Sensor initial drift fault online diagnosis method based on width neural network

Abstract

The invention discloses a sensor initial drift fault online diagnosis method based on a width neural network, relates to the technical field of data-driven fault diagnosis, and is directly applied to the field of sewage treatment. On the premise of considering the initial characteristics of the drift fault, a width neural network structure composed of a Fourier-based feature extraction layer, a gating attention enhancement layer and an output layer is designed, and the robustness and the initial fault diagnosis capability of the model are effectively improved. Meanwhile, enhanced nodes can be dynamically added to the network, the diagnosis precision is improved, the time cost is low, the problem that the sensor drift fault is difficult to diagnose timely and accurately at the initial stage in the sewage treatment process is solved, and safe and reliable operation of a sewage treatment plant is ensured.

Description

Technical Field

[0001] The present invention is an online diagnosis method for initial drift fault of a sensor based on a wideband neural network, aiming to realize online diagnosis of initial drift fault of a sensor in a sewage treatment process, including detecting the time of occurrence of the fault and locating the faulty sensor. Background Art

[0002] Sensors are an indispensable tool for evaluating the operation of the sewage treatment process, and their reliability is a prerequisite for ensuring the safety of sewage treatment plants and the quality of effluent water. However, due to environmental conditions such as high temperature, humidity, corrosion, and improper installation and maintenance, sensors are prone to failure. Sensor failures can be divided into the following categories: drift failure, deviation failure, accuracy degradation failure, spike failure, and stuck failure. Among them, drift failure is one of the most common types, which is characterized by slow and gradual changes over time. As drift failure develops, data will be significantly distorted, resulting in catastrophic effects such as control failure and substandard effluent water quality. However, major failures usually do not occur suddenly, but evolve from incipient failures. Incipient failure refers to the first change point when the sensor begins to deteriorate. Detecting the early stage of drift failure helps to take compensatory measures in time and control the severity of the failure. Therefore, timely and accurate detection of the occurrence of incipient drift failures and locating the faulty sensor are crucial to ensure the safe operation of sewage treatment plants.

[0003] At present, the early diagnosis of drift faults is still a major challenge. First, given the complex characteristics of the sewage treatment process, such as nonlinearity, strong coupling, and high time variation, the drift fault diagnosis of sensors is challenging. Secondly, the sewage treatment process data usually contains noise, which is characterized by occasional spikes or dips in the data, while the initial drift fault changes are weak. Therefore, it is difficult to distinguish between faults and noise, which can easily lead to missed diagnosis or misdiagnosis. Therefore, the present invention proposes an online diagnosis method for initial drift faults of sensors based on a wide neural network to achieve initial fault diagnosis of sensors in the sewage treatment process. Summary of the invention

[0004] The present invention proposes an online diagnosis method for sensor initial drift fault based on wide neural network, and realizes the diagnosis of multi-sensor initial drift fault in the presence of noise according to the data collected in the actual sewage treatment process. The present invention can not only handle the nonlinearity and dynamics in the process, but also has a simple network structure, fast update speed, high detection accuracy, and can realize online monitoring of sensors in the sewage treatment process.

[0005] The present invention proposes an online diagnosis method for sensor initial drift fault based on a wide neural network. The algorithm includes the following steps:

[0006] A method for online diagnosis of sensor initial drift fault based on wideband neural network, characterized by comprising the following steps:

[0007] Step 1: Establish a feature layer based on Fourier filter;

[0008] Step 1.1: At time t, the input is composed of an m-dimensional sample vector x(t) = [x 1 (t),…,x m (t)] T Representation; at the same time, the entire sample sequence is input into the feature layer based on Fourier filter through the sliding window mechanism, and the sample sequence is described as:

[0009]

[0010] Among them, m represents the sample dimension, T 0 Represents the sliding window size, a positive integer in the range of [5,30]; represents the field of real numbers;

[0011] Step 1.2: Using discrete Fourier transform, transform the i-th dimension into the sequence f i (t) Convert to the frequency domain and obtain the i-th frequency domain component F i (t) As shown in formula (2):

