Thin-wall structure dynamic parameter uncertainty quantification and vibration analysis method

Abstract

The invention discloses a thin-wall structure dynamic parameter uncertainty quantification and vibration analysis method, relates to the field of aircraft thin-wall structure dynamics in the civil aviation field, and aims to solve the problem that vibration characteristics of an aircraft thin-wall structure in the civil aviation field are difficult to accurately analyze due to the fact that the aircraft thin-wall structure is affected by multi-source uncertainty under complex working conditions. According to the method, the difficulties of uncertainty source coupling, parameter time varying, high dimension and strong nonlinearity of vibration characteristics and the like are analyzed, and corresponding solutions are provided: a multi-source uncertainty coupling analysis framework is constructed to realize accurate description of complex coupling uncertainty; establishing a time-varying uncertainty dynamic updating model, and quantizing parameter time-varying uncertainty in real time; and a high-efficiency high-dimension nonlinear vibration characteristic analysis method is developed, and the calculation cost is reduced. According to the method, the physical mechanism and the machine learning technology are combined, the uncertainty is described by adopting the probability model and the interval model, and the modeling precision of the aircraft thin-wall system structure dynamic model is improved.

Description

Technical Field

[0001] This invention relates to the field of aircraft thin-walled structure dynamics in civil aviation, and particularly to a method for quantifying the uncertainty of dynamic parameters and analyzing vibrations of thin-walled structures. Background Technology

[0002] In the aerospace field, thin-walled structures occupy a core position in aircraft and spacecraft due to their lightweight advantages. However, the dynamic behavior of these structures under complex operating conditions is affected by a variety of uncertainties, posing a significant challenge to the accurate analysis of their vibration characteristics. The uncertainties in dynamic parameters stem from multiple aspects: regarding material properties, even composite materials from the same batch can exhibit differences in parameters such as elastic modulus and Poisson's ratio due to slight fluctuations in manufacturing processes; in terms of geometry, the thickness and curvature of thin-walled structures are difficult to perfectly achieve design precision during processing, resulting in subtle deviations; boundary conditions are not entirely fixed in actual service, such as the potential loosening of connections in spacecraft solar panels, causing constraint stiffness to vary with operating conditions. Complex operating conditions further amplify the impact of these uncertainties. For example, aircraft face severe aerodynamic loads during high-speed flight, resulting in highly uneven temperature field distributions that cause nonlinear changes in material properties; spacecraft experience strong impact vibrations during launch, potentially leading to localized plastic deformation and irreversible changes in dynamic parameters. These uncertainties cause significant deviations between the vibration response of thin-walled structures and theoretical predictions, potentially leading to risks such as resonance and fatigue failure, seriously threatening the safety and reliability of equipment. Traditional deterministic analysis methods assume fixed parameters, failing to reflect actual uncertainties and thus struggling to meet the high-precision requirements for structural safety and reliability in the aerospace field. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a method for quantifying the uncertainty of dynamic parameters and analyzing vibration in thin-walled structures.

[0004] First, we analyze the difficulties in quantifying the uncertainty of structural dynamic parameters and analyzing vibration characteristics under complex working conditions: (1) Sources of uncertainty in thin-walled structures. These mainly include material parameter fluctuations, geometric dimension errors, boundary condition changes, and external load disturbances. These factors are coupled with each other, and the coupling effect of multiple sources of uncertainty makes the uncertainty of dynamic parameters exhibit complex nonlinear characteristics, which brings great difficulties to accurate quantification. (2) Time-varying characteristics of parameters under complex working conditions. During the takeoff, cruise, and landing phases of aircraft, and the launch, orbital operation, and reentry and return phases of spacecraft, the drastic changes in working conditions will cause the dynamic parameters of thin-walled structures to change dynamically and nonlinearly over time. The time-varying characteristics of parameters make it necessary for the uncertainty quantification model to have dynamic update capabilities. (3) High-dimensional and strongly nonlinear vibration characteristics. Thin-walled structures usually have complex geometric shapes, rich vibration modes, and high-dimensional dynamic equations. At the same time, under the influence of factors such as large amplitude vibration and material nonlinearity, the vibration characteristics of the structure exhibit strong nonlinear characteristics.

