Random degradation equipment residual life prediction method based on graph convolutional network

Abstract

The invention belongs to the technical field of reliability engineering, and relates to a multi-sensor random degradation equipment digital-analog residual life prediction method based on a graph convolutional network. The invention provides a method for predicting the residual life of random degradation equipment based on a graph convolutional network, and the method comprises the steps: S1, carrying out the normalization of the monitoring data of a j-th sensor collected on i-th equipment, and carrying out the further integration, and obtaining the degradation data of the i-th sensor; s2, regarding each sensor as a node, constructing a sensor network relation graph by calculating the similarity between the nodes, then learning interaction information between the sensors by adopting a graph convolutional network, and further constructing a composite health index sequence of monitoring data; s3, constructing a random degradation model of the random degradation equipment; s4, constructing a calculation model formula of the service life and the residual service life of the random degradation equipment; and S5, constructing a probability density function model and a cumulative distribution function model of the online service equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability engineering and relates to a method for predicting the digital-analog remaining life of multi-sensor randomly degraded equipment based on a graph convolutional network. Background Art

[0002] In many industrial and engineering applications, equipment maintenance and management are essential to ensure safety, reliability and economy. Prognostics and Health Management (PHM) is a feasible and effective technology that improves safety and reduces risks through proactive management activities. Since it was first proposed in the 1960s, it has been widely favored by scholars and engineers. PHM technology optimizes preventive health management activities by extracting information from various data sources, especially online condition monitoring (CM) data, evaluating the health status of equipment, and predicting the remaining useful life (Remaining Useful Life) of related equipment. Among them, the remaining useful life is defined as the time interval from the current moment to the failure of the equipment or equipment, providing reference information for maintenance planning and spare parts ordering, thereby extending the service life of the equipment and reducing maintenance costs and operating risks. Obviously, the remaining useful life prediction that links health management decisions with the health status of equipment has always played an important role in PHM. Due to the interaction between the internal degradation of materials and structures and external factors such as workloads and environmental conditions, the performance of most equipment exhibits random degradation, so it is called random degradation equipment. The prediction methods for randomly degraded equipment include methods based on physical models, data-driven methods, and their fusion. With the rapid development of data acquisition, conversion, storage, and processing technologies, data-driven methods have become dominant in the field of prediction of the remaining useful life of randomly degraded equipment. Generally speaking, the existing data-driven remaining useful life prediction methods for randomly degraded equipment are mainly divided into machine learning-based methods, statistical data-driven prediction methods, and hybrid methods.

[0003] Currently, machine learning techniques are combined with statistical data-driven predictions to achieve better remaining useful life predictions for complex stochastically degraded equipment with uncertainty characteristics. Two different technical routes can be summarized from the existing literature. The first method uses machine learning techniques to model the evolution of the complex health index of the relevant equipment. The second method uses a dedicated deep neural network to extract degradation features and construct a composite health index (CHI), which is more practical for equipment with multiple sensors. Usually, the constructed CHI is further described by a stochastic process model to represent temporal uncertainty. However, the data model interaction method in the existing methods constructs a one-dimensional CHI through weighted summation or deep neural networks, without specifically considering the correlation between multi-sensor data. In fact, during the operation of the equipment, its remaining useful life is affected by multiple sensors at the same time, and these sensors also interact with each other. Therefore, learning the relevant information between sensors is crucial to improve the accuracy of prediction. Summary of the invention

[0004] In view of the shortcomings of existing prediction methods, this paper proposes an interactive data model prediction method based on graph convolutional network (GCN) for the prediction of the remaining useful life of multi-sensor randomly degraded equipment. Specifically, sensors are regarded as nodes of a graph, and cosine similarity is used to evaluate the correlation between them. Then, a sensor network graph is constructed based on the calculated similarity, and GCN is used to propagate and aggregate information among sensors. This process learns the correlation between them and integrates them into the constructed CHI representing the health status of the equipment. On this basis, the evolution process of the constructed rules is modeled using a linear Wiener process model, and the corresponding remaining useful life of the rules under the concept of first hit time (FHT) is explicitly derived, as well as the rules and their variances of the expected rules. The method realizes parameter training by minimizing the cost function composed of the mean squared error (MSE) of the predicted rules, and automatically matches the extraction of CHI with random degradation modeling. Finally, the method is verified by the C-MAPSS dataset. The contribution of this paper is mainly to construct a data model remaining useful life prediction method for randomly degraded equipment considering the correlation between different sensors. According to the similarity of CM data, the relationship between sensors is described graphically, and the correlation between sensors is fully described into CHI, thereby improving the accuracy of remaining useful life prediction.

