Sensor signal anomaly detection method based on bidirectional fuzzy reasoning in resource-constrained scenarios

Abstract

The application discloses a kind of resource-restricted scene under bidirectional fuzzy inference sensor signal anomaly detection method, and industrial sensor multivariate signal anomaly detection technical field, the method formulates the abnormal identification mechanism based on " neighborhood-global " mode difference learning;Design the customization double-layer Fuzzy-KAN small volume network guided by this mechanism;Joint bidirectional learning strategy and four parallel Fuzzy-KAN network constructs bidirectional fuzzy inference anomaly detection model, executes " neighborhood-global " context mode difference learning in fuzzy domain from " history to future " and " future to history " two directions in Fuzzy-KAN network directly, identifies time point level anomaly in multivariate sensor signal under zero label.This application anomaly detection method realizes three goals of high detection speed, high detection precision and low resource consumption on the industrial equipment of limited resources, promotes the landing application of intelligent model in real industrial scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of anomaly detection of industrial sensor multi-element signals, and particularly relates to a sensor signal anomaly detection method based on bidirectional fuzzy reasoning in a resource-limited scenario. BACKGROUND

[0002] In order to manage and monitor industrial production processes, multiple heterogeneous sensors are integrated into devices to collect operational data at fixed time intervals, such as Figure 1 Data is transmitted to edge gateways through various networks (Wi-Fi, 5G, Ethernet) and protocols (Modbus, UDP, TCP), and then packaged and forwarded to cloud servers. Anomaly detection models are usually deployed on these servers to analyze data and return analysis results to the edge for timely alarms. Since existing time point level anomaly detection models are usually designed for deployment on resource-rich cloud servers, this design goal makes them tend to use complex neural networks with deep structures and large parameters, and detection accuracy as the core optimization goal. This approach, while ensuring detection accuracy, also has significant problems, namely, large model resource consumption and slow detection speed. With the advent of the big data era, the amount of sensor data is growing explosively, and cloud computing load is also rising exponentially, which makes communication delay and queuing problems increasingly prominent and becomes the main bottleneck restricting system performance. The cloud-based deployment mode is not up to the task when faced with the stringent real-time processing requirements of industrial scenarios, and it is difficult to meet the urgent requirements of detection timeliness in actual production. This reality has prompted a shift in intelligent model deployment strategies, with a move from the cloud to the edge becoming inevitable. However, edge devices are often limited in computing power and memory resources, making it difficult for existing complex intelligent anomaly detection models to run smoothly on edge devices, or even impossible to deploy effectively.

[0003] In resource-limited industrial scenarios, anomaly detection faces a very difficult core challenge of how to accurately and effectively balance the three mutually contradictory goals of detection speed, detection accuracy, and resource consumption. To achieve high detection accuracy, models usually need to have strong feature extraction capabilities, which often rely on deep neural networks with large parameters and complex structures. However, such models introduce high computational overhead during training and inference, not only leading to decreased detection speed, but also significantly increasing resource consumption and deployment costs. In contrast, shallow models can improve detection speed and reduce resource consumption by reducing parameter quantity and computational complexity, but their feature extraction capabilities are limited, often making it difficult to guarantee detection accuracy and showing weak robustness when dealing with diverse industrial scenarios.

[0004] To effectively address the "speed, accuracy and consumption difficult balance" problem faced by anomaly detection in resource-constrained industrial scenarios, current existing solutions are mainly divided into two categories: accuracy-oriented methods and speed-oriented methods, which are:

[0005] (1) Accuracy-oriented methods mainly rely on deep models to carry out anomaly detection work. Deep models have powerful feature extraction and pattern recognition capabilities due to their complex network structure and large number of parameters, and can theoretically achieve high-precision detection of industrial anomalies. At the same time, in order to alleviate the resource consumption problem caused by the large number of parameters of deep models, these methods usually apply compression techniques such as model pruning or knowledge distillation to reduce model size. However, since these methods are based on the inherent deep architecture, despite the use of compression techniques, the improvement in detection speed and resource consumption is still limited.

[0006] (2) Speed-oriented methods use shallow models with fewer parameters to prioritize fast inference and low resource consumption. Shallow models have simple structures and fewer parameters, requiring relatively low computational complexity and storage space during computation, so they can run quickly on resource-limited devices and meet the real-time detection needs of industrial production. Although speed-oriented methods usually introduce some accuracy improvement strategies to make up for their limited model performance, the shallow structure fundamentally limits the model's representation ability and inference performance. Due to the small number of layers, shallow models often have difficulty learning complex high-level features in the data, resulting in limited ability to identify anomalies, which makes the model's accuracy unstable in actual application and performs differently under different industrial scenarios and data distributions, making it vulnerable to noise and interference, resulting in false positives and false negatives.

[0007] (3) In the case of limited resources, shallow structures can achieve fast inference and low resource consumption, ensuring the continuity and stability of industrial production. However, improving the explainability and inference ability of shallow networks to enhance the detection accuracy of shallow networks is still a key challenge. Only by solving these two problems can speed-oriented methods play a greater role in resource-constrained industrial scenarios and achieve high-speed, low-consumption, and high-precision anomaly detection.

[0008] In the field of sensor signal analysis, various techniques have been applied to enhance the inference ability and explainability of shallow neural networks, specifically:

[0009] (1) Frequency domain analysis is the first commonly used technique, which uses Fourier transform or wavelet transform to improve inference ability and help extract key features. However, this technique requires an additional time-frequency transform process and cannot be directly integrated into neural networks, and will generate additional computational overhead.

[0010] (2) Fuzzy Inference is another excellent technique, which transfers the learning process from time domain to fuzzy domain, and can rely on expert knowledge to construct inference rules, or automatically learn rules through fuzzy neural networks, thereby improving inference ability. However, the traditional fuzzy neural network has a deep level, needs to go through the repeated conversion process of time domain-frequency domain-time domain, and has weak interpretability, resulting in additional computational overhead and performance degradation problems.

[0011] (3) KAN representation learning is the third technique, which uses Kolmogorov-Arnold representation learning theory to enhance the interpretability of neural networks, thereby improving the performance of shallow networks. However, its inference ability is also limited, and usually requires a deep network structure to achieve satisfactory performance.

