Method for reconstructing uncertainty response of thermal protection structure based on Bayesian theory

Abstract

The present invention relates to a method for reconstructing the uncertain response of a thermal protection structure based on Bayesian theory, including: constructing a reduced-order analysis model, which takes load uncertain variables as inputs and outputs the reduced-order global structural response data, and is established based on a neural network; selecting one of the uncertain variables constituting the load uncertain variables and its corresponding variable range, and randomly extracting sample points based on the Monte Carlo method so that the selected uncertain variable satisfies a Gaussian distribution within its corresponding variable range; inputting the sample point data into the reduced-order analysis model and outputting the corresponding structural response data; obtaining the prior probability density distribution of the structural response data as the response prior distribution for subsequent Bayesian inversion; experimentally obtaining the actual distribution of the selected uncertain variable, taking the response prior distribution and the actual distribution as inputs to the Bayesian formula, and performing Bayesian probability inversion to obtain the posterior distribution of the reconstructed structural response of the uncertain variable, thereby improving the accuracy and efficiency of response reconstruction.

Description

Technical Field

[0001] The present invention relates to the technical field of response reconstruction, and in particular to a method for reconstructing the uncertain response of a thermal protection structure based on Bayesian theory. Background Technique

[0002] The aerodynamic force and aerodynamic heat load suffered by aerospace vehicles during service exhibit complex time-varying dynamic characteristics. Their dynamic service environment makes the global mechanical environment of the thermal protection structure on the fuselage surface exhibit non-steady characteristics, which has an uncertain impact on the structural response characteristics. Accurately and efficiently identifying the mechanical environment of the thermal protection structure during the service process of the aircraft and monitoring and predicting its service state along the flight envelope are the key technologies to improve the reliability of the structural design and the effectiveness of strength assessment of aerospace vehicles.

[0003] During the service process of the aircraft, there are multi-dimensional uncertain factors in terms of its load, boundary, measurement conditions, etc., and there is a certain degree of randomness in the process of numerical simulation response reconstruction. Therefore, in order to accurately predict the mechanical environment of the aircraft structure under multi-field environments, it is necessary to quantitatively analyze the uncertain factors in the modeling.

[0004] Existing uncertainty analysis of response reconstruction usually adopts a single quantification method, including the stochastic perturbation method, the Monte Carlo method, the stochastic matrix method, etc. However, the uncertainty quantification results are only related to the established uncertainty of the input variables in the simulation, and cannot utilize effective information such as empirical data, index data or multi-sensor data in actual tests. Therefore, the uncertainty quantification results of structural response reconstruction based on such methods usually have a large deviation from the actual data in engineering applications, and at the same time, a large amount of computing time is required. In summary, there is an urgent need to develop a new type of uncertainty response reconstruction method that can effectively combine experimental information and simulation data with high efficiency and high precision. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention provides a method for reconstructing the uncertain response of a thermal protection structure based on Bayesian theory, aiming to improve the accuracy and efficiency of response reconstruction.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for reconstructing the uncertain response of a thermal protection structure based on Bayesian theory includes the following steps:

[0008] S1: Construct a reduced-order analysis model for the mapping relationship between load uncertain variables and structural responses. The reduced-order analysis model takes load uncertain variables as inputs and outputs the reduced-order global structural response data, and is established based on a neural network;

[0009] S2: Solve the prior distribution of the response, including:

[0010] Select one of the uncertain variables that make up the load uncertain variables and its corresponding variable range, and randomly extract sample points based on the Monte Carlo method so that the selected uncertain variable satisfies the Gaussian distribution within its corresponding variable range;

[0011] Input the sample point data into the reduced-order analysis model and output the corresponding structural response data;

[0012] Obtain the prior probability density distribution of the structural response data as the response prior distribution for subsequent Bayesian inversion;

[0013] S3: Perform response prior distribution inversion based on Bayesian probability:

[0014] Experimentally obtain the actual distribution of the uncertain variables selected in step S2, and use the response prior distribution and the actual distribution as the inputs of the Bayesian formula to perform Bayesian probability inversion to obtain the reconstructed structural response posterior distribution of the uncertain variables.