[0005] In order to achieve the above technical effects, the present invention proposes a method for predicting the remaining life of randomly degraded equipment based on a graph convolutional network, comprising:

[0006] S1: Normalize the monitoring data of the jth sensor collected on the i-th device, and further integrate it to obtain the degradation data of the i-th sensor;

[0007] S2: Each sensor is regarded as a node, and the sensor network relationship graph is constructed by calculating the similarity between nodes. Then, a graph convolutional network is used to learn the interaction information between sensors, and then a composite health index sequence of monitoring data is constructed;

[0008] S3: Based on S2, a random degradation model of randomly degraded equipment is constructed;

[0009] S4: Based on S3, a life and remaining life calculation model formula for randomly degraded equipment is constructed;

[0010] S5: Based on S4, construct the probability density function and cumulative distribution function model of online service equipment.

[0011] Preferably, S1 comprises:

[0012] S1.1: Monitoring data of the jth sensor collected on the i-th device The normalization operation is as follows:

[0013]

[0014] in, for After normalization, the monitoring data and are the maximum and minimum values ​​of all historical monitoring data of the jth sensor respectively;

[0015] S1.2: The monitoring data of the jth sensor of the i-th randomly degraded device after normalization is expressed as The degradation data of the i-th sensor obtained by integration is expressed as:

[0016]

[0017] in, The Sth sensor K of the i-th device i Data at the moment.

[0018] Preferably, S2 comprises:

[0019] S2.1: Consider the sensors used to collect data as nodes, determine the neighbor nodes of each node by calculating the cosine similarity between nodes, and calculate the weight A of the edges between nodes ij :

[0020]

[0021] in, x i and x j are the feature vectors of the nodes;

[0022] S2.2: GCN is used to learn the deep association information between nodes. The propagation rules between layers are defined as:

[0023]

[0024] Among them, the weight A ij Abbreviated as A, is the normalized adjacency matrix, I is the identity matrix, H (l) and H (l+1) are the node feature matrices of the lth layer and the l+1th layer, respectively, W (l) is the weight matrix of the lth layer, is the normalized degree matrix, σ is the nonlinear activation function;

[0025] S2.3: Construct monitoring moments One-dimensional composite health index sequence z i :

[0026]

[0027] For the i-th device The indicator of time, K i Represents the total number of all status monitoring points of the i-th device.

[0028] Preferably, S3 includes:

[0029] S3.1: Construct the random degradation model of the i-th (1≤i≤N) randomly degraded device at time t:

[0030] Z i (t) = z i,0 +θt+σB(t)

[0031] Among them, z i,0 is the initial degradation level, θ and σ are the drift coefficient and diffusion coefficient respectively, and B(t) is the standard Brownian motion reflecting the time-varying uncertainty of the degradation process;

[0032] S3.2: Express the θ and σ parameters to be estimated in S3.1 as θ = [θ, σ];

[0033] S3.3: Estimate the parameter Θ of S3.2 using the maximum likelihood estimation method:

[0034]

[0035] Where Δz i,k =z i,k -z i,k-1 , Δt=t i,k -t i,k-1 ; K i represents the total number of all status monitoring points of the i-th device; L(Θ) is the likelihood function, z i,k and z i,k-1 t i,k and t i,k-1 Composite health index at time, t i,k represents the kth monitoring time of the ith device, t i,k-1 represents the k-1th monitoring moment;

[0036] S3.4: In the formula of S3.3, θ and σ are 2 Taking the partial derivative and calculating its estimated value, we can get the maximum likelihood estimate of the degradation model parameter Θ of the i-th (1≤i≤N) randomly degraded device:

[0037]

[0038]

[0039] Among them, σ 2 is the square of the diffusion coefficient, For the i-th device Composite health index at each moment, K i represents the total number of all status monitoring points of the i-th device, z i,0 is the composite health indicator of the i-th device at time 0, and k represents the k-th measurement value of the i-th device.

