling process does not have requirements for these ancillary devices. This ICP registration can avoid the interference caused by these accessory devices. In Fig. According to the registration result, we can not only identify the equipment type but also obtain the pose of the corresponding model in the substation scene. We can also effectively evaluate the modeling accuracy based on the RMSE distance in the registration calculation.We have proposed a model-driven method for reconstructing three-dimensional laser-scanned scenes of substations, which is a fast and suitable approach for substation modeling. The processing results of real point cloud data from substations demonstrate the applicability of this method in reconstructing point cloud scenes with large data volumes and complex noise. We employed the VCHC method to segment the entire substation point cloud scene, leveraging both the computational efficiency of voxel-based clustering methods and the noise resistance of density-based clustering methods, resulting in a segmentation accuracy exceeding 90%.Building upon this, we adopted a classification approach that combines Dense SSD and ICP, achieving a classification accuracy of 92.86% for electrical equipment. Dense SSD accurately recognizes multiple device categories within fine-grained clusters, effectively avoiding inaccurate identification due to insufficient subdivisions. Moreover, ICP not only distinguishes different types of devices with subtle appearance differences but also accurately places the models into the substation scene.


Non-invasive skin characterization devices are emerging as a valuable tool in clinical skin research. In recent years, the range of available experimental techniques and methods used to determine the biomechanical properties of skin has increased considerably. Although a substantial amount of work has been devoted to assessing the working principle of macroscopic skin characterization devices individually, a rationalization and comparison between them is still lacking. This motivated the present study, which aimed to characterize and compare three commonly used working principles: suction, dynamic shear loading, and indentation. A synthetic model system with tunable mechanical properties was used to assess the three devices, and the results rationalized based on corresponding finite element models. In vivo measurements were performed on healthy volunteers to investigate the capability of differentiating the biomechanical properties of skin at different body locations, and to assess the intra- and inter-rater reliability of each device. The present comparative analysis indicates that the analyzed functional principles perceive the stiffness of human skin differently, with relevant implications for the interpretation of the respective measurement results. The skin is the largest organ of the human body, forming our primary protective barrier to the surrounding environment. From a mechanical perspective, skin is a highly complex material, capable of undergoing large deformations while displaying high fracture toughness as well as a capability of repairing injuries and growing –3. On thThe biomechanical properties of skin play a fundamental role in a wide range of medical applications and pathologies such as wound healing and the formation of scars, aging associated fragility as well as skin fibrosis –11. FurtMore recently, non-invasive in vivo skin characterization devices have developed into promising tools for measurements at the tissue length scale. The functional principle behind these devices can vary greatly, not to mention the nature of the extracted parameters, pointing to a lack of standardization . Only feFirst, measurements were performed with the different devices on elastomers with tunable mechanical properties in order to investigate the capability of each device to determine the substrate stiffness. Corresponding finite element (FE) simulations were performed to rationalize the measurements. In fact, correspondence between simulations and measurements indicated that the models reproduced the respective measurement principles well. Each device was then used to perform measurements on five human subjects in two different anatomical sites. The capability of distinguishing the two sites was assessed, as well as the intra- and inter-observer reliability through the means of the intra-class correlation coefficient (ICC) . Based oSuction experiments were performed with the Nimble, a skin suction device recently developed at ETH Zurich . One of − 1). The negative pressure inside the chamber induces deformations in the skin layers. Eventually, the elevation of the skin reaches the position h, effectively sealing the suction pipe. This event is easily recognizable in the pressure-time diagram, as the pressure difference ΔP between the suction line and the chamber will rapidly increase when the suction pipe closes . A figure showing the FE model boundary conditions and corresponding mesh can be found in the Appendix . The suction was induced by a negative pressure boundary condition. The vertical displacement of the apex point was monitored, allowing the closing pressure to be extracted from the pressure-elevation diagram. The mesh was generated with a free meshing technique with a minimum seed size of 25 μm using axisymmetric elements with quadratic interpolation , a device originally developed to characterize the biomechanical properties of