[0012] In summary, fuzzy inference and KAN representation learning are complementary and can be directly integrated with neural networks, so they are particularly suitable for enhancing the inference ability and interpretability of shallow networks. Currently, there is no existing work that combines fuzzy inference and KAN representation learning to build an anomaly detection model for multi-sensor signals. SUMMARY

[0013] In view of the above technical problems, the present application provides a sensor signal anomaly detection method based on bidirectional fuzzy inference in a resource-constrained scenario, which realizes fine-grained time point level anomaly detection on resource-limited industrial equipment by customizing a shallow small volume network and multiple precision improvement strategies, achieving high detection speed, high detection accuracy and low resource consumption.

[0014] To solve the above technical problems, the technical solution provided by the present application is:

[0015] A sensor signal anomaly detection method based on bidirectional fuzzy inference in a resource-constrained scenario, comprising the following contents:

[0016] Formulate an anomaly recognition mechanism based on "neighborhood-global" mode difference learning;

[0017] Design a double-layer small volume Fuzzy-KAN network guided by the anomaly recognition mechanism;

[0018] Joint bidirectional learning strategy and four parallel Fuzzy-KAN networks to build a bidirectional fuzzy inference anomaly detection model, which performs "neighborhood-global" context mode difference learning from "past to future" and "future to past" directions in the fuzzy domain of Fuzzy-KAN network, to identify time point level anomalies in multi-sensor signals under zero label.

[0019] Preferably, the abnormality identification mechanism based on "neighbor-global" pattern difference learning utilizes the physical property that periodic / seasonal features in normal sensor signals drive the "neighbor" and "global" context patterns similar at each time point, to generate a "neighbor" context consisting of multiple local neighbors and a "global" context consisting of multiple distant neighbors for each time point in the sensor signals; learn the pattern difference of the two contexts through a neural network, and judge the time points with large pattern difference as abnormal.

[0020] Preferably, the small-volume Fuzzy-KAN network consists of input neurons, hidden neurons, and output neurons, wherein and respectively represent the number of neighbors in the neighborhood and global contexts, is the number of fuzzy sets in the fuzzy domain, the input neurons and hidden neurons constitute a fuzzy mapping layer, and the hidden neurons and output neurons constitute a fuzzy reasoning layer, the fuzzy mapping layer is responsible for converting the time domain context data into fuzzy domain membership, and the fuzzy reasoning layer is responsible for "neighbor-global" fuzzy membership reasoning and learning of "neighbor-global" context pattern difference.

[0021] Preferably, the bidirectional fuzzy reasoning anomaly detection model consists of three parts:

[0022] Forward contrastive learning based on Fuzzy-KAN network, which adopts two Fuzzy-KAN networks to capture the "neighbor-global" context pattern difference of each time point in the fuzzy domain from "history to future" in the forward direction;

[0023] Reverse contrastive learning based on Fuzzy-KAN network, as a supplement to the forward process, which adopts another two Fuzzy-KAN networks to capture the "neighbor-global" context pattern difference in the fuzzy domain from "future to history" in the reverse direction;

[0024] Bidirectional joint abnormality scoring, which integrates the forward and reverse context pattern differences to calculate the joint abnormality score of each time point.

[0025] Preferably, the "history-to-future" forward contrastive learning comprises four parts: forward sampling, neighborhood-to-global membership inference, global-to-neighborhood membership inference and contrastive learning, specifically: first, forward sampling generates neighborhood context and global context for each time point; then, a Fuzzy-KAN network performs neighborhood-to-global membership inference in fuzzy domain, while another Fuzzy-KAN network performs global-to-neighborhood membership inference; finally, the results of the two membership inferences are contrasted to generate membership difference, which quantifies the context pattern change of each time point.

[0026] Preferably, in the "history-to-future" forward sampling, first, by extracting consecutive time points as neighborhood context of time point , then by selecting one time point every interval, a total of selections are made, i.e., from to , to obtain global context of time point , neighborhood context and global context are constructed based on historical data relative to , and time points are arranged in forward direction. Preferably, in the neighborhood-to-global membership inference, after forward sampling, a Fuzzy-KAN network is adopted to capture context pattern change in fuzzy domain; with neighbors in neighborhood context of each time point as input, each input connects

[0027] fuzzy sets to generate L membership, realizing mapping from time domain to fuzzy domain to obtain membership vector of neighborhood context in fuzzy domain, with size of S × S , then the membership vector of neighborhood context is passed to fuzzy inference layer, and global context membership vector with size of L × S is inferred through KAN representation learning, completing neighborhood-to-global membership inference. G S Preferably, in the global-to-neighborhood membership inference, another Fuzzy-KAN network is adopted to perform global-to-neighborhood membership inference in fuzzy domain with global context as input; with neighbors in global context generating global context membership vector through fuzzy mapping layer, with size of

[0028] × G , then global membership vector is input to fuzzy inference layer, and neighborhood context membership vector with size of G × S is inferred through KAN representation learning, completing global-to-neighborhood membership inference.L X S .

[0029] Preferably, the contrastive learning is used to confirm that the two Fuzzy-KAN networks generate the same neighborhood context membership vectors and the same global context membership vectors.

[0030] Preferably, the “future-to-past” reverse contrastive learning includes four parts: reverse sampling, neighborhood-to-global membership inference, global-to-neighborhood membership inference, and contrastive learning, specifically: first, the reverse sampling strategy first constructs the reverse neighborhood context and the reverse global context for each time point; then, the two Fuzzy-KAN networks perform global-to-neighborhood and neighborhood-to-global membership inference in the fuzzy domain in a contrastive learning manner; finally, the results of the two membership inferences are contrasted to produce membership differences, representing the reverse context mode changes at each time point.

[0031] Preferably, in the reverse sampling, from the future-to-past direction, from to , the consecutive time points constitute a reverse neighborhood context window, and every interval selects a time point, and times of consecutive selection are performed from to , generating a reverse global context window, and for time point , the forward and reverse contexts contain the same time points, but in reverse order.

[0032] Preferably, in the neighborhood-to-global membership inference, after reverse sampling, the third Fuzzy-KAN network takes the reverse neighborhood context as input, generates the membership vector of the reverse neighborhood context in the fuzzy domain through the fuzzy mapping layer, and then the neighborhood context membership vector is transmitted to the fuzzy inference layer to infer the membership vector of the reverse global context through KAN representation learning.

[0033] Preferably, in the global-to-neighborhood membership inference, the fourth Fuzzy-KAN network takes the reverse global context as input, generates the membership vector of the global context in the fuzzy mapping layer, and infers the membership vector of the reverse neighborhood context in the fuzzy inference layer through KAN representation learning.