[0040] Preferably, S4 includes:

[0041] S4.1: Lifetime T of the i-th (1≤i≤N) randomly degraded device i and the remaining life L i,k They are:

[0042] T i = inf{t i :Z i (t i )≥w|z i,0 <w}

[0043] L i,k = inf{l i,k :Z i (t i,k +li,k )≥w|z i,k <w}

[0044] Where w is the failure threshold, z i,k t i,k The composite health index sequence at the moment, l i,k t i,k The remaining life of the moment;

[0045] S4.2: Based on S4.1, life span T i and the remaining life L i,k It obeys the inverse Gaussian distribution parameterized by Θ = [θ,σ], then the lifetime of the i-th randomly degraded equipment T i The probability density function of and the cumulative distribution function for:

[0046]

[0047] Among them, t i represents the i-th monitoring moment;

[0048] Similarly, t i,k The remaining life of the i-th randomly degraded equipment at time L i,k The probability density function of and the cumulative distribution function for:

[0049]

[0050]

[0051] Therefore, the lifetime T of a randomly degraded device is i Expectations and variance They are:

[0052]

[0053] Among them, the result of life prediction is the expectation; the remaining life of the randomly degraded equipment L i,k Expectations and variance They are:

[0054]

[0055] S4.3: Construct a loss function to calculate the deviation between the predicted life value and the true value, and then the parameters in the training process. The specific calculation method of the loss function is as follows:

[0056]

[0057] Among them, T i and They represent the actual life and predicted life of the i-th (1≤i≤N) device respectively, N is the total number of devices, w is the failure threshold, W and b are the weight matrix and bias vector. The above parameters are optimized during the model training process. W, b, and w are all parameters optimized during the model training process.

[0058] Preferably, the probability density function of the remaining service life of S5 online service equipment is and the cumulative distribution function The expressions are:

[0059]

[0060]

[0061] Among them, l k represents the remaining life value of the online service equipment at the kth moment, and the deep degradation characteristic sequence of the online service equipment is z 0:k ={z0,z1,z2,...,z k}, θ i represents the initial degradation value of the i-th online service equipment, σ represents the randomness parameter of the online service equipment degradation, and w is the failure threshold; Z k is the composite health index of the online service equipment at time k, μ θ,K and is p(θ|z 0:K ) is the estimated parameter of the distribution of , and Φ represents the Φ function.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. The present invention designs a method for predicting the remaining life of multi-sensor randomly degraded equipment based on graph convolutional networks, which can efficiently integrate multi-sensor data features and effectively improve the prediction performance.

[0064] 2. The present invention combines the advantages of graph convolutional networks and Wiener processes to efficiently capture complex and relevant degradation information, thereby improving the accuracy of remaining life prediction.

[0065] 3. The present invention has strong generalization ability and can be effectively applied to equipment health status monitoring and remaining life prediction in complex industrial environments, providing reliable support for intelligent maintenance decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0067] In the attached picture:

[0068] Figure 1 is the sensor data information;

[0069] Figure 2 In the figure, (a) is the training set of the constructed composite health index; (b) is the test set of the constructed composite health index;

[0070] Figure 3 In the figure, (a) is the predicted remaining useful life and remaining useful life of engine No. 79; (b) is the predicted remaining useful life and remaining useful life of engine No. 82; (c) is the predicted remaining useful life and remaining useful life of engine No. 85; (d) is the predicted remaining useful life and remaining useful life of engine No. 88;

[0071] Figure 4 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0072] The following is combined with Figure 1 -Attached Figure 4 The preferred embodiments of the present invention are described. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0073] Example:

[0074] A method for predicting the remaining life of randomly degraded equipment based on a graph convolutional network, comprising:

