Dynamic load identification method of uncertain structure and related equipment

Abstract

The invention provides a dynamic load identification method for an uncertain structure and related equipment, and the method comprises the steps: obtaining an uncertain structure model, and determining the random structure parameters of the uncertain structure model; determining a to-be-identified load function of the uncertainty structure model according to the random structure parameters; determining a measurement response of the uncertain structure, and determining a linear relationship between the to-be-identified load and the measurement response according to the measurement response and the to-be-identified load function; and determining a sub-domain of a sample space formed by the random structure parameters and a corresponding assigned probability, and determining the distribution of the to-be-identified load according to the assigned probability, the linear relation and the measurement response. Measurement response is used as a known quantity, the measurement response can be represented by response linear superposition under the action of each to-be-identified load, the linear relation between the measurement response and the to-be-identified load is determined, and the to-be-identified load of an uncertain structure is converted into a deterministic load identification problem represented by representative points.

Description

Technical Field

[0001] The present application relates to the technical field of structural dynamic load identification research, and particularly to a method for identifying dynamic loads of an uncertain structure and related equipment. Background Art

[0002] Accurately describing the external loads borne by engineering structures such as launch vehicles, bridges, and high-rise buildings during service is the basis for research fields such as structural design and optimization, vibration control, and health monitoring. For complex engineering structures, the finite element method is generally used to construct the relationship between the input load and the output response. Therefore, establishing a reasonable and accurate finite element model plays a crucial role in the dynamic load identification of the structure. However, there will inevitably be uncertainties between the finite element model and the actual structure. These uncertainties may come from the deviations between the actual structure and the original design during manufacturing, processing, and assembly connection, unreasonable approximations and equivalences during the structure modeling process, and changes in material parameters caused by the environment and operating conditions during service. This will ultimately lead to deviations in the structural system matrix. At this time, if the uncertain factors existing in the structure are ignored and the original model is directly used for the dynamic load identification of the deterministic structure, the identification result often has a large error from the true load. Unreasonable dynamic load estimation will ultimately affect the optimal design of the structure and the assessment of the structural safety and reliability, thus causing hazards. Summary of the Invention

[0003] In view of this, the purpose of the present application is to propose a method for identifying dynamic loads of an uncertain structure and related equipment that overcomes the above problems or at least partially solves the above problems.

[0004] Based on the above purpose, in the first aspect of the present application, a method for identifying dynamic loads of an uncertain structure is provided, including:

[0005] Obtain an uncertain structure model, and determine the random structural parameters of the uncertain structure model;

[0006] Determine the load function to be identified of the uncertain structure model according to the random structural parameters;

[0007] Determine the measured response of the uncertain structure, and determine the linear relationship between the load to be identified and the measured response according to the measured response and the load function to be identified;

[0008] Determine the subdomain of the sample space composed of the random structural parameters and its corresponding assigned probability, and determine the distribution of the load to be identified according to the assigned probability, the linear relationship, and the measured response.

[0009] Optionally, the determining the load function to be identified of the uncertain structure model according to the random structural parameters includes:

[0010] Determine the basis coefficient and orthogonal polynomial basis function under the random structural parameters according to the random structural parameters;

[0011] Determine the load function to be identified by using the basis coefficient and orthogonal polynomial basis function;

[0012] The load function to be identified is expressed as:

[0013]

[0014] where Θ represents the first structural parameter, N c represents the order of the polynomial fitting selected, c jn (Θ) represents the basis coefficient under the first structural parameter, T n (t) represents the nth-order orthogonal polynomial basis function.

[0015] Optionally, the linear relationship between the load to be identified and the measured response is expressed as:

[0016]

[0017] where h ij (Θ,t) represents the impulse response function corresponding to the first structural parameter, represents the response of the deterministic structure at the corresponding position under the action of the basis function;

[0018] After determining the linear relationship between the first load function to be identified and the first measured response according to the first measured response and the impulse response function, it includes:

[0019] Discretize the linear relationship in the time domain to determine the relationship between the total measured response and the total basis coefficient:

[0020] Y = R(Θ)C f (Θ),

[0021] where, is the total basis coefficient corresponding to m f loads to be identified, and R(Θ) represents a polynomial.

[0022] Optionally, determining the subdomain of the sample space formed by the random structural parameters and its corresponding assigned probability, and determining the distribution of the load to be identified according to the assigned probability, the linear relationship and the measured response, includes:

[0023] Determine the preliminary probability density function of the load to be identified according to the load function to be identified and the Dirac δ function;

[0024] Determine the sample space composed of the random structure parameters, divide the sample space using the generalized F - deviation to form multiple representative points, and determine the Thiessen polygon unit corresponding to each representative point as a sub - domain of the sample space;

[0025] Use each representative point to approximately correspond to the assigned probability of the sub - domain;

[0026] According to the assigned probability of the sub - domain and the preliminary probability density function, determine the probability density function of the load to be identified;

[0027] According to the probability density function of the load to be identified, determine the distribution of the load to be identified.