[0034] Preferably, the contrastive learning is used to confirm that the two Fuzzy-KAN networks generate the same neighborhood and global context membership vectors.

[0035] Preferably, in the bidirectional joint anomaly scoring, after the forward and reverse contrast learning is completed, for a given time point to be tested , the scoring process is as follows:

[0036] S3-3-1, forward score calculation:

[0037] For a time point to be tested of a sensor signal containing variables , and its neighborhood context and global context, the forward contrast learning component generates membership contrast differences, the membership contrast difference of each variable being the sum of the global and neighborhood membership differences, the first maximum differences in the membership contrast differences are selected, and the average value thereof is defined as the forward anomaly score;

[0038] S3-3-2, reverse score calculation:

[0039] The reverse contrast learning component also generates N membership contrast differences for the variables of the sensor signal, the first maximum differences in the membership contrast differences are selected, and the average value thereof is defined as the reverse anomaly score;

[0040] S3-3-3, final score calculation:

[0041] The anomaly score of the time point is defined as the maximum of the forward score and the reverse score, and the anomaly score is compared with a predefined threshold to determine whether the time point to be tested is abnormal.

[0042] The sensor signal anomaly detection method for bidirectional fuzzy reasoning in a resource-constrained scenario provided by the present application has the following advantages compared with the prior art:

[0043] (1) The sensor signal anomaly detection method for bidirectional fuzzy reasoning in a resource-constrained scenario of the present application is based on a traditional fuzzy neural network, and through joint Kolmogorov-Arnold representation learning theory, a shallow Fuzzy-KAN network composed of only two layers of structure and a small number of parameters is designed after the process of repeatedly converting between "time domain-fuzzy domain" is simplified.

[0044] (2) The sensor signal anomaly detection method of bidirectional fuzzy reasoning in the resource-constrained scene of the application formulates an anomaly recognition mechanism based on "neighbor-global" mode difference learning, and a bidirectional learning strategy and four Fuzzy-KAN networks are used to drive the unsupervised bidirectional fuzzy reasoning fast anomaly detection model, which directly learns the context mode difference in the fuzzy domain rather than the time domain from "history to future" and "future to history".

[0045] (3) The sensor signal anomaly detection method of bidirectional fuzzy reasoning in the resource-constrained scene of the application is based on the learned bidirectional "global and neighborhood" context mode difference, and a customized anomaly scoring scheme is designed to generate a final anomaly score for each time point to achieve time point level anomaly detection, achieving the three goals of high detection speed, high detection accuracy and low resource consumption. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a schematic diagram of the anomaly detection process in a real scene.

[0047] Figure 2 is a schematic diagram of the anomaly recognition mechanism based on "neighbor-global" mode difference learning designed by the application.

[0048] Figure 3 is a traditional fuzzy neural network diagram.

[0049] Figure 4 is a two-layer Fuzzy-KAN small volume network diagram customized by the application.

[0050] Figure 5 is a bidirectional fuzzy reasoning anomaly detection model diagram designed by the application.

[0051] Figure 6 is a diagram of the forward and reverse sampling process of the model of the application.

[0052] Figure 7 is an anomaly detection visualization diagram of the 17th variable of the HAI data set from time point 16500 to 18000 in the verification test of the application.

[0053] Figure 8 is the deployment result of the application in the verification test on the resource-limited edge device Raspberry Pi 4b.

[0054] Figure 9 is the deployment result of the application in the verification test on the resource-limited edge device Jetson Xavier NX. DETAILED DESCRIPTION

[0055] The following provides a detailed description of specific embodiments of the present invention. It should be understood that the specific embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention.

[0056] The present invention provides a sensor signal anomaly detection method for bidirectional fuzzy inference in resource-constrained scenarios, which is applied to a system consisting of... A real-world industrial production process monitored by heterogeneous sensors. After several consecutive data acquisitions, the acquired sensor data constitute a multivariate time series, namely, a multivariate signal from an industrial sensor, represented as... ,in and These represent the number of sensors and the number of time points, respectively. For the first All sensor observations collected at each time point Indicates size is × A real matrix space. This multivariate sensor signal has two dimensions: a time dimension and a variable dimension. In the time dimension, ,in Indicates the first At any point in time The observation vectors of each sensor. In terms of variable dimensions, ,in Indicates the first One sensor in Observation vectors at each time point.

[0057] The sensor signal anomaly detection method of this invention designs a bidirectional fuzzy inference anomaly detection model to detect time-point anomalies in multi-sensor signals under resource-constrained scenarios. First, the anomaly detection model is trained using unlabeled historical multivariate time series (MTS) data collected from multiple industrial sensors. Second, the trained anomaly detection model generates an anomaly score for each test time point, expressed as:

[0058] (1)

[0059] FuKAN represents the designed bidirectional fuzzy inference anomaly detection model. Indicates a point in time Abnormal scores, Indicates the first At any point in time The observation vectors of each sensor. Finally, the anomaly score is compared with a predefined threshold. Compare to determine the point in time. Is it abnormal?

[0060] (2)

[0061] where, is the state label of time point , taking values 1 or 0. represents that time point is identified as abnormal, represents that time point is in normal state.

[0062] The resource-constrained scene bidirectional fuzzy reasoning sensor signal anomaly detection method of the application comprises the following steps:

[0063] Step S1, an abnormality identification mechanism based on "neighbor-global" mode difference learning is formulated.

[0064] In order to effectively identify the time point level anomaly in the multi-element sensor signal under zero label, the application designs an abnormality identification mechanism based on "neighbor-global" context mode difference learning. The mechanism generates the "neighbor-global" mode difference of each time point by analyzing the mode change of each time point in the neighbor context and the global context, so as to accurately distinguish the time point level anomaly in the sensor signal.

[0065] The anomaly in the sensor signal usually lasts for a period of time, that is, across multiple continuously collected time points, and is manifested as a change in the context mode. As shown in Figure 2 , and represent abnormal time points and normal time points respectively. The neighbor context mode around it is obviously inconsistent with its global context mode. On the contrary, due to the driving of physical characteristics such as periodicity / seasonality / trend in normal sensor signals, the neighbor context mode and the global context mode show strong similarity. Therefore, the change of the context mode provides an effective index for detecting the time point level anomaly in the sensor signal under zero label. Based on this principle, the application designs a simple and fast time point level anomaly identification mechanism, as shown in Figure 2As shown in the figure. In this mechanism, multiple adjacent time points of each time point are regarded as neighborhood context, and multiple distant time points are regarded as global context. Then, two shallow networks are employed to perform contrastive learning: one shallow network reconstructs the global context using the neighborhood context as input, and the other shallow network reconstructs the neighborhood context using the global context as input, and the two networks perform contrastive learning to ensure the consistency of the "neighborhood-global" context. Finally, the reconstruction difference of the "neighborhood-global" context in the two networks is taken as the anomaly score of the time point, thereby identifying anomalies under the zero label. Since the architecture of the present application only relies on shallow networks, it can ensure high detection speed and low resource consumption.