[0075] S1: Normalize the monitoring data of the jth sensor collected on the i-th device, and further integrate to obtain the degradation data of the i-th sensor; S1 includes:

[0076] S1.1: Monitoring data of the jth sensor collected on the i-th device The normalization operation is as follows:

[0077]

[0078] in, for After normalization, the monitoring data and are the maximum and minimum values ​​of all historical monitoring data of the jth sensor respectively;

[0079] S1.2: The monitoring data of the jth sensor of the i-th randomly degraded device after normalization is expressed as The degradation data of the i-th sensor obtained by integration is expressed as:

[0080]

[0081] in, The Sth sensor K of the i-th device i Each row represents the pre-processed monitoring data of the same sensor at different times, recording the operating status of the sensor at different time points; and each column corresponds to the monitoring data of all sensors at a certain moment.

[0082] S2: Unlike traditional structured data, a graph is a special data structure consisting of vertices and edges, which is used to describe pairwise relationships between targets and entities. In a graph, vertices represent targets or entities, and edges represent the relationships or connections between these targets or entities. Graphs can be directed or undirected, and edges can have weights to represent relationship strength or distance. Graph data can be described in the following ways:

[0083] G=(V,E,A) (3)

[0084] Among them, V and E represent the node set and edge set respectively, A∈R N×N is the adjacency matrix, and N is the number of nodes in the graph.

[0085] Each sensor is regarded as a node, and the sensor network relationship graph is constructed by calculating the similarity between nodes. Then, the graph convolutional network is used to learn the interaction information between sensors, and then a composite health index sequence of monitoring data is constructed. Specifically, it includes:

[0086] S2.1: Consider the sensors used to collect data as nodes, determine the neighbor nodes of each node by calculating the cosine similarity between nodes, and calculate the weight A of the edges between nodes ij :

[0087]

[0088] in, x i and x j are all feature vectors of nodes; for node x i , and its neighbor nodes are represented as

[0089]

[0090] S2.2: GCN is used to learn the deep association information between nodes. The propagation rules between layers are defined as:

[0091]

[0092] Among them, the weight A ij Abbreviated as A, is the normalized adjacency matrix, I is the identity matrix, H (l) and H (l+1) are the node feature matrices of the lth layer and the l+1th layer, respectively, W (l) is the weight matrix of the lth layer, is the normalized degree matrix, σ is the nonlinear activation function; the input layer feature H (0) is the degradation data feature X of each sensor i The graph convolution process is done by normalizing the adjacency matrix To spread node information, it avoids the impact of node degree imbalance on aggregation results.

[0093] When constructing CHI, X i As the initial input feature, the propagation information between layers is calculated through the above formula (6). Subsequently, a fully connected layer is used to fuse the data of each sensor to construct the degradation feature CHI sequence for subsequent degradation modeling.

[0094] S2.3: Construct monitoring moments One-dimensional composite health index sequence Z i :

[0095]

[0096] For the i-th device The indicator of time, K i Represents the total number of all status monitoring points of the i-th device.

[0097] S3: Based on S2, a random degradation model of random degradation equipment is constructed; including:

[0098] S3.1: Construct the random degradation model of the i-th (1≤i≤N) randomly degraded device at time t:

[0099] Z i (t) = z i,0 +θt+σB(t) (7)

[0100] Among them, z i,0 is the initial degradation level, θ and σ are the drift coefficient and diffusion coefficient respectively, and B(t) is the standard Brownian motion that reflects the time-varying uncertainty of the degradation process. This model can effectively capture the changes in the health status of the equipment and predict the remaining life.