[0028] Optionally, after using the generalized F - deviation to divide the sample space of the random structure parameters to form multiple representative points, and determining the Thiessen polygon unit corresponding to each representative point as a sub - domain of the sample space, it further includes:

[0029] Determine the marginal cumulative distribution function of the random structure parameters;

[0030] Determine the empirical marginal cumulative distribution function affected by the assigned probability of the sub - domain;

[0031] According to the marginal cumulative distribution function and the empirical marginal cumulative distribution function, determine the partitioning accuracy of the sample space.

[0032] Optionally, after determining the probability density function of the load to be identified according to the assigned probability of the sub - domain and the preliminary probability density function, it further includes:

[0033] Use kernel density estimation to determine the smoothing coefficient;

[0034] Use a continuous Gaussian function and the smoothing coefficient to smooth the Dirac δ function to determine the smoothed probability density function.

[0035] Based on the same inventive concept, in the second aspect of the embodiments of the present application, there is provided a dynamic load identification device for an uncertain structure, including:

[0036] An acquisition module, configured to acquire an uncertain structure model and determine the random structure parameters of the uncertain structure model;

[0037] A load - to - be - identified function module, configured to determine the load - to - be - identified function of the uncertain structure model according to the random structure parameters;

[0038] A linear relationship module, configured to determine the measurement response of the uncertain structure, and according to the measurement response, impulse response function and load - to - be - identified function, determine the linear relationship between the load to be identified and the measurement response;

[0039] A load distribution module, configured to determine a sub-domain of a sample space formed by the random structure parameters and their corresponding assigned probabilities, and determine the distribution of the load to be identified according to the assigned probabilities, the linear relationship, and the measured response.

[0040] Based on the same inventive concept, in a third aspect of the embodiments of the present application, an electronic device is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the dynamic load identification method for an uncertain structure as described in the first aspect is implemented.

[0041] Based on the same inventive concept, in a fourth aspect of the embodiments of the present application, a non-transitory computer-readable storage medium is provided. The non-transitory computer-readable storage medium stores computer instructions, characterized in that the computer instructions are used to cause a computer to execute the dynamic load identification method for an uncertain structure as described in the first aspect above.

[0042] As can be seen from the above, the dynamic load identification method and related devices provided in the present application, by taking the measured response as a known quantity, clarify that for a linear elastic structure, the measured response can be linearly superimposed and represented by the responses under the action of each load to be identified respectively, determine the linear relationship between the measured response and the load to be identified, then divide the sample space of the random structure parameters of the uncertain structure to obtain a small number of representative points, use the assigned probabilities of the representative points to determine the probability density function of the load to be identified in the uncertain structure, transform the load to be identified in the uncertain structure into a deterministic load identification problem represented by the representative points, thereby determining the distribution of the load to be identified, and the calculation time is much less than that of Monte Carlo simulation. Using the linear relationship, the load to be identified in the uncertain structure is obtained.

[0043] Finally, through function fitting and regularization methods, the noise influence in the processing process can be effectively identified, and it has strong anti-noise performance.

[0044] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the description. And in order to make the above and other purposes, features, and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention are specifically exemplified below. Description of the Drawings

[0045] In order to more clearly illustrate the technical solutions in the present application or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments or related technologies. Obviously, the drawings in the following description are only the embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0046] Figure 1 Flow chart of the dynamic load identification method 100 for the uncertainty structure according to the embodiment of the present application;

[0047] Figure 2 Schematic diagram of the planar truss model according to the embodiment of the present application;

[0048] Figure 3a 、 Figure 3b Schematic diagrams of the comparison between the probability density functions of two second loads to be identified and Monte Carlo simulation at the moment of 0.1 s when different representative points are selected according to the embodiment of the present application;

[0049] Figure 4a 、 Figure 4b Schematic diagrams of the comparison between the probability density functions of two second loads to be identified and Monte Carlo simulation at the moment of 0.3 s when different representative points are selected according to the embodiment of the present application;

[0050] Figure 5a 、 Figure 5b Schematic diagrams of the comparison between the mean and standard deviation of one second load to be identified and Monte Carlo simulation when different representative points are selected according to the embodiment of the present application;

[0051] Figure 6a 、 Figure 6b Schematic diagrams of the comparison between the mean and standard deviation of the other second load to be identified and Monte Carlo simulation when different representative points are selected according to the embodiment of the present application;

[0052] Figure 7a 、 Figure 7b Schematic diagrams of the comparison between the marginal cumulative distribution functions of two second loads to be identified and Monte Carlo simulation at the moment of 0.1 s when different representative points are selected according to the embodiment of the present application;

[0053] Figure 8a 、 Figure 8b Schematic diagrams of the comparison between the marginal cumulative distribution functions of two second loads to be identified and Monte Carlo simulation at the moment of 0.3 s when different representative points are selected according to the embodiment of the present application;