[0066] Step S2, constructing an abnormality identification mechanism guided double-layer small-volume Fuzzy-KAN network.

[0067] In order to balance high detection speed, high detection accuracy and low resource consumption in resource-constrained industrial scenarios, under the guidance of the abnormality identification mechanism in step S1, combined with fuzzy reasoning and KAN representation learning theory, the present application constructs a small-volume Fuzzy-KAN network with strong reasoning ability and high interpretability composed of only two layers of structure and a small number of parameters.

[0068] Shallow networks usually have limited and unstable representation and learning ability. To solve this problem, the present application introduces fuzzy reasoning into shallow networks. However, as shown in the figure, the existing fuzzy neural network (FNN) has the following three main problems and cannot be directly applied: (1) deep and complex structure; (2) poor interpretability of reasoning process; (3) repeated mapping between time domain and fuzzy domain results in high computational cost. In order to overcome these problems, the present application designs a small-volume Fuzzy-KAN network with only two layers of structure, reduces the traditional FNN, and introduces KAN learning into the FNN, as shown in the figure. Figure 3 Figure 4

[0069] In this embodiment, the design of the small-volume Fuzzy-KAN network includes the following two aspects:

[0070] (1) The reasoning process is entirely in the fuzzy domain. The traditional FNN needs to first map the time domain data to the fuzzy domain, then perform reasoning in the fuzzy domain, and finally transform the reasoning result back to the time domain. In contrast, the Fuzzy-KAN network first maps the time domain data to the fuzzy domain, then directly performs reasoning in the fuzzy domain, and learns the pattern difference between the input and the output, so that there is no need to map back to the time domain. This simplification reduces the network depth and avoids the computational overhead and instability caused by repeated domain conversion.

[0071] ​​(2) Embedding KAN representation learning in fuzzy inference to improve interpretability. In traditional FNN networks, the fuzzy inference process is a simple product-sum and normalization process of the membership degrees of all inputs in the same fuzzy set, which lacks strong reasoning and interpretability. In contrast, the present application uses a Kolmogorov-Arnold representation learning process as an inference learning process from input membership degrees to output, thereby improving fuzzy inference ability and interpretability.

[0072] In summary, the small-volume Fuzzy-KAN network designed by the present application is composed of two layers of structure and a small number of parameters, as shown in Figure 4 The small-volume network is composed of L input neurons, hidden neurons and output neurons, wherein L and G are the number of input and output values in the time domain, representing the number of neighbors in the neighborhood context and the global context at each time point in the model constructed by the present application, is the number of fuzzy sets in the fuzzy domain. The input neurons and hidden neurons in the network form a fuzzy mapping layer, which is responsible for converting the input values in the time domain into membership degrees in the fuzzy domain. The hidden neurons and output neurons form a fuzzy inference layer, which is responsible for inferring the membership degrees of the output values from the membership degrees of the input values in the fuzzy domain, thereby learning the pattern difference between "input-output". Specifically:

[0073] The fuzzy mapping layer process is as follows: since there are S fuzzy sets in the fuzzy domain, each input neuron will establish 1 mapping link with S fuzzy sets respectively. Therefore, L input neurons will establish S mapping links between fuzzy sets, and hidden neurons and mapping links are finally generated to generate fuzzy membership values. Each mapping link performs the following transformation process from the time domain to the fuzzy domain:

[0074] (3)

[0075] wherein represents the membership degree of the i input neuron in the j fuzzy set, i.e., the value of the i × j hidden neuron, x i is the value of the i input neuron, and the parameters and the mean and variance of the Gaussian membership function of the i-th input neuron to the j-th fuzzy set. i j

[0076] The fuzzy inference layer process is as follows: L S G S Kolmogorov-Arnold representation learning is introduced into the inference process of each link, and linear and nonlinear inference is performed as follows:

[0077] (4)

[0078] wherein, is the KAN inference result of the i-th hidden neuron to the j-th output neuron, is the value of the i-th hidden neuron, and and are the weights of nonlinear learning and linear learning respectively, is a nonlinear activation function used to learn nonlinear features, is a spline function, is the number of basis functions in the spline function, is the i-th basis sample function, and is the weight of the i-th basis spline function. j o j B V v v

[0079] Each output neuron is connected to hidden layer neurons, and KAN inference learning is performed times to generate link inference results. Therefore, the final output value of each output neuron is:

[0080] (5)

[0081] Benefiting from the guidance of the common anomaly recognition mechanism, the small-volume Fuzzy-KAN network directly performs membership inference of "input-output" in the fuzzy set, thereby learning the pattern difference of "input-output", and improving the detection accuracy and stability of the shallow network while ensuring high detection speed and low resource consumption.

[0082] Step S3, constructing a bidirectional fuzzy inference anomaly detection model. ​​​​​​​​​​​​​​​​​​​​​​​​​

[0083] To further increase the detection accuracy, under the guidance of the anomaly recognition mechanism, the bidirectional fuzzy reasoning learning strategy is combined with the four Fuzzy-KAN networks to jointly constitute a bidirectional fuzzy reasoning anomaly detection model, which learns the context pattern difference from "history to future" and "future to history" in the fuzzy domain instead of the time domain.

[0084] As shown in Figure 5 The bidirectional fuzzy reasoning anomaly detection model of the present application is composed of three parts:

[0085] (1) Forward contrast learning based on Fuzzy-KAN network.

[0086] This part uses the first two (first and second) Fuzzy-KAN networks to capture the "neighborhood-universe" context pattern difference in the "history to future" (forward) direction. First, the forward sampling strategy constructs the neighborhood context and the universe context for each time point. Then, the first Fuzzy-KAN network performs membership reasoning from neighborhood to universe in the fuzzy domain, while the other Fuzzy-KAN network performs membership reasoning from universe to neighborhood. Finally, the contrast learning of them produces "neighborhood membership difference + universe membership difference" to quantify the "neighborhood-universe" context pattern change of each time point.