[0101] S3.2: Express the θ and σ parameters to be estimated in S3.1 as θ = [θ, σ];

[0102] S3.3: Therefore, based on the Markov property of standard Brownian motion, the maximum likelihood estimation method is used to estimate the parameter Θ of S3.2:

[0103]

[0104] Where Δz i,k =z i,k -z i,k-1 , Δt=t i,k -t i,k-1 ; K i represents the total number of all status monitoring points of the i-th device; L(Θ) is the likelihood function, z i,k and z i,k-1 t i,k and t i,k-1 Composite health index at time, t i,k represents the kth monitoring time of the ith device, t i,k-1 represents the k-1th monitoring moment;

[0105] S3.4: In the formula of S3.3, θ and σ are 2 Taking the partial derivative and calculating its estimated value, we can get the maximum likelihood estimate of the degradation model parameter Θ of the i-th (1≤i≤N) randomly degraded device:

[0106]

[0107] Among them, σ 2 is the square of the diffusion coefficient, For the i-th device Composite health index at each moment, K i represents the total number of all status monitoring points of the i-th device, z i,0 is the composite health indicator of the i-th device at time 0, and k represents the k-th measurement value of the i-th device.

[0108] S4: Based on S3, a life and remaining life calculation model formula for randomly degraded equipment is constructed; including:

[0109] S4.1: Lifetime T of the i-th (1≤i≤N) randomly degraded device i and the remaining life L i，k They are:

[0110] T i = inf{t i :Z i (t i )≥w|z i,0 <w} ( 11 )

[0111] L i,k = inf{l i,k :Z i (ti,k +l i,k )≥w|z i,k <w} (12)

[0112] Where w is the failure threshold, z i,k t i,k The composite health index sequence at the moment, l i，k ;

[0113] S4.2: Based on S4.1, life span T i and the remaining life L i,k It obeys the inverse Gaussian distribution parameterized by Θ = [θ,σ], then the lifetime of the i-th randomly degraded equipment T i The probability density function of and the cumulative distribution function for:

[0114]

[0115] Among them, t i represents the i-th monitoring moment;

[0116] Similarly, t i,k The remaining life of the i-th randomly degraded equipment at time L i,k The probability density function of and the cumulative distribution function for:

[0117]

[0118] Therefore, the lifetime T of a randomly degraded device is i Expectations and variance They are:

[0119]

[0120] The remaining life of randomly degraded equipment L i,k Expectations and variance They are:

[0121]

[0122] The lifetime and remaining lifetime of the randomly degraded equipment are expressed by expectation. Based on the above extracted CHI and random degradation modeling, a loss function is constructed to calculate the deviation between the predicted lifetime value and the true value.

[0123] S4.3: Construct a loss function to calculate the deviation between the predicted life value and the true value, and then the parameters in the training process. This loss function can reversely optimize the parameters and failure threshold of CHI, so as to realize the interactive linkage of the equipment. The specific calculation method of the loss function is as follows:

[0124]

[0125] Among them, T i and They represent the actual life and predicted life of the i-th (1≤i≤N) device respectively, N is the total number of devices, w is the failure threshold, W and b are the weight matrix and bias vector. The above parameters are optimized during the model training process. W, b, and w are all parameters optimized during the model training process.

[0126] During the training process, continuous feedback optimization and adjustment are performed to achieve interaction between the construction of the composite health indicator and the random degradation modeling of the equipment, so as to enhance the matching degree between the composite health indicator and the degradation model.

[0127] S5: Based on S4, construct the probability density function and cumulative distribution function model of online service equipment.

[0128] For random degradation equipment in online service, there is more or less inter-unit variability between it and historically degraded equipment, and some degradation parameters need to be used as random variables to characterize this variability. Therefore, the main task of predicting the remaining service life of online service equipment is to update the parameters based on the real-time monitoring data obtained. Assume that the service life of the equipment in service is from the initial time to the current time t k The monitoring data is represented by X 0:K , the corresponding monitoring time is 0 = t0 < t1 < ... < t K During prediction, the acquired monitoring data is input into the trained model to obtain the CHI sequence z representing the health status of the equipment. 0:K ={z0,z1,z2,…,z K Then, the linear Wiener process model defined by equation (7) is used to model z 0:K The time evolution process of the equipment is analyzed, and finally the expectation and variance of the remaining useful life of the equipment in service are calculated.

