A dynamic fault prediction method based on state feature decomposition-prediction-reconstruction

Abstract

The application discloses a kind of dynamic fault prediction methods based on state feature decomposition-prediction-reconstruction, belongs to the field of mechanical component degradation feature decomposition and fault prediction, for the complex nonlinear original degradation feature of mechanical component, based on Box-Cox transformation Linearization of degradation trajectory, and the decomposition of original degradation feature is realized by different transformation coefficients;Afterwards, the transformed degradation feature is predicted using a linear model, and on this basis, the reconstruction of degradation feature is completed by Box-Cox inverse transformation, to realize fault probability prediction.The application adopts the above-mentioned kind of dynamic fault prediction method based on state feature decomposition-prediction-reconstruction, the original degradation feature of mechanical component is decomposed by Box-Cox transformation, on this basis, degradation feature modeling and performance prediction are carried out, and the reconstruction of degradation feature is completed using Box-Cox inverse transformation, to realize mechanical component fault probability prediction.

Description

Technical Field

[0001] This invention relates to the field of mechanical component degradation feature decomposition and fault prediction technology, and in particular to a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction. Background Technology

[0002] For mechanical components, the raw condition monitoring signals collected by sensors in the field contain rich equipment health information and are therefore widely used in degradation modeling and fault prediction. Preprocessing the raw signals to extract suitable features and build a degradation model is a crucial step in accurately predicting the performance degradation path of mechanical components. Currently, traditional methods typically select a single degradation feature from various candidate features based on indicators such as trend and predictability. However, a single feature often fails to comprehensively describe the performance degradation process of mechanical components and results in a large amount of useful information in the raw signal not being fully utilized. Decomposing and reconstructing the raw signal based on Box-Cox transform provides a new approach to improve the accuracy of degradation modeling and fault prediction for mechanical components. Summary of the Invention

[0003] The purpose of this invention is to provide a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction. The original degradation features of mechanical components are decomposed by Box-Cox transformation, degradation feature modeling and performance prediction are carried out on this basis, and degradation features are reconstructed by Box-Cox inverse transformation to realize fault probability prediction of mechanical components.

[0004] To achieve the above objectives, this invention provides a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction, comprising the following steps: Step 1, Decomposition of original degradation features: For the complex nonlinear original degradation features of mechanical parts, the degradation trajectory is linearized based on the Box-Cox transform. A series of candidate transformation coefficients are obtained according to the confidence interval of the optimal transformation coefficients. The original degradation features are decomposed by using different transformation coefficients. Step 2, Feature Prediction and Optimization: For the degradation features of the mechanical parts decomposed in Step 1, a linear model is used to fit and predict them, and the correlation coefficient is obtained. After sorting and selecting, the optimized transformation coefficient is obtained. Step 3, Degradation Feature Reconstruction: Based on the optimal transformation coefficients, the degradation features of the mechanical parts are reconstructed through the inverse Box-Cox transformation; Step 4, Failure Probability Prediction: Given the failure threshold of the mechanical component, the failure probability is predicted using the degradation characteristics of the mechanical component reconstructed in Step 3.

[0005] Preferably, the two basic settings for establishing this dynamic fault prediction method based on state feature decomposition-prediction-reconstruction are as follows: Basic setting 1: The original degradation characteristics of the mechanical parts satisfy the non-negativity condition for any detection time. The corresponding original degradation eigenvalue All are greater than 0, among which, , The number of times a mechanical part has undergone degradation testing; Basic setting 2: Failure threshold for given mechanical components Failure occurs when the original degradation characteristics of a mechanical component first exceed this threshold.

[0006] Preferably, in step one, Record the initial degradation characteristic value of the mechanical component at the time of detection. ,in, The linearity of the original degenerate features is improved by using the Box-Cox transformation method, and the transformed data for: ; in, Indicates the optimal transformation coefficients; The linear model satisfied by the degenerate feature trajectory after transformation is expressed as: ; in, This represents the intercept of the transformed linear model. This represents the slope of the transformed linear model; The error is expressed as a function of 0 and a standard deviation of 1. It follows a normal distribution.

