Multi-dimensional degradation control method and system based on self-encoding and fuzzy modeling

Abstract

The invention relates to a multi-dimensional degradation control method and system based on self-encoding and fuzzy modeling, and is suitable for health management and life prediction of industrial equipment. The system collects equipment degradation data through multiple sensors, constructs a three-dimensional tensor and performs data fusion and weight optimization by using CP decomposition and an entropy weight method; detecting a multi-dimensional collaborative change point by adopting a mahalanobis distance and a combined likelihood ratio; low-dimensional features are extracted through an auto-encoder, and degradation modes are divided in combination with a clustering algorithm; establishing a joint degradation equation fusing a drift term matrix, diffusion covariance and fractal Brownian motion, and depicting long-range dependence; on the basis of fuzzy Markov chain modeling state transition fuzziness, a multi-dimensional degradation path is generated in combination with a Copula-Monte Carlo algorithm, the sample weight is dynamically adjusted, and the residual life distribution is estimated and predicted by using kernel density. According to the method, the degradation modeling precision and working condition adaptability of the complex industrial equipment are improved, and technical support is provided for precise life prediction and health management.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment health management and intelligent modeling, and specifically relates to a degradation process control technology based on autoencoders and fuzzy modeling methods, which is suitable for application scenarios such as multi-dimensional degradation feature extraction, state identification and remaining life prediction of complex systems. Background Art

[0002] Traditional methods mainly rely on degradation process modeling, such as statistical model-based methods such as Markov chains, machine learning-based methods such as support vector regression, and deep learning-based methods such as LSTM and CNN.

[0003] Despite certain achievements, the following problems still exist in complex industrial scenarios: insufficient multi-dimensional data processing capabilities make it difficult to capture the collaborative degradation characteristics of multi-sensor data; long-term dependency modeling is missing, and the "memoryless" assumption of the Markov chain cannot describe the long-term evolution trend of the degradation process. Although it can characterize long-range dependencies, its parameter estimation relies on manual settings and its generalization is limited. Summary of the Invention

[0004] The present invention proposes a multi-dimensional degradation control method and system based on autoencoding and fuzzy modeling. Aiming at the limitations of existing single-dimensional degradation modeling methods, the present invention focuses on solving problems such as multi-parameter collaborative degradation, complex mode switching, and insufficient prediction accuracy.

[0005] In order to achieve the above objectives, the present invention provides a multi-dimensional degradation control method based on autoencoding and fuzzy modeling, the technical solution is as follows:

[0006] Step 1: Multi-dimensional data collection and preprocessing

[0007] First, based on the multi-dimensional degradation characteristics of complex equipment, multiple key degradation indicators (such as temperature, vibration, wear, etc.) are collected to construct a multi-dimensional degradation vector: X(t) = [x1(t), x2(t), ..., x n (t)],X(t)∈R T×D (T is the time step, D is the number of dimensions), where each component x i (t) represents the evolution of the i-th degradation indicator over time.

[0008] To improve data quality, standardization is used to remove dimensionality effects, and tensor decomposition is used for data fusion to reduce data redundancy and noise interference. Data preprocessing: The original data is constructed into a three-dimensional tensor X∈R T×D×M (T is the time step, D is the number of dimensions, and M is the number of device instances) Dimension weight calculation: Calculate the weight w of each dimension based on the entropy weight method i , reflecting its contribution to degradation. The standardized expression is as follows:

[0009]

[0010] Step 2: Multidimensional Change Point Detection

[0011] During multidimensional degradation, there may be mutation points (change points), which are critical moments when the device switches from one degradation mode to another. Traditional univariate change point detection methods cannot effectively identify multidimensional collaborative change points. Therefore, this paper introduces multivariate statistics (Mahalanobis distance and joint likelihood ratio) to detect mutation points and improve detection accuracy.

[0012] Mahalanobis distance D M (t), used to calculate the multivariate distance between adjacent time windows and detect joint degradation mutations. The expression is:

[0013] Formula 2:

[0014]

[0015] Among them, μ and Σ are the mean and covariance matrix of historical data respectively.