[0129] In order to characterize the variability of in-service equipment, the parameter θ in the model that can reflect the degradation rate of the equipment is selected as a random variable, assuming that θ obeys the mean μ θ,0 , the variance is In addition, the parameter σ in the model 2It is a fixed parameter that characterizes the common characteristics. As a commonly used model parameter update method, the Bayesian update method has been widely used in the parameter update of the remaining service life. Therefore, after obtaining new monitoring data, the Bayesian update method is used to calculate the posterior estimate of θ to dynamically update the parameters of the model. The core idea is to continuously correct the prior distribution of the model by combining the newly acquired observation data, and then generate a new posterior distribution, so as to more accurately reflect the real-time changes in the equipment status. When applying this method, it is first necessary to determine the prior distribution form of θ, σ 2 and the related hyperparameters therein.

[0130] Based on the above assumptions, the estimated values ​​of the mean and variance of θ can be calculated using equations (8) and (9), namely:

[0131]

[0132] σ 2 The estimated value of can be calculated by formula (12) The sample mean of is estimated as

[0133]

[0134] Based on the Bayesian updating method, at the current time t k , the posterior distribution of θ can be expressed as

[0135]

[0136] where p(θ) represents the prior distribution and p(z 0:K |θ) represents the joint probability density function under the condition of given θ. The specific form is

[0137]

[0138] Since p(z 0:K |θ) and p(θ) both obey the normal distribution, and the two form a conjugate relationship, so the posterior distribution p(θ|z 0:K ) also obeys the normal distribution, that is, Substituting (21) and (22) into (20), we can obtain t k The posterior estimate of the time parameter is

[0139]

[0140] Due to the randomness of parameter θ, its probability distribution should be integrated into the remaining useful life distribution during prediction. According to the total probability formula, t k The probability density function and cumulative distribution function of the remaining useful life of the equipment in service at the moment are expressed as follows

[0141]

[0142] in and Respectively represent θ and z 0:K The remaining useful life and cumulative distribution function of the condition.

[0143] Based on the above results, we can get t k Probability density function of the remaining service life of equipment in service at all times and the cumulative distribution function The expressions are:

[0144]

[0145] Among them, l k represents the remaining life value of the online service equipment at the kth moment, and the deep degradation characteristic sequence of the online service equipment is z 0:k ={z0,z1,z2,...,z k}, θ i represents the initial degradation value of the i-th online service equipment, σ represents the randomness parameter of the online service equipment degradation, and w is the failure threshold; Z k is the composite health index of the online service equipment at time k, μ θ,K and is p(θ|z 0:K ) is the estimated parameter of the distribution of , and Φ represents the Φ function.

[0146] Finally, the estimated parameters Substituting into equations (28) and (29) above, online prediction of the in-service system can be realized. Through the updated remaining useful life and cumulative distribution function, the point estimate of the remaining useful life and the predicted confidence interval can be calculated, and the uncertainty of the prediction can be quantified.

[0147] The life of a randomly degraded device is the time interval from time 0 to the time of failure, and the remaining life of a randomly degraded device is the time interval from the current time to the time of failure. The remaining service life of an in-service device is the time interval from the current time to the time of failure of the in-service device.

[0148] Verification experiment:

[0149] The implementation of the present invention is explained in combination with the experiment of the condition monitoring data of the aircraft engine. The experiment is conducted based on the simulation data set FD001 under a single working condition and a single failure mode. The specific steps include:

[0150] A. Data preprocessing and sensor selection

[0151] from Figure 1It can be observed that the monitoring data of some sensors (T2, P2, P15, epr, farB, Nf_dmd, PCNfR_dmd) have no obvious time-varying trend. Therefore, these sensor data are eliminated and 14 sensor data that can reflect the performance degradation of the engine equipment are selected for the experiment.

[0152] B. Set experimental parameters

[0153] The first 60 engines in the FD001 dataset were selected as the training set, and the last 40 engines were selected as the test set. The GCN network used in the model consists of two graph convolution layers and one fully connected layer. During the model training process, the Epoch was set to 1000, the Adams optimizer was used, the learning rate and L2 regularization parameters were set to 0.001, and the activation function was LeakReLU. The above experiments were run on an Intel Xeon Gold 5118CPU computer based on Linux and Python 3.8 environment and Pytorch 1.10 framework.

