Structure dynamic distribution load identification method based on pungent-preserving variation integral

Abstract

The invention provides a structure dynamic distribution load identification method based on pungent-preserving variational integration. Comprising the following steps: firstly, establishing a structural finite element model and setting upper and lower bounds of uncertain parameters, performing modal decomposition on a system, constructing a load reverse identification format of a Baochuang integral based on a discrete Burkhoff variation principle, and stably reconstructing a time domain load. A Gaussian process agent model is constructed in an uncertain parameter domain, and the upper bound and the lower bound of the load are respectively searched by adopting Bayesian optimization of upper and lower confidence bound acquisition functions through maximizing logarithmic edge likelihood adaptive learning kernel parameters and observation noise; and finally, converting a Gaussian process posterior mean value and a standard deviation into upper and lower bounds of a time history with given confidence. The method is high in sample efficiency, robust to noise and parameter uncertainty, and suitable for engineering application of load identification and safety margin verification.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, in particular to a structure dynamic distributed load identification method based on symplectic variational integration. BACKGROUND

[0002] In aerospace engineering, the distributed dynamic load borne by the aircraft structure during service is usually difficult to measure directly, while the dynamic response such as acceleration, speed or displacement of the structure under external excitation is easy to obtain. Therefore, how to inversely calculate the load time history based on the measurable response and combined with the mechanical equation is one of the key technologies to support the fine design, life evaluation and reliability verification of the structure. Existing load identification methods mainly include two types of frequency domain and time domain: the frequency domain method is intuitive in modeling, but it often needs to perform large-scale matrix inversion for wideband or non-stationary loads, and the calculation scale and ill-conditioned problem are significant; the time domain method can directly process transient processes, but it often involves discrete convolution in modal space, which is easy to cause error transmission and accumulation.

[0003] In addition, there are inevitable uncertainties such as material and connection parameter dispersion, environment and sensor noise in engineering practice. A large number of existing methods default the deterministic premise or rely on sufficient samples to establish the probability distribution. However, it is often not feasible to obtain sufficient data to accurately characterize the parameter distribution under the condition of limited flight test or ground test. Therefore, interval type uncertainty propagation has gradually attracted attention, with upper and lower bounds of parameters replacing complete distribution, which can still give a conservative outer bound of response under limited samples. However, the interval propagation based on traditional numerical simulation or Monte Carlo generally has problems such as large calculation overhead, low efficiency of extreme value search and insufficient explanation of boundary credibility, which is difficult to meet the engineering demand of high efficiency and high confidence in aerospace scenarios.

[0004] In view of the above bottlenecks: first, the symplectic variational integration which maintains the geometric structure of the system is introduced in the structural dynamics inversion, which can significantly improve the stability and energy consistency of the load time history reconstruction in long-time and strong coupling scenarios; second, under the condition of limited samples, only known parameter interval and noisy response, an uncertainty evaluation framework is needed which can efficiently search for extreme values and give confidence boundaries. Based on this, it is necessary to propose a method of using symplectic variational integration for robust load identification and combining Gaussian process Bayesian optimization to realize interval uncertainty propagation, so as to efficiently construct the upper and lower bounds of extreme values with explicit joint confidence under limited samples and noise interference, and provide a verifiable safety margin for the design and evaluation of aerospace structures. SUMMARY

[0005] To overcome the insufficient precision of load identification and lack of confidence evaluation under the conditions of small sample, interval type uncertainty and measurement noise, the present application proposes a structural dynamic distributed load identification method based on the symplectic variational integration. The method takes the structural dynamic response as the input, and uses the symplectic variational integration method to stably reconstruct the time-domain distributed load. In the case of only knowing the upper and lower bounds of the structural parameters, the Gaussian process Bayesian optimization is introduced to construct a proxy model of the parameter to the load extreme value, and the upper and lower confidence bounds are used to adaptively search for the extreme value in the parameter interval to obtain the confidence upper and lower bounds. The present application is suitable for the engineering scene with measurement noise, parameter uncertainty and limited data, and can realize accurate and robust distributed load identification and confidence evaluation of interval uncertainty envelope, thereby providing reliable basis for the design and safety margin verification of aerospace structures.

