Multi-body system model confirmation method and system considering random and cognitive uncertainty and storage medium

Abstract

The invention discloses a multi-body system model confirmation method and system considering random and cognitive uncertainty, and a storage medium. The method comprises the following steps: S1, establishing a dynamic model of a multi-body system considering random and cognitive uncertainty; s2, calculating a confidence region responded by the dynamic model by sampling random and cognitive uncertainty parameters; s3, performing a test to obtain test data, and calculating a confidence region of a test response according to the test data; s4, calculating a model confirmation measurement index according to the coincidence rate of the confidence regions of the dynamic model response and the test response in the time domain, judging whether the dynamic model meets the requirement or not, if so, confirming that the dynamic model is a final model, and otherwise, entering the step S5; s5, constructing a calibration optimization model used for correcting parameters of the kinetic model; calculating the confidence region of the kinetic model after parameter correction, and returning to the step S4; the device is suitable for a time-varying model, data can be comprehensively considered, and information cannot be lost.

Description

Technical Field

[0001] The present invention relates to multi-body system modeling, and in particular to a method, system and storage medium for multi-body system model validation considering random and epistemic uncertainties. Background Art

[0002] Multi-body system modeling technology has been widely applied to the modeling of motion mechanisms, gear transmissions, robots, etc. in the fields of automobiles, medical treatment, aviation, and aerospace. How to quantitatively evaluate the credibility of multi-body system dynamics models is a key issue in multi-body system modeling technology. Existing evaluations of multi-body system modeling accuracy usually compare the simulation and test errors under deterministic parameter conditions. However, due to machining errors, installation errors, measurement errors, etc., real multi-body systems have uncertainties. Uncertainties are classified into random uncertainties and epistemic uncertainties according to the completeness of their data. Model validation technology is to evaluate the credibility of simulation models considering uncertainties.

[0003] Model validation technology can be divided into two categories: model validation technology based on probability theory and model validation technology based on non-probability theory. Model validation technology based on probability theory mainly includes classical hypothesis testing method, Bayesian factor method, frequency index method and area measurement method. Model validation technology based on non-probability theory mainly includes model validation technology based on interval theory, model validation technology based on probability box and model validation technology based on evidence theory. These model validation technologies are only applicable to normal models and are no longer applicable to time-varying models such as multi-body system dynamics models. Based on this, model validation technology combining Mahalanobis distance (or Euclidean distance) with traditional model validation methods has emerged. Although the model validation technology based on Mahalanobis distance can handle general time-varying models, such as continuous degradation models, there are high-order vibrations in the dynamic response of multi-body systems. Transforming the dynamic response into a scalar through Mahalanobis distance and evaluating the model will have large errors, resulting in untrustworthy model validation results. Therefore, it is crucial to evaluate the accuracy of multi-body system dynamics models using the original dynamic response without data compression.

[0004] The present invention designs a multi-body system model validation index considering random and epistemic uncertainties based on a confidence region, and on this basis, proposes an optimization inversion method for multi-body system model parameters. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a method, system and storage medium for multi-body system model validation considering random and epistemic uncertainties that is applicable to time-varying models, can comprehensively consider data and will not lose information.

[0006] Technical Solution: The method for multi-body system model validation considering random and epistemic uncertainties according to the present invention includes the following steps:

[0007] S1. Establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify the random and epistemic uncertainty parameters.

[0008] S2. Calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters.

[0009] S3. Conduct tests on the multi-body system to obtain the mean and standard deviation of the test data, and calculate the confidence region of the test response based on this.

[0010] S4. Calculate the model confirmation metric by the coincidence rate of the confidence regions of the dynamic model response and the test response in the time domain. Based on this, determine whether the dynamic model meets the requirements. If it meets the requirements, confirm the dynamic model as the final model; otherwise, go to step S5.

[0011] S5. Construct a calibration optimization model for correcting the dynamic model parameters with the maximum value of the model confirmation metric as the optimization goal and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as the design variables; calculate the confidence region of the dynamic model after correcting the parameters and return to step S4.