[0154] C. Comparison of performance of different methods for predicting remaining useful life

[0155] like Figure 2 As shown, we constructed CHI for the training set and the test set. The optimized fault threshold in the training phase is -0.08699. It is obvious that the calculated CHI decreases as the number of operating cycles increases. In order to evaluate the effect of CHI, we used the Pearson correlation coefficient to quantitatively analyze the test set results. This coefficient ranges from -1 to 1, and its size indicates the strength of linear correlation. In addition, we also calculated the variance of CHI at failure to evaluate the consistency between similar devices under the same conditions. The comparison results are shown in Table 1. It is obvious that the absolute value of the Pearson correlation coefficient of the constructed CHI exceeds the absolute value of the correlation coefficient of a single sensor, indicating that the construction quality of CHI has been significantly improved. In addition, the variance of the fault threshold is smaller than the variance of a single sensor. Therefore, it can be proved that the CHI we constructed effectively captures the equipment degradation information.

[0156] Table 1 Comparison with other methods

[0157]

[0158]

[0159] It is compared with the state-of-the-art methods, including deep neural network based methods (CNN, ALSTM, GCN+EdgePool, GGCN). Table 2 summarizes the RMSE and SF values ​​of all prognostic methods for FD001. It can be seen that the RMSE and SF indicators show that the proposed method outperforms the baseline methods, indicating that the prediction accuracy can be significantly improved by utilizing inter-sensor information. In addition, compared with most competing methods, this method can provide uncertainty quantification, which helps to arrange a more reasonable maintenance plan.

[0160] Table 2 RMSE and SF

[0161]

[0162] By substituting the estimated parameters into equation (16), the probability distribution of the remaining useful life of the randomly degraded equipment is calculated. In addition, the remaining useful life probability density function (remaining useful life) of engines 79, 82, 85 and 88 in the test set is given. Figure 3 Among them, (a) is the predicted remaining service life and remaining service life of engine No. 79; (b) is the predicted remaining service life and remaining service life of engine No. 82; (c) is the predicted remaining service life and remaining service life of engine No. 85; (d) is the predicted remaining service life and remaining service life of engine No. 88. Figure 3 The predicted remaining useful life, actual remaining useful life, and remaining useful life curves of the three engines for the last 20 monitoring moments are shown. It can be seen that with the increase in the amount of monitoring data, the remaining useful life curve becomes more clear, indicating a reduction in prediction uncertainty and an improvement in the accuracy of the predicted remaining useful life results, verifying that the proposed method can effectively predict the remaining useful life and quantify the uncertainty.

[0163] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks, characterized by: include: S1: Normalize the monitoring data of the jth sensor collected on the i-th device, and further integrate it to obtain the degradation data of the i-th sensor; S2: Each sensor is regarded as a node, and the sensor network relationship graph is constructed by calculating the similarity between nodes. Then, a graph convolutional network is used to learn the interaction information between sensors, and then a composite health index sequence of monitoring data is constructed; S3: Based on S2, a random degradation model of randomly degraded equipment is constructed; S4: Based on S3, a life and remaining life calculation model formula for randomly degraded equipment is constructed; S5: Based on S4, construct the probability density function and cumulative distribution function model of online service equipment.

2. According to claim 1, a method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks is characterized in that: S1 includes: S1.1: Monitoring data of the jth sensor collected on the i-th device The normalization operation is as follows: in, for After normalization, the monitoring data and are the maximum and minimum values ​​of all historical monitoring data of the jth sensor respectively; S1.2: The monitoring data of the jth sensor of the i-th randomly degraded device after normalization is expressed as The degradation data of the i-th sensor obtained by integration is expressed as: in, The Sth sensor K of the i-th device i Data at the moment.

3. According to claim 2, a method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks is characterized in that: S2 includes: S2.1: Consider the sensors used to collect data as nodes, determine the neighbor nodes of each node by calculating the cosine similarity between nodes, and calculate the weight A of the edges between nodes ij : in, x i and x j are the feature vectors of the nodes; S2.2: GCN is used to learn the deep association information between nodes. The propagation rules between layers are defined as: Among them, the weight A ij Abbreviated as A, is the normalized adjacency matrix, I is the identity matrix, H (l) and H (l+1) are the node feature matrices of the lth layer and the l+1th layer, respectively, W (l) is the weight matrix of the lth layer, is the normalized degree matrix, σ is the nonlinear activation function; S2.3: Construct monitoring moments One-dimensional composite health index sequence z i : For the i-th device The indicator of time, K i Represents the total number of all status monitoring points of the i-th device.

