Mechanism reliability calculation method based on multi-fidelity active learning agent model

Abstract

The invention relates to the technical field of mechanism reliability analysis, and particularly discloses a mechanism reliability calculation method based on a multi-fidelity active learning agent model. Comprising the steps of determining a sample space, performing initial test design, constructing a multi-fidelity model, adding sample points based on an active learning function, updating the model, calculating a failure probability and a variable coefficient, obtaining a mechanism performance function and a reliability analysis result and the like. Compared with the prior art, the method has the advantages that the multi-fidelity agent model is constructed, so that the calculation cost for constructing the model is reduced on the premise of ensuring the fitting precision of the model; an active learning function is applied to screen and add an optimal sample point, and a multi-fidelity Kriging model is updated, so that the precision of the constructed proxy model is improved; by setting the TAEA convergence criterion, the calculation precision and the calculation efficiency of the model are balanced, and the calculation efficiency of the proxy model is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanism reliability analysis, and in particular to a mechanism reliability calculation method based on a multi-fidelity active learning agent model. Background Art

[0002] Reliability analysis of mechanical structures is to measure the reliability of various performance indicators of mechanical structures under uncertain factors such as random fluctuations in size, load, vibration and acceleration. Mechanical structures are usually composed of multiple components and key parts, and each component and its parts affect each other. Under the interaction of complex environment and random load, its internal relationship is complex and full of uncertainty, resulting in complex and diverse failure mechanisms and the coexistence of multiple failure modes, which increases the difficulty of accurately evaluating its reliability. In addition, in actual engineering, the mapping relationship between uncertainty variables and performance indicators is difficult to express explicitly with analytical physical equations, that is, the so-called "black box function". For the reliability calculation problem of mechanical structures with black box functions, the finite element model and Monte Carlo simulation are usually used for calculation. Although this method can obtain relatively satisfactory analysis results, it takes a long time to calculate and has low efficiency, making it difficult to be widely used. Summary of the invention

[0003] The purpose of the present invention is to provide a mechanism reliability calculation method based on a multi-fidelity active learning agent model to solve the problems of high calculation difficulty and low calculation efficiency caused by the existence of multiple uncertain variables in the mechanical structure reliability calculation in the prior art.

[0004] In order to solve the above technical problems, the present invention provides a method for calculating the reliability of a mechanism based on a multi-fidelity active learning agent model, comprising the following steps:

[0005] S1. Based on the existing multi-physics field coupling simulation system, the size and working conditions of the mechanism to be analyzed are set in the multi-physics field coupling simulation system to obtain a two-dimensional thermodynamic model, a three-dimensional multi-body dynamics model and a sample space of uncertainty variable parameters of the mechanism to be analyzed;

[0006] S2. Using the Latin hypercube method, based on the two-dimensional thermodynamic model of the mechanism to be analyzed, the three-dimensional multi-body dynamics model and the sample space of the set uncertainty variable parameters, an initial experimental design is performed, and the initial low-fidelity sample points of the mechanism to be analyzed are obtained from the sample space of the uncertainty variable parameters, and a certain proportion of the initial low-fidelity sample points are randomly selected as initial high-fidelity sample points from the initial low-fidelity sample points. The initial low-fidelity sample points and the initial high-fidelity sample points together constitute the current sample space;

[0007] S3. Calculate the low-fidelity sample response value and high-fidelity sample response value of the mechanism to be analyzed respectively using the multi-physics field coupling simulation system, the two-dimensional thermodynamic model of the mechanism to be analyzed, the three-dimensional multi-body dynamics model, and the sample space of the uncertainty variable parameters. Construct a multi-fidelity Kriging model based on low-fidelity sample points, high-fidelity sample points, low-fidelity sample response values, and high-fidelity sample response values. The multi-fidelity Kriging model includes a low-fidelity Kriging model and a high-fidelity Kriging model. Obtain the performance function of the mechanism to be analyzed based on the constructed multi-fidelity Kriging model. Calculate the failure probability and coefficient of variation of the mechanism to be analyzed based on the performance function. If the coefficient of variation meets the accuracy requirements, execute step S5, otherwise execute step S4;

[0008] S4, using the improved MRU active learning function to select the optimal sample points from the sample space of the uncertain variable parameters, and adding the optimal sample points to the current sample space, using the TAEA convergence criterion as the stop condition of the active learning process of the MRU active learning function, when the TAEA convergence criterion is met, the multi-fidelity Kriging model is updated, and step S3 is executed. When the TAEA convergence criterion is not met, this step is repeated until the TAEA convergence criterion is met;

[0009] S5. Output the performance function, failure probability and coefficient of variation of the mechanism to be analyzed, and obtain the reliability result of the mechanism.