[0005] Therefore, this invention proposes a method for quantifying the uncertainty of dynamic parameters and analyzing the vibration characteristics of thin-walled structures under complex working conditions, including the following steps:

[0006] Step 1, Multi-source Uncertainty Coupling Quantification, includes: constructing a multi-source uncertainty coupling analysis framework; using a sparse Bayesian network model to describe the dependencies between different uncertainty sources; identifying uncertainty factors and their coupling paths; for uncertainties in materials and geometric parameters, using a probability box-based stochastic-interval uncertainty quantification analysis method based on interval analysis theory; for uncertainties in boundary conditions and loads, using a stochastic process model to describe their spatial and temporal variations; and using a stochastic finite element method transfer algorithm based on adaptive polynomial chaotic expansion to quantify the multi-source uncertainty coupling effect into statistical characteristics of vibration response, thereby achieving a description of complex coupled uncertainties.

[0007] Step 2, dynamic update of time-varying uncertainty, includes: proposing a dynamic update method for time-varying uncertainty based on online learning, combining the structural vibration response data and working condition parameters collected in real time by sensors, establishing a time-varying model of dynamic parameters, using the Kalman filter algorithm to estimate the time-varying parameters in real time, and dynamically updating the parameters of the model through a sliding window. By dynamically updating the model, the real-time quantification of the time-varying uncertainty of parameters under complex working conditions can be achieved.

[0008] Step 3, high-dimensional nonlinear vibration characteristic analysis, includes: constructing a high-dimensional nonlinear vibration characteristic analysis method based on dimensionality reduction, using the active subspace method to perform eigenvalue decomposition on the gradient covariance matrix of the output response, determining the basis vectors of the dimensionality reduction, and for strongly nonlinear systems, introducing a Chebyshev expansion function based on truncated sequences, and constructing an approximate relationship between the vibration response and uncertainty parameters by adaptively selecting basis functions and sample points, combined with a radial basis function network model, thereby realizing uncertainty quantification.

[0009] The technical solution provided by this invention brings at least the following beneficial effects:

[0010] This invention addresses the parameter uncertainties in the dynamics of thin-walled structures under complex working conditions by combining physical mechanisms and machine learning techniques to handle the uncertainty quantification problem. It employs probabilistic and interval models to describe the uncertainties, thereby improving the modeling accuracy of the dynamics model of thin-walled system structures. Attached Figure Description

[0011] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0013] like Figure 1 As shown, this invention proposes a method for quantifying the uncertainty of dynamic parameters and analyzing the vibration characteristics of thin-walled structures under complex working conditions, including the following steps:

[0014] Step 1, Multi-source Uncertainty Coupling Quantification, includes: constructing a multi-source uncertainty coupling analysis framework; using a sparse Bayesian network model to describe the dependencies between different uncertainty sources; identifying uncertainty factors and their coupling paths; for uncertainties in materials and geometric parameters, using a probability box-based stochastic-interval uncertainty quantification analysis method based on interval analysis theory; for uncertainties in boundary conditions and loads, using a stochastic process model to describe their spatial and temporal variations; and using a stochastic finite element method transfer algorithm based on adaptive polynomial chaotic expansion to quantify the multi-source uncertainty coupling effect into statistical characteristics of vibration response, thereby achieving a description of complex coupled uncertainties.

[0015] Step 2, dynamic update of time-varying uncertainty, includes: proposing a dynamic update method for time-varying uncertainty based on online learning, combining the structural vibration response data and working condition parameters collected in real time by sensors, establishing a time-varying model of dynamic parameters, using the Kalman filter algorithm to estimate the time-varying parameters in real time, and dynamically updating the parameters of the model through a sliding window. By dynamically updating the model, the real-time quantification of the time-varying uncertainty of parameters under complex working conditions can be achieved.