[0054] Figure 9 Comparison between the upper and lower bounds of the 99.5% confidence interval of one second load to be identified and the true load according to the embodiment of the present application;

[0055] Figure 10 Comparison between the upper and lower bounds of the 99.5% confidence interval of the other second load to be identified and the true load according to the embodiment of the present application;

[0056] Figure 11a 、 Figure 11bSchematic diagrams of the comparison between the marginal cumulative distribution functions of two second payloads to be identified and Monte Carlo simulations at the moment of 0.1 s under different interference noises in the embodiments of the present application;

[0057] Figure 12a 、 Figure 12b Schematic diagrams of the comparison between the marginal cumulative distribution functions of two second payloads to be identified and Monte Carlo simulations at the moment of 0.3 s under different interference noises in the embodiments of the present application;

[0058] Figure 13a 、 Figure 13b Schematic diagrams of the comparison between the mean and standard deviation of one second payload to be identified and Monte Carlo simulations under different interference noises in the embodiments of the present application;

[0059] Figure 14a 、 Figure 14b Schematic diagrams of the comparison between the mean and standard deviation of the other second payload to be identified and Monte Carlo simulations under different interference noises in the embodiments of the present application;

[0060] Figure 15 Comparison between the upper and lower bounds of the 99.5% confidence interval of one second payload to be identified and the true payload under different interference noises in the embodiments of the present application;

[0061] Figure 16 Comparison between the upper and lower bounds of the 99.5% confidence interval of the other second payload to be identified and the true payload under different interference noises in the embodiments of the present application;

[0062] Figure 17 Schematic diagram of the dynamic load identification device for the uncertain structure in the embodiments of the present application;

[0063] Figure 18 Schematic diagram of an electronic device in the embodiments of the present application. Detailed implementation manners

[0064] To make the objectives, technical solutions and advantages of the present application clearer and more understandable, the following further describes the present application in detail with reference to specific embodiments and the accompanying drawings.

[0065] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of this application should have the ordinary meanings understood by those of ordinary skill in the field to which this application belongs. The "first", "second" and similar terms used in the embodiments of this application do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "including" or "comprising" mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Upper", "lower", "left", "right", etc. are only used to represent relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0066] As described in the background art section, accurately describing the external loads borne by engineering structures such as launch vehicles, bridges, and high-rise buildings during service is the basis for research fields such as structural design and optimization, vibration control, and health monitoring. For complex engineering structures, the finite element method is generally used to construct the relationship between the input load and the output response. Therefore, establishing a reasonable and accurate finite element model plays a crucial role in the dynamic load identification of structures. However, there will inevitably be uncertainties between the finite element model and the actual structure. These uncertainties may come from the deviations of the actual structure from the original design during manufacturing, processing, and assembly connections, unreasonable approximations and equivalences in the process of structure modeling, and changes in material parameters caused by the environment and operating conditions during service. This will ultimately lead to deviations in the structural system matrix. At this time, if the uncertain factors existing in the structure are ignored and the original model is directly used for the dynamic load identification of the deterministic structure, it often leads to a large error between the identification result and the true load. Unreasonable dynamic load estimation will ultimately affect the optimal design of the structure and the assessment of the structural safety and reliability, thus causing hazards.

[0067] In practical engineering problems, load identification research is usually based on deterministic single - measurement response samples. When considering the influence of random structural parameters, the load to be identified will also be introduced with uncertain attributes. Most of the research on related technologies is carried out based on interval models or fuzzy sets, and the upper and lower bounds or fuzzy descriptions of the dynamic loads acting on the structure are identified through interval perturbation methods or fuzzy theories, so as to give the influence brought by the structural uncertainty. Such methods cannot describe non - Gaussian load information completely. In addition, for dynamic problems considering structural uncertainty, in related technologies, Monte Carlo Simulation (MCS) is widely used because of its high solution accuracy, but along with it is a very high computational cost. Especially for large and complex structures, the calculation time is often unacceptable.

[0068] Therefore, the purpose of this application is to be able to completely describe the load information of an uncertain structure while improving the calculation efficiency and quickly obtaining the load information in the uncertain structure.

[0069] In view of this, the embodiments of this application provide a method, device, electronic device and storage medium for identifying dynamic loads of an uncertain structure. Among them, refer to Figure 1 As shown, it is a flowchart of the dynamic load identification method 100 for an uncertain structure according to the embodiment of this application. The dynamic load identification method 100 for the uncertain structure starts from step S101: Obtain an uncertain structure model and determine the random structural parameters of the uncertain structure model.

[0070] In this step, first assume that the uncertain structure contains n d mutually independent random structural parameters where the random structural parameters include material parameters (such as density, elastic modulus, etc.), geometric dimensions and boundary conditions of the uncertain structure. In practical engineering problems, it is usually based on deterministic single - measurement response samples. Due to the randomness of the random structural parameter Θ, the load to be identified is also introduced with randomness.