muscles and soft tissues , 22. Moramax represents the maximum acceleration  is applied over an interval of 7 ms, during which the displacement and acceleration of the probe are recorded  with a minimum seed size of 500 μm. An overview of the FE model boundary conditions and mesh can be found in the Appendix . The pre-force was applied quasi-statically to a reference point on the rigid disk to which the mass of 9 g was assigned. Thereafter, the impulse was implemented as a step function on the interval dix Fig. .R = 11.5 mm) and a central cylindrical indenter with a length and radius of 1.25 mm  . It is a skin indentation device composed of two different force sensors: a base plate , with a minimum seed size of 100 μm. The indentation was realized by enforcing a displacement-controlled boundary condition of the base plate and central indenter, which were modelled as rigid bodies. The indentation force could then be extracted from the diagram showing the reaction force on the rigid bodies, where the event of full contact with the base plate is easily recognizable due to the sudden increase in force. An overview of the FE model boundary conditions and mesh can be found in the Appendix . The samples were then degassed again before curing .A model system with controllable mechanical properties was selected to evaluate the different devices. For this purpose, silicone elastomers were prepared, for which Young’s modulus can be controlled by varying the density of crosslinks. Two different elastomers were manufactured: Ecoflex  mixed with a silicone thinner  (hereafter: EF) and polydimethylsiloxane  with a base-to-crosslinker ratio of 35:1  a layer of the 35:1 PDMS on top of an already cured sample of a much softer PDMS with a base-to-crosslinker ratio of 45:1. The particular parameters for spincoating were chosen such that a layer thickness of about 100 μm was achieved. This configuration was used to investigate the capability of each device to detect the spincoated layer, when compared to measurements on the uncoated sample.− 1 in steps of 0.2 μm. Each sample was indented in minimum 9 different locations separated by at least 500 μm. An apparent elastic modulus (E) was extracted from each force-displacement curve under the assumptions of the analytical Hertzian contact solution  and the elastic modulus of the material (E) is given by . Th. Th29]. Based upon the excellent agreement between the finite element model and experimental results on elastomers, an estimate of the perceived apparent modulus of each functional principle could be calculated from the in vivo measurements, where the mean of all measurements performed in each location was used as reference value Table . For thiIn vivo skin characterization devices play an important role in clinical research given their capability of measuring skin properties non-invasively. However, the breadth of experimental techniques used in different devices lead to a wide range of extracted parameters and corresponding biomechanical properties. Motivated by the lack of unification and standardization between the different working principles of skin characterization devices, the present study aimed to compare three common skin characterization techniques: suction experiments using the Nimble, dynamic shear force using the MyotonPRO, and indentation experiments using the SkinFibroMeter.A preliminary study on synthetic materials was conducted in order to rationalize the different functional principles. The reference material properties of the synthetic materials were determined using high-precision micro-indentation equipment, which made it possible to observe to what extent the different devices could capture the corresponding values of material stiffness. These properties then served to calibrate a corresponding finite element model that was developed in parallel for each functional principle.Overall, an excellent agreement was observed between the experimental results and corresponding numerical analysis for all three devices, with a maximal deviation of less than 10 %. The FE model of the dynamic shear force experiment did not account for rate dependent material behavior, which might be a contributing factor to the discrepancy between the computational and experimental results, as this device induces high shear rates. As shown herein, the measurements on the soft elastomer (EF) used in this study reported stiffness values comparable to healthy human skin. With stiffness values comparable to measurements on a matured scar, the stiff elastomer (PDMS) can be assumed to represent an upper bound of the physiological range of human skin stiffness . UltimatConsidering that all devices reported an increased stiffness in the layered elastomer configuration under controlled boundary conditions, it is clear that the different functional principles lead to fundamentally different ways of perceiving the mechanical properties of skin. All three devices were able to successfully distinguish the two measurement locations in the in vivo measurements, noting that the suction device failed to detect a significant difference in one subject. Interestingly, the average relative range for the suction experiments was considerably higher than the other two functional principles. In contrast to the suction and indentation experiments, the shear force experiments showed a consistent decrease in stiffness between the forehead and volar forearm for all volunteers. The same effect