[0087] (2) Reverse contrast learning based on Fuzzy-KAN network.

[0088] As a supplement to the forward process, this part captures the "neighborhood-universe" context pattern difference in the "future to history" (reverse) direction. First, the reverse sampling strategy constructs the reverse neighborhood context and the reverse universe context for each time point. Then, the last two (third and fourth) Fuzzy-KAN networks perform membership reasoning in the fuzzy domain in a contrast learning manner, respectively "universe to neighborhood" and "neighborhood to universe". Finally, the "neighborhood membership difference + universe membership difference" produced by contrast learning is used to represent the reverse context pattern change of each time point.

[0089] (3) Bidirectional joint anomaly scoring.

[0090] Integrate the forward and reverse context pattern differences to calculate the joint anomaly score of each time point.

[0091] The bidirectional fuzzy reasoning anomaly detection model specifically includes the following contents:

[0092] S3-1, forward contrast learning based on Fuzzy-KAN network.

[0093] The first two small-volume Fuzzy-KAN networks are used to construct the forward contrast learning component, as shown inFigure 5 As shown in section (a), this component is used to capture the “neighborhood-global” membership difference from the historical to the future (forward) direction at each time point in the fuzzy domain, as a “neighborhood-global” contextual pattern change. This component consists of four parts: forward sampling, neighborhood-to-global membership inference, global-to-neighborhood membership inference, and contrastive learning.

[0094] S3-1-1, Forward Sampling: To capture changes in contextual patterns, this invention designs a forward (history to future) sampling strategy to generate neighborhood context and global context for each time point. The process is as follows... Figure 6 As shown, the time points on variable 1 Let's take an example to illustrate. First, by starting from... arrive extract A series of consecutive time points are obtained to get the time points. The neighborhood context, denoted as Then, through each Each interval selects a time point and continues... Second choice (from) Beginning, to End), obtain time point The global context, denoted as Neighborhood context and global context are both based only on relative to the context. Historical data was constructed to avoid any risk of data leakage. Their time points are arranged in a forward direction from history to the future. This sampling process... Execution is performed independently on each variable, and parallel execution can be used to improve speed.

[0095] S3-1-2, Neighborhood-to-Global Membership Reasoning: After forward sampling, the first Fuzzy-KAN network is used, taking the neighborhood context as input, to directly perform neighborhood-to-global membership reasoning in the fuzzy domain rather than the temporal domain, thereby capturing the "neighborhood-to-global" contextual pattern changes. This network consists of... One input neuron, Hidden neurons and It consists of 1 output neuron, among which L and G The number of neighbors in the neighborhood context and the global context. S The number of fuzzy sets. Based on the time points of variable 1. For example, the membership inference from the neighborhood to the global domain is as follows:

[0096] ① Fuzzy mapping: time point t The length is L neighborhood context As input, the neighborhood membership vector of each input neuron in the fuzzy domain is generated by the fuzzy mapping layer, with length . Where each input neuron is connected to S fuzzy sets, and each connection employs a trainable Gaussian kernel function as the membership function to calculate its membership in the fuzzy domain:

[0097] (6)

[0098] Where represents the membership of the input neuron in the fuzzy set, is its input value, and parameters and are the trainable mean and variance of its Gaussian membership function, respectively.

[0099] In matrix form, the fuzzy mapping is represented as:

[0100] (7)

[0101] Where is the neighborhood context membership vector in fuzzy sets, and the item represents the Kronecker product, is an all-1 vector, is to copy each element of times to calculate the membership of all fuzzy sets. and are the trainable mean and variance matrices of all membership functions in the first Fuzzy-KAN network, respectively.

[0102] ② Fuzzy reasoning: Neighborhood context membership vector is then passed to the fuzzy reasoning layer, which estimates the global context membership through KAN representation learning. This layer is fully connected, consisting of inputs and outputs. Each connection simultaneously performs an interpretable nonlinear and linear learning process:

[0103] (8)

[0104] Where is the reasoning result of the input neuron to the output neuron, is the input value of the input neuron, ​and These are trainable parameters that are randomly initialized. The function provides a non-linear activation function, while The function is a first-order B-spline function used for linear learning, defined as follows:

[0105]

[0106] (9)

[0107] in, It is weighted The One B-spline basis function, It is the total number of basis functions.

[0108] Combining formulas (8) and (9), we can obtain:

[0109] (10)

[0110] The inference result of the j-th output neuron can be obtained by summing the results of all input neurons:

[0111] (11)

[0112] The reasoning process can be represented in matrix form as follows:

[0113] (12)

[0114] in, These are the trainable parameters for fuzzy inference in the first Fuzzy-KAN network. This is the neighborhood membership vector. This is the global membership vector obtained through reasoning.

[0115] S3-1-3, Global-to-Neighborhood Membership Reasoning: To more accurately capture changes in the "neighborhood-global" contextual pattern, a second Fuzzy-KAN network takes the global context as input and performs global-to-neighborhood membership reasoning in the fuzzy domain, thereby capturing these changes. This network consists of... One input neuron, Hidden neurons and It consists of several output neurons, where the input neurons and hidden neurons form a fuzzy mapping layer, and the hidden neurons and output neurons form a fuzzy inference layer.

[0116] ① Fuzzy mapping: time point t The length is G global context As input, the global membership vector of time point is generated by the fuzzy mapping layer

[0117] (13)

[0118] where are trainable mean and variance matrices of all membership functions in the second Fuzzy-KAN network, respectively.

[0119] 2. Fuzzy inference: When the global membership t of time point is input to this layer, KAN representation learning is employed to infer the neighborhood membership t of time point in the fuzzy domain:

[0120] (14)

[0121] where are trainable parameters for fuzzy inference in the second Fuzzy-KAN network. is the global membership vector, is the inferred neighborhood membership vector.

[0122] S3-1-4. Contrastive learning: The inference processes of the first and second Fuzzy-KAN networks constitute a self-supervised learning environment, so we employ contrastive learning to jointly optimize these two networks. The whole contrastive learning process uses mean square error (MSE) as the loss function, which is defined as:

[0123] (15)

[0124] where and denote the neighborhood membership vectors generated by the first and second Fuzzy-KAN networks, respectively, while and denote the global membership vectors generated by the first and second Fuzzy-KAN networks, respectively, and are the numbers of variables and time points in the sensor signal, respectively.