[0012]

[0013] Where F{} represents discrete Fourier transform, m represents the sample dimension, and each dimension of data is transformed by formula (2) to obtain the overall frequency component F(t) as shown in formula (3):

[0014]

[0015] in, represents the field of real numbers;

[0016] Step 1.3: Construct a Fourier-based characteristic filter R(t), as shown in formula (4):

[0017]

[0018] Among them, w(r) is the weight of the filter, r∈[1,L] is the row number of the filter, represents the field of real numbers, is the identity matrix, is an all-zero matrix, L represents the number of rows of the filter, and is calculated by formula (5):

[0019] L=η×T 0 (5)

[0020] Where η is the filtering rate, and its value range is (0,1); the output signal of the filter is shown in formula (6):

[0021]

[0022] Among them, F′(t) represents the sample after filtering at time t;

[0023] Step 1.4: Reconstruct each dimension of F′(t) in the time domain by inverse discrete Fourier transform, as shown in formula (7)

[0024]

[0025] in, stands for discrete Fourier transform, F i ′(t) represents the i-th dimension of F′(t), f i '(t) represents the i-th dimension of the data reconstructed in the time domain; furthermore, all dimensions of the sample are reconstructed in the time domain, expressed as formula (8):

[0026]

[0027] Where f′(t) represents the data matrix reconstructed in the time domain, and x′(t) represents the sample denoised by the Fourier eigenfilter at time t;

[0028] Step 1.5: Perform feature mapping on f′(t) and establish n groups of feature nodes, as shown in formula (9):

[0029]

[0030] Among them, Z j represents the jth group of feature nodes, n represents the number of feature node groups; φ is the feature mapping function, and is the weight and bias of the randomly generated feature layer; then the total output of the feature layer based on the Fourier filter is the total feature node Z n It can be expressed as Z n ≡[Z 1 ,Z 2 …,Z n ];

[0031] Step 2: Establish a gated attention enhancement layer;

[0032] Step 2.1: By mapping feature node Z n Get v groups of enhanced nodes, as shown in formula (10):

[0033]

[0034] Among them, H urepresents the u-th group of enhanced nodes, v represents the number of enhanced node groups, ξ is the activation function Tanh function, and are the randomly generated weights and biases of the enhancement layer;

[0035] Step 2.2: Define the gated attention function W AGA Formula (11):

[0036]

[0037] Among them, τ represents the normalization function, dct represents discrete cosine transform, and γ is a parameter used to adjust the decay rate;

[0038] Step 2.3: Define the uth group of gated enhancement nodes H u ' is formula (12):

[0039] H u '=W AGA ·H u ,u=1,2,…,v (12)

[0040] Define the total output of the gated attention enhancement layer, i.e., all gated enhancement nodes, as H v ≡[H′ 1 ,H′ 2 …,H′ v ];

[0041] Step 3: Establish the output layer;

[0042] Step 3.1: The feature layer Z based on the Fourier filter n With the gated attention enhancement layer H v Connect to form a new state matrix

[0043]

[0044] Step 3.2: Use ridge regression training to obtain the state matrix The connection weights to the output layer

[0045] Step 3.2.1: Input the label vector Y and define the smoothed label vector Y′ as formula (14):

[0046]

[0047] Among them, α is the label smoothing parameter, and its value range is (0,1); Y i,j ' and Y i,j Represent the i-th row and j-th column elements of the smoothed label Y′ and the original label vector Y respectively;

[0048] Step 3.2.2: Construct the objective function as shown in formula (15):

[0049]

[0050] Among them, the first term is the regularization term, λ is the regularization parameter, and its value range is [10 -10 ,10 -1 ]; the second term is the least squares error term;

[0051] Step 3.2.3: By making equation (15) about The derivative of is equal to 0, and the optimal connection weight can be solved as formula (16):

[0052]

[0053] Where I is the identity matrix; the state matrix The Moose-Penrose generalized quasi-matrix for:

[0054]

[0055] therefore,

[0056] Step 3.2.4: Get the network output label s(t) at time t:

[0057]

