Straddle type monorail train gearbox fault detection method based on data enhancement strategy

Abstract

The invention discloses a straddle type monorail train gearbox fault detection method based on a data enhancement strategy. The method comprises the steps that straddle type monorail train gearbox data is input into a trained fault detection model, and a predicted fault label is output; the training step of the fault detection model comprises the steps of expanding actually measured fault data based on a continuous variable mode decomposition algorithm; training a 1D MOPGAN model through the preliminary expansion sample and the health data; inputting the health data into a generator of the trained 1D MOPGAN model, and outputting virtual fault data; taking the generated virtual fault data and health data as a training set of a fault detection model; and training the fault detection model through the training set until the model converges or reaches the maximum number of iterations. According to the invention, the problem of small samples caused by various gearbox fault types and difficulty in data acquisition can be solved, so that the accuracy and reliability of fault detection of the gearbox of the straddle type monorail train are improved.

Description

Technical Field

[0001] The present invention relates to the field of Internet big data and fault detection, and in particular to a straddle-type monorail train gearbox fault detection method based on a data enhancement strategy. Background Art

[0002] Compared with traditional subways, straddle-type monorail trains are special urban rail transit systems. Their tracks are suspended on elevated structures, and they do not require underground tunnels. They are more adaptable to different terrains and reduce dependence on urban land. Gearboxes, as core components of the monorail transmission system, need to cope with tasks such as frequent starts and stops and high-speed and heavy loads. They often operate in harsh working environments, which inevitably lead to aging and various damages of their components, increasing the risk of failures. Effective fault detection technology can detect faults and assess fault levels early, thereby reducing the risk of urban rail transit safety issues and economic losses caused by faults, and reducing the operating and maintenance costs of equipment. It is of great significance to ensure the reliable operation and long-term economic benefits of straddle-type monorail trains.

[0003] In the field of mechanical equipment fault diagnosis, early signal processing-based fault diagnosis methods usually require strong expert knowledge and manually analyze signals to obtain equipment detection results. As equipment structures and components become increasingly complex, the collected signals contain more components and interference, which poses a great challenge to signal processing technology. With the development of computer science, data-driven intelligent fault diagnosis technology has also emerged. Unlike traditional fault diagnosis methods that require expert experience or manual feature extraction, intelligent fault detection technology can train fault detection models using equipment monitoring data to establish an effective mapping between measurement signals and equipment health status, thereby completing equipment health status maintenance.

[0004] Recently, with the gradual maturity and diversification of deep learning, its powerful data mining capabilities have attracted widespread attention from researchers. However, in order for the deep learning model to have excellent detection effects, a large number of balanced training samples are required to complete the training of the model in order to achieve its high performance characteristics. However, in actual engineering environments, especially in the field of rotating machinery fault detection, there is a situation where the monitoring data availability is low. On the one hand, although the condition monitoring system composed of multiple sensors can continuously collect data, the equipment is in normal operation most of the time, and the duration of the equipment in the fault state is short. Therefore, most of the collected data is healthy data, and fault samples account for a small number. On the other hand, the sensors of some equipment are complex to install, and equipment failures are often sudden, and it is impossible to plan and arrange data collection work in advance. Therefore, it is extremely difficult to obtain fault signals of some equipment.

[0005] For the above reasons, when the fault data samples are sparsely collected, it will lead to the small sample problem. In the field of fault detection, too small a number of fault samples will prevent the model from obtaining comprehensive information during the training process, and it will be difficult to capture the diversity and complexity of the equipment status, resulting in inaccurate detection of the equipment. Secondly, the model trained with small samples is difficult to generalize to new situations. The model may not be able to adapt to new data sets or actual engineering scenarios, resulting in performance degradation. These problems make the fault detection results under small samples likely to be inaccurate and unstable. Therefore, how to design a method that can improve the accuracy and reliability of gearbox fault detection for straddle-type monorail trains is a technical problem that needs to be solved urgently. Summary of the invention

[0006] In view of the deficiencies of the above-mentioned prior art, the technical problem to be solved by the present invention is: how to provide a gearbox fault detection method for a straddle-type monorail train based on a data enhancement strategy, expand the measured fault data through the SVMD algorithm, and generate virtual fault data by training a generative adversarial network model with the expanded data, and then train the fault detection model together with the generated virtual fault data and healthy data, which can solve the small sample problem caused by the diverse types of gearbox faults and the difficulty in data collection, thereby improving the accuracy and reliability of gearbox fault detection for straddle-type monorail trains.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] The gearbox fault detection method for straddle-type monorail train based on data enhancement strategy includes:

[0009] S1: Acquire the gearbox data of the straddle-type monorail train to be tested;

[0010] S2: Input the straddle-type monorail train gearbox data into the trained fault detection model and output the corresponding predicted fault label;

[0011] The training steps of the fault detection model include:

[0012] S201: Obtain health data and measured fault data of a straddle-type monorail train gearbox;

[0013] S202: Expanding the measured fault data based on the continuous variable mode decomposition algorithm to obtain a preliminary expanded sample;

[0014] S203: training a 1D MOPGAN model by preliminarily expanding samples and healthy data; wherein a generator of the 1D MOPGAN model is used to generate virtual fault data according to the healthy data, and a discriminator is used to distinguish between the virtual fault data and the measured fault data;

[0015] S204: inputting the healthy data into the generator of the trained 1D MOPGAN model and outputting the virtual fault data;

[0016] S205: using the generated virtual fault data and healthy data together as a training set for a fault detection model;

[0017] S206: training the fault detection model using the training set until the model converges or reaches a maximum number of iterations;

[0018] S3: Outputting the predicted fault label as the fault detection result of the straddle-type monorail train gearbox data to be detected.