[0071] Thus, the motion equation of the discretized structure with N degrees of freedom can be expressed as:

[0072]

[0073] where M(Θ), C(Θ) and K(Θ) respectively represent the structural mass matrix, damping matrix and stiffness matrix of the uncertain structure model, y(t), and respectively represent the displacement response, velocity response and acceleration response of the uncertain structure model. represents containing m fA load function to be identified affected by random structural parameters Θ, where W represents an N×m f configuration matrix of the acting positions of the loads to be identified.

[0074] After that, in step S102, the load function to be identified of the uncertain structural model is determined according to the random structural parameters.

[0075] Assume that the deterministic single measurement sample contains a total of m y measurement responses y i (t), i = 1, 2, … m y (which can be displacement, velocity, acceleration, etc. at any position of the structure). Without considering the measurement error interference caused by factors such as noise, for a linear elastic structure, the measurement response can be represented by the linear superposition of the responses under the action of each load to be identified. Combining with the Duhamel integral, the measurement response y i (t) is expressed as:

[0076]

[0077] where h ij (Θ, t) represents the corresponding impulse response function containing the first structural parameter, and f j (Θ, t) represents the first load to be identified.

[0078] To improve the accuracy of identifying the first load to be identified, the function fitting technology is introduced. For the load to be identified f j (Θ, t) that is continuously integrable on the acting interval [0, s], it is expanded into the form of an orthogonal polynomial combination, specifically:

[0079] According to the random structural parameters, determine the basis coefficients and orthogonal polynomial basis functions under the random structural parameters;

[0080] Use the basis coefficients and orthogonal polynomial basis functions for polynomial fitting to determine the load function to be identified.

[0081] The load function to be identified is expressed as:

[0082]

[0083] where N c represents the order of the polynomial fitting selected, c jn (Θ) is the basis coefficient under the random structural parameter Θ, and T n (t) is the nth-order orthogonal polynomial basis function.

[0084] After that, in step S103, determine the measurement response of the uncertain structure. According to the measurement response and the load function to be identified, determine the linear relationship between the load to be identified and the measurement response.

[0085] Substituting Equation (3) into Equation (2), the linear relationship between the measurement response and the load function to be identified can be expressed as:

[0086]

[0087] where represents the first measurement response at the corresponding position of the structure under the action of the basis function T n (t).

[0088] Regarding the measurement response and the load function to be identified in the linear relationship, there is a data at each time point for both, which is equivalent to the measurement response of N degrees of freedom. The measurement response of each degree of freedom contains a piece of load data to be identified in time. Therefore, the linear relationship (Equation 4) between the load to be identified and the measurement response is discretized in the time domain into n t time points. Then, for the relationship between the total measurement response of m y measurement responses and the total basis coefficients, it can be expressed as:

[0089] Y = P(Θ)C f (Θ) (5)

[0090] where is the total basis coefficient corresponding to m f loads to be identified, and R(Θ) represents a polynomial.

[0091] And

[0092]

[0093] where

[0094]

[0095] It can be seen from Equation (5) that based on the known total measurement response Y, the implicit relationship between the random structural parameter Θ and the load function f f (Θ) can be constructed with the help of the total basis coefficient C i (Θ,t), i = 1, 2,... m f . For a specific Θ, the corresponding total basis coefficient C f (Θ) can be obtained by combining the Tikhonov regularization and the generalized cross-validation criterion, and the load f j (Θ,t) to be identified can be obtained from Equation (3).

[0096] In the above embodiments, in the uncertainty structure model, the linear relationship between the load function to be identified and the measurement response is determined, and the implicit relationship between the random structural parameters and the load function to be identified is disclosed. The main purpose of this application is to determine the distribution and magnitude of the load to be identified for the uncertainty structure based on the above linear relationship and implicit relationship, and to derive and calculate them.

[0097] After that, in step S104, the subdomain of the sample space composed of random structural parameters and its corresponding assigned probability are determined, and the distribution of the load to be identified is determined according to the assigned probability, the linear relationship and the measurement response.

[0098] In some embodiments, step S104 includes:

[0099] Determine the preliminary probability density function of the load to be identified according to the load function to be identified and the Dirac δ function;

[0100] In this step, if no additional random factors are introduced during the action time of the load to be identified in the uncertainty structure, according to the conditional probability formula and the properties of the Dirac δ function, combined with the load function to be identified (formula 3), the load to be identified f i (θ, t) of the uncertainty structure under the given random structural parameter θ = Θ, the first probability density function (PDF) can be expressed as:

[0101]

[0102] Wherein, is the realization of f i .

[0103] Further determine the joint second density function of the load to be identified f i (θ, t) and the random structural parameter θ as:

[0104]

[0105] Combining formula (8) and formula (9), at any moment, the preliminary probability density function i of the load to be identified f and the preliminary probability density function p Θ (θ) of the random structural parameter θ, that is, the preliminary probability density function of the load to be identified is:

[0106]

[0107] Wherein, Ω Θ represents the sample space composed of random structural parameters.