[0007] Preferably, the steps for obtaining the estimated values ​​of each parameter of the linear model satisfied by the degenerate feature trajectory after the above transformation are as follows: Step 1, construct the log-likelihood function: Based on the transformed degradation characteristics, the log-likelihood function of the linear model parameters satisfied by the transformed degradation characteristic trajectory is constructed as follows: ; in, This represents the log-likelihood function of the linear model parameters satisfied by the degenerate feature trajectory after the transformation; Step 2, maximize the log-likelihood function: Maximizing the log-likelihood function in step one yields estimated values ​​for the linear model parameters satisfied by the degenerate feature trajectories after each transformation: ; in, Parameters The estimated value; Based on the optimal transformation coefficients, the log-likelihood is defined as follows: ; in, The log-likelihood ratio represents the transformation coefficients. The function is given by the function and follows a chi-square distribution with 1 degree of freedom; Given confidence level The confidence intervals for the transformation coefficients are calculated as follows: ; in, The quantiles of a chi-square distribution with 1 degree of freedom are represented. According to The minimum value of the calculated transformation coefficients is denoted as The maximum value is denoted as Then the confidence interval of the transformation coefficients at the given confidence level is: Given the number of candidate transform coefficients Select at equal intervals within the confidence interval These values ​​are taken as candidate transform coefficients and denoted as follows: Based on the determined candidate transform coefficients, the original degradation features are decomposed using Box-Cox transform, and the decomposed first... The degradation characteristics are: ; in, Indicates the first Candidate transformation coefficients.

[0008] Preferably, in step two, A linear model is used to fit and predict the degradation characteristics of the decomposed mechanical parts: ; in, Indicates the first The intercept of each decomposition and degradation feature. Indicates the first The slope of each decomposition and degradation feature; The error is expressed as a function of 0 and a standard deviation of 1. The normal distribution , .

[0009] Preferably, the above parameters The calculation formula is as follows: ; ; ; in and The calculation formula is: ; ; in, ; Based on parameter estimation, for the th The correlation coefficients obtained from the decomposition and degradation features are: ; correlation coefficient Sort them in ascending order, given the number of preferred transformation coefficients. Select the first sorted order The transformation coefficients corresponding to the correlation coefficients are taken as the optimized transformation coefficients, and they are denoted as follows: .

[0010] Preferably, in step three, For the decomposed first k A degenerative feature, in Predicted value at detection time for: ; in, Indicates based on the first Transformation coefficients The intercept of the linear model obtained after performing the Box-Cox transformation. Indicates based on the first Transformation coefficients The slope of the linear model obtained after performing the Box-Cox transformation; No. The corresponding Box-Cox inverse transform of each degenerate feature prediction value is: ; in, Indicates the first The result of inverse transformation of the predicted values ​​of each degradation feature; Based on the degradation characteristics of each decomposed component, the original degradation characteristics of the mechanical part are reconstructed: ; in, This indicates the original degradation characteristics of the reconstructed mechanical parts.

[0011] Preferably, in step four, Failure threshold of a given mechanical component For the decomposed first A degenerate feature, whose failure probability at any given time is: ; in, The cumulative distribution function represents the standard normal distribution. Indicates based on the first Transformation coefficients The standard deviation of the linear model obtained after performing the Box-Cox transformation. The failure threshold after the Box-Cox transformation is represented by the following formula: ; in, Indicates the decomposition of the first... The transformation coefficients corresponding to each degenerate feature; Based on the various decomposition and degradation characteristics, the failure probability of the mechanical component at time t is: .

[0012] Therefore, the present invention employs the above-mentioned dynamic fault prediction method based on state feature decomposition-prediction-reconstruction, and the beneficial effects are as follows: 1. This invention decomposes the original degradation features of mechanical parts through Box-Cox transformation, making full use of the degradation information of the parts and facilitating operation; 2. This invention uses a transformed linear model to predict the various decomposition and degradation features of mechanical parts, with low computational load and high accuracy; 3. This invention reconstructs the original degradation characteristics of mechanical components based on the Box-Cox inverse transform, which can predict the failure probability of mechanical components and has strong feasibility.

[0013] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating an embodiment of a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction according to the present invention. Figure 2 This is an original degradation feature map of a mechanical bearing, representing an embodiment of a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction according to the present invention. Figure 3 This is a decomposed mechanical bearing degradation feature map of an embodiment of the dynamic fault prediction method based on state feature decomposition-prediction-reconstruction according to the present invention. Figure 4 This is a reconstructed mechanical bearing degradation feature map based on a dynamic fault prediction method based on state feature decomposition-prediction-reconstruction according to an embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0016] It should be noted that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products, or devices.