[0019] Preferably, in step S202, the preliminary expansion sample is generated by the following steps:

[0020] S2021: Decomposing the measured fault data by a continuous variable mode decomposition algorithm to obtain a number of IMF components;

[0021] S2022: Calculate the kurtosis value of each IMF component;

[0022] S2023: Selecting an IMF component with a kurtosis value greater than a preset value as a target IMF;

[0023] S2024: Randomly weight the target component to obtain a weighted IMF;

[0024] S2025: reconstruct the weighted IMF and other unweighted IMF components to obtain a reconstructed signal x1;

[0025] S2026: Calculate the standard deviations a and b of the measured fault data and the reconstructed signal x1 respectively;

[0026] S2027: Calculate the initial expansion sample by reconstructing the signal x1 and the standard deviations a and b

[0027] Preferably, in step S202, the optimal balance parameters of the continuous variable mode decomposition algorithm are adaptively and iteratively searched through the GWO algorithm.

[0028] Preferably, in step S202, the processing steps of the GWO algorithm include:

[0029] S2121: Setting the fitness function of the GWO algorithm;

[0030] S2122: Initialize the gray wolf population of the GWO algorithm; each gray wolf individual in the gray wolf population represents a balance parameter of the continuous variable mode decomposition algorithm;

[0031] S2123: Calculate the fitness values ​​of all gray wolf individuals through the fitness function, then take the first three gray wolf individuals with the highest fitness values ​​as α wolf, β wolf and γ wolf, and take the gray wolf individuals other than α wolf, β wolf and γ wolf as ω wolf;

[0032] S2124: Hunting is performed based on the positions of wolf α, wolf β and wolf γ, and the positions of each individual gray wolf are updated;

[0033] S2125: Update the fitness value based on the position of the gray wolf individual, and record the optimal balance parameter corresponding to the current gray wolf individual;

[0034] S2126: Determine whether the termination condition is met: if so, output the optimal balance parameters; otherwise, return to step S2123.

[0035] Preferably, in step S2021, the processing steps of the continuous variable mode decomposition algorithm include:

[0036] 1) Decompose the measured fault data x(t) to obtain the L-order IMF component u L (t) and the residual signal x r (t);

[0037] The formula is described as:

[0038] x(t)=u L (t)+x r (t);

[0039] Residual signal x r (t) consists of two parts: the sum of all IMF components obtained before the L-th order IMF component and the unprocessed original signal x u (t);

[0040] 2) During the decomposition process, four constraints are set to obtain the Lth IMF component:

[0041] Constraint 1: Each IMF component should be compact around its center frequency;

[0042] The formula is described as:

[0043]

[0044] Where: represents the partial derivative with respect to time t; δ(t) represents the Dirac function; * represents the convolution operation; ω L represents the center frequency of the L-th order IMF component;

[0045] Constraint criterion 2: Make the L-th order IMF component u L (t) and the residual signal x r(t) to minimize the spectral overlap between them; this is achieved by the following filter:

[0046]

[0047] Where: α represents the equilibrium parameter;

[0048] The following criteria are used to minimize spectrum overlap:

[0049]

[0050] Constraint criterion 3: At the center frequency of the IMF component obtained before the Lth order, u L The energy of (t) is minimized; using a filter with the following frequency response

[0051] The formula is described as:

[0052]

[0053] Standard J3 is as follows:

[0054]

[0055] Constraint criterion 4: The original signal x(t) is reconstructed by the sum of all extracted IMF components and the unprocessed signal;

[0056] 3) When the L-1th order IMF component is known, the task of extracting the Lth order IMF component is converted into a constrained minimization problem;

[0057]

[0058] Where: α is the parameter for balancing J1, J2, and J3;

[0059] 4) Convert the constrained minimization problem into an unconstrained optimization problem: First, introduce the quadratic penalty term and Lagrange multiplier to establish the augmented Lagrangian function, then convert it into the frequency domain form according to Parseval's theorem, and finally use the multiplication alternating algorithm to iteratively solve it; that is, the iteration of the continuous variable mode decomposition algorithm is completed by the following formula:

[0060]

[0061] Where: represents the Fourier transform of the original signal x(t); Indicates the center frequency The L-th order mode at the n-th iteration Fourier transform of ; n represents the number of iterations.

[0062] Preferably, in step S2022, the kurtosis value of the IMF component is calculated by the following formula:

[0063]

[0064] Where: k represents the kurtosis value; x i represents the i-th value in the IMF component; represents the average value of the IMF component, and n represents the number of samples in the IMF component.

[0065] Preferably, in step S203, the 1D MOPGAN model is constructed based on a generative adversarial network, and the generator and discriminator of the generative adversarial network are replaced by a Self-ONN network from a CNN network.

[0066] Preferably, in step S203, the loss function for training the 1D MOPGAN model is as follows:

[0067]

[0068] L total =Loss BCE +λLoss MAE ;

[0069] Where: G represents the generator; D represents the discriminator; D(x) and D(G(z)) represent the output of the discriminator when the input is the measured fault data x and the virtual fault data G(z), respectively, and z is the one-dimensional healthy data; |·| represents the absolute value; x i Indicates the measured fault data; p i represents virtual fault data; λ represents the balance parameter; and represents the expectation; N represents the total number of samples.

[0070] Preferably, in step S206, the fault detection model is a randomly configured network.

[0071] Preferably, in step S206, the steps of constructing the random configuration network are as follows:

[0072] S20601: Construct a random configuration network with input layer, hidden layer and output layer;

[0073] S20602: Train the random configuration network using training data, where the output of the L-1 layer of the random configuration network is expressed as:

[0074]

[0075] Where: f L-1 (X) represents the output of the L-1th layer of the random configuration network; X = {x1, x2..., x N} represents training data; β jrepresents the output weight of hidden layer node j; g(·) represents the activation function; w j and b j They represent the input weight and bias of the jth node in the hidden layer respectively;

[0076] S20602: Calculate the residual e between the current random configuration network output and the true value using the following formula L-1 :

[0077] e L-1 =ff L-1 (X);

[0078] Where: f represents the output of the random configuration network;

[0079] S20603: If ‖e L-1 ‖ 2 The preset error ε is not reached or the maximum number of nodes L is not reached max , then add a new hidden layer node L under the supervision mechanism:

[0080]

[0081] Where: h L represents the output of the hidden layer node L; w L and b L They represent the candidate parameters of node L respectively; r∈(0,1); {μ L} represents a non-negative real number sequence; ξ L,q represents the supervision mechanism; q = 1, 2, ... m;

[0082] S20604: Globally evaluate the output weights of the hidden layer nodes of the random configuration network by the least squares method;

[0083] β=argmin β ||Hβ-Y|| 2 =H + Y;

[0084] Where: β represents the output weight; H represents the hidden layer output matrix; H + represents the Moore-Penrose generalized inverse of H; Y = {y1, y2..., y N} represents label data;

[0085] S20605: Calculate the output result f=Hβ of the random configuration network based on the output weight and the hidden layer output matrix;

[0086] S20606: Repeat steps S20602 to S20605 to incrementally generate hidden layer nodes of the randomly configured network.

