Method for predicting residual life of mechanical system based on physical guidance chaos Gaussian model
A physically guided chaotic Gaussian model addresses the inaccuracy of traditional methods by enhancing mechanical system life prediction through fatigue characteristic extraction, normalization, and optimization, achieving high-precision and uncertainty quantification in complex systems.
Patent Information
- Application Number
- CN202411352137.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-26
- Publication Date
- 2024-12-31
AI Technical Summary
Traditional life prediction methods for mechanical systems, relying on empirical formulas and finite element analysis, lack accuracy when dealing with complex nonlinear systems, especially under varying operating environments and workloads, leading to inadequate safety and service life estimation.
A physically guided chaotic Gaussian model is established to predict remaining life, involving fatigue characteristic extraction, normalization, and optimization, using a physically guided chaotic Gaussian model with a loss function that incorporates data fitting and physical constraints to enhance accuracy and uncertainty quantification.
The method effectively captures nonlinear evolution in mechanical systems, providing high-precision remaining life estimation by accurately fitting data and quantifying uncertainty, thus improving safety and service life prediction.
Smart Images
Figure CN119227538A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a high-precision result remaining life prediction method, in particular to a mechanical system remaining life prediction method based on a physics-guided chaotic Gaussian model. Background Art
[0002] During the long-term operation of mechanical systems, fatigue, wear and environmental factors will cause the structure to gradually develop cracks, corrosion and other damage, seriously affecting the safety and service life of the mechanical system. Traditional life prediction methods mainly rely on empirical formulas and finite element analysis, which often lack accuracy when dealing with complex nonlinear systems. In addition, as the operating environment and workload of mechanical systems become more and more complex, accurately predicting their remaining life faces more challenges. In this context, it is necessary to propose a new method to accurately estimate the remaining life of mechanical systems and improve system accuracy, which has important practical research significance. Summary of the invention
[0003] Purpose of the invention: The purpose of the invention is to provide a method for predicting the remaining life of a mechanical system based on a physically guided chaotic Gaussian model.
[0004] Technical solution: The present invention comprises the following steps:
[0005] (1) Extraction and characterization of fatigue characteristics of mechanical systems;
[0006] (2) Normalization optimization and determination of fatigue characteristics;
[0007] (3) Establishment of physically guided chaotic Gaussian model;
[0008] (4) Optimization of physically guided chaotic Gaussian models;
[0009] (5) Prediction of mechanical system life based on physically guided chaotic Gaussian model.
[0010] Furthermore, the step (1) comprises:
[0011] According to the state of the mechanical system, the fatigue characteristics of crack parameters that affect the service life of the mechanical system are measured, including the crack length a, radius r, depth d, and angle θ of the crack.
[0012] Furthermore, the step (1) comprises:
[0013] By collecting the vibration acceleration signal a(t) of the mechanical system in operation, we can obtain deeper fatigue characteristics.
[0014] For the signal a(t), the signal is converted into the frequency domain A(ω) through Fourier transform, and then the displacement is obtained by integration.
[0015]
[0016] Where ω is the angular frequency and X(ω) is the expression of displacement in the frequency domain;
[0017] Then, by inverse Fourier transforming back to the time domain, we get the displacement X(t):
[0018] X(t)=fft -1 [X(ω)]
[0019] In the case of vibration and crack growth, the stress intensity factor K is usually related to the crack length a, the vibration-induced stress σ, and the geometry of the crack tip Y:
[0020]
[0021] The stress σ is derived from the vibration signal. The stress is calculated from the vibration displacement X(t) and the known structural stiffness k:
[0022] σ=kX(t)
[0023] Combining the process of deriving displacement from acceleration signal, the comprehensive expression of stress intensity factor K is as follows:
[0024]
[0025] Due to the change in the vibration acceleration signal, we can calculate the stress intensity factor difference ΔK, the expression is as follows:
[0026] ΔK=K max -K min
[0027] Calculate each fatigue characteristic X according to ΔK, expressed as:
[0028] X=[a,r,d,θ,ΔK]
[0029] Finally, the fatigue characteristics X of the mechanical system are determined.
[0030] Furthermore, the step (2) comprises:
[0031] According to the fatigue characteristic X extracted and characterized in step (1), X is composed of multiple fatigue characteristics, and the characteristics are scaled to [0, 1] by using data scaling technology.
[0032] Furthermore, each X in the fatigue characteristic X obtained by extraction and characterization i , the normalization process is:
[0033]
[0034] Among them, min(X i) and max(X i ) represent the minimum and maximum values of the i-th feature respectively. Through normalization, the differences in different scales of the input features are eliminated.