[0058] Among them, m represents the sample dimension;

[0059] Step 3.2.5: Store the weight parameters in each sliding window

[0060] Step 4: Online testing;

[0061] Step 4.1: Use the sliding window to input the test samples in sequence, calculate the cosine similarity between the test samples and the training samples in each window, and use the weight parameter corresponding to the training sample with the largest similarity Conduct testing;

[0062] Step 4.2: Repeat step 4.1 until all test samples are slid to obtain the network output label. If the label is 0, it means there is no sensor fault, 1 means the first sensor fault, and so on, the fault diagnosis is preliminarily completed;

[0063] Step 5: When the initial diagnosis accuracy does not meet the requirements, add d additional enhanced nodes for incremental learning training, where d represents the number of additional enhanced nodes, and the trial-and-error method is used to select any positive integer;

[0064] Step 5.1: Define additional enhancement node H ν+1 for:

[0065]

[0066] Among them, ξ is the activation function Tanh function, and are randomly set weights and biases;

[0067] Step 5.2: Repeat steps 2.2 to 2.3 to obtain additional gated enhancement nodes H ν+1 ';

[0068] Step 5.3: Convert the state matrix With additional gate enhancement node H ν+1 'Connect to get a new extended state matrix As shown in formula (20):

[0069]

[0070] Step 5.4: Calculate new connection weights according to Greville's theorem As shown in formula (21):

[0071]

[0072] Among them, the transformation matrix B T , difference term C, and projection term D are defined as:

[0073]

[0074] Among them, C + and Represent the difference term C and the state matrix respectively of pseudo-rebellion;

[0075] Step 5.5: Get the network output label:

[0076]

[0077] Among them, m represents the sample dimension;

[0078] Step 5.6: Store the weight parameters in each sliding window after incremental learning

[0079] Step 5.7: Calculate the incremental learning training accuracy;

[0080] Step 5.8: Repeat steps 5.1 to 5.7 until the training accuracy decreases or remains unchanged;

[0081] Step 6: Incremental learning test;

[0082] Step 6.1: Use the sliding window to input the test samples one by one, and use the weight parameters updated incrementally Conduct testing;

[0083] Step 6.2: Get the network output label. If the label is 0, it means there is no sensor failure, 1 means the first sensor failure, and so on.

[0084] Step 6.3: Calculate the fault diagnosis accuracy and complete the fault diagnosis; the sliding window size T in the above steps is 0 , the filtering rate η, the parameter Υ used to adjust the decay rate, the label smoothing parameter α, and the regularization parameter λ can be determined by grid searching within the value range and selecting the corresponding parameter with the highest fault diagnosis accuracy.

[0085] Compared with the prior art, the present invention has the following obvious advantages and beneficial effects:

[0086] The present invention utilizes Fourier filters to attenuate low-frequency signals and remove high-frequency noise signals, thereby improving the robustness of the model from a frequency domain perspective. Secondly, a gated attention enhancement layer is designed based on the initial characteristics of drift faults to improve the detectability of initial faults from a time domain perspective. In addition, the label smoothing mechanism can effectively prevent model overfitting and improve model classification performance. Finally, by dynamically enhancing nodes, the model structure can be adjusted online to improve the model diagnostic performance. Therefore, the present invention has the technical advantages of being robust to noise, having high diagnostic accuracy, being adaptable to dynamic processes, having fast learning speed, and having strong interpretability. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 is a network structure diagram of the present invention;

[0088] Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0089] The present invention obtains an online diagnosis method for sensor initial drift fault based on wide neural network, realizes accurate diagnosis of sensor initial drift fault according to data collected in actual sewage treatment process, accurately detects fault occurrence time online and locates faulty sensor, reduces safety risks and economic losses in sewage treatment process;

[0090] The experimental data comes from 2309 sets of samples from a sewage treatment plant in Beijing, China from April to November 2021. The sensor variables selected include (1) inlet ammonia nitrogen, (2) inlet flow, (3) effluent BOD, and (4) effluent COD. The data are rounded and divided into 5 groups. A 5-fold cross-validation is performed. 4 groups are selected for training and 1 group for testing. In each group, drift faults with drift rates of -10%, -5%, +5%, and +10% are added to each variable in turn. The specific fault settings are shown in Table 1;