[0087] Compared with the prior art, the straddle-type monorail train gearbox fault detection method based on data enhancement strategy in the present invention has the following beneficial effects:

[0088] The present invention expands the measured fault data based on the Continuous Variable Mode Decomposition (SVMD) algorithm, and then trains the 1D MOPGAN (Generative Adversarial Network) model through the expanded samples and healthy data, so that virtual fault data can be generated based on the healthy data through the generator of the 1D MOPGAN model. First, the SVMD algorithm can generate new samples with similar characteristics but not completely the same as the original fault data by decomposing and reconstructing the measured fault data, increasing the diversity and quantity of fault data, and ensuring the training effect of the 1D MOPGAN model. In addition, the SVMD algorithm can highlight the characteristic components of the fault signal during the decomposition process, so that the expanded data is more focused on the fault characteristics, which helps the 1D MOPGAN model to capture fault information more accurately during the training process, thereby assisting in improving the accuracy of the gearbox fault detection of the straddle-type monorail train. Secondly, the generator of the 1D MOPGAN model can learn the potential relationship between the healthy data and the fault data and generate realistic virtual fault data. These virtual data not only increase the number of training samples, but also enrich the diversity of fault types. Finally, the discriminator continuously distinguishes between real fault data and generated virtual fault data, prompting the generator to continuously improve the quality of the data it generates, making the generated virtual fault data closer to the real fault data, thereby improving the authenticity and credibility of the data.

[0089] The present invention generates a virtual fault number through a generator of a 1D MOPGAN model, and then trains a fault detection model through a training set of virtual fault data and measured health data. First, in practical applications, fault data is often more scarce than health data. By generating virtual fault data through a 1D MOPGAN model, the proportion of health data and fault data in the training set can be balanced, so that the model can fully learn the difference between the health state and the fault state during the training process. Secondly, the fault detection model trained with virtual fault data and measured health data can learn more comprehensive signal features, thereby solving the problem of small samples caused by the variety of gearbox fault types and data collection difficulties, and helping the model to more accurately judge the state of the gearbox during the detection process, thereby improving the accuracy and reliability of gearbox fault detection of straddle-type monorail trains. Finally, by training virtual data containing multiple fault types, the fault detection model can better adapt to the detection requirements under different working conditions and fault conditions, thereby improving the robustness and adaptability of the model.

[0090] The fault detection model of the present invention uses a random configuration network (SCN) model. First, the random configuration network simplifies the model building process by randomly generating network structures and weights, making the fault detection model more efficient during the training process and able to quickly adapt to different detection tasks. Secondly, the random configuration network has a strong nonlinear mapping capability and can handle complex nonlinear relationships, which is conducive to better completing the gearbox fault detection of straddle-type monorail trains. Finally, the random configuration network model introduces a certain regularization effect through randomness, which helps to prevent the model from overfitting, so that the model can maintain stable detection accuracy under different working conditions and fault conditions. At the same time, compared with other complex neural network models, the random configuration network model requires fewer computing resources during the training process, which is conducive to improving the efficiency of fault detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0092] Figure 1 The overall process framework of the fault detection model.

[0093] Figure 2 This is the training flow chart of the 1D MOPGAN model.

[0094] Figure 3 This is the network structure diagram of SCN.

[0095] Figure 4 Time domain comparison between original data and preliminary expanded data.

[0096] Figure 5 Frequency domain comparison between original data and preliminary expanded data.

[0097] Figure 6 Comparison of data correlation coefficients with and without the initial expansion strategy.

[0098] Figure 7 Displays the time domain and frequency domain of the DGLC dataset.

[0099] Figure 8 Comparison of correlation coefficients between generated and real data for different faults.

[0100] Fig. 9 Generate correlation coefficients for different models and compare them with real data.

[0101] Fig.10 Frequency domain visualization of real and generated data for different faults in DGLC.

[0102] Fig.11 Comparison of experimental results of DGLC data.

[0103] Fig.12 It is a confusion matrix diagram. DETAILED DESCRIPTION

[0104] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but only represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0105] The following is a further detailed description through specific implementation methods:

[0106] Example:

[0107] This embodiment discloses a straddle-type monorail train gearbox fault detection method based on a data enhancement strategy.

[0108] like Figure 1 As shown, the gearbox fault detection method for straddle-type monorail train based on data enhancement strategy includes:

[0109] S1: Acquire the gearbox data of the straddle-type monorail train to be tested;

[0110] S2: Input the straddle-type monorail train gearbox data into the trained fault detection model and output the corresponding predicted fault label;

[0111] The training steps of the fault detection model include:

[0112] S201: Obtain health data and measured fault data of a straddle-type monorail train gearbox;

[0113] S202: Expand the measured fault data based on the Successive Variational Mode Decomposition (SVMD) algorithm to obtain a preliminary expanded sample;

[0114] S203: training a 1D MOPGAN (one-dimensional operation generative adversarial network based on mean absolute error) model by preliminarily expanding samples and healthy data; the generator of the 1D MOPGAN model is used to generate virtual fault data according to the healthy data, and the discriminator is used to distinguish the virtual fault data from the measured fault data;

[0115] S204: inputting the healthy data into the generator of the trained 1D MOPGAN model and outputting the virtual fault data;

[0116] S205: using the generated virtual fault data and healthy data together as a training set for a fault detection model;

[0117] S206: training the fault detection model using the training set until the model converges or reaches a maximum number of iterations;

[0118] S3: Outputting the predicted fault label as the fault detection result of the straddle-type monorail train gearbox data to be detected.