[0012] Based on the above method, the present invention comprehensively deals with random uncertainty and epistemic uncertainty by integrating probability theory and interval theory, significantly improving the robustness of the multi-body system model; the use of sampling to dynamically generate the confidence region of the dynamic model response in the time domain can fully reflect the fluctuation range of the system behavior, and combine the mean and standard deviation of the test data to construct the confidence region of the test response. The coincidence rate of the two confidence regions in the time domain is used as the model confirmation metric to quantify the model accuracy, retain the complete time-domain response information of the dynamics, and avoid the errors caused by traditional scalar compression; construct an optimization model with the maximization of the model confirmation metric as the goal, use the calibration optimization model to correct the random parameters and the boundaries of the interval parameters, and form a "modeling-verification-calibration" closed-loop process to ensure the dynamic correction ability of complex time-varying systems.

[0013] In summary, this method simultaneously considers random and epistemic uncertainties, avoids the one-sidedness of the finally confirmed model, and takes into account the completeness and incompleteness of the test data; moreover, the model confirmation metric is used as the model confirmation standard, retaining the complete time-domain response information, avoiding the loss of high-order vibration information caused by compressing the response into a scalar in traditional methods. Without introducing parameter distribution assumptions under the condition of making full use of the test data, it can more truly reflect the consistency between the multi-body system simulation model and the test data; also, the calibration optimization model enables the parameters to have dynamic correction ability, ensuring that the finally confirmed model has sufficient credibility.

[0014] The multi-body system model validation system considering random and epistemic uncertainties described in the present invention, the system includes:

[0015] Dynamic model construction module: used to establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify random and epistemic uncertainty parameters;

[0016] Model confidence region calculation module: used to calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters;

[0017] Test confidence region calculation module: used to conduct tests on the multi-body system to obtain the mean and standard deviation of the test data, and calculate the confidence region of the test response accordingly;

[0018] Model qualification determination module: used to calculate the model validation metric by the coincidence rate of the confidence regions of the dynamic model response and the test response in the time domain, and judge whether the dynamic model meets the requirements accordingly. If it meets the requirements, the dynamic model is confirmed as the final model, otherwise it enters the model optimization module;

[0019] Model optimization module: used to construct a calibration optimization model with the maximum value of the model validation metric as the optimization goal, and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as design variables to correct the parameters of the dynamic model; calculate the confidence region of the dynamic model after correcting the parameters and return it to the model qualification determination module.

[0020] The computer-readable storage medium storing one or more programs described in the present invention, including one or more programs including instructions, which when executed by a computing device, cause the computing device to execute any of the above methods.

[0021] Advantageous effects: Compared with the prior art, the present invention has the following remarkable effects: The present invention simultaneously considers random and epistemic uncertainties, avoids the one-sidedness of the finally confirmed model, and uses the model validation metric as the model validation standard, retaining the complete time-domain response information, avoiding the loss of high-order vibration information caused by compressing the response into a scalar in the traditional method, and also enabling the parameters to have the ability of dynamic correction through the calibration optimization model, ensuring that the finally confirmed model has sufficient credibility. Brief description of the drawings

[0022] Figure 1 It is the overall flow schematic diagram of the present invention;

[0023] Figure 2 It is the schematic diagram of the crank-slider mechanism in the embodiment;

[0024] Figure 3 It is the diagram of the four model validation metric results in the embodiment;

[0025] Figure 4 It is the graph of the change of the model correction fitness value in the embodiment. Specific implementation manners

[0026] As shown in the figure, the multi-body system model confirmation method considering random and epistemic uncertainties according to the present invention includes the following steps:

[0027] S1. Establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify the random and epistemic uncertainty parameters;

[0028]

[0029] Among them, M is the mass matrix, Φ and Φ q are the constraint equations and the Jacobian matrix corresponding to the constraint equations respectively, is the generalized acceleration, is the generalized velocity, Φ qt is the partial derivative of the Jacobian matrix corresponding to the constraint equation with respect to time, Φ tt is the second-order partial derivative of the constraint equation with respect to time, α and β are both Baumgarte coefficients, g is the generalized force, a = [a1, ···, a nS and e M = [e M1 , ···, e MnL are the random uncertainty vector and the epistemic uncertainty vector respectively, a nS and e MnL are the nS-th random uncertainty parameter and the nL-th epistemic uncertainty parameter respectively, and nS and nL are the total numbers of random uncertainty and epistemic uncertainty parameters respectively.