[0015] The further technical solution is:

[0016] In step S1, the acquisition of the input and output data of the neural network includes:

[0017] S11. Determine the variable range of the load uncertain variables, select a number of sample points within the variable range using the optimized Latin hypercube method, and obtain the global structural response matrix of the sample points through finite element pre-analysis;

[0018] S12. Project the global structural response matrix onto a set of optimal orthogonal bases based on the proper orthogonal decomposition method, and perform dimensionality reduction on the global structural response matrix by truncating the basis vectors to obtain the reduced-dimensional mapping vector of the global response matrix.

[0019] In step S3, the reconstructed structural response posterior distribution of the uncertain variables includes: the maximum likelihood solution, expectation, variance, and confidence interval of the reconstructed structural response.

[0020] The load uncertain variables include multiple uncertain variables: the temperature on the surface and inside the thermal protection structure, and the pressure on the surface of the thermal protection structure.

[0021] The structural response includes displacement response or strain response.

[0022] The beneficial effects of the present invention are as follows:

[0023] Through technical methods such as numerical simulation, neural network models, and efficient reduced-order analysis models, this application constructs an uncertainty analysis framework for response reconstruction under the Bayesian theory, effectively combines the prior distribution of responses obtained from simulation and the sensor measurement load distribution obtained from small-sample tests, and obtains posterior distribution information of reconstructed responses that is closer to the actual situation, with high reconstruction accuracy and engineering application value.

[0024] This application establishes a reduced-order analysis model guided by load variables for the response reconstruction object, efficiently obtains the prior distribution of structural responses corresponding to load uncertain variables within a set range, combines it with an efficient Monte Carlo based on a surrogate model, and performs response data inversion and uncertainty verification under the Bayesian framework by analyzing load measurement data and prior response data obtained from simulation, significantly improving the accuracy of uncertainty quantification of structural reconstructed responses.

[0025] The present invention can effectively utilize the results of small-sample tests, combine with the prior information of responses obtained from simulation, and perform secondary calibration on the response reconstruction results, thereby further improving the accuracy of uncertainty quantification of thermal protection structure response reconstruction.

[0026] Other features and advantages of the present invention will be described in the following specification, and in part, will be obvious from the specification, or will be understood by implementing the present invention. Brief Description of the Drawings

[0027] Figure 1 It is a flowchart of the method according to an embodiment of the present invention.

[0028] Figure 2 It is a schematic diagram of a finite element model of a stitched sandwich thermal protection structure according to an embodiment of the present invention.

[0029] Figure 3 It is a comparison diagram of the prior temperature distribution and the actual measured temperature distribution of sensors of a stitched sandwich thermal protection structure according to an embodiment of the present invention.

[0030] Figure 4 It is a comparison diagram of uncertainty quantification results of the displacement response of a stitched sandwich thermal protection structure with respect to the temperature of the bottom panel according to an embodiment of the present invention. Detailed Description of the Invention

[0031] The following describes the specific embodiments of the present invention with reference to the drawings.

[0032] Refer to Figure 1 , a method for uncertainty response reconstruction of a thermal protection structure based on the Bayesian theory of this application includes the following steps:

[0033] S1: Construct a reduced-order analysis model for the mapping relationship between load uncertain variables and structural responses. The reduced-order analysis model takes load uncertain variables as inputs and the reduced-order global structural response data as outputs, and is established based on a neural network.

[0034] S2: Solve the response prior distribution, including:

[0035] Select an uncertain variable from the load uncertain variables and its corresponding uncertain variable range, and randomly extract sample points based on the Monte Carlo method so that the selected uncertain variable satisfies the Gaussian distribution within its corresponding uncertain variable range.

[0036] Input the uncertain variables of the sample points into the reduced-order analysis model, and output the corresponding structural response data.

[0037] Simulate and obtain the prior probability density distribution of the structural response data as the response prior distribution for subsequent Bayesian inversion.

[0038] S3: Invert the response prior distribution based on Bayesian probability:

[0039] Experimentally obtain the actual distribution of the uncertain variables, input the response prior distribution and the actual distribution into the Bayesian formula for Bayesian probability inversion, and then obtain the reconstructed structural response posterior distribution of the uncertain variables.