[0125] The forward contrastive learning processes of variables in the multi-sensor signal are independent of each other and can be executed in parallel, and all variables share the same two Fuzzy-KAN networks (the first and second Fuzzy-KAN networks).

[0126] S3-2. Backward contrastive learning based on Fuzzy-KAN networks.

[0127] The context patterns of sensor signals can be analyzed from two complementary directions: forward (from history to future) and backward (from future to history). For an anomaly that lasts for multiple consecutive time points, its boundary points are often the most difficult to detect. At the starting boundary point of an anomaly, the forward context often does not show a pattern change, but the backward context shows a clear pattern change; conversely, at the ending boundary point of an anomaly, the forward context shows a clear pattern change, but the backward context does not show a clear change.

[0128] To further improve the detection accuracy, the present application uses a third and a fourth small-volume Fuzzy-KAN network to construct a backward contrast learning component, as shown in part (b) of Figure 5 , for capturing the "neighborhood-universe" membership difference in the fuzzy domain from the future to the history (backward) direction at each time point, to complement the forward contrast learning component. This component also contains four parts: backward sampling, neighborhood-to-universe membership reasoning, universe-to-neighborhood membership reasoning, and contrast learning.

[0129] S3-2-1, Backward Sampling: Unlike forward sampling, backward sampling faces a key challenge: potential data leakage, because future data cannot be obtained at the current time point. To solve this problem, the present application designs a backward sampling strategy that only relies on historical data to eliminate the risk of leakage, as shown in Figure 6 . Taking the time point of variable 1 as an example, in the future-to-history direction, the consecutive time points from to form the backward neighborhood context, denoted as . Similarly, in the same direction, every interval selects a time point, and consecutive selections are made, starting from to , to generate the backward universe context, denoted as .

[0130] For time point , the neighborhood and universe contexts in the forward and backward directions contain the same time points, but in reverse order. For example, is the forward neighborhood context (from history to future), while is the backward neighborhood context (from future to history).

[0131] S3-2-2, Neighborhood-to-Global Membership Reasoning: Consistent with the forward learning, the third Fuzzy-KAN network takes the reverse neighborhood context as input, performs neighborhood-to-global membership reasoning from the future to the past, thereby capturing the "neighborhood-global" context pattern change. Take the time point t on variable 1 as an example, the reverse fuzzy reasoning process is as follows:

[0132] ① Fuzzy Mapping: The length of the time point t is L The reverse neighborhood context goes through the fuzzy mapping layer to obtain the neighborhood membership vector in the fuzzy domain :

[0133] (16)

[0134] wherein is the trainable mean and variance matrix of all membership functions in the third Fuzzy-KAN network.

[0135] ② Fuzzy Reasoning: The generated neighborhood membership vector is then input to the fuzzy reasoning layer to estimate the membership vector of the reverse global context using KAN representation learning, and the formula is:

[0136] (17)

[0137] wherein is the trainable parameter of fuzzy reasoning in the third Fuzzy-KAN network.

[0138] S3-2-3, Global-to-Neighborhood Membership Reasoning: Similarly, the fourth Fuzzy-KAN network takes the reverse global context as input to perform global-to-neighborhood membership reasoning. At the time point , the reasoning process for variable 1 is as follows.

[0139] ① Fuzzy Mapping: The length of the time point t is L The reverse global context goes through the fuzzy mapping layer to obtain the global membership vector in the fuzzy domain :

[0140] (18)

[0141] wherein is the trainable mean and variance matrix of all membership functions in the fourth Fuzzy-KAN network.

[0142] ② Fuzzy Reasoning: Then the input is fed into the fuzzy inference layer, where KAN representation learning is used to predict the membership vectors of the reverse neighborhood context in the fuzzy domain :

[0143] (19)

[0144] where, is the trainable parameter of fuzzy inference in the fourth Fuzzy-KAN network.

[0145] S3-2-4, Contrastive Learning: In line with the forward learning, contrastive learning is performed on the third and fourth Fuzzy-KAN networks, with the loss function defined as :

[0146] (20)

[0147] where, and represent the neighborhood membership vectors generated by the third and fourth Fuzzy-KAN networks, respectively, and represent the global membership vectors generated by the third and fourth Fuzzy-KAN networks, respectively.

[0148] S3-3, Bidirectional Joint Anomaly Scoring.

[0149] When the training is complete, the invention designs a bidirectional joint scoring strategy to determine whether the time point to be tested is abnormal, as shown in (c) of Figure 5 For a given time point to be tested , the scoring process is as follows:

[0150] S3-3-1, Forward Scoring Calculation.

[0151] For a time point to be tested containing variables, and its neighborhood context and global context, the forward contrastive learning component will generate N membership contrast differences on variables, with the formula as follows:

[0152] (21)

[0153] where, F represents forward learning, represents the set of forward membership contrast differences for time point t , containing N values.

[0154] Select the top values in The average value of the largest differences defines the forward abnormality score at time point t

[0155] (22)

[0156] S3-3-2, Reverse score calculation.

[0157] The reverse contrast learning component also generates N a variable number of membership contrast differences for the sensor signals , which is formulated as:

[0158] (23)

[0159] wherein B denotes the reverse learning, denotes the set of reverse membership contrast differences at time point t , which contains N values.

[0160] The reverse abnormality score is defined as the average value of the first largest differences , which is formulated as:

[0161] (24)

[0162] S3-3-3, Final score calculation.

[0163] The final abnormality score at time point is defined as the maximum value between the forward score and the reverse score:

[0164] (25)

[0165] Based on this final score, the formula (2) is applied to determine whether the time point under test is abnormal or not.

[0166] Verification experiment:

[0167] Eight publicly available real-world industrial sensor multivariate signal datasets were adopted to evaluate the proposed model, as shown in Table 1. These datasets cover multiple fields such as intelligent manufacturing, industrial control, and Internet of Things, thereby ensuring the diversity and fairness of experimental evaluation.

[0168] Table 1 Eight real-world industrial sensor multivariate signal datasets

[0169]

[0170] ​​In particular, the SKAB dataset provides multivariate sensor signals collected from an industrial testbed. The GECCO dataset contains water quality measurement data acquired from Internet of Things sensors. The PUMP dataset records 51 -dimensional operational data from an industrial pump, while the HAI dataset contains measurement data from pumps, valves, pressure sensors, and other industrial equipment. The WADI dataset provides 127-dimensional monitoring data from a large industrial control system, and the Genesis dataset contains 5 continuous signals and 13 discrete signals from industrial Internet of Things devices. In addition, the SMAP dataset provides telemetry data and soil measurement data from NASA's Mars rover. Finally, the SWAT dataset contains 51 -dimensional sensor data from a water treatment plant testbed.