[0006] The technical solution of the present application is a structural dynamic distributed load identification method based on symplectic variational integration, which comprises the following steps:

[0007] First step: first, a finite element model of the structure to be identified is established, the geometry, material and boundary conditions are defined, the structure is discretized, and the mass matrix, damping matrix and stiffness matrix are obtained; the finite element model is mapped to modal coordinates through characteristic decomposition to obtain modal mass matrix, modal damping matrix and modal stiffness matrix;

[0008] Second step: then, the parameter interval of the uncertain input is determined, the lower and upper bounds of each parameter are given, and the structural parameter interval description is formed; the real parameter interval is linearly mapped to the standard normalized space;

[0009] Third step: deterministic load identification, including: in the modal space, the discrete Birkhoff variational method is used to variational modeling of the dynamic relationship of adjacent time steps, the discrete action is taken to the extreme value, and the algebraic update formula corresponding to the time step is obtained, and the external load is taken as the to-be-identified quantity and solved together;

[0010] Fourth step: in the given uncertain parameter upper and lower bounds, first, the target confidence is selected, the Latin hypercube sampling method is used to generate a small number of uniformly dispersed initial sample points in the normalized parameter domain, for each initial sample, the deterministic load identification of the third step is called to solve the scalar response of the corresponding time sequence or key moment, and the input-output observation pair is formed;

[0011] Fifth step: based on the initial observation pair, a Gaussian process regression model is constructed, the kernel parameter and observation noise are adaptively learned by maximizing the log marginal likelihood; at the same time, the posterior mean field is obtained, which describes the central tendency of the response under different parameter values; the posterior standard deviation field is obtained, which quantifies the model uncertainty and noise influence;

[0012] Sixth step: based on the fitted Gaussian process, the coefficients in the acquisition function are calculated according to the given confidence Instantiation; construct the upper and lower boundary corresponding acquisition function: the upper boundary adopts the upper confidence limit function UCB, the lower boundary adopts the lower confidence limit function LCB, respectively maximize the UCB function and minimize the LCB function in the parameter domain, obtain a new sampling point;

[0013] Step 7: calling the deterministic load identification of step 3 for the new sampling point to obtain the corresponding response value; incorporating the new data into the sample set, updating the Gaussian process model, making the posterior mean and standard deviation shrink with data accumulation, repeating the selection, calculation and updating until the termination is met, finally outputting the time series envelope on the parameter domain under the target confidence, and the average value of the upper and lower boundaries is the nominal value of the identified load.

[0014] Compared with the prior art, the present application has the following advantages:

[0015] (1) The present application adopts the symplectic variational integration to establish the load identification discrete format, maintains the geometric structure characteristics of the dynamic system, significantly suppresses the long-term energy drift and error accumulation, and can still stably reconstruct the distributed load time course under the condition of strong coupling and weak damping.

[0016] (2) The present application introduces the Gaussian process Bayesian optimization under the condition of only parameter interval and limited measurement, jointly learns the mean and variance and outputs the upper and lower boundaries with explicit confidence, converges to the extreme value outer boundary with a small amount of evaluation, and significantly reduces the simulation or test cost. DETAILED DESCRIPTION

[0017] Figure 1 is the structural dynamic distributed load identification method flowchart based on the symplectic variational integration of the present application;

[0018] Figure 2 is a schematic diagram of a cantilever plate structure model subjected to two-dimensional dynamic load according to the present application;

[0019] Figure 3 is a deterministic load identification result diagram for the cantilever plate structure according to the present application;

[0020] Figure 4 is an uncertain load identification result diagram for the cantilever plate structure according to the present application, and the upper and lower boundaries of the time domain load at the node where the maximum load occurs. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other. In order to achieve the above purpose, the technical scheme of the present application is as follows.

[0022] As Figure 1 indicated, the application provides a structural dynamic distributed load identification method based on a preservation variation integral, comprising the following steps:

[0023] First step: firstly, a finite element model of a structure to be subjected to load identification is established, the definition of geometry, material and boundary conditions is completed, the structure is discretized, and mass matrix , damping matrix and stiffness matrix are obtained. The damping can be in the form of proportional damping, and the corresponding parameters are calibrated by experience or test. The finite element model is mapped to modal coordinates by eigenvalue decomposition, and modal mass matrix , modal damping matrix and modal stiffness matrix are obtained, and the specific form is:

[0024] (1)

[0025] Wherein, , and represent the first diagonal element of matrix , and , respectively, and represents the total degree of freedom of the system.