[0091] Table 1 Fault settings

[0092] Serial number Sensor Status Proportion Drift rate 0 normal 0.6 0 1 Outlet COD fault 0.1 -10％，-5％，+5％，+10％ 2 Ammonia nitrogen fault in outlet water 0.1 -10％，-5％，+5％，+10％ 3 Inlet water PH fault 0.1 -10％，-5％，+5％，+10％ 4 Inlet COD fault 0.1 -10％，-5％，+5％，+10％

[0093] Step 1: Establish a feature layer based on Fourier filter;

[0094] Step 1.1: At time t, the input is composed of an m-dimensional sample vector x(t) = [x 1 (t),…,x m (t)] T Representation; at the same time, the entire sample sequence is input into the feature layer based on Fourier filter through the sliding window mechanism, and the sample sequence is described as:

[0095]

[0096] Among them, m represents the sample dimension, T 0 Represents the sliding window size, which is 5 in this example; represents the field of real numbers;

[0097] Step 1.2: Using discrete Fourier transform, transform the i-th dimension into the sequence f i (t) Convert to the frequency domain and obtain the i-th frequency domain component F i (t) As shown in formula (2):

[0098]

[0099] in, Represents discrete Fourier transform, m represents the sample dimension, in this example m is 4, each dimension of data is transformed by formula (2) to obtain the overall frequency component F(t) as shown in formula (3):

[0100]

[0101] in, represents the field of real numbers;

[0102] Step 1.3: Construct a Fourier-based characteristic filter R(t), as shown in formula (4):

[0103]

[0104] Among them, w(r) is the weight of the filter, r∈[1,L] is the row number of the filter, represents the field of real numbers, is the identity matrix, is an all-zero matrix, L represents the number of rows of the filter, and is calculated by formula (5):

[0105] L=η×T 0 (5)

[0106] Wherein, η is the filtering rate, which is 0.7 in this example; the output signal of the filter is shown in formula (6):

[0107]

[0108] Among them, F′(t) represents the filtered sample at time t.

[0109] Step 1.4: Reconstruct each dimension of F′(t) in the time domain by inverse discrete Fourier transform, as shown in formula (7):

[0110]

[0111] in, stands for discrete Fourier transform, F i ′(t) represents the i-th dimension of F′(t), f i '(t) represents the i-th dimension of the data reconstructed in the time domain; furthermore, all dimensions of the sample are reconstructed in the time domain, expressed as formula (8);

[0112]

[0113] Where f′(t) represents the data matrix reconstructed in the time domain, and x′(t) represents the sample denoised by the Fourier eigenfilter at time t;

[0114] Step 1.5: Perform feature mapping on f′(t) and establish n groups of feature nodes, as shown in formula (9):

[0115]

[0116] Among them, Z j represents the jth group of feature nodes, n represents the number of feature node groups, which is 10 in this example, and φ is the feature mapping function. and is the weight and bias of the randomly generated feature layer; then the total output of the feature layer based on the Fourier filter is the total feature node Z n It can be expressed as Z n ≡[Z 1 ,Z 2 …,Z n ];

[0117] Step 2: Establish a gated attention enhancement layer;

[0118] Step 2.1: By mapping feature node Z n Get v groups of enhanced nodes, as shown in formula (10):

[0119]

[0120] Among them, H u represents the u-th group of enhanced nodes, v represents the number of enhanced node groups, which is 1 in this example, ξ is the activation function Tanh function, and are the randomly generated weights and biases of the enhancement layer;

[0121] Step 2.2: Define the gated attention function W AGA Formula (11):

[0122]

[0123] Among them, τ represents the normalization function, dct represents discrete cosine transform, and γ is a parameter used to adjust the decay rate, which is 0.25 in this example;

[0124] Step 2.3: Define the uth group of gated enhancement nodes H u ' is formula (12):

[0125] H u '=W AGA ·H u ,u=1,2,…,v (12)