[0016] Joint likelihood ratio test Λ, assuming that the distribution consistency of two consecutive windows is tested, if the likelihood ratio exceeds the threshold λ th , is determined as a change point, and the expression is Formula 3:

[0017]

[0018] Step 3: Multi-feature cluster analysis

[0019] After detecting the change point, the partition characteristics of the degradation pattern are further analyzed by feature clustering. Feature extraction is divided into local features and global features. In the local feature, the slope vector of each degradation segment (η=[η1,η2,…,η D ]), and the covariance matrix C∈R D×D In the global features, the first k principal components are extracted by principal component analysis (PCA), and 95% variance contribution rate is retained.

[0020] Deep embedding clustering, using autoencoders to map high-dimensional features to a low-dimensional space Z∈R d (d-dimensional real space), minimize the reconstruction loss The expression is Formula 4:

[0021]

[0022] The K-means algorithm is applied in the embedding space Z(t), and the number of clusters K is optimized by the silhouette coefficient. The embedded representation of each time t is mapped to the corresponding cluster label, Φ(t)∈{1,2,…,K}, which represents the degradation mode of the device at different times during the degradation process.

[0023] Step 4: Multi-dimensional degradation model construction

[0024] The joint degradation equation is as follows:

[0025]

[0026] Among them, the drift term matrix Λ∈R D×K , represents the multidimensional drift rate under each degradation mode. Diffusion covariance Σ H ∈R D×D , used to describe the correlation of multidimensional noise. Multidimensional fractal Brownian motion B H (t), H is the Hurst index, which ranges from H∈(0,1) and is used to characterize the long-range dependence of the degradation process; B H The incremental covariance of (t) is expressed as Equation 6:

[0027]

[0028] Step 5: Parameter estimation and remaining life prediction

[0029] In the multi-mode degradation modeling stage, the present invention defines a continuous-time Markov chain to characterize the transition behavior between degradation modes. The element q of the state transition rate matrix Q is ij , represents the switching rate from mode i to mode j. In order to deal with the boundary fuzziness problem in the mode switching process, a fuzzy Markov chain is introduced to deal with the boundary fuzziness. The expression is formula 7:

[0030]

[0031] Among them, μ i (t) is the membership degree of pattern i at time t, which is determined by the cluster embedding space Z(t) and the pattern center c i The similarity calculation is obtained, and the Gaussian kernel function is used for smoothing. The expression is formula 8:

[0032]

[0033] c i is the cluster center of the i-th category, σ is the bandwidth parameter, and is optimized through cross-validation.

[0034] The drift and diffusion parameters are solved by maximizing the log-likelihood function, which is expressed as Equation 9:

[0035]

[0036] In order to obtain the state transition rate q defined in the above equation 7 ij The present invention adopts an estimation method based on statistical counting, and the Markov chain transfer rate is estimated by counting method. The expression is formula 10:

[0037]

[0038] Where Nij represents the number of times switching from mode i to mode j, Δt k is the duration of mode k.

[0039] Hamiltonian Monte Carlo (HMC) sampling is introduced for high-dimensional parameters to accelerate the convergence of the posterior distribution.

[0040] The present invention is based on the improved Monte Carlo residual life prediction, adopts Copula function to model multi-dimensional correlation, and generates a joint degradation path: F(X1, X2, ..., X D )=C(F1(X1),F2(X2),…,F D (X D ), where C is the Gaussian Copula function, F i is the marginal distribution. The Monte Carlo sample weights are dynamically adjusted according to real-time data.

[0041] For each path X (i) (t), calculate the time when the failure threshold ω is first exceeded

[0042] The remaining life distribution is obtained by kernel density estimation (KDE), and the expression is formula 11:

[0043]

[0044] The bandwidth parameter h is set according to the Silverman criterion, and the expression is Equation 12:

[0045] h=0.9·min(σ,IQR / 1.34)·N -1 / 5 (Formula 12)

[0046] The overall framework flow chart of the system of the present invention is as follows Figure 1 shown.

[0047] The present invention also provides a multi-dimensional degradation control system based on autoencoding and fuzzy modeling, comprising:

[0048] Data acquisition module, used to acquire multi-sensor data in real time and construct three-dimensional tensors;

[0049] The preprocessing module is connected to the acquisition module and performs data standardization, tensor decomposition and entropy weight calculation;

[0050] The change point detection module is connected to the preprocessing module and identifies multi-dimensional collaborative mutation points based on Mahalanobis distance and joint likelihood ratio;

[0051] The feature analysis module is connected to the change point detection module and divides the degradation pattern through the autoencoder and clustering algorithm;