[0016] Step 3, high-dimensional nonlinear vibration characteristic analysis, includes: constructing a high-dimensional nonlinear vibration characteristic analysis method based on dimensionality reduction, using the active subspace method to perform eigenvalue decomposition on the gradient covariance matrix of the output response, determining the basis vectors of the dimensionality reduction, and for strongly nonlinear systems, introducing a Chebyshev expansion function based on truncated sequences, and constructing an approximate relationship between the vibration response and uncertainty parameters by adaptively selecting basis functions and sample points, combined with a radial basis function network model, thereby realizing uncertainty quantification.

[0017] Step 1 is as follows:

[0018] Based on the logic of "dependency modeling - source quantification - coupling transmission", a multi-source uncertainty coupling analysis framework is constructed, adopting a three-level logic: ① Sparse Bayesian network modeling of four types of uncertainty sources (material parameter fluctuations) Geometric dimensional error Boundary condition changes External load disturbance ① Dependence; ② Material / geometric uncertainties are quantified using probability boxes and boundary / load uncertainties using stochastic processes; ③ Adaptive polynomial chaotic expansion-stochastic finite element transfer of uncertainties.

[0019] A multi-source uncertainty coupling analysis framework is constructed, employing a sparse Bayesian network model, which includes:

[0020] Parent node ;

[0021] in, For elastic modulus, Poisson's ratio, For thickness, Let k be the length, k be the stiffness constraint, and c be the damping. For dynamic loads.

[0022] child nodes ;

[0023] Where K is stiffness and φ is transmission efficiency.

[0024] Output vibration displacement , This is a vibration response.

[0025] The optimal sparse network is selected using the L1 regularized Bayesian information criterion, and the joint probability distribution is:

[0026] ;

[0027] in, Let be the marginal probability of the material parameters. Let be the marginal probability of the geometric dimensions. Let be the marginal probability of the boundary condition. Let be the marginal probability of the external load. Stiffness matrix rely and The conditional probability, For transmission efficiency rely and The conditional probability, Vibration displacement Dependence on K and load transfer efficiency The conditional probability.

[0028] Describes the dependencies between different sources of uncertainty. Dependencies are categorized as follows:

[0029] Direct dependency path: geometric dimension error (Thickness h decreases) → Boundary conditions (k decreases) → Load transfer efficiency (φ decreases) → Vibration displacement Z (u increases);

[0030] Indirect dependency path: material elastic modulus (E increases) → Stiffness (K increases) → Vibration displacement Z (u decreases).

[0031] Identify key uncertainty factors and their coupling paths:

[0032] The key uncertainty factors are identified using the Sobol exponent formula, and the coupling path formula is as follows:

[0033] ;

[0034] in, for right Sensitivity; for right Sensitivity.

[0035] For uncertainties in materials and geometric parameters, a probability box-based stochastic-interval uncertainty quantification analysis method is adopted based on interval analysis theory:

[0036] Based on interval analysis theory, the probability box describes both the "deterministic fluctuation range" and the "uncertainty distribution" of material and geometric parameters through "interval range + upper and lower bounds of probability distribution," and is divided into three steps:

[0037] 1) Determine the interval boundaries of the parameters:

[0038] First, determine the deterministic fluctuation range of material and geometric parameters through experimental measurement or manufacturing tolerances:

[0039] ;

[0040] ;

[0041] Where E is a material parameter (such as elastic modulus), E min and E max These are their minimum and maximum values, respectively; h is a geometric parameter (such as structural thickness), h min and h max These are its minimum and maximum values, respectively.