[0010] Preferably, in step S3, the performance function of the mechanism to be analyzed is: ;

[0011] in, is the performance function of the mechanism to be analyzed, is the performance threshold of the institution to be analyzed, Predict values ​​for the multi-fidelity Kriging model.

[0012] Preferably, in step S3, the failure probability of the mechanism to be analyzed is: ;

[0013] in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

[0014] Preferably, in step S3, the coefficient of variation of the mechanism to be analyzed is: ;

[0015] in, is the coefficient of variation of the institution to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0016] Preferably, in step S4, the MRU active learning function is: ;

[0017] in, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, For the constructed low-fidelity Kriging model, A high-fidelity Kriging model was constructed. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function.

[0018] Preferably, in step S4, the multi-fidelity correlation function is: ;

[0019] in, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model.

[0020] Preferably, in step S4, the cost ratio function is: ;

[0021] in, .

[0022] Preferably, in step S4, the TAEA convergence criterion includes a convergence criterion A and a convergence criterion B, and the TAEA convergence criterion expression is: ;

[0023] in, is the failure probability predicted by the multi-fidelity Kriging model, The number of samples generated for the Monte Carlo method, is the cumulative distribution function.

[0024] Preferably, in step S5, the mechanism performance function of the mechanism to be analyzed is: ;

[0025] in, is the mechanism performance function of the mechanism to be analyzed, is the threshold of institutional performance, Predicted value for the current active learning Kriging model.

[0026] The failure probability of the mechanism to be analyzed is: ;

[0027] in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

[0028] The coefficient of variation of the institution to be analyzed is: ;

[0029] in, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The present invention reduces the computational cost of constructing a model while ensuring the model fitting accuracy by constructing a multi-fidelity proxy model; applies active learning MRU function to screen and add optimal sample points, and updates the multi-fidelity Kriging model, thereby improving the accuracy of the constructed proxy model; and balances the model calculation accuracy and efficiency by setting the TAEA convergence criterion, thereby improving the computational efficiency of the proxy model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of an embodiment of the present invention;

[0033] Figure 2 The fitting accuracy variation curve of the multi-fidelity Kriging model of the first embodiment of the present invention;

[0034] Figure 3 It is a schematic diagram of a dynamic model of a piston-cylinder group of an aero-engine according to a second embodiment of the present invention;

[0035] Figure 4 is the thermodynamic prediction result of Example 2 of the present invention;

[0036] Figure 5 is the multi-body dynamics prediction result of the second embodiment of the present invention;

[0037] Figure 6 Failure probability curve of the second embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0039] Embodiment 1: Figure 1 As shown, this embodiment provides a method for calculating the reliability of an organization based on a multi-fidelity active learning agent model, comprising the following steps:

[0040] S1. Based on the existing multi-physics field coupling simulation system, the size and working conditions of the mechanism to be analyzed are set in the multi-physics field coupling simulation system, and a two-dimensional and three-dimensional digital model of the mechanism to be analyzed and a sample space of uncertainty variable parameters are constructed. In this embodiment, the two-dimensional and three-dimensional digital models are a two-dimensional thermodynamic model and a three-dimensional multi-body dynamics model of the mechanism to be analyzed;

[0041] S2. Using the Latin hypercube method, based on the two-dimensional thermodynamic model and three-dimensional multi-body dynamics model of the mechanism to be analyzed constructed in step S1, and the sample space of the set uncertainty variable parameters, an initial experimental design is performed, and the initial low-fidelity sample points of the mechanism to be analyzed are obtained from the sample space of the uncertainty variable parameters, and a certain proportion of the initial low-fidelity sample points are randomly selected as initial high-fidelity sample points from the initial low-fidelity sample points. In this embodiment, the selection ratio is 25%, and the initial low-fidelity sample points and the initial high-fidelity sample points together constitute the current sample space;