[0119] The present invention expands the measured fault data based on the Continuous Variable Mode Decomposition (SVMD) algorithm, and then trains the 1D MOPGAN (Generative Adversarial Network) model through the expanded samples and healthy data, so that virtual fault data can be generated based on the healthy data through the generator of the 1D MOPGAN model. First, the SVMD algorithm can generate new samples with similar characteristics but not completely the same as the original fault data by decomposing and reconstructing the measured fault data, increasing the diversity and quantity of fault data, and ensuring the training effect of the 1D MOPGAN model. In addition, the SVMD algorithm can highlight the characteristic components of the fault signal during the decomposition process, so that the expanded data is more focused on the fault characteristics, which helps the 1D MOPGAN model to capture fault information more accurately during the training process, thereby assisting in improving the accuracy of the gearbox fault detection of the straddle-type monorail train. Secondly, the generator of the 1D MOPGAN model can learn the potential relationship between the healthy data and the fault data and generate realistic virtual fault data. These virtual data not only increase the number of training samples, but also enrich the diversity of fault types. Finally, the discriminator continuously distinguishes between real fault data and generated virtual fault data, prompting the generator to continuously improve the quality of the data it generates, making the generated virtual fault data closer to the real fault data, thereby improving the authenticity and credibility of the data.

[0120] The present invention generates a virtual fault number through a generator of a 1D MOPGAN model, and then trains a fault detection model through a training set of virtual fault data and measured health data. First, in practical applications, fault data is often more scarce than health data. By generating virtual fault data through a 1D MOPGAN model, the proportion of health data and fault data in the training set can be balanced, so that the model can fully learn the difference between the health state and the fault state during the training process. Secondly, the fault detection model trained with virtual fault data and measured health data can learn more comprehensive signal features, thereby solving the problem of small samples caused by the variety of gearbox fault types and data collection difficulties, and helping the model to more accurately judge the state of the gearbox during the detection process, thereby improving the accuracy and reliability of gearbox fault detection of straddle-type monorail trains. Finally, by training virtual data containing multiple fault types, the fault detection model can better adapt to the detection requirements under different working conditions and fault conditions, thereby improving the robustness and adaptability of the model.

[0121] The fault detection model of the present invention uses a random configuration network (SCN) model. First, the random configuration network simplifies the model building process by randomly generating network structures and weights, making the fault detection model more efficient during the training process and able to quickly adapt to different detection tasks. Secondly, the random configuration network has a strong nonlinear mapping capability and can handle complex nonlinear relationships, which is conducive to better completing the gearbox fault detection of straddle-type monorail trains. Finally, the random configuration network model introduces a certain regularization effect through randomness, which helps to prevent the model from overfitting, so that the model can maintain stable detection accuracy under different working conditions and fault conditions. At the same time, compared with other complex neural network models, the random configuration network model requires fewer computing resources during the training process, which is conducive to improving the efficiency of fault detection.

[0122] In order to better introduce the technical solution of the present invention, this embodiment is described through the following parts.

[0123] 1. Preliminary expansion of samples

[0124] In actual engineering scenarios, the number of healthy samples in the collected equipment data is far greater than that of faulty samples. In this case, it is difficult to train a generative adversarial network model with good performance. Therefore, the present invention uses GWO to optimize the data initial expansion strategy of SVMD, with the aim of helping 1D MOPGAN learn more data features to generate higher quality generated samples.

[0125] In this embodiment, the initial expansion sample is generated through the following steps:

[0126] S2021: Decompose the measured fault data by using the SVMD algorithm to obtain several IMF components;

[0127] S2022: Calculate the kurtosis value of each IMF component;

[0128] S2023: Selecting an IMF component whose kurtosis value is greater than a preset value (the preset value is 3) as a target IMF;

[0129] S2024: Randomly weight the target component to obtain a weighted IMF;

[0130] In this embodiment, the weighted values ​​are from a preset range of uniform distribution;

[0131] S2025: reconstruct the weighted IMF and other unweighted IMF components to obtain a reconstructed signal x1;

[0132] In this embodiment, signal reconstruction refers to adding the weighted IMF and other unweighted IMF components.

[0133] S2026: Calculate the standard deviations a and b of the measured fault data and the reconstructed signal x1 respectively;

[0134] S2027: Calculate the initial expansion sample by reconstructing the signal x1 and the standard deviations a and b

[0135] 1. GWO algorithm

[0136] In this embodiment, the GWO algorithm (Gray Wolf Optimization Algorithm) is used to adaptively iterate and search for the optimal balance parameters of the SVMD algorithm. The Gray Wolf Algorithm divides the wolf pack into four pyramid-shaped levels, namely α, β, γ and ω. Among them, α, β and γ wolves belong to the leadership class, which can more keenly perceive the potential location of prey than ω wolves, and are responsible for leading the wolf pack to search, track and approach prey. Therefore, in the optimization decision, the position of the prey (optimal solution) is determined by the position of the α, β and γ wolves (optimal candidate solution). The ω wolf is responsible for surrounding the prey from all directions under the command of the α, β and γ wolves, and starts to prey when the encirclement is small enough.

[0137] The specific steps include:

[0138] S2121: Setting the fitness function of the GWO algorithm;

[0139] S2122: Initialize the gray wolf population of the GWO algorithm; each gray wolf individual in the gray wolf population represents a balance parameter of the SVMD algorithm;

[0140] S2123: Calculate the fitness values ​​of all gray wolf individuals through the fitness function, then take the first three gray wolf individuals with the highest fitness values ​​as α wolf, β wolf and γ wolf, and take the gray wolf individuals other than α wolf, β wolf and γ wolf as ω wolf;

[0141] S2124: Hunting is performed based on the positions of wolf α, wolf β and wolf γ, and the positions of each individual gray wolf are updated;

[0142] S2125: Update the fitness value based on the position of the gray wolf individual, and record the optimal balance parameter corresponding to the current gray wolf individual;

[0143] S2126: Determine whether the termination condition is met: if so, output the optimal balance parameters; otherwise, return to step S2123.

[0144] During hunting, the distance between the gray wolf and the prey is calculated by the following formula:

[0145]

[0146] Where: D represents the distance between the gray wolf and the prey; t represents the number of iterations of the current algorithm; Represents the prey position vector is the gray wolf position vector; represents a random vector;

[0147] Used to prevent the algorithm from falling into local optimality, defined as:

[0148]

[0149] Where: The modulus of is a random number in [0,1].