[0042] 2) Constructing a univariate probability box (random-interval combination):

[0043] For a single parameter (such as E or h), the upper and lower bounds of all possible cumulative distribution functions are described by a univariate probability box, as follows:

[0044] ;

[0045]

[0046] in, Denotes the true cumulative distribution function of E. The minimum possible cumulative probability, This represents the maximum possible cumulative probability. Represents the true cumulative distribution function of h. The minimum possible cumulative probability, This represents the maximum possible cumulative probability.

[0047] 3) Joint probability box (considering parameter correlation):

[0048] Material and geometric parameters may be correlated (e.g., materials with a large E have smaller manufacturing errors in h). The correlation between these two parameters can be linked using a Gaussian Copula function:

[0049] ;

[0050] ;

[0051] in, This represents the minimum correlation probability between the material and its geometric parameters. This represents the maximum correlation probability between material and geometric parameters. This represents the Gaussian Copula function, describing the correlation between parameters.

[0052] For uncertainties in boundary conditions and loads, a stochastic process model is used to describe their variation with space and time.

[0053] Described using a stochastic process model, such as load (t is time, x is spatial coordinate):

[0054] ;

[0055] in, It is a mean function. , Covariance function eigenvalues ​​and eigenfunctions It is an independent standard random variable. For time Spatial coordinates Load at time, For time Spatial coordinates Load at that time.

[0056] The coupling effect of multi-source uncertainties is quantified into statistical characteristics of vibration response, enabling a precise description of complex coupled uncertainties. The statistical characteristics of vibration response mainly include the mean and variance of the time-domain waveform, as well as the spectral distribution characteristics in the frequency domain.

[0057] Adaptive polynomial chaotic expansion-stochastic finite element method is used to transmit coupling effects:

[0058] 1) Control equations of the vibration system (stochastic finite element form):

[0059] ;

[0060] in , , Let be the random mass, damping, and stiffness matrices, respectively, and z be the nodal displacement vector. Let θ be a random load vector, and let θ represent a random variable.

[0061] 2) Adaptive polynomial chaotic expansion:

[0062] Will Represented as orthogonal basis functions ( A linear combination of vectors of random variables:

[0063] ;

[0064] Where s is the expansion order, The coefficients to be determined are shown. s is adjusted using an adaptive algorithm, with an error less than 10. -4 Stop at certain times to ensure a balance between accuracy and efficiency.

[0065] 3) Response statistical characteristics:

[0066] Calculation using adaptive polynomial chaotic expansion coefficients:

[0067] mean ;

[0068] variance ;

[0069] Achieve precise quantification of uncertainties arising from multi-source coupling. 2 To find the second norm.

[0070] Step 2 is as follows:

[0071] A time-varying uncertainty dynamic update method based on online learning is proposed. This method combines real-time structural vibration response data acquired by sensors with load parameters (such as temperature and load) to establish a time-varying model of dynamic parameters. Using the structural vibration response (sensor-acquired) and load parameters as inputs, a time-varying model of the dynamic parameters is constructed to reflect the correlation between the parameters and the load conditions. The specific time-varying model of the dynamic parameters is as follows:

[0072] State vector definition: Let the vibration state of the structure be displacement. ,speed Time-varying dynamic parameters (such as stiffness) Damping )for The operating parameters (temperature T(t), load F(t)) are as follows: Then the state vector is Time-varying state equations (continuous time domain):

[0073] ;

[0074] Where A is the state transition matrix (which varies with dynamic parameters). The damping-stiffness matrix of the vibration system is time-varying (e.g., the damping-stiffness matrix of the vibration system), and B is the input matrix. For process noise (following a Gaussian distribution N(0, ..., ...), ... )), For covariance.

[0075] Observation equation (corresponding to sensor data):

[0076] ;

[0077] in, The vibration response is collected in real time by the sensor. These are displacement observations. For velocity observations, Let υ(t) be the observation matrix (extracting measurable variables from the state), and υ(t) be the observation noise (following a Gaussian distribution N(0, 1)). )).