[0040] Preferably, in step S1, the acquisition of the input and output data of the neural network includes:

[0041] S11: Use the optimized Latin hypercube method to select sample points within the set range of load uncertain variables, and obtain the global structural response matrix of the sample points through finite element pre-analysis.

[0042] S12: Use the proper orthogonal decomposition (POD) method to perform principal component analysis on the global structural response: project the global structural response matrix onto a set of optimal orthogonal bases, and perform dimensionality reduction on the global structural response matrix by truncating the basis vectors to obtain the reduced-dimensional mapping vector of the global response matrix. The calculation process is as follows:

[0043]

[0044] In the formula, H is the dimensionality reduction coefficient, u i is the global structural response matrix obtained through finite element pre-simulation, is the optimal orthogonal basis vector obtained by the POD method; n is the number of vectors after dimensionality reduction;

[0045] Transform the above formula to get:

[0046]

[0047] In the formula, is the dimensionality reduction function with respect to the basis vectors, and λ is the eigenvalue of the matrix composed of the basis vectors;

[0048] Let U = {u1, u2,... u n}, and taking the partial derivative of the above formula gives:

[0049]

[0050] Let Z = UU T , that is, transforming the above problem into solving the eigenvalues and eigenvectors of the matrix Z:

[0051]

[0052] Solve the relevant parameters of the matrix Z through the singular value decomposition method, and judge the truncation range through the numerical value of the data energy percentage. The larger its value, the more complete the matrix information it contains. The subset can be selected from the full set with reference to the error tolerance range, and usually more than 99% of the information is retained. The data energy percentage I(r) is defined as:

[0053]

[0054] The eigenvectors corresponding to the first r eigenvalues are the optimal orthogonal basis vectors sought The global response reduction model based on the proper orthogonal decomposition method is obtained as:

[0055]

[0056] In the formula, α r is the modal mapping coefficient corresponding to the r-th basis vector, R represents the number of truncated basis vectors, and the reduced-dimensional data obtained can be reconstructed through the corresponding mapping coefficients subsequently.

[0057] Specifically, in step S3, the response prior distribution and the actual load distribution are used as the inputs of the Bayes formula, that is, the prior information and the likelihood function, to perform Bayesian probability inversion, and the Bayesian posterior probability calculation expression is obtained as follows:

[0058]

[0059] Among them, d is the actual load distribution data of N dimensions, m is the structural response data of M dimensions, p(d) is the normalization constant, p(m) is the prior probability density distribution of the structural response data, obtained by simulation, p(m|d) is the conditional probability of m with respect to d, that is, the statistical inversion solution, p(d|m) is the likelihood function, usually written as L(m), representing the conditional probability of d with respect to m, and is expressed as a multi-dimensional Gaussian distribution:

[0060]

[0061] where d(m) is the forward data, and C d is the covariance matrix of the relationships between various variables; N is the dimension of the load variables.

[0062] According to the Bayesian posterior probability, the posterior distribution of the reconstructed structural response of the uncertain variable can be obtained, including statistical characteristics such as the maximum likelihood solution, expectation, variance, and confidence interval of the reconstructed structural response.

[0063] Specifically, the load uncertain variables include multiple uncertain variables: the temperature of the surface and internal regions of the thermal protection structure, and the pressure on the surface of the thermal protection structure.

[0064] Specifically, the structural response includes a displacement response or a strain response.

[0065] The probability theory under the Bayesian framework quantifies the possibility of an event by combining the empirical reasoning of a phenomenon with a certain prior. The method for reconstructing the uncertainty response of the thermal protection structure based on the Bayesian theory in this application effectively combines the prior distribution of the response obtained by simulation and the sensor measurement load distribution obtained by small-sample tests, obtains a posterior distribution of the reconstructed response closer to the real situation, performs secondary calibration on the results of the structural response reconstruction, and at the same time combines the neural network-based reduced-order analysis technology to greatly reduce the computational cost, thereby effectively improving the efficiency and accuracy of the quantification of the uncertainty of the reconstructed response, and having practical theoretical value and broad application prospects.