[0150] During the hunting process, the gray wolf position is updated using the following formula:

[0151]

[0152] Where: Represents the command vector, which is used to command the ω wolf to deviate from the prey to search for a better target or approaching prey to hunt represents the gray wolf position vector; represents the prey position vector; represents the convergence vector, which decreases linearly from 2 to 0 as t increases; The modulus of is a random number in [0,1].

[0153] During hunting, the prey position is tracked using the following formula:

[0154]

[0155] It's in front This formula defines a random vector;

[0156] It's in front The coefficient vector in this formula;

[0157] Where: Denote the positions of α wolf, β wolf and γ wolf respectively; D α , D β , D γ Respectively represent the distances between α wolf, β wolf, γ wolf and each ω wolf; Represents the distance and direction that the ω wolf individual moves towards the α wolf, β wolf and γ wolf.

[0158] The present invention optimizes the balance parameter selection of SVMD through GWO (Grey Wolf Optimization Algorithm), and utilizes the advantages of GWO algorithm such as simplicity, few control parameters, strong global search capability, and balance between solution accuracy and convergence speed. It efficiently and accurately selects the optimal balance parameters for the SVMD algorithm to give full play to its signal decomposition performance, that is, it can achieve high-precision signal decomposition to obtain several IMF components.

[0159] In the specific implementation process, the fuzzy entropy of the bearing fault signal is used as the fitness function of the GWO algorithm, and the minimum value of the fuzzy entropy is used as the fitness value of the gray wolf individual. Fuzzy entropy is a measure of the probability of the generation of a new pattern. The larger the entropy value, the greater the probability of the generation of a new pattern.

[0160] 2. SVMD algorithm

[0161] In this embodiment, the processing steps of the SVMD algorithm include:

[0162] 1) Decompose the measured fault data to obtain the L-order IMF component u L (t) and the residual signal x r (t);

[0163] The formula is described as:

[0164] x(t)=u L (t)+x r (t);

[0165] Residual signal x r (t) consists of two parts: the sum of all IMF components obtained before the L-th order IMF component and the unprocessed original signal x u (t);

[0166] 2) During the decomposition process, four constraints are set to obtain the Lth IMF component:

[0167] Constraint 1: Each IMF component should be compact around its center frequency; three of the constraints are the same as those of VME: Each IMF component should be compact around its center frequency.

[0168] The formula is described as:

[0169]

[0170] Where: represents the partial derivative with respect to time t; δ(t) represents the Dirac function; * represents the convolution operation; ω L represents the center frequency of the L-th order IMF component;

[0171] Constraint criterion 2: Make the L-th order IMF component u L (t) and the residual signal x r (t) to minimize the spectral overlap between them; this is achieved by the following filter:

[0172]

[0173] Where: α represents the equilibrium parameter;

[0174] The following criteria are used to minimize spectrum overlap:

[0175]

[0176] Constraint criterion 3: At the center frequency of the IMF component obtained before the Lth order, u L The energy of (t) is minimized; using a filter with the following frequency response

[0177] The formula is described as:

[0178]

[0179] Standard J3 is as follows:

[0180]

[0181] Constraint criterion 4: The original signal x(t) is reconstructed by the sum of all extracted IMF components and the unprocessed signal;

[0182] 3) When the L-1th order IMF component is known, the task of extracting the Lth order IMF component is converted into a constrained minimization problem;

[0183]

[0184] Where: α is the parameter for balancing J1, J2, and J3;

[0185] 4) Convert the constrained minimization problem into an unconstrained optimization problem: First, introduce the quadratic penalty term and Lagrange multiplier to establish the augmented Lagrangian function, then convert it into frequency domain form according to Parseval's theorem, and finally use the multiplication alternating algorithm to iteratively solve it; that is, the iteration of the SVMD algorithm is completed by the following formula:

[0186]

[0187] Where: represents the Fourier transform of the original signal x(t); Indicates the center frequency The L-th order mode at the n-th iteration Fourier transform of ; n represents the number of iterations; is the power spectrum center of the new IMF component.

[0188] S305: Obtaining an update equation of the Lagrange multiplier λ by a double ascent method;

[0189] The formula is described as:

[0190]

[0191] Where: τ represents the iteration step length.

[0192] 3. Calculation of kurtosis value

[0193] In this embodiment, the kurtosis value of the IMF component is calculated by the following formula:

[0194]

[0195] Where: k represents the kurtosis value; x i represents the i-th value in the IMF component; represents the average value of the IMF component, and n represents the number of samples in the IMF component.

[0196] 2. 1D MOPGAN Model

[0197] In this embodiment, the 1D MOPGAN model is built based on a generative adversarial network, specifically replacing the generator and discriminator of the generative adversarial network from the original CNN network to a Self-ONN (Self-organized Operational Neural Networks) network. The Self-ONN network is an upgrade and improvement of the operational neural network (ONN). It approximates the function based on Taylor expansion, without pre-defining the operator set library, avoiding the cost of searching for the best operator set. The lightweight configuration of the Self-ONN network makes it more convenient for real-time processing and suitable for deployment on low-power devices.

[0198] Self-ONN has higher flexibility and expressiveness in processing complex dynamic data by generating neurons and Taylor series to approximate nonlinear transformations.

[0199]

[0200] Where: f(x) represents the expression of function f with respect to x; f (n) (0) represents the nth derivative of function f at x=0; n! represents the factorial of x; (x) n represents x to the power of x;

[0201] The Qth-order truncated approximation, formally called the Taylor polynomial, takes the form of the following finite summation.