[0078] This model incorporates operating condition parameters such as temperature and load into the state transition matrix, directly linking the physical logic of "operating condition change - time-varying dynamic parameters - vibration response", thus providing a foundation for subsequent parameter estimation.

[0079] The Kalman filter algorithm is used to estimate time-varying parameters in real time.

[0080] By using a "prediction-update" iteration, the estimated values ​​of dynamic parameters are corrected using real-time observation data, thus achieving unbiased optimal estimation.

[0081] Prediction step (based on the previous time-estimation):

[0082] ;

[0083] ;

[0084] in, This is the prior estimate of the parameters at time t. This is the parameter transition matrix (describing the evolution of parameters over time). Let U be the input gain matrix, and U(t) be the input vector at time t. This is the prior covariance matrix (quantifying the uncertainty of the prior estimate). The posterior estimate of the parameters at time t-1 is... Let be the posterior covariance matrix of the parameter estimation error at time t-1.

[0085] Update step (incorporating current observation data):

[0086] ;

[0087] ;

[0088] ;

[0089] in, Kalman gain (balancing the weights of prior estimates and observed data), The covariance matrix of the observation noise, This represents the posterior estimate (final real-time estimate) of the parameter at time t. Let be the posterior covariance matrix (to quantify the uncertainty of the estimation results). I is the identity matrix.

[0090] Kalman filtering dynamically adjusts the gain. It can still achieve real-time parameter tracking even under noise interference. For example, when a sudden increase in temperature causes a decrease in stiffness k(t), the vibration response can be used to track the parameter. Quickly correct the estimated value.

[0091] The parameters of the uncertainty quantification model are dynamically updated using the sliding window technique.

[0092] By using a "sliding window" to filter the most recent valid estimates, the statistical parameters (such as mean and variance) of the uncertainty model are updated in real time, avoiding the lag caused by old data.

[0093] Sliding window definition: A sliding window of length N is used to retain the parameter estimates for the most recent N time steps. The data within the window are... .

[0094] Uncertainty parameter update formula (taking Gaussian distribution quantization as an example):

[0095] ;

[0096] ;

[0097] in: Let be the mean of the uncertainty model at time t (the central tendency of the parameter estimates). Variance (quantifies the degree of dispersion of the parameter estimate, i.e., the magnitude of uncertainty).

[0098] As the window slides over time, it automatically removes old data at or before time tN and incorporates new estimates at time t, ensuring that uncertainty quantification always reflects the true fluctuations of the “most recent N times” (such as periodic fluctuations of parameters under alternating loads) and avoids interference from historical data with current uncertainty.

[0099] For typical complex operating conditions such as high temperature and alternating loads, a neural network model based on physical information is developed. This model integrates physical laws such as material constitutive relations and heat conduction equations into the neural network, improving the accuracy and generalization ability of time-varying parameter prediction. By dynamically updating the model, real-time quantification of the time-varying uncertainty of parameters under complex operating conditions is achieved.

[0100] By incorporating physical laws such as material constitutive properties and thermal conduction as constraints into neural networks, the problem of insufficient generalization ability of pure data-driven models under high temperature and alternating loads can be solved.

[0101] Physical information neural network structure definition: Input is operating condition parameters Given time t, the output is the predicted value of the dynamic parameters. Network loss functions are divided into "data loss" and "physical constraint loss".

[0102] Total loss function formula:

[0103] ;

[0104] in, For data loss, For physical constraint loss, These are the weighting coefficients for physical constraints, used to balance the consistency between data fitting and physical laws.

[0105] a. Data loss (real-time estimate of the fitted Kalman filter):

[0106] ;

[0107] Where M is the number of training samples, This is the true estimate from the Kalman filter.

[0108] b. Physical constraint loss (residuals incorporating physical laws):

[0109] Thermal conduction constraint (temperature field satisfies Fourier's law):

[0110] ;

[0111] Where α is the thermal diffusivity of the material.