[0066] The following further illustrates the implementation manner of this application with specific embodiments.

[0067] (1) Refer to Figure 2 , the stitched sandwich thermal protection structure is composed of a composite material load-bearing panel 1, an aerogel core layer 2, and puncture sutures 3, and is used as an integrated whole of structure and function by being bonded to a metal bottom plate 4 in the actual engineering application environment.

[0068] The load uncertain variables include four uncertain variables: the temperatures T1, T2, and T3 of the upper, middle, and lower layers of the stitched sandwich thermal protection structure, and the aerodynamic pressure P of the upper panel. The variable ranges (set ranges) corresponding to the four uncertain variables are respectively: [600, 1000] °C, [300, 600] °C, [20, 300] °C, [1, 300] kPa.

[0069] Establish a finite element analysis model of the stitched sandwich structure as Figure 2As shown in the figure, finite element preventive simulation analysis is carried out. Initially, the optimal Latin hypercube method is used to select 150 sample points within the set load range. Through automated simulation, the displacement response results of the fixed-end structure at both ends under thermo-mechanical coupling conditions included in the sample space are obtained, thereby constructing a mapping relationship dataset between the load and the displacement response, and obtaining a high-order displacement response matrix with the dimension of "the number of finite element model nodes × the number of load sample points".

[0070] The principal component analysis of the response data is carried out using the proper orthogonal decomposition method: project the high-order displacement response matrix onto a set of optimal orthogonal bases, and reduce the dimension of the matrix by truncating the basis vectors to obtain a reduced-dimensional mapping vector. To control the error of the reduced-order result to be less than 1%, the first 6 eigenvectors are selected as the reduced-order target subset, and the reduced-dimensional mapping vector of the global displacement response matrix with a data energy percentage greater than 99.8% is obtained.

[0071] Taking the temperature T1, T2, T3, and the pneumatic pressure P of the upper panel as four uncertain variables as the input, and the reduced-order displacement response as the output, an approximate analysis model of the input load sample points and the proper orthogonal decomposition reduced-dimensional mapping vector is established based on the BP neural network model, thereby constructing a reduced-order analysis model of the load variables with respect to the global response.

[0072] Among them, the learning and training process of the BP neural network model is carried out by alternately cycling through two steps: forward propagation of information and backpropagation of errors to adjust the weights and thresholds layer by layer until the error limit requirement is met or the maximum number of iterations is reached. Set 70% of the training samples, 15% of the validation samples, 15% of the test samples, and the number of neuron layers is 10.

[0073] (2) In order to analyze the influence of the temperature T3 of the lower panel of the stitched sandwich thermal protection structure on the structural displacement response, 10,000 sample points are randomly selected based on the Monte Carlo method so that T3 satisfies the Gaussian distribution in the range of [20, 300] °C, that is, in the actual service environment of the stitched sandwich thermal protection structure, the initial dynamic uncertainty change of the temperature T3 of the lower panel relative to the statistical expected value can be approximately regarded as a Gaussian distribution, that is, the prior distribution of the temperature T3 of the lower panel satisfies the Gaussian distribution.

[0074] Substitute the load sample point data into the reduced-order analysis model for response reconstruction for efficient statistical experiments, that is, quickly calculate the displacement response of the uncertain load variables through a large number of simulations, analyze the statistical relationship between the temperature T3 of the lower panel and the reconstructed displacement response of the target key nodes, and obtain the initial uncertain reconstructed displacement response field of the reconstructed displacement response under uncertain load conditions, that is, obtain the prior distribution of the displacement response, which is used as the prior data of the reconstructed response in the subsequent Bayesian inversion process.

[0075] (3) Measure the actual distribution of the temperature T3' of the lower panel through sensors, and compare the actual distribution with the prior distribution of the temperature of the lower panel Figure 3As shown. From Figure 3 it can be seen that there is a relatively large gap between the prior temperature distribution and the actual temperature distribution measured by the sensor.