[0202]

[0203] Where: f(x) (Q) It represents the Q-order Taylor expansion of the function f(x) at a certain point, and Q represents the number of terms in the expansion;

[0204] The above formula can fully approximate any function f(x) around 0. By using an activation function that restricts the neuron input feature map to be within the range of 0, a composite node operator can be formed using formula (9), where the power coefficient can be used as a learning parameter during network training. The node operator of the kth generator neuron in the lth layer can take the following general form:

[0205]

[0206] where Y l-1 is the corresponding input, is a three-dimensional weight matrix, and yes The qth slice of . The 0th order term (i.e., DC bias) can be ignored, and its effect can be replaced and compensated by the learnable bias parameters in the neuron. Now it becomes very easy to backpropagate through this node operator. The following two equations provide the relative input Y l-1 and the weight of the qth slice The derivative of :

[0207]

[0208] Where: represents the node operator of the k-th generator neuron in the l-th layer.

[0209] During the learning process, as the weights are updated through BP, this representation enables the network to produce new node transformations that are optimized to achieve a given learning objective.

[0210] Specifically, the loss function for training the 1D MOPGAN model is as follows:

[0211]

[0212] L total =Loss BCE +λLoss MAE ;

[0213] Where: G represents the generator; D represents the discriminator; D(x) and D(G(z)) represent the output of the discriminator when the input is the measured fault data x and the virtual fault data G(z), respectively, and z is the one-dimensional healthy data; |·| represents the absolute value; x i Indicates the measured fault data; p i represents virtual fault data; λ represents the balance parameter; and represents the expectation; N represents the total number of samples.

[0214] In order to further reduce the difference between generated data and real data, the present invention improves the loss function and designs a hybrid loss function of binary cross entropy combined with mean absolute error. At the same time, the balance parameter λ is introduced in GAN training to adjust the weight between binary cross entropy loss (BCE) and mean absolute error loss (MAE), so as to balance the two loss functions more flexibly to better meet task requirements.

[0215] Combination Figure 2 As shown, the use of 1D MOPGAN to expand the data set can be divided into two parts. The training part and the data generation part. At present, most scholars use random noise as the input of the generator, but random noise as the input of the generator usually lacks clear structure or semantic information, which causes the generated samples to deviate from the real data in semantic consistency and structural characteristics. Therefore, the present invention adopts an equipment health data conversion strategy to convert the equipment health data collected in the actual working environment into frequency domain data as the generator input, so as to improve the authenticity of the generated samples in structure, characteristics and practical applications, and overcome the problem that the difference in fault characteristics in time domain signals is not obvious.

[0216] 3. Randomly configure the network

[0217] In this embodiment, the fault detection model is a random configuration network. Since the traditional feedforward neural network faces the problems of high computational complexity and high modeling cost when processing high-dimensional nonlinear industrial data, the present invention proposes to use a random configuration network (SCN) with simple structure and low computational complexity for modeling. Its structure is as follows Figure 3 shown.

[0218] The steps to construct a random configuration network are as follows:

[0219] S20601: Construct a random configuration network with input layer, hidden layer and output layer;

[0220] S20602: Train the random configuration network using training data. The output of the L-1 layer of the random configuration network is expressed as:

[0221]

[0222] Where: f L-1 (X) represents the output of the L-1th layer of the random configuration network; X = {x1, x2..., x N} represents training data, and represents a d-dimensional real number space and an m-dimensional real number space; β j represents the output weight of hidden layer node j; g(·) represents the activation function; w j and b j They represent the input weight and bias of the jth node in the hidden layer respectively;

[0223] S20602: Calculate the residual e between the current random configuration network output and the true value using the following formula L-1 :

[0224] e L-1 =ff L-1 (X);

[0225] Where: f represents the output of the random configuration network;

[0226] S20603: If ‖e L-1 ‖ 2 The preset error ε is not reached or the maximum number of nodes L is not reached max , then add a new hidden layer node L under the supervision mechanism:

[0227]

[0228] Where: h L represents the output of the hidden layer node L; w L and b L They represent the candidate parameters of node L respectively; r∈(0,1); {μ L} represents a sequence of non-negative real numbers, where satisfy The candidate node parameter with the maximum value is taken as the Lth node parameter; ξ L,q represents the supervision mechanism; q = 1, 2, ... m;

[0229] S20604: Globally evaluate the output weights of the hidden layer nodes of the random configuration network by the least squares method;

[0230] β=argmin β ||Hβ-Y|| 2 =H + Y;

[0231] Where: β represents the output weight; H represents the hidden layer output matrix; H + denotes the Moore-Penrose generalized inverse of H; Y = {y1, y2..., y N} represents the corresponding label data,

[0232] S20605: Calculate the output result f=Hβ of the random configuration network based on the output weight and the hidden layer output matrix;

[0233] S20606: Repeat steps S20602 to S20605 to incrementally generate hidden layer nodes of the randomly configured network.

[0234] 4. Experimental Description

[0235] In order to verify the effectiveness of the model proposed in this invention, the straddle-type monorail train gearbox dataset (DGLC for short) collected by this research team was used for experimental verification. In this experiment, the DGLC dataset is divided into three categories, category 1 is inner ring fault, category 2 is assembly error, and category 3 is normal signal of the gearbox. The sampling rate of the measured data is 10240Hz. Next, a small sample dataset will be constructed to simulate the small sample situation, and then the algorithm will be experimentally verified. Assume that the sampling length is 1024, and each fault state is sampled 40 times, as shown in Table 1.

[0236] Table 1 DGLC dataset

[0237]

[0238] 1. Validation of the preliminary data expansion architecture

[0239] In order to avoid overfitting of the generative adversarial network, the SVMD based on GWO optimization is used for preliminary data enhancement. The one-dimensional time domain vibration signal of the equipment operation status and working condition information is expanded, and then the frequency domain data is obtained by Fourier transform as the input of the generator, thereby generating sufficient training data and improving the generalization performance of the model. Table 2 shows the comparison of the quantity before and after data expansion.

[0240] Table 2 Comparison of the number of fault data before and after the initial expansion

[0241]

[0242] Figure 4 (a) and Figure 4 (b) shows the time domain waveforms of the original data and expanded data of the gearbox inner ring fault. Figure 4 (c) and Figure 4 (d) shows the time domain waveforms of the original data and the expanded data of the gearbox assembly error. By comparison, the original data and the expanded data are consistent in the periodic vibration part, indicating that the expanded data effectively retains the fault characteristics. After further Fourier transformation, Figure 5 (a) and Figure 5 (b) shows the frequency domain waveform of the original and expanded data of the inner race fault. Figure 5 (c) and Figure 5 (d) shows the frequency domain waveforms of the original and augmented data of the assembly error, both of which show that the frequency components of the augmented data are highly consistent with the original data. Therefore, the comparison between the time domain and the frequency domain verifies that the augmented data can effectively retain the fault characteristics, providing sufficient basis for training the generator.