[0126] Define the total output of the gated attention enhancement layer, i.e., all gated enhancement nodes, as H v ≡[H′ 1 ,H′ 2 …,H′ v ];

[0127] Step 3: Establish the output layer;

[0128] Step 3.1: The feature layer Z based on the Fourier filter n With the gated attention enhancement layer H v Connect to form a new state matrix

[0129]

[0130] Step 3.2: Use ridge regression training to obtain the state matrix The connection weights to the output layer

[0131] Step 3.2.1: Input the label vector Y and define the smoothed label vector Y′ as formula (14):

[0132]

[0133] Among them, α is the label smoothing parameter, which is 0.1 in this example; Y i,j ' and Y i,j Represent the i-th row and j-th column elements of the smoothed label Y′ and the original label vector Y respectively;

[0134] Step 3.2.2: Construct the objective function as shown in formula (15):

[0135]

[0136] The first term is the regularization term, and λ is the regularization parameter. In this example, it is set to 10. -8 ; The second term is the least squares error term;

[0137] Step 3.2.3: By making equation (15) about The derivative of is equal to 0, and the optimal connection weight can be solved as formula (16):

[0138]

[0139] Where I is the identity matrix; the state matrix The Moose-Penrose generalized quasi-matrix for:

[0140]

[0141] therefore,

[0142] Step 3.2.4: Get the network output label s(t) at time t:

[0143]

[0144] Among them, m represents the sample dimension;

[0145] Step 3.2.5: Store the weight parameters in each sliding window

[0146] Step 4: Online testing;

[0147] Step 4.1: Use the sliding window to input the test samples in sequence, calculate the cosine similarity between the test samples and the training samples in each window, and use the weight parameter corresponding to the training sample with the largest similarity Conduct testing;

[0148] Step 4.2: Repeat step 4.1 until all test samples are slid to obtain the network output label. If the label is 0, it means there is no sensor fault, 1 means the first sensor fault, and so on, the fault diagnosis is preliminarily completed;

[0149] Step 4.3: Define the following evaluation indicators to evaluate the test results;

[0150] ①SN=the number of sampling points where the method detects the initial fault after the actual fault occurs;

[0151] ② False alarm rate FAR = FP / (FP+TN);

[0152] ③ Missing alarm rate MAR = FN / (TP+FN);

[0153] ④Accuracy ACC = (TP + TN) / (TP + FN + TN + FP);

[0154] Among them, TP, TN, FP, and FN represent the number of true positive cases, true negative cases, false positive cases, and false negative cases, respectively; Table 2 is the preliminary fault diagnosis result of the present invention;

[0155] Table 2 Preliminary fault diagnosis results of the present invention at different fault rates

[0156]

[0157]

[0158] Step 5: When the initial diagnosis accuracy does not meet the requirements, add d additional enhancement nodes for incremental learning training, where d represents the number of additional enhancement nodes, and in this example, 10 is used.

[0159] Step 5.1: Define additional enhancement node H ν+1 for:

[0160]

[0161] Among them, ξ is the activation function Tanh function, and are randomly set weights and biases;

[0162] Step 5.2: Repeat steps 2.2 to 2.3 to obtain additional gated enhancement nodes H ν+1 ';

[0163] Step 5.3: Convert the state matrix With additional gate enhancement node H ν+1 'Connect to get a new extended state matrix As shown in formula (20):

[0164]

[0165] Step 5.4: Calculate new connection weights according to Greville's theorem As shown in formula (21):

[0166]

[0167] Among them, the transformation matrix B T , difference term C, and projection term D are defined as:

[0168]

[0169] Among them, C + and Represent the difference term C and the state matrix respectively of pseudo-rebellion;

[0170] Step 5.5: Get the network output label:

[0171]

[0172] Among them, m represents the sample dimension;

[0173] Step 5.6: Store the weight parameters in each sliding window after incremental learning

[0174] Step 5.7: Calculate the incremental learning training accuracy;

[0175] Step 5.8: Repeat steps 5.1 to 5.7 until the training accuracy decreases or remains unchanged;

[0176] Step 6: Incremental learning test;

[0177] Step 6.1: Use the sliding window to input the test samples one by one, and use the weight parameters updated incrementally Conduct testing;

[0178] Step 6.2: Get the network output label. If the label is 0, it means there is no sensor failure, 1 means the first sensor failure, and so on.