[0035] Furthermore, the step (3) comprises:
[0036] According to the normalized fatigue characteristic X obtained in step (2) i，norm , in order to pass X i，norm To predict the remaining life of mechanical systems, a physical guided chaotic Gaussian model was established. i，nomn As input to the model;
[0037] When predicting the output, the input features are linearly transformed, biased, and activated by the nonlinear activation function ReLu through the physical guidance hidden layer, ensuring that the network can represent complex nonlinear relationships. The physical guidance hidden layer is expressed by the following general formula:
[0038] H l =σ(W l H l-1 +b1)=f l (H l-1 )
[0039] Among them, H l is the output of the,th layer, H l-1 is the output of the l-1th layer. In the case of the 1st layer, it is the input data X, H1 = σ(W1X+b1)W l is the weight matrix of the lth layer, describing the connection between the neurons in the l-1th layer and the lth layer, b l is the bias vector of the lth layer, σ(·) is the activation function, which introduces nonlinear characteristics;
[0040] σ(x)=max(0,x)
[0041] Through the activation function, nonlinear transformation is performed, and finally the remaining life span N is predicted through the output layer. p
[0042]
[0043] Among them, f PINN Represents the mapping function of physical guidance, f l is the mapping function of the lth layer network, with a total of L layers, γ PINN is the set of physically guided parameters, including the weights and biases of each layer, It is a composite operation of functions, and the output of each layer is passed layer by layer as the input of the next layer.
[0044] Furthermore, the physical guidance chaotic Gaussian model is a chaotic Gaussian modeling based on physical guidance, and the physical guidance is used as the basic network to predict the remaining life N p , and then passed to Chaos Gaussian, through Chaos Gaussian modeling, the physically guided output is further modified and the uncertainty is quantified:
[0045] p(N DGP |N p )=GP(μ(N p ),∑(N p ))
[0046] Among them, N DGP is the predicted value of remaining life after DGP correction, μ(N p ) is the chaotic Gaussian prediction of the final remaining life, Σ(N p ) is the covariance function of DGP to prediction uncertainty;
[0047] The mean function μ(N p ) is usually used to predict the output prediction under a given input, and the mean function is assumed to be a zero-mean process, that is, μ(N p )=0, but a more flexible choice is to express the mean function through a regression model, that is, to obtain the function form through learning, such as a linear regression model or a polynomial regression. For prediction tasks, the commonly used ones are:
[0048] μ(N p )=ω T N p +b
[0049] Among them, ω is the weight vector and b is the bias term. Through training data, DGP will learn the appropriate weight ω and bias term b, so that the mean function fits the actual remaining life as much as possible;
[0050] The covariance function is used to describe the correlation between different inputs. In the Gaussian process, the covariance function determines the smoothness and complexity of the function. The common covariance function form is the radial basis function, and its formula is:
[0051]
[0052] Among them, N p and N′ p are two different input points, i.e., the life prediction values of two different samples. is the amplitude parameter, which controls the overall length of the kernel function, and l is the length scale parameter, which controls the speed at which the function changes, that is, the speed at which the correlation between different points decays with distance.
[0053] Furthermore, the covariance function in the Gaussian process is used to calculate the similarity between each pair of inputs, and the uncertainty of the model output is adjusted according to the similarity.
[0054] Furthermore, the step (4) comprises:
[0055] According to the physical guided chaotic Gaussian model established in step (3), the model is optimized, where the design of the loss function is the core of model optimization. The loss function is composed of the data fitting loss L data and the physical constraint loss L p It consists of two parts.
[0056]
[0057]
[0058] Among them, n is the number of samples of the total data, N p，i is the remaining life value of the ith operating condition initially predicted by the PINN model, N t，i is the true value of the remaining life under the i-th condition, is the crack growth rate predicted by the model under the i-th working condition. The remaining life N is calculated from the output of the model through automatic differentiation. p The derivative of ΔK p，i is the difference of stress intensity factors under the i-th working condition predicted by the model, C and m are constants of the material;
[0059] The loss function design of Chaos Gaussian is based on the maximum likelihood estimation of Gaussian process, including mean correction error and uncertainty quantification. Chaos Gaussian corrects the mean of the physical guidance output to minimize the error between the corrected prediction value and the actual remaining life. The loss term L DGP The mean function of the Gaussian process is used to evaluate the accuracy of the predicted mean and improve the preliminary prediction results guided by physics:
[0060]
[0061] Among them, N DGP，i is the predicted value of the remaining life under the i-th working condition after DGP correction, which is obtained by correcting the preliminary prediction result of PINN by DGP. t，i is the true value of the remaining life under the i-th condition, is the uncertainty estimate of the DGP model for the i-th working condition;
[0062] The total loss function of the physically guided chaotic Gaussian model achieves compliance with physical constraints, high-precision fitting of data, and reasonable estimation of uncertainty. The expression is:
[0063] Ltotal =λ1(L data +L p )+λ2L DGP
[0064] Among them, λ1 controls the contribution of PINN loss to the total loss function, which determines the degree of optimization of the model in terms of physical constraints and data fitting; λ2 controls the contribution of DGP loss to the total loss function, which determines the degree of optimization of the model for uncertainty quantification and prediction mean correction.