[0026] Second step: then, the interval of uncertain input parameters (such as structural elastic modulus, density and other material parameters) is determined. These parameter variables are expressed as , the lower limit and upper limit of each parameter variable are given, and the interval description for subsequent analysis is formed. In order to unify the scale, the real parameter interval is linearly mapped to the standard normalized space , wherein is the number of uncertain parameters.

[0027] Third step: in the modal space, the discrete Birkhoff variation integral method is used to model the dynamic relationship of adjacent time steps, the extremum of the discrete action is obtained, the algebraic update relationship corresponding to the time step is obtained, and the external load is taken as the to-be-identified quantity and solved. The load identification formula of the discrete Birkhoff variation integral in the modal space is:

[0028] (2)

[0029] Wherein, represents the modal space degree of freedom index, is the to-be-identified external load in the modal space at the time step ,common (time step) and The first and second are respectively the first in the modal space. Displacement and velocity responses at time steps For time step.

[0030] Combined with the measured response sequence and By proceeding step by step, the modal load matrix can be obtained. ,in For the first Load time series vector of modal degrees of freedom. The load matrix in the actual physical space is obtained through inverse modal transformation. This step is the deterministic load identification process, and the results provide a benchmark input for subsequent uncertainty analysis and confidence boundary assessment.

[0031] Step 4: Within the given upper and lower bounds of the uncertainty parameter, first select the target confidence level (e.g., 90%, 95%, or 99%). This applies to the uncertainty parameter defined in Step 2. (Domain is) The Latin hypercube sampling method is used to generate a small number of uniformly distributed initial sample points within the normalized parameter domain. ,in This represents the initial number of sample points. For each initial sample, the deterministic load identification method from step three is called to obtain the load. Record the first Load of each sample for Ultimately formed Input-output observation pairs .

[0032] Step 5: Given an initial observation set back( The initial sample set contains the number of samples. For input, (For the corresponding observations), a Gaussian process regression model is constructed based on the initial observations. The kernel parameters and observation noise are adaptively learned by maximizing the log-marginal likelihood. Initial observation set any test point Noise-containing observations at the location The conditional distribution is:

[0033] (3)

[0034] in,

[0035] (4)

[0036] here, , The kernel function matrix, It is the identity matrix. represents the hyperparameters of the Gaussian process model, obtained by maximizing the likelihood function. represents the column vector of covariance between the test point and all training points, expressed as:

[0037] (5)

[0038] Based on equation (4), we can simultaneously obtain: the posterior mean field, which characterizes the central trend of the response under different parameter values; and the posterior standard deviation field, which quantifies the uncertainty of the model and the influence of noise.

[0039] Step 6: Based on the fitted Gaussian process, adjust the coefficients in the acquisition function according to the predetermined confidence level. Instantiation is used to define the specific form of the sampling function. This function is used to select the next most valuable sampling point. For a given confidence level... ,coefficient The instantiation formula is:

[0040] (6)

[0041] in, This is the cumulative distribution function of the standard normal distribution.

[0042] Construct the acquisition functions corresponding to the upper and lower bounds: the upper bound uses the UCB function, and the lower bound uses the LCB function. In the step iteration, the forms of the UCB and LCB functions are:

[0043] (7)

[0044] in, and Let be the posterior mean function and posterior standard deviation function of the Gaussian process model obtained in this iteration. In the parameter domain... The UCB function is maximized and the LCB function is minimized respectively, where d represents the dimension of the parameter space, to obtain new sampling points, expressed as:

[0045] (8)

[0046] (9)

[0047] and New sampling points corresponding to the upper and lower bounds, respectively. Indicates the uncertainty of parameters Domain Upsampling.