[0076] Taking the prior distribution of the displacement response obtained by simulation and the actual distribution of the T3' temperature measurement value obtained by experiment as the input of the Bayesian formula, substituting the prior information and the likelihood function for Bayesian probability inversion, the posterior distribution of the displacement reconstruction response corresponding to the actual load uncertainty variable is obtained, that is, statistical characteristics including the maximum likelihood solution, expectation, variance, and confidence interval of the reconstructed displacement response.

[0077] Comparing the uncertainty analysis results based on the Monte Carlo method, the uncertainty quantification results after the secondary verification based on the Bayesian theory, and the actual displacement response distribution, as Figure 4 shown. From Figure 4 it can be seen that the uncertainty quantification results after the secondary verification based on the Bayesian theory adopted in this application are closer to the actual displacement response distribution, indicating that the reconstruction method of this application has high accuracy.

[0078] The uncertainty response reconstruction method of the thermal protection structure based on the Bayesian theory in this embodiment establishes a reduced-order analysis model guided by load variables for the response reconstruction object, efficiently obtains the prior distribution of the structural response corresponding to the analysis variables within the set variable range, combines the efficient Monte Carlo of the surrogate model, and through analyzing the load measurement data and the prior response data obtained by simulation, conducts response data inversion and uncertainty verification under the Bayesian framework, significantly improving the accuracy of the uncertainty quantification of the structural reconstruction response. Refer to Figure 1 It can be seen that the method proposed in this application can effectively utilize the results of small-sample experiments, combine the prior response information obtained by simulation, and conduct secondary calibration on the response reconstruction results, thereby further improving the accuracy of the uncertainty quantification of the thermal protection structure response reconstruction.

[0079] Those of ordinary skill in the art can understand that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for reconstructing the uncertain response of a thermal protection structure based on Bayesian theory, characterized in that, It includes the following steps: S1: Construct a reduced-order analysis model for the mapping relationship between load uncertain variables and structural responses. The reduced-order analysis model takes load uncertain variables as inputs and reduced-order global structural response data as outputs, and is established based on a neural network; S2: Solve the prior distribution of the response, including: Select one of the uncertain variables that make up the load uncertain variables and its corresponding variable range, and randomly extract sample points based on the Monte Carlo method so that the selected uncertain variable satisfies a Gaussian distribution within its corresponding variable range; Input the sample point data into the reduced-order analysis model and output the corresponding structural response data; Obtain the prior probability density distribution of the structural response data as the prior distribution of the response for subsequent Bayesian inversion; S3: Perform inversion of the prior distribution of the response based on Bayesian probability: Experimentally obtain the actual distribution of the uncertain variable selected in step S2, use the prior distribution of the response and the actual distribution as inputs to the Bayesian formula, and perform Bayesian probability inversion to obtain the posterior distribution of the reconstructed structural response of the uncertain variable.

2. The method for reconstructing the uncertainty response of the thermal protection structure based on the Bayesian theory according to claim 1, characterized in that, In step S1, the acquisition of the input and output data of the neural network includes: S11. Determine the variable range of the load uncertain variables, select several sample points within the variable range using the optimized Latin hypercube method, and obtain the global structural response matrix of the sample points through finite element pre-analysis; S12. Project the global structural response matrix onto a set of optimal orthogonal bases based on the proper orthogonal decomposition method, and perform dimensionality reduction on the global structural response matrix by truncating the basis vectors to obtain the reduced-dimensional mapping vector of the global response matrix.

3. The method for reconstructing the uncertain response of the thermal protection structure based on the Bayesian theory according to claim 1, wherein In step S3, the posterior distribution of the reconstructed structural response of the uncertain variable includes: the maximum likelihood solution, expectation, variance, and confidence interval of the reconstructed structural response.

4. The method for reconstructing the uncertain response of the thermal protection structure based on the Bayesian theory according to claim 1, characterized in that, The load uncertain variables include multiple uncertain variables: the temperature of the surface and internal regions of the thermal protection structure, and the pressure on the surface of the thermal protection structure.

5. The method for reconstructing the uncertain response of the thermal protection structure based on the Bayesian theory according to claim 1, wherein The structural response includes displacement response or strain response.

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