[0065] Furthermore, the step (5) comprises:
[0066] According to the optimization of the physically guided chaotic Gaussian model in step (4), the remaining life of the mechanical system is estimated, and the characteristics are fitted by the Matern kernel and the SE kernel. The solution is as follows:
[0067]
[0068] Among them, N final is the final life expectancy prediction value, k(N p , N e ) is the test point N p With training data N e The covariance between e , N e ) is the covariance matrix between training data, is the noise variance, usually used to control the noise in the data, N t is the true value of the training data, that is, the true lifespan.
[0069] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: it can fully characterize the remaining life of the mechanical system, extract fatigue characteristics, and construct a physically guided chaotic Gaussian model to predict the complex nonlinear system; it can effectively capture the nonlinear evolution in the complex system, accurately and efficiently estimate the remaining life of the mechanical system, and has important practical research significance. BRIEF DESCRIPTION OF THE DRAWINGS
[0070] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION
[0071] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.
[0072] like Figure 1 As shown, the present invention comprises the following steps:
[0073] (1) Extraction and characterization of fatigue characteristics of mechanical systems;
[0074] According to the state of the mechanical system, firstly, the fatigue characteristics of the crack parameters that affect the operating life of the mechanical system are measured, including the crack length a, radius r, depth d, and angle θ of the crack. Secondly, the vibration acceleration signal a(t) of the operating state of the mechanical system is collected to obtain deeper fatigue characteristics.
[0075] For the signal a(t), the signal is converted into the frequency domain A(ω) through Fourier transform, and then the displacement is calculated by integration.
[0076]
[0077] Here, ω is the angular frequency and X(ω) is the expression of the displacement in the frequency domain.
[0078] Then, through the inverse Fourier transform back to the time domain, we get the displacement X(t)
[0079] X(t)=fft -1 [X(ω)]
[0080] In the case of vibration and crack growth, the stress intensity factor K is usually related to the crack length a, the vibration-induced stress σ, and the geometry Y of the crack tip.
[0081]
[0082] The stress σ can be derived from the vibration signal. Using the vibration displacement X(t) and the known structural stiffness k, the stress can be calculated:
[0083] σ=kX(t)
[0084] Combining the process of deriving displacement from acceleration signal, the comprehensive expression of stress intensity factor K is as follows:
[0085]
[0086] Due to the change in the vibration acceleration signal, we can calculate the stress intensity factor difference ΔK, the expression is as follows:
[0087] ΔK=K max -K min
[0088] Finally, the fatigue characteristics X of the mechanical system are determined and expressed as:
[0089] X=[a,r,d,θ,ΔK]
[0090] (2) Normalization optimization and determination of fatigue characteristics;
[0091] According to the fatigue characteristic X extracted and characterized in step (1), X is composed of multiple fatigue characteristics. In order to avoid the influence of the difference of different dimensional characteristics on the subsequent, the characteristics are scaled to [0, 1] by data scaling technology.
[0092] For each X in the fatigue characteristic X i , the normalization process is:
[0093]
[0094] Among them, min(X i ) and max(X i ) represent the minimum and maximum values of the i-th feature respectively. Through normalization, the differences in different scales of the input features are eliminated, which improves the performance of subsequent use.
[0095] (3) Establishment of physically guided chaotic Gaussian model;
[0096] According to the normalized fatigue characteristic X obtained in step (2) i，nnorm , in order to pass X i，norm To predict the remaining life of mechanical systems, a physical guided chaotic Gaussian model was established. i，norm as input to the model.