[0042] S3. Calculate the low-fidelity sample response value and high-fidelity sample response value of the mechanism to be analyzed respectively using the multi-physics field coupling simulation system, the two-dimensional thermodynamic model of the mechanism to be analyzed, the three-dimensional multi-body dynamics model, and the sample space of the uncertainty variable parameters. Construct a multi-fidelity Kriging model based on low-fidelity sample points, high-fidelity sample points, low-fidelity sample response values, and high-fidelity sample response values. The multi-fidelity Kriging model includes a low-fidelity Kriging model and a high-fidelity Kriging model. Obtain the performance function of the mechanism to be analyzed based on the constructed multi-fidelity Kriging model. Calculate the failure probability and coefficient of variation of the mechanism to be analyzed based on the performance function. If the coefficient of variation meets the accuracy requirements, execute step S5, otherwise execute step S4;

[0043] The performance function of the mechanism to be analyzed is: ;

[0044] in, is the performance function of the mechanism to be analyzed, is the performance threshold of the institution to be analyzed, Predicted values ​​for the multi-fidelity Kriging model;

[0045] The failure probability of the mechanism to be analyzed is: ;

[0046] in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable;

[0047] The coefficient of variation of the institution to be analyzed is: ;

[0048] in, is the coefficient of variation of the institution to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0049] S4. Use the improved MRU active learning function to select the optimal sample points from the sample space of the uncertain variable parameters, and add the optimal sample points to the current sample space. Use the TAEA convergence criterion as the stop condition of the active learning process of the MRU active learning function. When the TAEA convergence criterion is met, update the multi-fidelity Kriging model, such as Figure 2 The figure shows the fitting accuracy change curve of the multi-fidelity Kriging model of the first embodiment of the present invention. When step S3 is executed and the TAEA convergence criterion is not met, this step is repeated until the TAEA convergence criterion is met.

[0050] The MRU active learning function is: ;

[0051] in, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, For the constructed low-fidelity Kriging model, A high-fidelity Kriging model was constructed. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function;

[0052] The multi-fidelity correlation function is: ;

[0053] in, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model;

[0054] The cost ratio function is: ;

[0055] in, .

[0056] The TAEA convergence criterion includes convergence criterion A and convergence criterion B. The TAEA convergence criterion expression is: ;

[0057] in, is the failure probability predicted by the multi-fidelity Kriging model, The number of samples generated for the Monte Carlo method, is the cumulative distribution function.

[0058] S5. Output the performance function, failure probability and coefficient of variation of the mechanism to be analyzed, and obtain the reliability result of the mechanism;

[0059] The performance function of the mechanism to be analyzed is: ;

[0060] in, is the performance function of the mechanism to be analyzed, is the performance threshold of the institution to be analyzed, Predict values ​​for the multi-fidelity Kriging model.

[0061] The failure probability calculation expression of the mechanism to be analyzed is: ;

[0062] in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

[0063] The coefficient of variation of the institution to be analyzed is: ;

[0064] in, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0065] Embodiment 2: This embodiment provides a method for calculating the reliability of an organization based on a multi-fidelity active learning agent model, comprising the following steps:

[0066] S1. Based on the existing multi-physics coupling simulation system, by setting the parameters such as mechanism size and working conditions in the multi-physics coupling simulation system, the piston-cylinder group thermodynamic model and the crankshaft-connecting rod mechanism multi-body dynamics model of the aircraft engine are obtained in turn, and the sample space of the uncertainty variable parameters of the analyzed mechanism is obtained through the multi-physics coupling simulation system.

[0067] The principle of thermodynamic analysis is to establish a two-dimensional cylinder-piston group model. The purpose of thermodynamic analysis is to obtain the cylinder pressure change required for multi-body analysis. The rigid adiabatic cylinder-piston group established in this analysis is based on the following assumptions and simplifications: in the cylinder, only air is considered as fluid; the heat generated by combustion is evenly distributed in space; the convection effect inside the cylinder is ignored; all equations are solved in the original domain, and the influence of the volume change of the cylinder is analyzed in the equations.

[0068] This heat transfer equation is used to simulate the temperature distribution of the air in the cylinder. When the piston does work, the temperature rises and the pressure work increases. The pressure distribution in the air is simulated using the ideal gas equation. Its expression is: ;

[0069] in, They represent the in-cylinder pressure, air mass, in-cylinder current volume, specific gas constant, and in-cylinder temperature respectively.