[0112] Material constitutive constraints (the relationship between stiffness and temperature):

[0113] ;

[0114] Where k0 is the stiffness at room temperature, and β is the stiffness temperature coefficient.

[0115] Total physical loss:

[0116] ;

[0117] pass The network output is forced to conform to basic physical laws such as heat conduction and material constitutive properties. For example, under high temperature conditions (sudden increase in T(t)), the network will not predict results that violate the law that "stiffness decreases with increasing temperature", thereby improving the prediction accuracy and generalization ability under complex conditions.

[0118] Step 3 specifically involves:

[0119] Using the mean / variance of the vibration response output from step 1 as initial data, a dimensionality reduction analysis is performed using the active subspace method. This develops a high-dimensional nonlinear vibration characteristic analysis method based on dimensionality reduction technology. The active subspace method is used to perform eigenvalue decomposition on the gradient covariance matrix of the output response to determine the basis vectors for dimensionality reduction, thus reducing the dimensionality of the uncertainty parameter space. For strongly nonlinear systems, a Chebyshev expansion function based on truncated sequences is introduced. By adaptively selecting basis functions and sample points, the computational efficiency of uncertainty propagation is improved. Combined with a radial basis function network model, an approximate relationship between the vibration response and uncertainty parameters is constructed, replacing the complex dynamic calculation model. This significantly reduces the computational cost of vibration characteristic analysis for high-dimensional, strongly nonlinear systems, achieving efficient uncertainty quantification.

[0120] Dimensionality reduction using active subspace method: for high-dimensional uncertain parameters (d>50), reduced to a lower dimensional space using the active subspace method. ( ).

[0121] 1) Calculate the response gradient covariance matrix:

[0122] ;

[0123] Where Y(θ) is the nonlinear vibration response (such as amplitude A(θ)). The gradient with respect to θ is calculated using the finite difference method.

[0124] 2) Eigenvalue decomposition and active subspace construction:

[0125] Perform eigenvalue decomposition on C:

[0126] ;

[0127] in, For eigenvalues, ; This is the eigenvector matrix.

[0128] Take the eigenvectors corresponding to the first m largest eigenvalues Construct an active subspace:

[0129] ;

[0130] in, Let η be the nominal value of the parameter, and η be a low-dimensional parameter (satisfying...) (Ensure that the retention rate of uncertain information is ≥95%).

[0131] Chebyshev expansion accelerates nonlinear transfer:

[0132] For strongly nonlinear systems, a Chebyshev expansion function based on truncated sequences is introduced to approximate the response Y(η):

[0133] 1) Parameter normalization: Mapped to [-1,1]: ;

[0134] 2) Chebyshev expansion:

[0135] ;

[0136] in, It is an nth-order Chebyshev polynomial. , , .

[0137] Expansion coefficient:

[0138] ;

[0139] By adaptively selecting N (such as when (Time cut-off), balancing accuracy and computational load.

[0140] Radial basis function network approximation modeling:

[0141] By combining radial basis function networks (RBF) to construct an approximate relationship between vibration response and uncertainty parameters, RBF can be used to replace complex nonlinear dynamic calculations, enabling rapid response prediction.

[0142] 1) Sample point selection: M samples are generated within the active subspace η using Latin hypercube sampling (LHS). The corresponding response was calculated using the original dynamic model. ;

[0143] 2) Radial basis function network approximation:

[0144] ;

[0145] in, It is a Gaussian radial basis function network function. ε is the shape parameter of the radial basis function, ω i The network weights satisfy a system of linear equations. ω is obtained by directly solving the system of linear equations. i Ultimately, this enables rapid prediction of vibration response.