[0017] Similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0018] like Figure 1 As shown, the dynamic fault prediction method based on state feature decomposition-prediction-reconstruction described in this invention requires the following basic settings: Basic setting 1: The original degradation characteristics of the mechanical parts satisfy the non-negativity condition, that is, for any detection time... The corresponding original degradation eigenvalue All are greater than 0, among which, , The number of times a mechanical part has undergone degradation testing; Basic setting 2: Failure threshold for given mechanical components Failure occurs when the original degradation characteristics of a mechanical component first exceed this threshold.

[0019] The dynamic fault prediction method based on state feature decomposition-prediction-reconstruction includes the following steps: Step 1: Decomposition of original degradation features; For the complex and nonlinear original degradation features of mechanical parts, the degradation trajectory is linearized based on the Box-Cox transform. A series of candidate transformation coefficients are obtained according to the confidence interval of the optimal transformation coefficients. The original degradation features are decomposed by using different transformation coefficients.

[0020] Record the initial degradation characteristic value of the mechanical component at the time of detection. ,in, The linearity of the original degenerate features is improved by using the Box-Cox transformation method, and the transformed data for: (1); in, Indicates the optimal transformation coefficients; The linear model satisfied by the degenerate feature trajectory after transformation is expressed as: (2); in, This represents the intercept of the transformed linear model. This represents the slope of the transformed linear model; The error is expressed as a function of 0 and a standard deviation of 1. It follows a normal distribution.

[0021] The steps to obtain the estimated values ​​of each parameter of the linear model satisfied by the degenerate feature trajectory after the above transformation are as follows: Step 1, construct the log-likelihood function: Based on the transformed degradation characteristics, the log-likelihood function of the linear model parameters satisfied by the transformed degradation characteristic trajectory is constructed as follows: (3); in, This represents the log-likelihood function of the linear model parameters satisfied by the degenerate feature trajectory after the transformation; Step 2, maximize the log-likelihood function: Maximizing the log-likelihood function expressed in equation (3), we obtain the estimated values ​​of the linear model parameters satisfied by the degenerate feature trajectories after each transformation: (4); in, Parameters The estimated value; Based on the optimal transformation coefficients, the log-likelihood is defined as follows: (5); in, The log-likelihood ratio represents the transformation coefficients. The function is given by the function and follows a chi-square distribution with 1 degree of freedom; Given confidence level The confidence intervals for the transformation coefficients are calculated as follows: (6); in, The quantiles of a chi-square distribution with 1 degree of freedom are represented. The minimum value of the transformation coefficients calculated according to equation (6) is denoted as The maximum value is denoted as Then the confidence interval of the transformation coefficients at the given confidence level is: Given the number of candidate transform coefficients Select at equal intervals within the confidence interval These values ​​are taken as candidate transform coefficients and denoted as follows: Based on the determined candidate transform coefficients, the original degradation features are decomposed using Box-Cox transform, and the decomposed first... The degradation characteristics are: (7); in, Indicates the first Candidate transformation coefficients.

[0022] This embodiment focuses on a certain mechanical bearing, and the degradation of its inner diameter wear over time is shown in Table 1. The bearing wear data is in millimeters, and the time is in months.

[0023] Table 1. Degradation data of wear on the inner diameter of mechanical bearings

[0024] The original degradation trajectory of the mechanical bearing is as follows: Figure 2 As shown.

[0025] The model parameters corresponding to the optimal transformation coefficients are calculated based on equations (3) and (4). The estimated values ​​of each parameter are as follows: ; Given confidence level The confidence intervals of the transformation coefficients are calculated according to equations (5) and (6), and the results are as follows: ; Given the number of candidate transform coefficients Select at equal intervals within the confidence interval The following values ​​were selected as candidate transformation coefficients: 3.0620, 3.1390, 3.2160, 3.2930, 3.3700, 3.4470, 3.5240, 3.6010, 3.6780, and 3.7550. Based on the candidate transformation coefficients, the 10 decomposed degradation features can be obtained through equation (7).

[0026] Step 2, Feature Prediction and Optimization: For the degradation features of the mechanical parts decomposed in Step 1, a linear model is used to fit and predict them, and the correlation coefficients are obtained. After sorting and selection, the optimized transformation coefficients are obtained.

[0027] For the degradation characteristics of mechanical parts after Box-Cox transformation decomposition, a linear model is used for fitting and prediction, namely: (8); in, Indicates the first The intercept of each decomposition and degradation feature. Indicates the first The slope of each decomposition and degradation feature; The error is expressed as a function of 0 and a standard deviation of 1. The normal distribution , .