[0052] The degradation modeling module is connected to the feature analysis module to construct the joint degradation equation and estimate the parameters;

[0053] The life prediction module is connected to the degradation modeling module, and uses the Copula-Monte Carlo algorithm to generate the degradation path and output the remaining life distribution. Figure 2 The system module structure diagram of the present invention is shown as follows. Figure 3 The present invention provides a multi-dimensional degradation control method and system based on autoencoding and fuzzy modeling, which has the following beneficial effects:

[0054] (1) Through CP decomposition and entropy weight method, deep fusion and weight optimization of multi-sensor degradation data are achieved, which significantly improves the accuracy of feature extraction and data utilization;

[0055] (2) Multi-dimensional collaborative change point detection based on Mahalanobis distance and joint likelihood ratio can capture the mutation points of equipment degradation patterns in real time, enhancing the sensitivity to early fault signals;

[0056] (3) The autoencoder is combined with the clustering algorithm to perform low-dimensional embedding and pattern division of degradation features, effectively depicting the diversity and stages of the complex degradation process;

[0057] (4) The introduction of the joint degradation equation of fractal Brownian motion and diffusion covariance matrix can model long-range dependencies and improve the physical consistency of degradation process modeling;

[0058] (5) Fuzzy Markov chains are used to handle the uncertainty of state transitions, and the Copula-Monte Carlo algorithm is combined to generate multidimensional degradation paths and dynamically adjust sample weights, which greatly improves the accuracy and stability of remaining life prediction;

[0059] (6) The remaining life distribution is accurately constructed through kernel density estimation, and the bandwidth parameter is optimized using the Silverman criterion, achieving efficient and reliable health management and decision support. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flow chart of the overall framework of the system of the present invention;

[0061] Figure 2This is a flow chart of the life prediction part of the present invention;

[0062] Figure 3 This is a system module structure diagram of the present invention. DETAILED DESCRIPTION

[0063] The present invention relates to a multi-dimensional degradation process control system that combines deep reinforcement learning with degradation modeling technology to accurately model and predict the remaining life of complex industrial equipment based on the multi-mode degradation characteristics. The overall framework flow chart of the system is as follows: Figure 1 The following describes the embodiments of the present invention in detail through specific examples.

[0064] Step 1: Multi-dimensional data collection and preprocessing. For industrial equipment with multi-dimensional degradation characteristics (such as rotating machinery, gas turbines, etc.), first deploy a multi-sensor network to collect key degradation indicator data in real time, including temperature, vibration, wear, pressure, etc., and construct a multi-dimensional degradation vector X(t) = [x1(t), x2(t), ..., x n (t)],X(t)∈R T×D , where T is the time step, D is the number of dimensions, and M is the number of device instances. The data sampling frequency is set to 1Hz to 100Hz according to the device characteristics. To improve data quality, the data of each dimension is Z-score normalized to eliminate dimensional differences, and then the raw data is constructed as a three-dimensional tensor X∈R T×D×M , and uses CP decomposition (Canonical Polyadic Decomposition) for data fusion, extracting the core tensor G and factor matrix, significantly reducing data redundancy and noise interference. On this basis, the weight w of each dimension is calculated based on the entropy weight method i , the standardized expression is Formula 1:

[0065]

[0066] The weight values are used for feature weighted fusion in subsequent degradation modeling.

[0067] Step 2: Multi-dimensional change point detection. After data preprocessing, in order to capture possible sudden changes in various degradation indicators of the equipment, this embodiment adds a multi-dimensional change point detection module. The specific implementation steps are as follows:

[0068] Using Mahalanobis distance D M (t), using the above mean vector and covariance matrix, the difference between the statistical characteristics of the current time window and the historical data is quantified, and the expression is formula 2:

[0069]

[0070] where Xt is the multidimensional data vector within the current window. This distance quantifies the degree of deviation between the current window data and the overall historical characteristics. For multidimensional data, it can effectively eliminate the impact of different scales and correlations.

[0071] In addition to the Mahalanobis distance, in order to further improve the reliability of detection, a joint likelihood ratio test Λ is performed on the data distribution consistency of two adjacent time windows. Assume that the distribution consistency of two consecutive windows is tested. If the likelihood ratio exceeds the threshold λ th , is determined as a change point, and the expression is Formula 3:

[0072]

[0073] When it is detected that the statistics (Mahalanobis distance and joint likelihood ratio) in multiple consecutive windows exceed the set threshold, the system automatically marks the moment as a change point.