[0030] Random uncertainties (such as machining errors and measurement noises) usually follow a probability distribution (such as a normal distribution). The present invention quantifies such parameters through probability theory to ensure that the model can reflect the statistical characteristics of the actual system. Epistemic uncertainties (such as unknown parameter intervals) usually appear in the form of intervals (such as gap size ranges). The present invention uses interval theory to describe such parameters to avoid model deviations caused by insufficient information.

[0031] By combining probability theory and interval theory, the model can simultaneously capture randomness and epistemic uncertainty, significantly improving the comprehensiveness and applicability of the multi-body system dynamic model.

[0032] S2. Calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters;

[0033] S2.1. Set the number of random and epistemic uncertainty samplings to m and n respectively;

[0034] S2.2. Draw m groups of random uncertainty vectors according to the probability distribution to construct a random uncertainty vector group, and draw n groups of epistemic uncertainty vectors according to Latin hypercube sampling to construct an epistemic uncertainty vector group.

[0035] Sampling according to the probability distribution (random uncertainty parameters) and Latin hypercube sampling (epistemic uncertainty parameters) ensures a high sample coverage rate and a uniform distribution, avoiding the confidence region deviation caused by insufficient sampling in traditional methods.

[0036] S2.3. Draw any vector from the epistemic uncertainty vector group, and calculate the confidence region of this vector and each vector in the random uncertainty vector group in the dynamic model response. The formula for this confidence region (that is, the confidence region of the response of any drawn epistemic uncertainty vector and each random uncertainty vector in the dynamic model) is

[0037]

[0038] where, is the k-th epistemic uncertainty vector, t is time, is the given epistemic uncertainty vector considering only random uncertainty vectors, and are the lower and upper boundaries of the confidence region of the given epistemic uncertainty vector considering only random uncertainty respectively. is the cumulative distribution function of the given epistemic uncertainty vector considering only random uncertainty vectors at time t. is the dynamic response y(t) when the cumulative distribution function value is 2.5%, that is d , namely is the dynamic response y(t) when the cumulative distribution function value is 97.5%, that is u , namely

[0039] S2.4. Confirm whether all vectors in the uncertainty vector group have been drawn. If so, go to step S2.5; otherwise, put forward the drawn vectors in the uncertainty vector group and return to step S2.3;

[0040] S2.5. Synthesize the confidence region results of all epistemic uncertainty vectors to generate the confidence region of the dynamic model response considering random uncertainty and epistemic uncertainty. The formula for this confidence region (that is, the confidence region of the dynamic model response considering random uncertainty and epistemic uncertainty) is

[0041]

[0042] where y(t) d and y(t) u are the lower and upper bounds of the confidence region considering random and epistemic uncertainties, respectively. The lower bound of the confidence region considering random and epistemic uncertainties is the minimum of the lower bounds of the confidence regions of the responses of all given epistemic uncertainty vectors and each random uncertainty vector in the dynamic model, i.e., y(t) d = min(y(t|e M )) d ); the upper bound of the confidence region considering random and epistemic uncertainties is the maximum of the upper bounds of the confidence regions of the responses of all given epistemic uncertainty vectors and each random uncertainty vector in the dynamic model, i.e., y(t) u = max(y(t|e M )) u ).

[0043] This step generates the confidence region of the dynamic response in the time domain through multi-level sampling of double uncertainty parameters, which can comprehensively reflect the fluctuation range of the system behavior.