[0028] The above parameters The calculation formula is as follows: (9); (10); (11); in, , S xy and S xx The calculation formula is: (12); (13); in, ; Based on parameter estimation, for the th The correlation coefficients obtained from the decomposition and degradation features are: (14); correlation coefficient Sort them in ascending order, given the number of preferred transformation coefficients. Select the first sorted order The transformation coefficients corresponding to the correlation coefficients are taken as the optimized transformation coefficients, and they are denoted as follows: .

[0029] In this embodiment, the decomposed degradation features are fitted according to equation (8), and the model parameters and correlation coefficients are shown in Table 2: Table 2 Fitting results of decomposition degradation features

[0030] Given the number of preferred transformation coefficients Select the first few after sorting from smallest to largest The transformation coefficients corresponding to the correlation coefficients are taken as the optimized transformation coefficients and are denoted as follows: 3.2160, 3.2930, 3.3700, 3.4470, 3.5240, and 3.6010. The six decomposition degradation features obtained from the optimized transformation coefficients are as follows: Figure 3 As shown.

[0031] Step 3, Degradation Feature Reconstruction: Based on the optimized transformation coefficients, the degradation features of the mechanical parts are reconstructed through Box-Cox inverse transformation.

[0032] For the decomposed first A degenerative feature, in Predicted value at detection time for: (15); No. The corresponding Box-Cox inverse transform of each degenerate feature prediction value is: (16); in, Indicates the first The result of inverse transformation of the predicted values ​​of each degradation feature; Based on the degradation characteristics of each decomposed component, the original degradation characteristics of the mechanical part are reconstructed: (17); in, This indicates the original degradation characteristics of the reconstructed mechanical parts.

[0033] In this embodiment, based on the preferred transformation coefficients, an inverse transformation is performed on each decomposed degradation feature according to equations (15) and (16), and the results are shown in Table 3, where the unit of the degradation feature after the inverse transformation is millimeters: Table 3 Degradation characteristics after inverse transform

[0034] The original degradation characteristics of the mechanical bearing are reconstructed using equation (17). The reconstructed degradation characteristics are as follows: Figure 4 As shown.

[0035] Step 4, Fault Probability Prediction: Failure threshold of a given mechanical component For the decomposed first A degenerate feature, whose failure probability at any given time is: (18); in, The cumulative distribution function represents the standard normal distribution. Indicates based on the first Transformation coefficients The standard deviation of the linear model obtained after performing the Box-Cox transformation. The failure threshold after the Box-Cox transformation is represented by the following formula: (19); in, Indicates the decomposition of the first... The transformation coefficients corresponding to each degenerate feature; Based on the various decomposition and degradation characteristics, the failure probability of the mechanical component at time t is: (20).

[0036] In this embodiment, a failure threshold for a given mechanical component is defined. Based on equations (18)-(20), the failure probability of the mechanical bearing in the month is: ; The results show that the method proposed in this invention can decompose, predict and reconstruct the original degradation characteristics of mechanical parts, and can predict the failure probability of mechanical parts, thus achieving the expected purpose.

[0037] Therefore, this invention adopts the above-mentioned dynamic fault prediction method based on state feature decomposition-prediction-reconstruction. The original degradation features of mechanical components are decomposed by Box-Cox transformation, degradation feature modeling and performance prediction are carried out on this basis, and degradation features are reconstructed by Box-Cox inverse transformation, thereby improving the accuracy of mechanical component fault probability prediction.