[0048] Step 7: Apply the load identification method from Step 3 to the new sampling points to obtain the corresponding observations. Incorporate the new data into the sample set and update the Gaussian process model so that its posterior mean and standard deviation shrink as the data accumulates. Repeat the selection, calculation, and update until one of the termination conditions is met: (1) the maximum number of updates is reached. (2) The changes in the maximum / minimum values ​​in the two most recent iterations are both less than the preset threshold. ,Right now:

[0049] (10)

[0050] The final output is the time series envelope (i.e., the upper and lower bounds of the time-domain load) in the parameter domain at the target confidence level, and its form is:

[0051] (11)

[0052] in, and These are the posterior mean and posterior standard deviation functions obtained after iteration termination. Upper and lower bounds. and The sum of the values ​​can be used to obtain the nominal value of the identified load.

[0053] Example:

[0054] To better understand the features of this invention and its applicability to engineering practice, this invention focuses on distributed load identification for aircraft control surface structures subjected to two-dimensional dynamic distributed loads. This control surface structure can be equivalent to a cantilever plate structure, such as... Figure 2 As shown. The three regions of this cantilever plate have different material parameters, and their elastic modulus ranges are respectively... , and The density parameter is the same: 4510 kg / m³ 3 The structure is subjected to a gust of wind load, the specific form of which is:

[0055] (12)

[0056] in, and For regularized coordinates, and These are the chord length and the span, respectively, both of which are taken as 1 m in this example. For load amplitude coefficient, It is the chord gradient coefficient. It is the gust bandwidth parameter.

[0057] Using the center value of the elastic modulus as input, the deterministic load identification results and errors are shown in [the table below]. Figure 3 The figures show (a) a comparison of the overall load identification results, (b) an absolute error cloud map, (c) an absolute error surface plot, (d) a relative error cloud map, and (e) a relative error surface plot. The results demonstrate the effectiveness and high accuracy of the load identification method based on symplectic variational integral in this invention. Considering uncertainty, using the uncertain interval of the elastic modulus as input and a confidence level of 95%, the time-domain load boundary at the node with the maximum uncertain load is shown in the figure. Figure 4 The results in the figure show that the identified load boundary can effectively enclose the actual load.

[0058] The above are merely specific steps of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of protection of the present invention.

[0059] The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A method for identifying structural dynamic distributed loads based on symplectic variational integrals, characterized in that, Includes the following steps: Step 1: First, establish a finite element model of the structure to be identified under load, define the geometry, materials and boundary conditions, discretize the structure, and obtain the mass matrix, damping matrix and stiffness matrix. The finite element model is mapped to modal coordinates through eigenvalue decomposition to obtain the modal mass matrix, modal damping matrix, and modal stiffness matrix; Step 2: Then determine the parameter range of the uncertain input, give the lower and upper bounds of each parameter, and form a description of the structural parameter range; Linearly map the true parameter range to the standard normalized space; The third step is deterministic load identification, which includes: using the discrete Burkhov variational method in the modal space to perform variational modeling of the dynamic relationship between adjacent time steps, letting the discrete action take extreme values, obtaining the algebraic update formula corresponding to the time step, and solving the external load as a variable to be identified. Step 4: Within the given upper and lower bounds of the uncertain parameters, first select the target confidence level, and use the Latin hypercube sampling method to generate a small number of uniformly dispersed initial sample points in the normalized parameter domain. For each initial sample, call the deterministic load identification in step 3 to solve the scalar response of the corresponding time series or key moment to form an input-output observation pair. Step 5: Construct a Gaussian process regression model based on the initial observation pair, and adaptively learn the kernel parameters and observation noise by maximizing the log marginal likelihood; at the same time, obtain: the posterior mean field, which describes the central trend of the response under different parameter values; and the posterior standard deviation field, which quantifies the uncertainty of the model and the influence of noise. Step 6: Based on the fitted Gaussian process, adjust the coefficients in the acquisition function according to the predetermined confidence level. Instantiate; construct the acquisition functions corresponding to the upper and lower bounds: the upper bound uses the upper confidence limit function UCB, and the lower bound uses the lower confidence limit function LCB. Maximize the UCB function and minimize the LCB function in the parameter domain to obtain new sampling points; Step 7: Call the deterministic load identification in step 3 for the new sampling points to obtain the corresponding response values; incorporate the new data into the sample set, update the Gaussian process model so that its posterior mean and standard deviation shrink as the data accumulates, repeat the selection of points, calculation, and update until the termination condition is met, and finally output the time series envelope in the parameter domain under the target confidence level. The average value of the upper and lower bounds is used to obtain the nominal value of the identified load.