[0171] Nine representative state-of-the-art (SOTA) models were selected as benchmark models, namely TransDe (2025), NRdetector (2025), KANAD (2025), MGBOD (2025), COUTA (2024), DTAAD (2024), PatchAD (2024), FuzzyIF (2024), and DCdetector (2023). The reasons for selecting these models are twofold. From the perspective of deep and shallow structures: TransDe, NRdetector, DTAAD, PatchAD, DCdetector, and KANAD are deep models with multi-layer architectures and large parameter scales, while MGBOD, COUTA, FuzzyIF, and FuzzyKAN are shallow models with relatively fewer parameters. From the perspective of whether fuzzy domain reasoning is used: MGBOD, FuzzyIF, and FuKAN are models based on fuzzy domain reasoning, while the other models are based on time domain.

[0172] I. Accuracy Experiment

[0173] Six evaluation indicators were used to compare the bidirectional fuzzy reasoning anomaly detection model (abbreviated as FuKAN) of the present application with nine benchmark models on eight real-world industrial sensor multivariate signal datasets.

[0174] (1) Accuracy: Table 2 summarizes the anomaly detection results of ten models on eight datasets, with the best performance in bold and the second best performance underlined. The following observations can be made:

[0175] 1) Overall performance: The FuKAN model of the present invention consistently outperforms the other models, followed by the DCdetector, TransDe, COUTA, PatchAD, and KANAD, while the FuzzyIF, DTAAD, NRdetector, and MGBOD perform the worst. For example, on the SWAT dataset, the accuracy of FuKAN reaches 0.9940, while that of TransDe is 0.9921, KANAD is 0.9899, and COUTA is 0.9630.

[0176] 2) Stability: FuKAN, DCdetector, and TransDe exhibit the most stable performance across all six metrics. Notably, FuKAN ranks first in each metric on SKAB, PUMP, WADI, and SWAT.

[0177] 3) Fuzzy region reasoning: Although the performance of fuzzy region reasoning-based models (FuzzyIF and MGBOD) is inferior to that of time region reasoning models (COUTA and DCdetector), the FuKAN model of the present invention outperforms all baseline models. Its advantage lies in the combination of fuzzy reasoning and KAN representation learning, and further improvement of detection accuracy through bidirectional learning and contrastive learning. For example, on the HAI dataset, the VUS_ROC values are 0.7902 (FuzzyIF), 0.5346 (MGBOD), 0.8928 (DCdetector), 0.9086 (TransDe), and 0.9202 (FuKAN), respectively.

[0178] 4) Shallow architecture: The detection performance of shallow models generally lags behind deep models; however, despite the shallow architecture of FuKAN, its performance is superior to that of deep and shallow benchmark models. On WADI, the VUS_PR of FuKAN reaches 0.9460, significantly higher than that of DCdetector (0.9386), TransDe (0.8006), and NRdetector (0.6139).

[0179] Table 2 Accuracy analysis

[0180]

[0181] (2) Visualization: Figure 7 The abnormality detection results of ten models on the 17th variable of the HAI dataset at 16,500 to 18,000 time points are shown. The black curve represents the true value, and the red curve represents the true / predicted label (peak value represents abnormality, and valley value represents normal state). From the figure, two results can be obtained.

[0182] 1) Accuracy: FuKAN, COUTA, KANAD, DCdetector, and TransDe were highly consistent with the ground truth, successfully detecting anomalies between 16,950 and 17,150 time points. In contrast, the remaining models produced multiple misclassifications, either missing true anomalies or producing false detections.

[0183] 2) False Positives: FuKAN and DCdetector produced significantly fewer false positives than the other models, with the FuKAN model of the present invention performing best overall. For example, FuKAN produced only 7 false positives on normal data, while DCdetector produced 17 false positives and COUTA produced 31 false positives.

[0184] The experimental results demonstrate that the bidirectional fuzzy reasoning anomaly detection model of the present invention achieves superior and stable performance in multivariate sensor signal time point level anomaly detection. Specifically, the model consistently ranks first or second in six evaluation metrics on multiple datasets, outperforming multiple deep models. These findings confirm the effectiveness of the customized Fuzzy-KAN network, bidirectional learning, "neighborhood-global" mode difference learning, and fuzzy domain reasoning in the present invention.

[0185] II. Deployability and timeliness experiments

[0186] To complete the deployability and timeliness experiments, ten models were deployed on a PC, as well as two resource-limited edge devices to perform anomaly detection on the PUMP dataset. The Raspberry Pi 4B is equipped with a 1.5 GHz ARM Cortex-A72 processor and 2 GB of RAM, while the Jetson Xavier NX is equipped with a 6-core Carmel ARMv8.2 processor and 8 GB of RAM.

[0187] (1) Deployability: Figure 8 and Figure 9 The deployment results on the two edge devices are shown, where all models except PatchAD were successfully deployed. Overall, shallow models exhibit higher deployability than deep models on resource-limited industrial devices. In industrial environments where process changes frequently, models must be updated regularly to ensure reliable detection. In this case, shallow models have an advantage because they can be updated directly on edge devices with minimal data and communication overhead, making them more suitable for dynamic industrial environments.

[0188] (2) Timeliness and resource consumption: Table 3 shows the timeliness and resource consumption of the ten models on a PC and two edge devices, where ot represents out-of-memory, summarizing key observations:

[0189] 1) Model parameters: Our FuKAN model is very compact, containing only 8.8K parameters, while COUTA has 121.1K parameters, TransDe has 231.1K parameters, KANAD has 274K parameters, and PatchAD has 1,263.4K parameters. In general, shallow models contain far fewer parameters than deep models.

[0190] 2) Timeliness: Shallow models (FuKAN, FuzzyIF, and COUTA) complete training and testing significantly faster than deep models, except for MGBOD. For example, on a PC with a batch size of 128, FuKAN only takes 16.9 seconds to complete all time point tests, while DCdetector takes 83.1 seconds, and PatchAD takes 168.7 seconds.

[0191] 3) Computational consumption: The CPU and GPU occupancy of shallow models is much lower than that of deep models. On Jetson Xavier NX, FuKAN only occupies 29.2% of the CPU, while DCdetector and TransDe occupy 77.6% and 65.2%, respectively.