[0108] After that, a sample space composed of random structural parameters is determined. The generalized F - deviation is used to divide the sample space to form multiple representative points, and the Thiessen polygon cell corresponding to each representative point is determined as a sub - domain of the sample space.

[0109] Here, when considering that there are multiple random structural parameters and the random influence of multiple random structural parameters, the high - order integral operation involved in the preliminary probability density function (Equation 10) is very difficult to solve directly. Therefore, a point - selection technique of generalized F - deviation is introduced to divide the sample space Ω Θ formed by random structural parameters, and a point set p containing n representative points is constructed, and the Thiessen polygon (Voronoi) cell of each representative point is used as a sub - domain of the sample space. The Voronoi cell of the q - th (q = 1, 2, …, n p ) representative point θ q is defined as:

[0110]

[0111] where, ‖x‖ represents the Euclidean norm of x. Thus, the sample space Ω Θ is divided into a series of non - overlapping sub - domains, and satisfies and for any q≠j, there is

[0112] After that, the assigned probability of each sub - domain is approximated by the corresponding representative point. That is, the probability information of each sub - domain is approximated by the corresponding representative point, and we get:

[0113]

[0114] where, P q represents the assigned probability of the sub - domain Ω Θ,q , and satisfies that the sum of the assigned probabilities of all sub - domains is 1, that is V q represents the volume of the sub - domain Ω Θ,q .

[0115] After that, the probability density function of the load to be identified is determined according to the assigned probability of the sub - domain and the preliminary probability density function.

[0116] That is, the integral formula of the preliminary density probability function of the load to be identified in Equation (10) can be approximately transformed into the following discrete summation form:

[0117]

[0118] where, represents the probability of the load under the sub - domain Ω Θ,q .

[0119] Finally, determine the distribution of the load to be identified according to the probability density function of the load to be identified.

[0120] Thus, the identification problem of the load to be identified for the uncertain structure with random structural parameters is transformed into n p deterministic load identification problems, that is, based on Equation (5), use an appropriate regularization algorithm to solve for the coefficients c p under n q deterministic structural parameters θ in (θ q ).

[0121] In some embodiments, the sample space of the random structural parameters is divided using the generalized F - deviation to form multiple representative points, and the Thiessen polygon unit corresponding to each representative point is determined as a sub - domain of the sample space. After that, it further includes:

[0122] Determine the marginal cumulative distribution function of the random structural parameters;

[0123] Determine the empirical marginal cumulative distribution function of the probability influence assigned to the sub - domain;

[0124] Determine the partitioning accuracy of the sample space according to the marginal cumulative distribution function and the empirical marginal cumulative distribution function.

[0125] In practice, the selection of the number of representative points n p will affect the accuracy and efficiency of the solution. Usually, the generalized F - deviation D GF is introduced as an index to evaluate the partitioning accuracy of the sample space Ω Θ , and its expression can be written as:

[0126]

[0127] where, represents the marginal cumulative distribution function (Cumulative Distribution Function, CDF) of the th random structural parameter, is the empirical marginal CDF considering the influence of the assigned probability P q and can be expressed as:

[0128]

[0129] where I(·) is the indicator function, and I(x) = 1 if and only if x is true, otherwise I(x) = 0.

[0130] In some embodiments, according to the assigned probability of the sub - domain and the preliminary probability density function, determine the probability density function of the load to be identified. After that, it further includes:

[0131] Determine the smoothing coefficient using kernel density estimation;

[0132] Smooth the Dirac delta function using a continuous Gaussian function and the smoothing coefficient to determine the smoothed probability density function.

[0133] In this embodiment, due to certain errors in the recognition result of the load to be recognized and the discontinuity of the Dirac delta function, if not enough representative points are selected, the probability density function of the load to be recognized directly obtained from formula (13) will have severe numerical oscillations and large errors. However, in order to ensure the calculation efficiency, the actual situation does not allow selecting too many representative points. Therefore, a continuous Gaussian function is selected to smooth the Dirac delta function, effectively improving the recognition accuracy of the load to be recognized. The smoothed probability density function of the load to be recognized is expressed as:

[0134]

[0135] Among them, ε is the smoothing coefficient that determines the smoothing degree of the Dirac delta function and has a great influence on the solution accuracy of the probability density of the load to be recognized. In the embodiment of the present application, the smoothing parameter ε is selected based on the adaptive empirical method of kernel density estimation, that is

[0136]

[0137] Among them, the smoothing factor β ∈ (0, 1), and iqr(·) represents the interquartile range. Thus, for an uncertain structure, the smoothed probability density function of the load to be recognized can be analytically expressed by formula (16).

[0138] So far, for an uncertain structure, the position and size of the load to be recognized in the uncertain structure are determined according to the smoothed probability density function for recognition.