2. The structural dynamic distributed load identification method based on symplectic variational integral as described in claim 1, characterized in that, In the first step, the modal mass matrix Modal damping matrix With modal stiffness matrix The specific form is as follows: （1） in, , and Represent matrices respectively , and The One main diagonal element, This represents the total number of degrees of freedom of the system.

3. The structural dynamic distributed load identification method based on symplectic variational integral according to claim 1, characterized in that, In the second step, the parameters include the structural elastic modulus and density, which are expressed as... .

4. The structural dynamic distributed load identification method based on basic variational integral according to claim 3, characterized in that, In the third step, the load identification formula for the discrete Berkhoff variational integral in modal space is: （2） in, Indicates the degree of freedom index in modal space. For the first in modal space The external load to be identified at the time step and The first and second are respectively the first in the modal space. Displacement and velocity responses at time steps For time step; , and Corresponding modal space mass matrix Damping matrix and stiffness matrix The first on the diagonal One element; Combined with the measured response sequence and By proceeding step by step, the modal load matrix can be obtained. ,in For the first The load time series vector of the modal degrees of freedom, The load matrix in the actual physical space is obtained through inverse modal transformation. .

5. The structural dynamic distributed load identification method based on stoichiometric variational integral according to claim 4, characterized in that, For the uncertain parameters defined in the second step The domain is defined as follows: a small number of uniformly dispersed initial sample points are generated within the normalized parameter domain using the Latin hypercube sampling method. ,in This represents the initial number of sample points; For each initial sample, the deterministic load identification method in step three is called to obtain the load. ; Record the first Load of each sample for Ultimately formed Input-output observation pairs .

6. The structural dynamic distributed load identification method based on symplectic variational integral according to claim 1, characterized in that, In the fifth step, given the initial observation set Subsequently, a Gaussian process regression model is constructed based on the initial observations. The kernel parameters and observation noise are adaptively learned by maximizing the log-marginal likelihood. any test point Noise-containing observations at the location The conditional distribution is: （3） in, （4） here, , The kernel function matrix, It is the identity matrix. The hyperparameters of the Gaussian process model are obtained by maximizing the likelihood function. The column vector representing the covariance between the test point and all training points is expressed as: （5） Based on equation (4), we simultaneously obtain: the posterior mean field, which characterizes the central trend of the response under different parameter values; and the posterior standard deviation field, which quantifies the uncertainty of the model and the influence of noise.

7. The structural dynamic distributed load identification method based on symplectic variational integral according to claim 6, characterized in that, In step six, for a given confidence level... ,coefficient The instantiation formula is: （6） in, The cumulative distribution function of the standard normal distribution; The acquisition functions corresponding to the upper and lower bounds are: the upper bound uses the UCB function, and the lower bound uses the LCB function. In the step iteration, the forms of the UCB and LCB functions are: （7） in, and Let be the posterior mean function and posterior standard deviation function of the Gaussian process model obtained in this iteration; in the parameter domain The UCB function is maximized and the LCB function is minimized respectively, where d represents the dimension of the parameter space, to obtain new sampling points, expressed as: （8） （9） in, and New sampling points corresponding to the upper and lower bounds, respectively. Indicates the uncertainty of parameters Domain Upsampling.

8. The structural dynamic distributed load identification method based on stoichiometric variational integral according to claim 7, characterized in that, In step seven, the termination condition is: (1) the maximum number of updates is reached. ; or (2) the changes in the maximum / minimum values ​​of the two most recent iterations are both less than the preset threshold. ,Right now: （10） The final output is the time series envelope in the parameter domain at the target confidence level, in the following form: （11） in, and Let the upper and lower bounds be the posterior mean function and the posterior standard deviation function obtained after the iteration terminates. and The sum of the values ​​yields the nominal value of the identified load.

9. The structural dynamic distributed load identification method based on symplectic variational integral according to claim 1, characterized in that, In the fourth step, the target confidence level is selected as 90%, 95%, or 99%.

10. The structural dynamic distributed load identification method based on symplectic variational integral according to claim 1, characterized in that, In the first step, the damping adopts the form of proportional damping, and the corresponding parameters are calibrated by experience or experiment.

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