[0044] S3. Conduct experiments on the multi-body system to obtain the mean and standard deviation of the experimental data, and calculate the confidence region of the experimental response accordingly. The specific calculation formula is

[0045]

[0046] where is the confidence region of the experimental response, t is time, T is the test time interval, is the k-th epistemic uncertainty vector, y obs (t) d and y obs (t) u are the lower and upper bounds of the confidence region respectively, and are the mean and standard deviation of the dynamic response of the multi-body system obtained from the experiment under the given epistemic uncertainty parameters, nE is the number of epistemic uncertainty samples in the experiment, and nA is the number of random uncertainty samples in the experiment.

[0047] Generating the confidence region of the experimental response through the mean and standard deviation of the experimental data provides an objective benchmark for model verification.

[0048] S4. Calculate the model confirmation metric through the coincidence rate of the confidence regions of the dynamic model response and the experimental response in the time domain. Accordingly, judge whether the dynamic model meets the requirements. If it meets, confirm the dynamic model as the final model; otherwise, enter step S5;

[0049] The calculation formula for the model confirmation metric is

[0050]

[0051] where, is the model confirmation metric, and respectively represent the confidence regions of the dynamic model response and the test response, and t0 and t d are the start time and end time of the time domain respectively.

[0052] A threshold can be set. When W is higher than the threshold, it is considered qualified, and this dynamic model is taken as the final model; traditional methods (such as the model confirmation technology based on Mahalanobis distance) need to compress the dynamic response into a scalar, resulting in the loss of high-order vibration information. The present invention retains the complete time-domain response through the model confirmation metric, that is, the confidence region coincidence rate, and is particularly applicable to multi-body systems containing high-frequency vibrations.

[0053] S5. Construct a calibration optimization model for correcting the dynamic model parameters with the maximum value of the model confirmation metric value as the optimization objective and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as the design variables; calculate the confidence region of the dynamic model after correcting the parameters and return to step S4.

[0054] The calibration optimization model is

[0055]

[0056] s.t. μ min ≤ μ ≤ μ max

[0057] σ min ≤ σ ≤ σ max

[0058]

[0059] where, μ and σ are the mean and standard deviation of the random uncertainty parameters to be corrected respectively, μ min and μ max are the minimum and maximum values of the means of all random uncertainty parameters in the dynamic model respectively, σ min and σ max are the minimum and maximum values of the standard deviations of all random uncertainty parameters in the dynamic model respectively, θ L and θ U are the lower and upper bounds of the epistemic uncertainty parameters to be corrected respectively, and are the minimum value of the lower bounds of all epistemic uncertainty parameters in the dynamic model and the maximum value of the upper bounds respectively.

[0060] After the parameters are corrected, the confidence region of the dynamic model response is regenerated and W is calculated to form a "modeling-verification-calibration" closed loop until the model passes the threshold of the model confirmation metric. This process ensures that the model maintains high accuracy under complex working conditions and is applicable to dynamic systems in engineering practice.

[0061] The multi-body system model confirmation system considering random and epistemic uncertainties described in the present invention, the system includes:

[0062] Dynamic model construction module: used to establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify random and epistemic uncertainty parameters;

[0063] Model confidence region calculation module: used to calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters;

[0064] Test confidence region calculation module: used to conduct tests on the multi-body system to obtain the mean and standard deviation of the test data, and calculate the confidence region of the test response accordingly;

[0065] Model qualification determination module: used to calculate the model confirmation metric by the coincidence rate of the confidence regions of the dynamic model response and the test response in the time domain, and judge whether the dynamic model meets the requirements accordingly. If it meets the requirements, the dynamic model is confirmed as the final model; otherwise, it enters the model optimization module;

[0066] Model optimization module: used to construct a calibration optimization model with the maximum value of the model confirmation metric as the optimization goal, and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as the design variables, for correcting the parameters of the dynamic model; calculate the confidence region of the dynamic model after the corrected parameters and return it to the model qualification determination module.

[0067] The computer-readable storage medium storing one or more programs described in the present invention includes one or more programs including instructions, and when the instructions are executed by a computing device, the computing device is caused to execute any of the methods according to the above methods.