[0139] In some embodiments, the method further includes:

[0140] Determine the noise level and random noise that satisfies the standard normal distribution;

[0141] Add interference noise to the first measurement response according to the noise level and the random noise that satisfies the standard normal distribution to determine the actual measurement response.

[0142] In this embodiment, since the signal of the actual measurement response has noise interference, in order to explore the influence of the noise interference on the load to be recognized, artificial interference noise information is added in the uncertain structure to simulate the interference noise existing in the actual situation.

[0143]

[0144] Among them, Y meis the total value of the true measurement response, used to identify the dynamic load conditions on the deterministic structure. Y is the total value of the calculated measurement response, and l is the noise level. is the random noise that satisfies the standard normal distribution.

[0145] Determine the probability density function of the load to be identified under the Monte Carlo simulation;

[0146] Use the relative entropy divergence to determine the difference between the probability density function of the load to be identified under the Monte Carlo simulation and the smoothed probability density function;

[0147] Determine the mean and variance of the second load to be identified, and use the mean and variance to verify the accuracy of the second load to be identified.

[0148] To verify the accuracy of the second load to be identified, in the example of the planar truss structure, the results of 10 6 times of Monte Carlo simulation (MCS) are used as the reference solution, and by introducing the relative entropy (Kullback-Leibler, KL) divergence, it is expressed as:

[0149]

[0150] Use the relative entropy divergence to compare the difference between the probability density function of the load to be identified under the Monte Carlo simulation and the smoothed probability density function. Among them, p MC (f) is the probability density function of the load to be identified based on the Monte Carlo simulation, and p(f) is the smoothed probability density function calculated using the method of this article. The smaller D KL is, the closer the two are.

[0151] On this basis, the mean and variance of the load to be identified at each moment can also be obtained, and the mean and variance are respectively expressed as:

[0152]

[0153] Among them, f(t) represents the load to be identified.

[0154] Similarly, in order to quantitatively check the accuracy of the dynamic load identification method for the uncertain structure in the embodiment of this application, the relative errors (R μ , R σ ) of the mean and standard deviation of the load to be identified are taken as evaluation indicators, that is:

[0155]

[0156] Among them, μ MC (t) and σ MC (t) are respectively the mean and standard deviation of the load to be identified obtained by MCS.

[0157] To describe the influence of the uncertainty structure on the load to be identified, a confidence interval is introduced for measurement. For the 1-γ confidence interval of the load f(t) to be identified can be expressed as [f lb (t), f ub (t)], where the upper and lower bounds f lb (t) and f ub (t) of the confidence interval correspond to the CDFs of and In the numerical example of this paper, γ = 0.5% is taken, that is, the 99.5% confidence interval. At the same time, through the relative errors R ub and R lb quantitatively describe the deviation between f ub (t) and f lb (t) and the true load f tr (t), that is:

[0158]

[0159] In this part, through a plane truss model, as Figure 2 shown, the effectiveness of the method of this patent for the multi-point load identification problem considering random structural parameters is verified. Here, the displacement response of the structural measurement points is selected as the measurement response, and the generalized Chebyshev orthogonal polynomial is selected as the basis function to fit the load on the action interval [0, s].

[0160]

[0161] Two-point load identification without the influence of noise. In the embodiment of this application, the load identification of the embodiment of this application without interference noise is verified by comparing it with the load identification under Monte Carlo simulation to verify its effectiveness. The lengths of all horizontal and vertical rods are 5 m, and the cross-sectional area is 10 -3 m 2 . It is assumed that the damping of the structure is proportional damping, and the coefficient related to the mass matrix is 0 s -1 . Considering that the plane truss has 7 random structural parameters, as shown in Table 1. The Young's modulus and density of the remaining rods are determined constants, which are 2.1×10 11 Pa and 7800 kg / m 3 respectively. A load f1 and f2 acting horizontally to the left are applied at nodes 11 and 9 respectively, and their true magnitudes are:

[0162]

[0163] Under the action of 1 and 2, when the random structural parameters take the average value, the displacement response of nodes 5, 8 and 10 in the x direction without noise influence is taken as the measurement response, and the load on the structure is identified without considering the influence of measurement noise. The load action time is 0.5s, and the time interval Δt=2×10 -3 s, the Chebyshev polynomial base order is selected as 30. In terms of accuracy and efficiency, the dynamic load identification method of the uncertain structure of the embodiment of the application is compared with 10 6 The load identification under the Monte Carlo simulation (MCS) is compared.

[0164] Table 1 Plane truss random structural parameters

[0165]

[0166] Table 2 shows the generalized F deviation corresponding to the description of 7 random structural parameters by different numbers of representative points and the method of the embodiment of the present application and 10 6 Combining the relative entropy (Kullback-Leibler, KL) divergence, mean and standard deviation and the relative error of the MCS result, it can be seen that the dynamic load identification method of the uncertain structure of the embodiment of the present application has high accuracy and has a great advantage in efficiency. Figure 3a , Figure 3b and Figure 4a and Figure 4b A comparison between the probability density function curve of the load to be identified by the dynamic load identification method of the uncertain structure in the embodiment of the present application and the MCS kernel density estimation curve at two time points is given. When 1000 representative points are selected, the peak value of the probability density function of the load to be identified will be slightly lower than the MCS result, but when 1200 and 1500 representative points are selected, it is closer to the MCS result.