[0192] 4) Storage consumption: Deep models require higher memory overhead. On a Raspberry Pi 4B with 2GB of RAM, FuKAN only occupies 199.4MB, while TransDe occupies 451.5MB, and NRdetector occupies 409.8MB.

[0193] Table 3 Timeliness and resource consumption analysis

[0194]

[0195] The experimental results show that the resource-constrained scene bidirectional fuzzy reasoning sensor signal anomaly detection method of the application can be applied and stably operated in resource-constrained industrial scenes under the support of the shallow architecture of the small-volume Fuzzy-KAN network.

[0196] The above implementation cases are only preferred embodiments of the application and do not limit the application in any form. Although the application has been disclosed as above with preferred embodiments, it is not intended to limit the application. Therefore, any simple modification, equivalent change and modification made to the above embodiments without departing from the technical solution of the application, according to the technical essence of the application, should fall within the scope of protection of the technical solution of the application.

Claims

1. A method for sensor signal anomaly detection based on bidirectional fuzzy reasoning in a resource-constrained scenario, characterized in that, The application relates to an abnormality identification mechanism based on a "neighbor-global" mode difference learning method. The application relates to a double-layer small-size Fuzzy-KAN network guided by the abnormality identification mechanism. The application relates to a bidirectional fuzzy reasoning abnormality detection model constructed by combining a bidirectional learning strategy and four parallel Fuzzy-KAN networks. The model performs "neighbor-global" context mode difference learning in a fuzzy domain from "history to future" and "future to history" directions to identify time point level abnormalities in multi-sensor signals under zero labels. The abnormality identification mechanism based on the "neighbor-global" mode difference learning method uses the periodic / seasonal characteristics of normal sensor signals to drive the "neighbor" and "global" context modes of each time point to be similar in physical properties, generates a "neighbor" context composed of multiple local neighbors and a "global" context composed of multiple remote neighbors for each time point in the sensor signals, learns the mode difference between the two contexts through a neural network, and judges the time points with large mode differences as abnormal. The small volume Fuzzy-KAN network is composed of one input neuron, one hidden neuron and one output neuron, wherein and respectively represent the number of neighbors in the neighborhood and global context, is the number of fuzzy sets in the fuzzy domain, the input neuron and the hidden neuron constitute a fuzzy mapping layer, and the hidden neuron and the output neuron constitute a fuzzy reasoning layer, the fuzzy mapping layer is responsible for converting the time domain context data into fuzzy domain membership, the fuzzy reasoning layer is responsible for "neighborhood-global" fuzzy membership reasoning and learning the "neighborhood-global" context mode difference; The bidirectional fuzzy reasoning abnormality detection model is composed of three parts. Forward contrast learning based on the Fuzzy-KAN network, two Fuzzy-KAN networks are used to capture the "neighbor-global" context mode difference of each time point in the fuzzy domain from the forward direction of "history to future". Reverse contrast learning based on the Fuzzy-KAN network, as a supplement to the forward process, another two Fuzzy-KAN networks are used to capture the "neighbor-global" context mode difference in the fuzzy domain from the reverse direction of "future to history". Bidirectional joint abnormality scoring, the context mode differences of the forward and reverse directions are integrated to calculate the joint abnormality score of each time point.

2. The method of claim 1, wherein, The "history to future" forward contrast learning includes four parts: forward sampling, neighborhood to global membership reasoning, global to neighborhood membership reasoning and contrast learning.

3. The method of claim 2, wherein, In the aforementioned "history to future" forward sampling, firstly, by starting from... Extract to t Each consecutive time point is used as the neighborhood context of time point t, and then, through each Each interval selects a time point and continues... The second choice, that is, from Starting from point t and ending at point t, we obtain the global context at time point t. The neighborhood context and global context are constructed based on historical data relative to t, with time points arranged in a forward order.

4. The method of claim 3, wherein, In the neighborhood to global membership reasoning, after forward sampling, a Fuzzy-KAN network is used to capture the context mode difference in the fuzzy domain. Each of the L neighbors in the neighborhood context of each time point is taken as input, S fuzzy sets are generated for each input, S membership degrees are generated, time domain to fuzzy domain mapping is realized, a neighborhood context membership vector in the fuzzy domain is obtained, and the size of the vector is LXS. The neighborhood context membership vector is transmitted to the fuzzy reasoning layer, a global context membership vector is inferred through KAN representation learning, the size of the vector is GXS, and neighborhood to global membership reasoning is completed.

5. The method of claim 4, wherein, In the global-to-neighborhood membership reasoning, another Fuzzy-KAN network is used to perform global-to-neighborhood membership reasoning in the fuzzy domain with global context as input; G neighbors in the global context generate a global context membership vector through a fuzzy mapping layer, with a size of GxS, and the global membership vector is input into a fuzzy reasoning layer to infer a neighborhood context membership vector with a size of LxS through KAN representation learning.

6. The method of claim 1, wherein, The "future-to-history" reverse contrast learning includes four parts: reverse sampling, neighborhood-to-global membership reasoning, global-to-neighborhood membership reasoning, and contrast learning, specifically: first, the reverse sampling strategy first constructs a reverse neighborhood context and a reverse global context for each time point; then, two Fuzzy-KAN networks perform global-to-neighborhood and neighborhood-to-global membership reasoning in the fuzzy domain in a contrast learning manner; finally, the results of the two membership reasonings are compared to generate a membership difference, representing the reverse context pattern change at each time point.

7. The method of claim 1, wherein, In the bidirectional joint anomaly scoring, after the forward and reverse contrast learning is completed, for a given time point t to be tested, the scoring process is as follows: S3-3-1, forward score calculation: For a time point t of a sensor signal to be tested comprising variables, and its neighborhood context and global context, the forward contrast learning component generates membership contrast differences, the membership contrast difference for each variable being the sum of the global and neighborhood membership differences, the top maximal differences among the membership contrast differences are selected, the average of which defines the forward anomaly score; S3-3-2, reverse score calculation: The reverse contrast learning component also produces membership contrast differences for the N variables of the sensor signal, selects the top membership contrast difference, and an average of the top membership contrast differences is defined as the reverse anomaly score. S3-3-3, final score calculation: The anomaly score of time point t is defined as the maximum of the forward score and the reverse score, and the anomaly score is compared with a predefined threshold to determine whether the time point t to be tested is abnormal.

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