[0074] Step 3: Feature extraction and cluster analysis. After detecting the change point, it is necessary to further analyze the partition characteristics of the degradation pattern. First, extract local features and global features: the local features include the slope vector η = [η1, η2, ..., η D ], and the covariance matrix C∈R D×D ; The global features are extracted by principal component analysis (PCA) to extract the first k principal components (retaining 95% variance contribution rate). Subsequently, an autoencoder is used to map the high-dimensional features to a low-dimensional embedding space Z∈R d , minimize the reconstruction loss, the expression is formula 4:

[0075]

[0076] Optimize the feature representation and apply the K-means algorithm for clustering in the embedding space. Use the silhouette coefficient to determine the optimal number of clusters K to achieve partition identification of degradation patterns. Map the embedding representation at each time t to the corresponding cluster label Φ(t)∈{1,2,…,K}.

[0077] Step 4: Multi-dimensional degradation model construction. The degradation process is modeled as a joint equation, and the expression is Equation 5:

[0078]

[0079] Where the drift matrix Λ∈R D×K represents the drift rate of each mode, and the diffusion covariance matrix Σ H ∈R D×D Describing multidimensional noise correlation, fractal Brownian motion B H (t) The long-range dependence is characterized by the Hurst index H∈(0,1), and its incremental covariance is expressed as Equation 6:

[0080]

[0081] Step 5: Parameter estimation and remaining life prediction. Use fuzzy Markov chain to model state transition and define the membership function μ i (t) Quantify the mode switching fuzziness and accelerate parameter convergence through Hamiltonian Monte Carlo (HMC) sampling. The fuzzy Markov chain expression is as follows:

[0082]

[0083] μ i (t) is the membership degree of pattern i at time t, which is determined by the cluster embedding space Z(t) and the pattern center c i The similarity calculation is obtained, and the Gaussian kernel function is used for smoothing. The expression is formula 8:

[0084]

[0085] c i is the cluster center of the i-th class, σ is the bandwidth parameter, which is optimized through cross-validation. The specific symbols are shown in Table 1:

[0086]

[0087] Table 1

[0088] The drift and diffusion parameters are solved by maximizing the log-likelihood function, which is expressed as Equation 9:

[0089]

[0090] The Markov chain transition rate is estimated by the counting method, and the expression is Equation 10:

[0091]

[0092] Use Gaussian Copula function to model multi-dimensional correlation F(X1,X2,…,X D )=C(F1(X1),F2(X2),…,F D (X D )), where Fi is the marginal distribution, and the Monte Carlo sample weight is dynamically adjusted to adapt to real-time data. Simulate and generate multiple degradation paths X (i) (t), record the time when each path first exceeds the failure threshold ω, and finally calculate the remaining life distribution through kernel density estimation (KDE), the expression is formula 11:

[0093]

[0094] The bandwidth h is set according to the Silverman criterion to ensure that the prediction results have physical consistency and high accuracy. The expression is Equation 12:

[0095] h=0.9·min(σ,IQR / 1.34)·N -1 / 5 (Formula 12)

[0096] Based on the above technical background and prior art, in order to more clearly illustrate the technical solution and implementation methods of the present invention, the system architecture, workflow and other aspects of the present invention are described in detail below. By elaborating on specific embodiments, it is intended to enable those skilled in the art to better understand and implement the present invention, thereby achieving the intended technical effects.

[0097] In a specific implementation, the system architecture is divided into a data acquisition module, a data preprocessing module, a feature extraction and analysis module, a degradation modeling and prediction module, and a result display and decision support module. The data acquisition module is responsible for acquiring data from each sensor and performing preliminary formatting processing to ensure the uniformity and standardization of the data. The data preprocessing module performs denoising and standardization on the collected data to ensure data quality. The feature extraction and analysis module extracts key features from the preprocessed data, performs pattern recognition and trend analysis, and reveals the operating status of the equipment. The degradation modeling and prediction module establishes a degradation model based on the analysis results, predicts the remaining life of the equipment, and provides maintenance decision support. The life prediction flow chart is as follows: Figure 2 shown.

[0098] The system module structure diagram is as follows Figure 3 shown.