4. According to claim 3, a method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks is characterized in that: S3 includes: S3.1: Construct the random degradation model of the i-th (1≤i≤N) randomly degraded device at time t: Z i (t)=z i,0 +θt+σB(t) Among them, z i,0 is the initial degradation level, θ and σ are the drift coefficient and diffusion coefficient respectively, and B(t) is the standard Brownian motion reflecting the time-varying uncertainty of the degradation process; S3.2: Express the θ and σ parameters to be estimated in S3.1 as θ = [θ, σ]; S3.3: Estimate the parameter Θ of S3.2 using the maximum likelihood estimation method: Where Δz i,k =z i,k -z i,k-1 , Δt=t i,k -t i,k-1 ; K i represents the total number of all status monitoring points of the i-th device; L(Θ) is the likelihood function, z i,k and z i,k-1 t i,k and t i,k-1 Composite health index at time, t i,k represents the kth monitoring time of the ith device, t i,k-1 represents the k-1th monitoring moment; S3.4: In the formula of S3.3, θ and σ are 2 Taking the partial derivative and calculating its estimated value, we can get the maximum likelihood estimate of the degradation model parameter Θ of the i-th (1≤i≤N) randomly degraded device: Among them, σ 2 is the square of the diffusion coefficient, For the i-th device Composite health index at each moment, K i represents the total number of all status monitoring points of the i-th device, z i,0 is the composite health indicator of the i-th device at time 0, and k represents the k-th measurement value of the i-th device.

5. According to claim 4, a method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks is characterized in that: S4 includes: S4.1: Lifetime T of the i-th (1≤i≤N) randomly degraded device i and the remaining life L i，k They are: T i =inf{t i :Z i (t i )≥w|z i,0 <w} L i,k =inf{l i,k :Z i (t i,k +l i,k )≥w|z i,k <w} Where w is the failure threshold, z i,k t i,k The composite health index sequence at the moment, l i,k t i,k The remaining life of the moment; S4.2: Based on S4.1, life span T i and the remaining life L i,k It obeys the inverse Gaussian distribution parameterized by Θ = [θ,σ], then the lifetime of the i-th randomly degraded equipment T i The probability density function of and the cumulative distribution function for: Among them, t i represents the i-th monitoring moment; Similarly, t i,k The remaining life of the i-th randomly degraded equipment at time L i,k The probability density function of and the cumulative distribution function for: Therefore, the lifetime T of a randomly degraded device is i Expectations and variance They are: Among them, the result of life prediction is the expectation; the remaining life of the randomly degraded equipment L i,k Expectations and variance They are: S4.3: Construct a loss function to calculate the deviation between the predicted life value and the true value, and then the parameters in the training process. The specific calculation method of the loss function is as follows: Among them, T i and They represent the actual life and predicted life of the i-th (1≤i≤N) device respectively, N is the total number of devices, w is the failure threshold, W and b are the weight matrix and bias vector. The above parameters are optimized during the model training process. W, b, and w are all parameters optimized during the model training process.

6. The method for predicting the remaining life of randomly degraded equipment based on graph convolutional networks according to claim 5 is characterized in that: S5 Probability density function of remaining service life of online service equipment and the cumulative distribution function The expressions are: Among them, l k represents the remaining life value of the online service equipment at the kth moment, and the deep degradation characteristic sequence of the online service equipment is z 0:k ={z0,z1,z2,...,z k }, θ i represents the initial degradation value of the i-th online service equipment, σ represents the randomness parameter of the online service equipment degradation, and w is the failure threshold; Z k is the composite health index of the online service equipment at time k, μ θ,K and is p(θ|z 0:K ) is the estimated distribution parameter of , and Φ represents the φ function.

Images