Claims

1. A method for quantifying the uncertainty of dynamic parameters and analyzing vibration in thin-walled structures, characterized in that, Includes the following steps: Step 1, Multi-source Uncertainty Coupling Quantification, includes: constructing a multi-source uncertainty coupling analysis framework; using a sparse Bayesian network model to describe the dependencies between different uncertainty sources; identifying uncertainty factors and their coupling paths; for uncertainties in materials and geometric parameters, using a probability box-based stochastic-interval uncertainty quantification analysis method based on interval analysis theory; for uncertainties in boundary conditions and loads, using a stochastic process model to describe their spatial and temporal variations; and using a stochastic finite element method transfer algorithm based on adaptive polynomial chaotic expansion to quantify the multi-source uncertainty coupling effect into statistical characteristics of vibration response, thereby achieving a description of complex coupled uncertainties. Step 2, dynamic update of time-varying uncertainty, includes: proposing a dynamic update method for time-varying uncertainty based on online learning, combining the structural vibration response data and working condition parameters collected in real time by sensors, establishing a time-varying model of dynamic parameters, using the Kalman filter algorithm to estimate the time-varying parameters in real time, and dynamically updating the parameters of the model through a sliding window. By dynamically updating the model, the real-time quantification of the time-varying uncertainty of parameters under complex working conditions can be achieved. Step 3, high-dimensional nonlinear vibration characteristic analysis, includes: constructing a high-dimensional nonlinear vibration characteristic analysis method based on dimensionality reduction, using the active subspace method to perform eigenvalue decomposition on the gradient covariance matrix of the output response, determining the basis vectors of the dimensionality reduction, and for strongly nonlinear systems, introducing a Chebyshev expansion function based on truncated sequences, and constructing an approximate relationship between the vibration response and uncertainty parameters by adaptively selecting basis functions and sample points, combined with a radial basis function network model, thereby realizing uncertainty quantification.

2. The method according to claim 1, characterized in that, In step 1, the sparse Bayesian network is selected as the optimal sparse network using the L1 regularized Bayesian information criterion, and the conditional probability table between uncertainty sources is output for subsequent probability box and stochastic process model parameter assignment.

3. The method according to claim 1, characterized in that, In step 1, the random-interval uncertainty quantification analysis method based on probability boxes uses a Gaussian Copula function to describe the correlation between material and geometric parameters, and outputs the upper and lower bounds of the joint probability box as inputs for the random variables of the adaptive polynomial chaotic expansion.

4. The method according to claim 1, characterized in that, In step 1, the adaptive polynomial chaotic expansion is performed at an expansion order P such that the response variance error is less than 1 / 2. It will stop automatically when the time comes.

5. The method according to claim 1, characterized in that, In step 2, the time-varying model of dynamic parameters directly embeds temperature and load conditions into the time-varying state transition matrix, so that the Kalman filter gain automatically balances the sudden changes in conditions and observation noise.

6. The method according to claim 1, characterized in that, In step 2, the sliding window length is such that only the parameter estimates of the most recent N times are retained, and the data within the window is used to refresh the mean and variance of uncertainty in real time to suppress the lag of historical data.

7. The method according to claim 1, characterized in that, Step 2 further includes: incorporating the material constitutive model and heat conduction equation as physical constraints into the neural network loss function to form a physical information neural network, so as to improve the extrapolation accuracy of time-varying parameter prediction under high temperature and alternating load.

8. The method according to claim 1, characterized in that, In step 3, the active subspace method determines the dimension m of dimensionality reduction by retaining ≥95% of the uncertainty information as a threshold, so that the high-dimensional parameter space is reduced to m≤10 dimensions.

9. The method according to claim 1, characterized in that, In step 3, the Chebyshev expansion function is truncated according to the expansion coefficient. Automatically truncates.

10. The method according to claim 1, characterized in that, In step 3, the radial basis function network generates training samples in the dimensionality-reduced space using Latin hypercube sampling, and solves the network weights in one go through a system of linear equations to achieve millisecond-level prediction of vibration response.

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