[0097] When predicting the output, the input features are transformed linearly, biased, and activated by the nonlinear activation function ReLu to ensure that the network can represent complex nonlinear relationships. The physical guidance hidden layer is expressed by the following general formula:
[0098] H l =σ(W l H l-1 +b1)=f l (N l-1 )
[0099] Among them, H l is the output of layer l. l-1 is the output of the l-1th layer. In the case of the 1st layer, it is the input data X, H1 = σ(W1X+b1). l is the weight matrix of the lth layer, describing the connection between the neurons in the -1th and ,th layers. l is the bias vector of the lth layer. σ(·) is the activation function, which introduces nonlinear characteristics.
[0100] σ(x)=max(0,x)
[0101] Through the activation function, nonlinear transformation is performed, and finally the remaining life span N is predicted through the output layer. p
[0102]
[0103] Among them, f PINN Represents the mapping function of physical guidance. l is the mapping function of the lth layer of the network, with a total of L layers. PINN is the set of physically guided parameters, including the weights and biases of each layer. It is a composite operation of functions, and the output of each layer is passed layer by layer as the input of the next layer.
[0104] Chaos Gaussian performs uncertainty modeling based on physical guidance. Physical guidance is used as the basic network to predict the remaining life N p , and then passed to Chaos Gaussian. Through Chaos Gaussian modeling, the output of physical guidance is further modified and the uncertainty is quantified.
[0105] p(N DGP |N p )=GP(μ(N p ),Σ(N p ))
[0106] Among them, N DGP is the predicted value of remaining life after DGP correction, μ(N p ) is the mean prediction of the final remaining life by chaotic Gaussian, ∑(N p ) is the covariance function of DGP with respect to prediction uncertainty.
[0107] The mean function μ(N p ) is usually used to predict the output given the input. In general, the mean function is assumed to be a zero-mean process, that is, μ(N p )=0. But a more flexible option is to express the mean function through a regression model, that is, to obtain a functional form through learning, such as a linear regression model or polynomial regression. For prediction tasks, commonly used ones are:
[0108] μ(N p )=ω T N p +b
[0109] Among them, ω is the weight vector and b is the bias term. Through training data, DGP will learn the appropriate weight ω and bias term b so that the mean function fits the actual remaining life as closely as possible.
[0110] The covariance function is used to describe the correlation between different inputs. In the Gaussian process, the covariance function determines the smoothness and complexity of the function. The common form of the covariance function is the radial basis function, and its formula is:
[0111]
[0112] Among them, N p and N′ p are two different input points, that is, the life expectancy prediction values of two different samples. is the amplitude parameter, which controls the overall length of the kernel function. l is the length scale parameter, which controls the speed at which the function changes, that is, the speed at which the correlation between different points decays with distance.
[0113] Through the covariance function in the Gaussian process, we can calculate the similarity between each pair of inputs, and the Gaussian process will adjust the uncertainty of the model output based on these similarities.
[0114] (4) Optimization of physically guided chaotic Gaussian models;
[0115] According to the physical guided chaotic Gaussian model established in step (3), the model is optimized. The design of the loss function is the core of model optimization, which directly affects the degree to which the model follows the physical laws and the fitting accuracy of the data.
[0116] In physics guidance, it is necessary to ensure that the model can fit the observed data and conform to the laws of physics. To this end, the loss function is composed of the data fitting loss L data and the physical constraint loss L p It consists of two parts.
[0117]
[0118]
[0119] Among them, n is the number of samples of the total data, N p，i is the remaining life value of the ith operating condition initially predicted by the PINN model, N t，i is the true value of the remaining life under the i-th condition, is the crack growth rate predicted by the model under the i-th working condition. The remaining life N is calculated from the output of the model through automatic differentiation. p The derivative of ΔK p，i is the difference in stress intensity factor under the i-th condition predicted by the model. C and m are constants of the material.
[0120] The output of the physical guidance is used as the input of the Chaotic Gaussian to further correct the preliminary prediction results and provide uncertainty estimates. To achieve this goal, the loss function of the Chaotic Gaussian is designed based on the maximum likelihood estimation of the Gaussian process, which mainly includes mean correction error and uncertainty quantification. The Chaotic Gaussian corrects the mean of the physical guidance output to minimize the error between the corrected prediction value and the true remaining life. This part of the loss term L DGPThe mean function of the Gaussian process is used to evaluate the accuracy of the predicted mean and improve the preliminary prediction results guided by physics:
[0121]
[0122] Among them, N DGP,i is the predicted value of the remaining life under the i-th working condition after DGP correction, which is obtained by correcting the preliminary prediction result of PINN by DGP. t，i is the true value of the remaining life under the i-th working condition. is the uncertainty estimate of the DGP model for the i-th operating condition.