[0099] The system's workflow includes data acquisition, data transmission, data processing, feature analysis, modeling and prediction, and result presentation. Sensors collect real-time equipment operating data and transmit it to the data storage and processing unit via a communication interface. The data preprocessing module processes the raw data to ensure data quality. The feature extraction and analysis module analyzes the processed data to identify key features. The degradation modeling and prediction module uses the analysis results to develop a degradation model and predict the remaining life of the equipment.

[0100] The specific embodiments described above further illustrate the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-dimensional degradation control method based on autoencoding and fuzzy modeling, characterized in that: The following steps are involved: Step 1: Multi-dimensional data collection and preprocessing: Collect multi-dimensional degradation indicator data of industrial equipment, construct a three-dimensional tensor, and perform data fusion and weight calculation through tensor decomposition and entropy weight method; Step 2: Multidimensional change point detection: Use multivariate statistics to detect the collaborative mutation points in the degradation process; Step 3: Multi-feature clustering analysis: extract local and global features, and divide the degradation pattern by combining autoencoder dimensionality reduction with clustering algorithm; Step 4: Multi-dimensional degradation model construction: Establish a joint degradation equation including the drift term matrix, diffusion covariance matrix and fractal Brownian motion; Step 5: Parameter estimation and remaining life prediction: Based on the fuzzy Markov chain modeling state transition, the Copula-Monte Carlo algorithm is used to generate the joint degradation path, and the remaining life distribution is calculated by kernel density estimation.

2. The method according to claim 1, characterized in that In step 1: The three-dimensional tensor is constructed as X∈R T×D×M , where T is the time step, D is the number of dimensions, and M is the number of device instances; data fusion uses CP decomposition to extract core tensors and factor matrices; dimension weights are calculated using the entropy weight method and are expressed as Equation 1 3. The method according to claim 1, characterized in that In step 2: The multivariate statistics include Mahalanobis distance and joint likelihood ratio; The Mahalanobis distance calculation method is expressed as formula 2: Among them, μ and Σ are the mean and covariance matrix of historical data respectively; The joint likelihood ratio test determines the change point by comparing the distribution consistency of adjacent time windows. The expression is Equation 3:

4. The method according to claim 1, wherein In step 3: The local features include the degradation segment slope vector η and the covariance matrix C. The global features are extracted by principal component analysis to retain the top k principal components with a 95% variance contribution rate. The autoencoder optimizes the low-dimensional embedding space by minimizing the reconstruction loss, which is expressed as Equation 4: The clustering algorithm uses K-means, and the optimal cluster number K is determined by the silhouette coefficient.

5. The method according to claim 1, wherein In step 4: The joint degradation equation is expressed as Equation 5: Among them, Λ is the drift matrix, Σ H is the diffusion covariance matrix, B H (t) is a fractal Brownian motion, and its Hurst exponent H∈(0,1). H (t) Incremental covariance, expressed as Equation 6:

6. The method according to claim 1, wherein In step 5: The fuzzy Markov chain handles boundary fuzziness, and the expression is Equation 7: The state transition rate of the fuzzy Markov chain is calculated by the membership function, which is expressed as Equation 8:

7. The method according to claim 1, characterized in that In step 5: The drift and diffusion parameters are solved by maximizing the log-likelihood function, which is expressed as Equation 9: The Markov chain transition rate is estimated by counting method, which is expressed as Equation 10:

8. The method according to claim 1, characterized in that In step 5, the remaining life distribution is obtained by kernel density estimation (KDE), which is expressed as formula 11:

9. The method according to claim 1, characterized in that In step 5, the bandwidth calculation formula for kernel density estimation is 12: h = 0.9·min(σ, IQR / 1.34)·N -1 / 5 ; (Equation 12) 10. A multi-dimensional degradation control system based on autoencoding and fuzzy modeling, characterized in that: include: Data acquisition module, used to acquire multi-sensor data in real time and construct three-dimensional tensors; The preprocessing module is connected to the acquisition module and performs data standardization, tensor decomposition and entropy weight calculation; The change point detection module is connected to the preprocessing module and identifies multi-dimensional collaborative mutation points based on Mahalanobis distance and joint likelihood ratio; The feature analysis module is connected to the change point detection module and divides the degradation pattern through the autoencoder and clustering algorithm; The degradation modeling module is connected to the feature analysis module to construct the joint degradation equation and estimate the parameters; The life prediction module, connected to the degradation modeling module, uses the Copula-Monte Carlo algorithm to generate the degradation path and output the remaining life distribution.

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