[0243] Figure 6 The Pearson correlation coefficient between the generated data and the real data in the first 700 iterations when different models are trained using the DGLC dataset with or without data augmentation strategies is shown. The results show that after adopting the data augmentation strategy, the similarity between the data generated by each model and the real data is significantly improved, which verifies that the initial data augmentation strategy effectively improves the quality of generated data and provides training data that is more in line with real working conditions for subsequent training.

[0244] 2. 1D MOPGAN Effectiveness Verification

[0245] The present invention uses Self-ONN as a generator and discriminator. Unlike traditional CNN, Self-ONN has self-organizing learning capabilities and can adapt to complex data patterns. The nonlinearity, non-stationarity and multi-frequency components of mechanical fault vibration signals enable the Self-ONN generator to capture signal features more effectively. In order to cope with the noise interference of fault features in time domain signals, the present invention converts the initially expanded time domain data into frequency domain data, improves the generator's learning ability for fault features and improves the quality of generated data. Figure 7 The time domain and frequency domain data of the inner ring fault, assembly error and normal operation status of the straddle-type monorail train gearbox are displayed after preliminary data expansion.

[0246] Figure 8The correlation coefficients between generated data and real data are shown when the unmodified 1D OpGAN and GAN networks are trained using the DGLC dataset. As can be seen from the figure, the similarity between the fault data generated by 1D OpGAN and the real data is significantly higher than that of GAN. Therefore, it is more appropriate to use Self-ONN as the generator and discriminator network, which can more effectively capture complex features and generate high-quality samples.

[0247] In order to reduce the difference between generated data and real data, the present invention designs a hybrid loss function that combines binary cross entropy and mean absolute error. Fig. 9 The correlation coefficients between generated data and real data when training each generative model on the DGLC dataset are shown. The results show that the similarity of the data generated by 1D MOPGAN using a mixed loss function is significantly higher than that of other generative models. After the introduction of the mean absolute error, the closeness between the generated data and the real data is significantly improved, which enhances the performance of the generator.

[0248] To evaluate the quality of generated data after data augmentation, the generated data are randomly selected and compared with the frequency domain features of the real data. Fig.10 The real and generated frequency domain signals of the inner ring fault and assembly error fault of the straddle-type monorail train gearbox are shown. The results show that the generated samples are highly consistent with the real samples in terms of characteristic frequencies, which verifies the ability of the generator to capture the fault frequency of mechanical equipment vibration signals. This shows that the generated data can effectively simulate the frequency domain characteristics of actual faults, provide real and reliable training data for subsequent fault diagnosis, and improve the accuracy of diagnosis.

[0249] 3. Experiments based on 1D SVMD-MOPGAN and SCN fault detection models

[0250] This experiment is based on the DGLC dataset to evaluate the effectiveness of the 1D SVMD-MOPGAN-SCN fault detection architecture. Five sets of comparative experiments are set up to compare the SCN method without data augmentation with the following fault detection methods with data augmentation: 1D SVMD-MOPGAN-SCN, 1D SVMD-OpGAN-SCN, SVMD-GAN-SCN, SVMD-WGAN-SCN and SVMD-WGANgp-SCN. Table 3 shows the number of training and test sets for these methods, among which the number of training and test sets for the five data augmentation methods is the same.

[0251] Table 3. Number of training data and test data after data augmentation

[0252]

[0253] The experimental results are as follows Fig.11As shown in the figure, the model using the data enhancement method generally shows higher fault detection accuracy in five experiments. Although in some cases, the accuracy of the method of the present invention is comparable to that of other methods, the detection effect of the method of the present invention is more stable on small sample data sets. In general, the method of the present invention is superior to other comparative methods in fault detection accuracy.

[0254] Fig.12 The confusion matrix of the test set of the first set of experiments of the 1D SVMD-MOPGAN-SCN method is shown. The model can correctly classify in most cases, but there are misclassifications, such as the inner ring fault is mistakenly identified as a normal signal. This may be because the characteristic frequency of the inner ring fault is similar to that of the normal signal, or it is interfered by noise, resulting in poor performance in the frequency domain. Or the generated fault data has unclear frequency domain performance, which affects the model recognition ability. Nevertheless, combined with Fig.11 Other experimental results in show that the fault detection accuracy and stability of the proposed method on a small sample data set are superior to those of other methods.

[0255] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A straddle-type monorail train gearbox fault detection method based on data enhancement strategy, characterized in that: include: S1: Acquire the gearbox data of the straddle-type monorail train to be tested; S2: Input the straddle-type monorail train gearbox data into the trained fault detection model and output the corresponding predicted fault label; The training steps of the fault detection model include: S201: Obtain health data and measured fault data of a straddle-type monorail train gearbox; S202: Expanding the measured fault data based on the continuous variable mode decomposition algorithm to obtain a preliminary expanded sample; S203: training a 1D MOPGAN model by preliminarily expanding samples and healthy data; wherein a generator of the 1D MOPGAN model is used to generate virtual fault data according to the healthy data, and a discriminator is used to distinguish between the virtual fault data and the measured fault data; S204: inputting the healthy data into the generator of the trained 1D MOPGAN model and outputting the virtual fault data; S205: using the generated virtual fault data and healthy data together as a training set for a fault detection model; S206: training the fault detection model using the training set until the model converges or reaches a maximum number of iterations; S3: Outputting the predicted fault label as the fault detection result of the straddle-type monorail train gearbox data to be detected.

2. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 1, characterized in that: In step S202, a preliminary expansion sample is generated through the following steps: S2021: Decomposing the measured fault data by a continuous variable mode decomposition algorithm to obtain a number of IMF components; S2022: Calculate the kurtosis value of each IMF component; S2023: Selecting an IMF component with a kurtosis value greater than a preset value as a target IMF; S2024: Randomly weight the target component to obtain a weighted IMF; S2025: reconstruct the weighted IMF and other unweighted IMF components to obtain a reconstructed signal x1; S2026: Calculate the standard deviations a and b of the measured fault data and the reconstructed signal x1 respectively; S2027: Calculate the initial expansion sample by reconstructing the signal x1 and the standard deviations a and b 3. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 1, characterized in that: In step S202, the optimal balance parameters of the continuous variable mode decomposition algorithm are searched adaptively and iteratively through the GWO algorithm.

4. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 3, characterized in that: In step S202, the processing steps of the GWO algorithm include: S2121: Setting the fitness function of the GWO algorithm; S2122: Initialize the gray wolf population of the GWO algorithm; each gray wolf individual in the gray wolf population represents a balance parameter of the continuous variable mode decomposition algorithm; S2123: Calculate the fitness values ​​of all gray wolf individuals through the fitness function, then take the first three gray wolf individuals with the highest fitness values ​​as α wolf, β wolf and γ wolf, and take the gray wolf individuals other than α wolf, β wolf and γ wolf as ω wolf; S2124: Hunting is performed based on the positions of wolf α, wolf β and wolf γ, and the positions of each individual gray wolf are updated; S2125: Update the fitness value based on the position of the gray wolf individual, and record the optimal balance parameter corresponding to the current gray wolf individual; S2126: Determine whether the termination condition is met: if so, output the optimal balance parameters; otherwise, return to step S2123.

5. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 2, characterized in that: In step S2021, the processing steps of the continuous variable mode decomposition algorithm include: 1) Decompose the measured fault data x(t) to obtain the L-order IMF component u L (t) and the residual signal x r (t); The formula is described as: x(t)=u L (t)+x r (t); Residual signal x r (t) consists of two parts: the sum of all IMF components obtained before the L-th order IMF component and the unprocessed original signal x u (t); 2) During the decomposition process, four constraints are set to obtain the Lth IMF component: Constraint 1: Each IMF component should be compact around its center frequency; The formula is described as: Where: θ t represents the partial derivative with respect to time t; δ(t) represents the Dirac function; * represents the convolution operation; ω L represents the center frequency of the L-th order IMF component; Constraint 2: Make the L-th order IMF component u L (t) and the residual signal x r (t) to minimize the spectral overlap between them; this is achieved by the following filter: Where: α represents the equilibrium parameter; The following criteria are used to minimize spectrum overlap: Constraint criterion 3: At the center frequency of the IMF component obtained before the Lth order, u L The energy of (t) is minimized; using a filter with the following frequency response The formula is described as: Standard J3 is as follows: Constraint criterion 4: The original signal x(t) is reconstructed by the sum of all extracted IMF components and the unprocessed signal; 3) When the L-1th order IMF component is known, the task of extracting the Lth order IMF component is converted into a constrained minimization problem; Where: α is the parameter for balancing J1, J2, and J3; 4) Convert the constrained minimization problem into an unconstrained optimization problem: First, introduce the quadratic penalty term and Lagrange multiplier to establish the augmented Lagrangian function, then convert it into the frequency domain form according to Parseval's theorem, and finally use the multiplication alternating algorithm to iteratively solve it; that is, the iteration of the continuous variable mode decomposition algorithm is completed by the following formula: Where: represents the Fourier transform of the original signal x(t); Indicates the center frequency The L-th order mode at the n-th iteration Fourier transform of ; n represents the number of iterations.

6. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 2, characterized in that: In step S2022, the kurtosis value of the IMF component is calculated by the following formula: Where: k represents the kurtosis value; x i represents the i-th value in the IMF component; represents the average value of the IMF component, and n represents the number of samples in the IMF component.

7. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 1, characterized in that: In step S203, the 1D MOPGAN model is constructed based on the generative adversarial network, and the generator and discriminator of the generative adversarial network are replaced by the Self-ONN network from the CNN network.

8. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 7, characterized in that: In step S203, the loss function for training the 1D MOPGAN model is as follows: L total =Loss BCE +λLoss MAE ; Where: G represents the generator; D represents the discriminator; D(x) and D(G(z)) represent the output of the discriminator when the input is the measured fault data x and the virtual fault data G(z), respectively, and z is the one-dimensional healthy data; |·| represents the absolute value; x i Indicates the measured fault data; p i represents virtual fault data; λ represents the balance parameter; and represents the expectation; N represents the total number of samples.

9. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 1, characterized in that: In step S206, the fault detection model is a randomly configured network.

10. The method for detecting gearbox faults of straddle-type monorail trains based on data enhancement strategy according to claim 9, characterized in that: In step S206, the steps of constructing the random configuration network are as follows: S20601: Construct a random configuration network with input layer, hidden layer and output layer; S20602: Train the random configuration network using training data, where the output of the L-1 layer of the random configuration network is expressed as: Where: f L-1 (X) represents the output of the L-1th layer of the random configuration network; X = {x1, x2..., x N } represents training data; β j represents the output weight of hidden layer node j; g(·) represents the activation function; w j and b j They represent the input weight and bias of the jth node in the hidden layer respectively; S20602: Calculate the residual e between the current random configuration network output and the true value using the following formula L-1 : e L-1 =f-f L-1 (X); Where: f represents the output of the random configuration network; S20603: If ‖e l-1 ‖ 2 The preset error ε is not reached or the maximum number of nodes L is not reached max , then add a new hidden layer node L under the supervision mechanism: Where: h L represents the output of the hidden layer node L; w L and b L They represent the candidate parameters of node L respectively; r∈(0,1); {μ L } represents a non-negative real number sequence; ξ L,q represents the supervision mechanism; q = 1, 2, ... m; S20604: Globally evaluate the output weights of the hidden layer nodes of the random configuration network by the least squares method; β=argmin β ||Hβ-Y|| 2 =H + Y; Where: β represents the output weight; H represents the hidden layer output matrix; H + represents the Moore-Penrose generalized inverse of H; Y = {y1, y2..., y N } represents label data; S20605: Calculate the output result f=Hβ of the random configuration network based on the output weight and the hidden layer output matrix; S20606: Repeat steps S20602 to S20605 to incrementally generate hidden layer nodes of the randomly configured network.

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