[0070] The expression of piston displacement changing with crankshaft rotation angle is: ;

[0071] In the formula, is the piston displacement, is the crank radius, Connecting rod length is the crank angle.

[0072] The dynamic model of the cylinder-piston group is as follows: Figure 3 The dynamic expression of the piston cylinder group is: ;

[0073] In the formula, To break out the pressure, is the connecting rod force, is the oil film pressure, is the friction force between the bushing wall and the piston sleeve, is the torque around the piston pin, caused by the oil film pressure, and are the normal force and tangential force of the equivalent ring acting on the piston, is the piston mass, is the moment of inertia of the piston about the pin, is the nominal diameter of the piston, They are Figure 3 The distance shown, is the reciprocating inertia force.

[0074] S2. Use the Latin hypercube method to perform initial experimental design, obtain the initial low-fidelity sample points of the institution to be analyzed from the sample space of the uncertainty variable parameters, and randomly select 25% of the samples from the low-fidelity samples as the initial high-fidelity sample points.

[0075] The variable parameters in this embodiment are: piston radius, connecting rod length, crankshaft length and combustion heat.

[0076] S3. Calculate the response values ​​of low-fidelity samples and high-fidelity samples respectively using a multi-physics field coupling simulation system. Construct an initial multi-fidelity Kriging model based on the initial sample points and the corresponding response values. Obtain the performance function of the mechanism based on the constructed multi-fidelity Kriging model, and calculate the failure probability and coefficient of variation of the mechanism based on the performance function. If the coefficient of variation meets the accuracy requirements, execute step S6, otherwise execute step S4.

[0077] The calculation expression of the multi-fidelity active learning function MRU is: ;

[0078] in, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, For the constructed low-fidelity Kriging model, A high-fidelity Kriging model was constructed. is the multi-fidelity correlation function, is the cost ratio function, is the probability density function.

[0079] The multi-fidelity correlation function is: ;

[0080] in, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model;

[0081] The cost ratio function is: ;

[0082] in, .

[0083] The TAEA convergence criterion includes convergence criterion A and convergence criterion B. The TAEA convergence criterion expression is: ;

[0084] in, is the failure probability predicted by the multi-fidelity Kriging model, The number of samples generated for the Monte Carlo method, is the cumulative distribution function.

[0085] S4. Use the improved MRU learning function to select the optimal sample points from the sample space and add them to the current sample space. Use the TAEA convergence criterion as the stop condition of the active learning process. When the convergence criterion is met, update the multi-fidelity Kriging model and execute step S3. Otherwise, execute step S5.

[0086] S5. Repeat step S4 until it meets the TAEA convergence criterion.

[0087] S6. According to the current multi-fidelity Kriging model, the current mechanism performance function is obtained, and the current mechanism performance function is output to calculate the failure probability and coefficient of variation of the mechanism.

[0088] The calculation expression of the mechanism performance function is: ;

[0089] in, is the mechanism performance function, is the threshold of institutional performance, Predicted value for the current active learning Kriging model.

[0090] The failure probability calculation expression is: ;

[0091] in, is the failure probability, is an n-dimensional random vector, is the probability density function of the random variable.

[0092] The expression for calculating the coefficient of variation is: ;

[0093] in, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

[0094] The dynamic model of the aircraft engine piston cylinder group is as follows Figure 3 As shown in Figure 2, the thermodynamic prediction results and multi-body dynamics prediction results of the aircraft engine are shown in Figure 2. Figure 4 , 5 As shown in Figure 2, the failure probability curve of the multi-fidelity active learning Kriging model is as follows: Figure 6 As shown in the table below, it can be seen that the failure probability prediction results of the method of the present invention have higher accuracy under different cost ratios. In addition, the proposed method reduces the waste of calculation cost while ensuring the prediction accuracy.

[0095] ;

[0096] The embodiments of the present invention are given for the purpose of illustration and description, and are not intended to be exhaustive or to limit the invention to the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for specific uses.