[0179] Step 6.3: Calculate the fault diagnosis accuracy and complete the fault diagnosis;

[0180] The test results of incremental learning are shown in Table 3. The test results of incremental learning show that the present invention successfully achieves zero-delay diagnosis of initial drift faults with a shorter retraining time through incremental learning, while maintaining a low false alarm rate and missed alarm rate, as well as a high diagnostic accuracy;

[0181] Table 3 Fault diagnosis results of the present invention before and after incremental learning at different fault rates

[0182]

[0183] In order to verify the effectiveness of each component, a series of ablation experiments are conducted to verify the effectiveness of the proposed method. The experimental results are shown in Table 4, where FEBNN is the method of the present invention, FEBLS is the method of the present invention to remove label smoothing, FLBLS is the method of the present invention to remove the gated attention mechanism, ELBLS is the method of the present invention to remove the Fourier filter-based method, FBLS is the method of the present invention to retain only the Fourier filter-based method, EBLS is the method of the present invention to retain only the gated attention mechanism, LBLS is the method of the present invention to retain only label smoothing, and BLS is the basic width learning system. The experimental results show that the present invention has the best diagnostic performance and can achieve delay-free detection of initial drift faults; in addition, each component of the present invention has an improvement effect on the overall performance;

[0184] Table 4 Ablation test results under different drift failure rates

[0185]

[0186]