was observed in a recent study done by Rosicka et al., where the skin stiffness was evaluated in different body locations using the MyotonPRO with indentation and shear probes, respectively . Herein,High repeatability and reliability are highly relevant for a skin characterization device to be considered for clinical use. In this study, suction experiments provided high values of inter-rater and intra-rater reliability. The inter-rater reliability was found to be zero for both measures  and ICC) for the indentation experiments in the FH location. This indicates an incapability of distinguishing the different subjects. On the other hand, indentation provided the highest intra-rater reliability at VF, showing great repeatability. At FH, the intra-rater reliability was highest for the dynamic shear force device.The comparative analysis indicated a positive intra-location correlation between the suction and indentation experiments, which supports the validity of both measurements.Motivated by the agreement between the experimental results and corresponding numerical simulations on the synthetic model system, an apparent modulus was calculated using the corresponding FE model for each measurement principle in each location. This analysis indicated a good agreement between the suction and indentation technique in the FH measurement site, whereas the indentation device reported a larger increase in stiffness value for the VF measurement site. This effect could be related to the influence of deeper layers at this location, increasing the apparent stiffness for compressive loads.Notably, the dynamic shear force device operates at a deformation rate orders of magnitude higher than the other two devices used in this study, which can explain the different skin assessments. Furthermore, the neo-Hookean model applied in the present work represents a simplification not only of the tissue response but also for the elastomers considered in this study. A multilayer, time-dependent numerical model of the skin and the underlying structures could help explain the differences in measurement outcomes and facilitate the interpretation of the results from each device. In conclusion, it is evident that the reported apparent moduli can vary greatly between the different functional principles, so that a direct comparison of the stiffness descriptors is not possible.In this study, three different devices for in vivo skin characterization were analyzed and compared. Using synthetic materials and corresponding FE simulations, a framework for rationalizing the different functional principles was established. The subsequent analysis showed that the apparent moduli detected by the different devices on the synthetic materials were in excellent agreement. Moreover, all three devices were able to reliably detect a thin, stiff coating on a soft substrate. When performing measurements on healthy volunteers, the agreement between the devices was partially lost, as both the relative values and magnitude of the skin stiffness detected in each location differed between the devices. It is clear that the different devices respond differently to the complex structure of the skin at each anatomical location, which ultimately motivates a careful interpretation of the descriptors and the comparison between them.


The mode converter, as a passive mode conversion device in transmission lines, is well-investigated and widely implemented in various electromagnetic systems. However, most traditional mode converters can only realize a single conversion mode. Thus, a mode converter achieving multiple controllable output modes is urgently needed. In this paper, a reconfigurable mode converter operating in the microwave range is achieved by embedding a deformable all-dielectric material with quadrilateral shape into a rectangular waveguide based on coupled-mode theory. It can achieve different target modes with controllable output for the same input by exciting the deformable all-dielectric material. The design principle of the mode converter is expounded concretely and simulation is carried out using HFSS software 2022 R2. Experimental results, consisting of the simulation results, demonstrate that the proposed mode converter can achieve various mode conversions with mode purity higher than 95%. This article innovatively applies deformable materials to waveguide mode conversion, expanding the application of deformable memory materials in electromagnetic devices. Waveguide mode refers to the type of electromagnetic (EM) field that can propagate in a waveguide. Practically, an EM system requires various waveguide modes as input, such as electron cyclotron resonance heating , radar , antennaThere are three common approaches for mode conversion: phase matching ,13,14,15Another approach involves using photonic crystals to control EM waves in the waveguide. The tapered-slot mode converter and the photonic crystal structure mentioned in References ,29 are eIn the field of mode conversion, one common approach is to introduce a perturbation in the refractive index of the waveguide along with controlling the propagation directions. This can be achieved by etching gaps in the waveguide, which is the most popular method for realizing mode conversion. There have been various designs and structures proposed for mode converters in different frequency ranges. For example, Ohana  designedTo tackle the need for multiple controllable output modes in waveguide