[0167] Table 2 Comparison of efficiency and accuracy between this method and MCS

[0168]

[0169]

[0170] Figure 5a , Figure 5b as well as Figure 6a and Figure 6bThe comparison of the mean and standard deviation curves of the identified loads and the MCS results for the dynamic load identification method of the uncertain structure in the embodiments of the present application under different representative points is given. It can be seen that the identified mean is basically consistent with the MCS result. Except that the standard deviation of the identified load f2 fluctuates slightly at t = 0.3 s, the standard deviation identified by the method of the embodiments of the present application at other times is basically consistent with the MCS result. To better describe the influence of the uncertain structure on load identification, the dynamic load identification method of the uncertain structure in the embodiments of the present application gives the upper and lower bounds of the 99.5% confidence interval of the identified load through CDF and compares it with the identification result of MCS. From Figure 7a and Figure 7b as well as Figure 8a and Figure 8b it can be seen that the CDF obtained by the dynamic load identification method of the uncertain structure in the embodiments of the present application at two time points is basically consistent with the MCS result. Figure 9 and Figure 10 give the upper and lower bounds of the confidence interval of the identified load over the entire time period, describing the deviation that may be caused to the identified load due to the uncertain structure. It can be seen that the upper and lower bounds obtained by the dynamic load identification method of the uncertain structure in the embodiments of the present application are basically consistent with the MCS result. At the same time, it can also be seen that the error caused by uncertainty is mainly reflected in the peak position of the load, and the deviation caused by other positions is relatively small.

[0171] Table 3 Comparison of the upper and lower bounds of the 99.5% confidence interval of the identified load with the true load at some time points

[0172]

[0173]

[0174] Table 3 gives the magnitude of the deviation and the relative errors R ub and R lb of the upper and lower bounds of the confidence interval from the true load at some time points near the peak. The maximum deviation at the peak time point exceeds 60%, and the deviations of the upper and lower bounds of the confidence intervals of loads f1 and f2 exceed 13% and 19% respectively. It can be seen that the influence of the uncertain structure on load identification is relatively large. If only directly considering identifying the dynamic load based on a set of possible structural parameters, the identification result is very likely to have a large deviation from the actual load, which is often unacceptable. Therefore, it is very necessary to fully reduce the influence of uncertain factors in the actual modeling process in order to identify and obtain more accurate loads.

[0175] Two-point load identification considering the influence of noise. From the above embodiments, it can be seen that in the dynamic load identification method of the uncertain structure of the present application, the probability density functions of the loads f1 and f2 to be identified can be well identified, and there is a great advantage in efficiency compared with MCS. Here, the influence of measurement noise is further considered, and the total measurement response including noise interference is given by formula (18), so as to explore the influence of noise on the identification results of loads f1 and f2. It can be seen from Table 4 that as the noise level increases, the errors of the probability density function, mean value and standard deviation of the identified load will increase slightly, but the overall high accuracy is maintained. In addition, the errors between the upper and lower bounds of the 99.5% confidence interval given by the CDF and the true load are also given, and it can be seen that it is basically not affected by noise, verifying the good anti-noise performance of the dynamic load identification method of the uncertain structure in the embodiments of the present application. By Figure 11a , Figure 11b and Figure 12a , Figure 12b shown, the probability density functions at the time points when the two loads are at the peak are given. It can be seen that as the noise level increases, the probability density functions of the identified loads f1 and f2 will only produce a small shift compared with the case without noise. By Figure 13a , Figure 13b and Figure 14a , Figure 14b shown, as the noise level increases, the mean value of the identified load is basically consistent with that without noise, and at the same time, the standard deviation also maintains a high identification accuracy. Figure 15 and Figure 16 give the upper and lower bounds of the confidence interval of the identified load under the influence of 10% noise in the entire time period, describing the deviation caused by the uncertain structure to the load identification in the real situation. Except that the peak position is slightly different from the case without noise, the results at other times are basically the same as those without noise.

[0176] Table 4 Identification accuracy of the method of the present application under different noise levels

[0177]

[0178] It should be noted that the method of the embodiments of the present application can be executed by a single device, such as a computer or a server, etc. The method of this embodiment can also be applied to a distributed scenario and completed by multiple devices cooperating with each other. In this case of a distributed scenario, one of the multiple devices can only execute one or more steps of the method of the embodiments of the present application, and these multiple devices will interact with each other to complete the described method.