[0123] The total loss function of the physically guided chaotic Gaussian model achieves compliance with physical constraints, high-precision fitting of data, and reasonable estimation of uncertainty. Its expression is:
[0124] L total =λ1(L data +L p )+λ2L DGP
[0125] Among them, λ1 controls the contribution of PINN loss to the total loss function, which determines the degree of optimization of the model in terms of physical constraints and data fitting. λ2 controls the contribution of DGP loss to the total loss function, which determines the degree of optimization of the model for uncertainty quantification and prediction mean correction.
[0126] (5) Prediction of mechanical system life based on physically guided chaotic Gaussian model;
[0127] According to the optimization of the physical guided chaotic Gaussian model in step (4), the remaining life of the mechanical system is estimated. The characteristics are fitted by Matem kernel and SE kernel, and the solution is as follows:
[0128]
[0129] Among them, N final is the final life expectancy prediction value, k(N p , N e ) is the test point N p With training data N e The covariance between ∑(N e , N e ) is the covariance matrix between the training data. is the noise variance, usually used to control the noise in the data. t is the true value of the training data, that is, the true lifespan.
Claims
1. A method for predicting the remaining life of a mechanical system based on a physically guided chaotic Gaussian model, characterized in that: The method comprises the following steps: (1) Extraction and characterization of fatigue characteristics of mechanical systems; (2) Normalization optimization and determination of fatigue characteristics; (3) Establishment of physically guided chaotic Gaussian model; (4) Optimization of physically guided chaotic Gaussian models; (5) Prediction of mechanical system life span based on physically guided chaotic Gaussian model.
2. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (1) comprises: According to the state of the mechanical system, the fatigue characteristics of crack parameters that affect the service life of the mechanical system are measured, including the crack length a, radius r, depth d, and angle θ of the crack.
3. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (1) comprises: By collecting the vibration acceleration signal a(t) of the mechanical system in operation, we can obtain deeper fatigue characteristics. For the signal a(t), the signal is converted into the frequency domain A(ω) through Fourier transform, and then the displacement is calculated by integration. Where ω is the angular frequency and X(ω) is the expression of displacement in the frequency domain; Then, by inverse Fourier transforming back to the time domain, we get the displacement X(t): X(t)=fft -1 [X(ω)] In the case of vibration and crack growth, the stress intensity factor K is usually related to the crack length a, the vibration-induced stress σ, and the geometry of the crack tip Y: The stress σ is derived from the vibration signal. Using the vibration displacement X(t) and the known structural stiffness k, the stress is calculated: σ=kX(t) Combining the process of deriving displacement from acceleration signal, the comprehensive expression of stress intensity factor K is as follows: Due to the change in the vibration acceleration signal, we can calculate the stress intensity factor difference ΔK, the expression is as follows: ΔK=K max -K min Calculate each fatigue characteristic X according to ΔK, expressed as: X=[a,r,d,θ,ΔK] Finally, the fatigue characteristics X of the mechanical system are determined.
4. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (2) comprises: According to the fatigue characteristic X extracted and characterized in step (1), X is composed of multiple fatigue characteristics, and the characteristics are scaled to [0, 1] by using data scaling technology.
5. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 4, characterized in that: Each of the fatigue characteristics X obtained by the extraction and characterization i , the normalization process is: Among them, min(X i ) and max(X i ) represent the minimum and maximum values of the i-th feature respectively. Through normalization, the differences in different scales of the input features are eliminated.
6. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (3) comprises: According to the normalized fatigue characteristic X obtained in step (2) i，norm , in order to pass X i，norm To predict the remaining life of mechanical systems, a physical guided chaotic Gaussian model was established. i，norm As input to the model; When predicting the output, the input features are linearly transformed, biased, and activated by the nonlinear activation function ReLu through the physical guidance hidden layer, ensuring that the network can represent complex nonlinear relationships. The physical guidance hidden layer is expressed by the following general formula: H l =σ(W l H l-1 +b1)=f l (H l-1 ) Among them, H l is the output of the,th layer, H l-1 is the output of the l-1th layer. In the case of the 1st layer, it is the input data X, H1 = σ(W1X+b1)W l is the weight matrix of the lth layer, describing the connection between the neurons in the l-1th layer and the lth layer, b l is the bias vector of the lth layer, σ(·) is the activation function, which introduces nonlinear characteristics; σ(x)=max(0,x) Through the activation function, nonlinear transformation is performed, and finally the remaining life span N is predicted through the output layer. p Among them, f PINN Represents the mapping function of physical guidance, f l is the mapping function of the lth layer network, with a total of L layers, γ PINN is the set of physically guided parameters, including the weights and biases of each layer, It is a composite operation of functions, and the output of each layer is used as the input of the next layer and passed layer by layer.
7. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 6, characterized in that: The physical guidance chaotic Gaussian model is a chaotic Gaussian modeling of uncertainty based on physical guidance. Physical guidance is used as a basic network to predict the remaining life N p , and then passed to Chaos Gaussian, through Chaos Gaussian modeling, the physically guided output is further modified and the uncertainty is quantified: p(N DGP |N p )=GP(μ(N p ),∑(N p )) Among them, N DGP is the predicted value of remaining life after DGP correction, μ(N p ) is the mean prediction of the final remaining life by chaotic Gaussian, ∑(N p ) is the covariance function of DGP to prediction uncertainty; The mean function μ(N p ) is usually used to predict the output prediction under a given input, and the mean function is assumed to be a zero-mean process, that is, μ(N p )=0, but a more flexible choice is to express the mean function through a regression model, that is, to obtain the function form through learning, such as a linear regression model or a polynomial regression. For prediction tasks, the commonly used ones are: μ(N p )=ω T N p +b Among them, ω is the weight vector and b is the bias term. Through training data, DGP will learn the appropriate weight ω and bias term b, so that the mean function fits the actual remaining life as much as possible; The covariance function is used to describe the correlation between different inputs. In the Gaussian process, the covariance function determines the smoothness and complexity of the function. The common covariance function form is the radial basis function, and its formula is: Among them, N p and N′ p are two different input points, i.e., the life prediction values of two different samples. is the amplitude parameter, which controls the overall length of the kernel function, and l is the length scale parameter, which controls the speed at which the function changes, that is, the speed at which the correlation between different points decays with distance.
8. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 7, characterized in that: The covariance function in the Gaussian process is used to calculate the similarity between each pair of inputs, and adjust the uncertainty of the model output according to the similarity.
9. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (4) comprises: According to the physical guided chaotic Gaussian model established in step (3), the model is optimized, where the design of the loss function is the core of model optimization. The loss function is composed of the data fitting loss L data and the physical constraint loss L p It consists of two parts. Among them, n is the number of samples of the total data, N p，i is the remaining life value of the ith operating condition initially predicted by the PINN model, N t，i is the true value of the remaining life under the i-th working condition, is the crack growth rate predicted by the model under the i-th working condition. The remaining life N is calculated from the output of the model through automatic differentiation. p The derivative of ΔK p，i is the difference of stress intensity factors under the i-th working condition predicted by the model, C and m are constants of the material; The loss function design of Chaos Gaussian is based on the maximum likelihood estimation of Gaussian process, including mean correction error and uncertainty quantification. Chaos Gaussian corrects the mean of the physical guidance output to minimize the error between the corrected prediction value and the actual remaining life. The loss term L DGP The mean function of the Gaussian process is used to evaluate the accuracy of the predicted mean and improve the preliminary prediction results guided by physics: Among them, N DGP，i is the predicted value of the remaining life under the i-th working condition after DGP correction, which is obtained by correcting the preliminary prediction result of PINN by DGP. t，i is the true value of the remaining life under the i-th working condition, is the uncertainty estimate of the DGP model for the i-th working condition; The total loss function of the physically guided chaotic Gaussian model achieves compliance with physical constraints, high-precision fitting of data, and reasonable estimation of uncertainty. The expression is: L total =λ1(L data +L p )+λ2L DGP Among them, λ1 controls the contribution of PINN loss to the total loss function, which determines the degree of optimization of the model in terms of physical constraints and data fitting; λ2 controls the contribution of DGP loss to the total loss function, which determines the degree of optimization of the model for uncertainty quantification and prediction mean correction.
10. The method for predicting the remaining service life of a mechanical system based on a physically guided chaotic Gaussian model according to claim 1, characterized in that: The step (5) comprises: According to the optimization of the physically guided chaotic Gaussian model in step (4), the remaining life of the mechanical system is estimated, and the characteristics are fitted by the Matern kernel and the SE kernel. The solution is as follows: Among them, N final is the final life expectancy prediction value, k(N p , N e ) is the test point N p With training data N e The covariance between e , N e ) is the covariance matrix between training data, is the noise variance, usually used to control the noise in the data, N t is the true value of the training data, that is, the true lifespan.