[0068] In order to verify the effectiveness and effect of the method of the present invention, the method of the present invention is applied in an example as follows:

[0069] Taking a crank-slider mechanism with clearance considering random and epistemic uncertainties as an example, the schematic diagram of the crank-slider mechanism is shown in Figure 2。The mass of the slider is 0.14 kg, the rotational speed of the crank is 5000 rpm, the radius of the shaft is 10 mm. The crank and the connecting rod are rods with uniform cross-sections, and the mass per unit length is 6 kg / m and 1.75 kg / m respectively. The lengths of the crank and the connecting rod are random uncertainty parameters, and the clearance size is an interval uncertainty parameter. Table 1 lists the uncertainty parameter distributions of 4 simulation models, where Model 1 is consistent with the real model.

[0070] Table 1 Uncertainty parameter distributions of four simulation models

[0071]

[0072] The results of the confirmation metrics for the four simulation models are shown in Figure 3 , and it can be found that: the closer the simulation model is to the real multi-body system model, the closer the model confirmation metric result is to 1, and the sample numbers of random uncertainty and epistemic uncertainty will affect the model confirmation metric result. Specifically, the value of the model confirmation metric index tends to be stable as the sample numbers of both increase.

[0073] As Figure 4 shown, for Simulation Model 3 that does not meet the requirements of the confirmation metric, after parameter correction, the model confirmation metric index gradually approaches 1.

Claims

1. A method for model validation of a multi-body system considering random and epistemic uncertainties, characterized in that, It includes the following steps: S1. Establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify the random and epistemic uncertainty parameters; S2. Calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters; S3. Conduct experiments on the multi-body system to obtain the mean and standard deviation of the experimental data, and calculate the confidence region of the experimental response based on this; S4. Calculate the model confirmation metric by the coincidence rate of the confidence regions of the dynamic model response and the experimental response in the time domain, and judge whether the dynamic model meets the requirements based on this. If it meets the requirements, confirm the dynamic model as the final model; otherwise, go to step S5; S5. Construct a calibration optimization model for correcting the dynamic model parameters with the maximum value of the model confirmation metric as the optimization goal, and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as the design variables; Calculate the confidence region of the dynamic model with the corrected parameters and return to step S4.

2. The method according to claim 1, characterized in that: The dynamic model of the multi-body system established in step S1 is where M is the mass matrix, Φ and Φ q are the constraint equation and the Jacobian matrix corresponding to the constraint equation respectively, is the generalized acceleration, is the generalized velocity, Φ qt is the partial derivative of the Jacobian matrix corresponding to the constraint equation with respect to time, Φ tt is the second-order partial derivative of the constraint equation with respect to time, α and β are both Baumgarte coefficients, g is the generalized force, a = [a1, ···, a nS and e M = [e M1 , ···, e MnL are the stochastic uncertainty vector and the epistemic uncertainty vector respectively, a nS and e MnL are the nS-th stochastic uncertainty parameter and the nL-th epistemic uncertainty parameter respectively, and nS and nL are the total numbers of the stochastic uncertainty and the epistemic uncertainty parameters respectively.

3. The method according to claim 2, wherein The solution of the confidence region of the dynamic model in step S2 includes the following sub-steps: S2.

1. Set the sampling numbers of random and epistemic uncertainties as m and n respectively; S2.

2. Extract m groups of random uncertainty vectors according to the probability distribution to construct a random uncertainty vector group, and extract n groups of epistemic uncertainty vectors according to Latin hypercube sampling to construct an epistemic uncertainty vector group; S2.

3. Extract any vector in the epistemic uncertainty vector group, calculate the responses of this vector and each vector in the random uncertainty vector group in the dynamic model, and calculate the confidence region; S2.

4. Confirm whether all the vectors in the epistemic uncertainty vector group have been extracted. If so, go to step S2.5; otherwise, remove the extracted vectors in the epistemic uncertainty vector group and return to step S2.3; S2.