mode converters, we present a phase-matching technique utilizing an embedding reconfigurable waveguide mode converter in this work. The mode converter is designed to alter the refractive index of the standard rectangular waveguide, achieving high-purity mode conversion. Additionally, as shown in According to the coupled-mode theory, if a perturbation is introduced into a waveguide, one waveguide mode can be coupled into another mode. Assuming the dielectric constant of the medium filled in the original waveguide is In the absence of perturbation, degenerate modes remain constant along the propagation direction The amplitude of each mode along the propagation direction is determined by :(3)ddzAmMode conversion is essentially the co-directional coupling of two modes in the waveguide. When considering the co-directional coupling between the two modes, (3) can be rewritten as a set of differential equations:fined as :(5)kmn=ωThe proposed device functions as a co-directional coupler, facilitating the coupling of two eigenmodes that propagate in the same direction within a single multimode waveguide. Solving the mode coupling Equation (4) under the phase matching condition reveals a periodic exchange of power between the modes as they propagate . The solTheoretically, the period of the structure is rbations . In thisrbations , we adopWe obtained the approximate parameters of the coupled mode theory.Therefore, finding suitable parameters to satisfy (7) is the key to the design of the mode converter. In order to further improve the performance of the device, we selected an approximate interval containing parameter In this work, the numerical results were obtained by ANSYS HFSS 2022 R2 based on the finite element method. In simulations, the temperature-controlled deformable material Verowhiteplus is set to a dielectric constant To evaluate device feasibility, we investigated fabrication tolerance by examining the effects of geometry deviation on performance. We first analyzed the conversion efficiency and mode purity versus variation in angle According to the theoretical calculations, the mode converter can be applied to other waveguides to realize higher-order mode conversion. To verify the generality of the mode converter, we designed another mode converter that realizes the conversion between TE10 and TE30 modes embedded in the WR-229 waveguide with cross-sectional parameters To assess the robustness of the designed mode converter, we conducted an analysis of the effects of length and angle parameters on transmission efficiency and mode purity, as displayed in To verify our simulation results and the feasibility of the proposed mode converter, we punch on the waveguide and measure the electric field amplitude propagating through the temperature-controlled deformable material to compare with the simulation results. According to the simulation results, we designed the position of the circular holes to ensure that both the high- and low-energy positions of the EM waves can be detected. The punched waveguide is shown in For the measurement, we employed the setup shown in We test the energy of the electric field at 7.8 GHz at the trepanning position of the waveguide with The mode-oriented coupling/decoupling combiner proposed in Reference  achievesIn comparison to these previous works, the proposed mode converter distinguishes itself with a compact structure, robustness, exceptional mode purity, and a relatively broad bandwidth. Notably, this article innovatively leverages the characteristics of SMMs to design a mode converter that offers reversible and controllable mode output with the potential for higher-order mode conversions. However, practical applications should consider temperature variations in the waveguide environment to mitigate errors stemming from spontaneous material changes. Finally, the deformation capacity of SMMs is not infinite, and the degree of deformation of SMMs should also be considered in practical engineering applications.In this work, a reconfigurable rectangular waveguide mode converter operating at the microwave range has been investigated and verified. The actual effect of the mode converter was consistent with the simulation results, which proves the effectiveness of our design theory. Based on the 3D printing technology, the proposed mode converter achieved different waveguide mode conversions by spontaneous deformation through temperature-controlled materials instead of modifying the structure of the device. Compared to other forms of mode converters in the microwave section, the mode converter proposed in this work can achieve higher purity mode conversion in a smaller size. Although this reconfigurable method is convenient and accurate, it still faces the problems of long deformation time and limited deformation degree. Moreover, numerical simulations showed that the mode converter could be extended to other frequencies by modifying the parameters of the device. The embedded features of the mode converter enable it to be applied in different kinds of rectangular waveguides. This light structure expands the application of shape memory materials to electromagnetic devices, providing an alternative to constructing novel waveguide mode converters. In the future, reconfigurable waveguide mode converters based on SMMs will definitely be applied in highly integrated microwave systems, effectively avoiding some additional operations, such as system reconstruction.