Claims

1. A method for calculating mechanism reliability based on a multi-fidelity active learning agent model, characterized in that: The following steps are involved: S1. Based on the existing multi-physics field coupling simulation system, the size and working conditions of the mechanism to be analyzed are set in the multi-physics field coupling simulation system to obtain a two-dimensional thermodynamic model, a three-dimensional multi-body dynamics model and a sample space of uncertainty variable parameters of the mechanism to be analyzed; S2. Using the Latin hypercube method, based on the two-dimensional thermodynamic model of the mechanism to be analyzed, the three-dimensional multi-body dynamics model and the sample space of the set uncertainty variable parameters, an initial experimental design is performed, and the initial low-fidelity sample points of the mechanism to be analyzed are obtained from the sample space of the uncertainty variable parameters, and a certain proportion of the initial low-fidelity sample points are randomly selected as initial high-fidelity sample points from the initial low-fidelity sample points. The initial low-fidelity sample points and the initial high-fidelity sample points together constitute the current sample space; S3, using a multi-physics field coupling simulation system, a two-dimensional thermodynamic model of the mechanism to be analyzed, a three-dimensional multi-body dynamics model and a sample space of uncertainty variable parameters, respectively calculating the low-fidelity sample response value and the high-fidelity sample response value of the mechanism to be analyzed, constructing a multi-fidelity Kriging model based on the low-fidelity sample points, the high-fidelity sample points, the low-fidelity sample response values ​​and the high-fidelity sample response values, the multi-fidelity Kriging model including a low-fidelity Kriging model and a high-fidelity Kriging model, obtaining a performance function of the mechanism to be analyzed according to the constructed multi-fidelity Kriging model, calculating the failure probability and the coefficient of variation of the mechanism to be analyzed according to the performance function, if the coefficient of variation meets the accuracy requirement, executing step S5, otherwise executing step S4; S4, using the improved MRU active learning function to select the optimal sample points from the sample space of the uncertain variable parameters, and adding the optimal sample points to the current sample space, using the TAEA convergence criterion as the stop condition of the active learning process of the MRU active learning function, when the TAEA convergence criterion is met, the multi-fidelity Kriging model is updated, and step S3 is executed. When the TAEA convergence criterion is not met, this step is repeated until the TAEA convergence criterion is met; S5. Output the performance function, failure probability and coefficient of variation of the mechanism to be analyzed, and obtain the reliability result of the mechanism.

2. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S3, the performance function of the mechanism to be analyzed is: ； in, is the performance function of the mechanism to be analyzed, is the performance threshold of the institution to be analyzed, Predict values ​​for the multi-fidelity Kriging model.

3. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S3, the failure probability of the mechanism to be analyzed is: ； in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable.

4. The method for calculating the reliability of an organization based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S3, the coefficient of variation of the mechanism to be analyzed is: ； in, is the coefficient of variation of the institution to be analyzed, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

5. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S4, the MRU active learning function is: ； in, is the MRU active learning function, is the predicted mean of the high-fidelity Kriging model, is the standard deviation of the high-fidelity Kriging model, is the model fidelity, For the constructed low-fidelity Kriging model, To construct a high-fidelity Kriging model, is the multi-fidelity correlation function, is the cost ratio function, is the probability density function.

6. The method for calculating the reliability of an organization based on a multi-fidelity active learning agent model according to claim 5, characterized in that: In step S4, the multi-fidelity correlation function is: ； in, is the predicted mean of the low-fidelity Kriging model, is the standard deviation of the low-fidelity Kriging model.

7. The method for calculating the reliability of an organization based on a multi-fidelity active learning agent model according to claim 5, characterized in that: In step S4, the cost ratio function is: ； in, .

8. The method for calculating the reliability of a mechanism based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S4, the TAEA convergence criterion includes convergence criterion A and convergence criterion B. The TAEA convergence criterion expression is: ； in, is the failure probability predicted by the multi-fidelity Kriging model, The number of samples generated for the Monte Carlo method, is the cumulative distribution function.

9. The method for calculating the reliability of an organization based on a multi-fidelity active learning agent model according to claim 1, characterized in that: In step S5, the performance function of the mechanism to be analyzed is: ； in, is the performance function of the mechanism to be analyzed, is the threshold value of the institution to be analyzed, Predicted values ​​for the multi-fidelity Kriging model; The failure probability of the mechanism to be analyzed is: ； in, is the failure probability of the mechanism to be analyzed, is an n-dimensional random vector, is the probability density function of the random variable; The coefficient of variation of the institution to be analyzed is: ； in, is the failure probability predicted by the multi-fidelity Kriging model, is the total number of sample points in the sample space.

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