5. Synthesize the confidence region results of all the epistemic uncertainty vectors to generate the confidence region of the dynamic model response considering random and epistemic uncertainties.

4. The method according to claim 3, wherein: The calculation formula for the confidence region of the response of any extracted epistemic uncertainty vector and each random uncertainty vector in the dynamic model in step S2.3 is wherein, is the k-th epistemic uncertainty vector and the confidence region of the response of each random uncertainty vector in the dynamic model, t is time, and are the lower and upper bounds of the confidence region considering only random uncertainties given the k-th epistemic uncertainty vector, respectively; represents the dynamic response at time t given the epistemic uncertainty vector when the cumulative distribution function value considering only the random uncertainty vector is 2.5%, represents the dynamic response at time t given the epistemic uncertainty vector when the cumulative distribution function value considering only the random uncertainty vector is 97.5%, 5. The method according to claim 3, characterized in that: The calculation formula for the confidence region of the dynamic model response considering random and epistemic uncertainties in step S2.5 is where y(t) d and y(t) u are the lower and upper bounds of the confidence region considering random and epistemic uncertainties, respectively.

6. The method according to claim 1, characterized in that: The calculation formula for the confidence region of the experimental response in step S3 is Among them, is the confidence region of the test response, t is the time, T is the test time interval, is the k-th epistemic uncertainty vector, y obs (t) d and y obs (t) u are the lower and upper boundaries of the confidence region respectively, and are the mean and standard deviation of the dynamic response of the multi-body system obtained from the test under the given epistemic uncertainty parameters. nE is the number of epistemic uncertainty samples in the test, and nA is the number of random uncertainty samples in the test.

7. The method according to claim 1, wherein: The calculation formula for the model confirmation metric in step S4 is Among them, is the model confirmation metric, and represent the confidence regions of the kinetic model response and the test response respectively, and t0 and t d are the start time and end time of the time domain respectively.

8. The method according to claim 1, wherein: The calibration optimization model in step S5 is where μ and σ are the mean and standard deviation of the random uncertainty parameters to be corrected, respectively, and μ min and μ max are the minimum and maximum values of the means of all the random uncertainty parameters in the kinetic model, respectively, and σ min and σ max are the minimum and maximum values of the standard deviations of all the random uncertainty parameters in the kinetic model, respectively, and θ L and θ U are the lower and upper bounds of the epistemic uncertainty parameters to be corrected, respectively, and are the minimum value of the lower bounds and the maximum value of the upper bounds of all the epistemic uncertainty parameters in the kinetic model, respectively.

9. A multi-body system model validation system considering random and epistemic uncertainties, characterized in that, The described system includes: A dynamic model construction module: used to establish a dynamic model of a multi-body system considering random and epistemic uncertainties based on probability theory and interval theory, and quantify the random and epistemic uncertainty parameters; A model confidence region calculation module: used to calculate the confidence region of the dynamic model response by sampling the quantified random and epistemic uncertainty parameters; An experimental confidence region calculation module: used to conduct experiments on the multi-body system to obtain the mean and standard deviation of the experimental data, and calculate the confidence region of the experimental response based on this; Model Qualification Judgment Module: It is used to calculate the model confirmation metric by the coincidence rate of the confidence regions of the dynamic model response and the test response in the time domain, and accordingly judge whether the dynamic model meets the requirements. If it meets the requirements, the dynamic model is confirmed as the final model; otherwise, it enters the Model Optimization Module. Model Optimization Module: It is used to construct a calibration optimization model for correcting the dynamic model parameters, with the maximum value of the model confirmation metric as the optimization goal and the mean and variance of the random uncertainty vector and the lower and upper bounds of the epistemic uncertainty vector as the design variables; calculate the confidence region of the dynamic model after the corrected parameters and return it to the Model Qualification Judgment Module.

10. A computer-readable storage medium storing one or more programs, characterized in that: Comprising one or more programs including instructions which, when executed by a computing device, cause the computing device to execute any of the methods according to claims 1 to 8.

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