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A dynamic fault prediction method based on state feature decomposition-prediction-reconstruction, characterized in that, Includes the following steps: Step 1, Decomposition of original degradation features: For the complex nonlinear original degradation features of mechanical parts, the degradation trajectory is linearized based on the Box-Cox transform. A series of candidate transformation coefficients are obtained according to the confidence interval of the optimal transformation coefficients. The original degradation features are decomposed by using different transformation coefficients. Step 2, Feature Prediction and Optimization: For the degradation features of the mechanical parts decomposed in Step 1, a linear model is used to fit and predict them, and the correlation coefficient is obtained. After sorting and selecting, the optimized transformation coefficient is obtained. Step 3, Degradation Feature Reconstruction: Based on the optimal transformation coefficients, the degradation features of the mechanical parts are reconstructed through the inverse Box-Cox transformation; Step 4, Failure Probability Prediction: Given the failure threshold of the mechanical component, the failure probability is predicted using the degradation characteristics of the mechanical component reconstructed in Step 3. The two basic settings for this dynamic fault prediction method based on state feature decomposition-prediction-reconstruction are as follows: Basic setting 1: The original degradation characteristics of the mechanical parts satisfy the non-negativity condition for any detection time. The corresponding original degradation eigenvalue All are greater than 0, among which, , The number of times a mechanical part has undergone degradation testing; Basic setting 2: Given a failure threshold for a mechanical component, failure occurs when the initial degradation characteristics of the mechanical component first exceed this threshold; In step one, the initial degradation characteristic value of the mechanical component at the time of detection is recorded. ,in, The linearity of the original degenerate features is improved by using the Box-Cox transformation method, and the transformed data for: ； in, Indicates the optimal transformation coefficients; The linear model satisfied by the degenerate feature trajectory after transformation is expressed as: ； in, This represents the intercept of the transformed linear model. This represents the slope of the transformed linear model; The error is expressed as a function of 0 and a standard deviation of 1. The normal distribution; The steps to obtain the estimated values ​​of each parameter of the linear model satisfied by the degenerate feature trajectory after the above transformation are as follows: Step 1, construct the log-likelihood function: Based on the transformed degradation characteristics, the log-likelihood function of the linear model parameters satisfied by the transformed degradation characteristic trajectory is constructed as follows: ； in, This represents the log-likelihood function of the linear model parameters satisfied by the degenerate feature trajectory after the transformation; Step 2, maximize the log-likelihood function: Maximizing the log-likelihood function in step one yields estimated values ​​for the linear model parameters satisfied by the degenerate feature trajectories after each transformation: ； in, Parameters The estimated value; Based on the optimal transformation coefficients, the log-likelihood is defined as follows: ； in, The log-likelihood ratio represents the transformation coefficients. The function is given by the function and follows a chi-square distribution with 1 degree of freedom; Given confidence level The confidence intervals for the transformation coefficients are calculated as follows: ； in, The quantiles of a chi-square distribution with 1 degree of freedom are represented. According to The minimum value of the calculated transformation coefficients is denoted as The maximum value is denoted as Then the confidence interval of the transformation coefficients at the given confidence level is: Given the number of candidate transform coefficients Select at equal intervals within the confidence interval These values ​​are taken as candidate transform coefficients and denoted as follows: Based on the determined candidate transform coefficients, the original degradation features are decomposed using Box-Cox transform, and the decomposed first... The degradation characteristics are: ； in, Indicates the first One candidate transformation coefficient; In step two, a linear model is used to fit and predict the degradation characteristics of the decomposed mechanical parts: ； in, Indicates the first The intercept of each decomposition and degradation feature. Indicates the first The slope of each decomposition and degradation feature; The error is expressed as a function of 0 and a standard deviation of 1. The normal distribution , ; The above parameters The calculation formula is as follows: ； ； ； in and The calculation formula is: ； ； in, ; Based on parameter estimation, for the th The correlation coefficients obtained from the decomposition and degradation features are: ； correlation coefficient Sort them in ascending order, given the number of preferred transformation coefficients. Select the first sorted order The transformation coefficients corresponding to the correlation coefficients are taken as the optimized transformation coefficients, and they are denoted as follows: ; In step three, for the decomposed first... k A degenerative feature, in Predicted value at detection time for: ； in, Indicates based on the first Transformation coefficients The intercept of the linear model obtained after performing the Box-Cox transformation. Indicates based on the first Transformation coefficients The slope of the linear model obtained after performing the Box-Cox transformation; No. The corresponding Box-Cox inverse transform of each degenerate feature prediction value is: ； in, Indicates the first The result of inverse transformation of the predicted values ​​of each degradation feature; Based on the degradation characteristics of each decomposed component, the original degradation characteristics of the mechanical part are reconstructed: ； in, This indicates the original degradation characteristics of the reconstructed mechanical parts.

2. The dynamic fault prediction method based on state feature decomposition-prediction-reconstruction according to claim 1, characterized in that: In step four, Failure threshold of a given mechanical component For the decomposed first A degenerate feature, whose failure probability at any given time is: ； in, The cumulative distribution function represents the standard normal distribution. Indicates based on the first Transformation coefficients The standard deviation of the linear model obtained after performing the Box-Cox transformation. The failure threshold after the Box-Cox transformation is represented by the following formula: ； in, Indicates the decomposition of the first... The transformation coefficients corresponding to each degenerate feature; Based on the various decomposition and degradation characteristics, the failure probability of the mechanical component at time t is: 。

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