Claims

1. A method for online diagnosis of sensor initial drift fault based on wide neural network, characterized in that: The following steps are involved: Step 1: Establish a feature layer based on Fourier filter; Step 1.1: At time t, the input is an m-dimensional sample vector x(t) = [x1(t),…,x m (t)] T Representation; at the same time, the entire sample sequence is input into the feature layer based on Fourier filter through the sliding window mechanism, and the sample sequence is described as: Where m represents the sample dimension, T0 represents the sliding window size, and the value range is a positive integer [5,30]; represents the field of real numbers; Step 1.2: Using discrete Fourier transform, transform the i-th dimension into the sequence f i (t) Convert to the frequency domain and obtain the i-th frequency domain component F i (t) As shown in formula (2): in, Represents discrete Fourier transform, m represents the sample dimension, and each dimension of data is transformed by formula (2) to obtain the overall frequency component F(t) as shown in formula (3): in, represents the field of real numbers; Step 1.3: Construct a Fourier-based characteristic filter R(t), as shown in formula (4): Among them, w(r) is the weight of the filter, r∈[1,L] is the row number of the filter, represents the field of real numbers, is the identity matrix, is an all-zero matrix, L represents the number of rows of the filter, and is calculated by formula (5): L=η×T0 (5) Where η is the filtering rate, and its value range is (0,1); the output signal of the filter is shown in formula (6): Among them, F′(t) represents the sample after filtering at time t; Step 1.4: Reconstruct each dimension of F′(t) in the time domain by inverse discrete Fourier transform, as shown in formula (7): in, stands for discrete Fourier transform, F′ i (t) represents the i-th dimension of F′(t), f′ i (t) represents the i-th dimension of the data reconstructed in the time domain; furthermore, all dimensions of the sample are reconstructed in the time domain, expressed as formula (8): Where f′(t) represents the data matrix reconstructed in the time domain, and x′(t) represents the sample denoised by the Fourier eigenfilter at time t; Step 1.5: Perform feature mapping on f′(t) and establish n groups of feature nodes, as shown in formula (9): Among them, Z j represents the jth group of feature nodes, n represents the number of feature node groups; φ is the feature mapping function, and is the weight and bias of the randomly generated feature layer; then the total output of the feature layer based on the Fourier filter is the total feature node Z n Represented as Z n ≡[Z1,Z2…,Z n ]; Step 2: Establish a gated attention enhancement layer; Step 2.1: By mapping feature node Z n Get v groups of enhanced nodes, as shown in formula (10): Among them, H u represents the u-th group of enhanced nodes, v represents the number of enhanced node groups, ξ is the activation function Tanh function, and are the randomly generated weights and biases of the enhancement layer; Step 2.2: Define the gated attention function W AGA Formula (11): Among them, τ represents the normalization function, dct represents discrete cosine transform, is a parameter used to adjust the decay rate; Step 2.3: Define the uth group of gated enhancement nodes H u ' is formula (12): H u '=W AGA ·H u ,u=1,2,…,v (12) Define the total output of the gated attention enhancement layer, i.e., all gated enhancement nodes, as H v ≡[H′1,H′2…,H′ v ]; Step 3: Establish the output layer; Step 3.1: The feature layer Z based on the Fourier filter n With the gated attention enhancement layer H v Connect to form a new state matrix Step 3.2: Use ridge regression training to obtain the state matrix The connection weights to the output layer Step 3.2.1: Input the label vector Y and define the smoothed label vector Y′ as formula (14): Among them, α is the label smoothing parameter, and its value range is (0,1); Y i,j ' and Y i,j Represent the i-th row and j-th column elements of the smoothed label Y′ and the original label vector Y respectively; Step 3.2.2: Construct the objective function as shown in formula (15): Among them, the first term is the regularization term, λ is the regularization parameter, and its value range is [10 -10 ,10 -1 ]; the second term is the least squares error term; Step 3.2.3: By making equation (15) about The derivative of is equal to 0, and the optimal connection weight is solved as formula (16): Where I is the identity matrix; the state matrix The Moose-Penrose generalized quasi-matrix for: therefore, Step 3.2.4: Get the network output label s(t) at time t: Among them, m represents the sample dimension; Step 3.2.5: Store the weight parameters in each sliding window Step 4: Online testing; Step 4.1: Use the sliding window to input the test samples in sequence, calculate the cosine similarity between the test samples and the training samples in each window, and use the weight parameter corresponding to the training sample with the largest similarity Conduct testing; Step 4.2: Repeat step 4.1 until all test samples are slid to obtain the network output label. If the label is 0, it means there is no sensor fault, 1 means the first sensor fault, and so on, the fault diagnosis is preliminarily completed; Step 5: When the initial diagnosis accuracy does not meet the requirements, add d additional enhanced nodes for incremental learning training, where d represents the number of additional enhanced nodes, and the trial-and-error method is used to select any positive integer; Step 5.1: Define additional enhancement node H ν+1 for: Among them, ξ is the activation function Tanh function, and are randomly set weights and biases; Step 5.2: Repeat steps 2.2 to 2.3 to obtain additional gated enhancement nodes H ν+1 '; Step 5.3: Convert the state matrix With additional gate enhancement node H ν+1 'Connect to get a new extended state matrix As shown in formula (20): Step 5.4: Calculate new connection weights according to Greville's theorem As shown in formula (21): Among them, the transformation matrix B T , difference term C, and projection term D are defined as: Among them, C + and Represent the difference term C and the state matrix respectively of pseudo-rebellion; Step 5.5: Get the network output label: Among them, m represents the sample dimension; Step 5.6: Store the weight parameters in each sliding window after incremental learning Step 5.7: Calculate the incremental learning training accuracy; Step 5.8: Repeat steps 5.1 to 5.7 until the training accuracy decreases or remains unchanged; Step 6: Incremental learning test; Step 6.1: Use the sliding window to input the test samples one by one, and use the weight parameters updated incrementally Conduct testing; Step 6.2: Get the network output label. If the label is 0, it means there is no sensor failure, 1 means the first sensor failure, and so on. Step 6.3: Calculate the fault diagnosis accuracy and complete the fault diagnosis; the sliding window size T0, the filter rate η, the parameter Υ for adjusting the attenuation rate, the label smoothing parameter α, and the regularization parameter λ in the above steps are determined by grid searching within the value range and selecting the corresponding parameters with the highest fault diagnosis accuracy.

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