[0179] It should be noted that some embodiments of the present application have been described above. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the above embodiments and still achieve the desired results. Additionally, the processes depicted in the drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0180] Based on the same inventive concept, corresponding to any of the above-described method embodiments, the present application further provides a dynamic load identification device for an uncertain structure.

[0181] Referring to Figure 17 , the dynamic load identification device for the uncertain structure includes:

[0182] An acquisition module 1701, configured to acquire an uncertain structure model and determine random structure parameters of the uncertain structure model;

[0183] A load function to be identified module 1702, configured to determine a load function to be identified for the uncertain structure model according to the random structure parameters;

[0184] A linear relationship module 1703, configured to determine a measured response of the uncertain structure, and determine a linear relationship between the load to be identified and the measured response according to the measured response, an impulse response function, and the load function to be identified;

[0185] A load distribution module 1704, configured to determine a sub-domain of a sample space constituted by the random structure parameters and its corresponding assigned probability, and determine the distribution of the load to be identified according to the assigned probability, the linear relationship, and the measured response.

[0186] For the convenience of description, when describing the above device, it is divided into various modules according to functions and described separately. Of course, when implementing the present application, the functions of each module can be implemented in one or more software and / or hardware.

[0187] The device in the above embodiment is used to implement the corresponding dynamic load identification method for the uncertain structure in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be elaborated herein.

[0188] Based on the same inventive concept, corresponding to any of the above-described method embodiments, the present application further provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the dynamic load identification method for the uncertain structure described in any of the above embodiments when executing the program.

[0189] Figure 18 FIG. 1 shows a more specific schematic diagram of the hardware structure of the electronic device provided in this embodiment. The device may include: a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. Among them, the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are communicatively connected to each other inside the device through the bus 1050.

[0190] The processor 1010 may be implemented in a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, etc., and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0191] The memory 1020 may be implemented in the form of a ROM (Read Only Memory), a RAM (Random Access Memory), a static storage device, a dynamic storage device, etc. The memory 1020 may store an operating system and other application programs. When implementing the technical solutions provided in the embodiments of this specification through software or firmware, the relevant program codes are stored in the memory 1020 and are called and executed by the processor 1010.

[0192] The input / output interface 1030 is used to connect to an input / output module to implement information input and output. The input / output module may be configured as a component in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Among them, the input device may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device may include a display, a speaker, a vibrator, an indicator light, etc.

[0193] The communication interface 1040 is used to connect to a communication module (not shown in the figure) to implement communication interaction between this device and other devices. Among them, the communication module may implement communication in a wired manner (such as USB, network cable, etc.) or in a wireless manner (such as mobile network, WIFI, Bluetooth, etc.).

[0194] The bus 1050 includes a path for transmitting information between various components of the device (such as the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040).

[0195] It should be noted that although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040, and the bus 1050, in the specific implementation process, the device may also include other components necessary for normal operation. In addition, those skilled in the art can understand that the above device may also only include the components necessary to implement the solution of the embodiments of this specification, and does not necessarily include all the components shown in the figure.

[0196] The electronic device of the above embodiment is used to implement the dynamic load identification method of the corresponding uncertainty structure in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be elaborated here.

[0197] Based on the same inventive concept, corresponding to the method of any of the above embodiments, the present application also provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to cause the computer to execute the dynamic load identification method of the uncertainty structure as described in any of the foregoing embodiments.

[0198] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible by a computing device.

[0199] The computer instructions stored in the storage medium of the above embodiment are used to cause the computer to execute the dynamic load identification method of the uncertainty structure as described in any of the foregoing embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be elaborated here.

[0200] Based on the same inventive concept, corresponding to the method for identifying dynamic loads of an uncertainty structure described in any of the above embodiments, the present disclosure also provides a computer program product, which includes computer program instructions. In some embodiments, the computer program instructions can be executed by one or more processors of a computer to cause the computer and / or the processor to execute the color correction method. Corresponding to the execution entities corresponding to the steps in each embodiment of the color correction method, the processor that executes the corresponding steps can belong to the corresponding execution entity.

[0201] The computer program product of the above embodiment is used to cause the computer and / or the processor to execute the method for identifying dynamic loads of an uncertainty structure described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be elaborated here.

[0202] Those of ordinary skill in the art should understand that: The discussion of any of the above embodiments is only exemplary and is not intended to imply that the scope of the present application (including the claims) is limited to these examples; Under the concept of the present application, the technical features in the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations in different aspects of the embodiments of the present application as described above, and they are not provided in detail for the sake of brevity.

[0203] In addition, for simplicity of description and discussion, and in order not to make the embodiments of the present application difficult to understand, the well-known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. In addition, the device may be shown in block diagram form to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform on which the embodiments of the present application will be implemented (that is, these details should be fully within the understanding of those skilled in the art). In the case where specific details (such as circuits) are set forth to describe the exemplary embodiments of the present application, it will be apparent to those skilled in the art that the embodiments of the present application can be implemented without these specific details or with variations of these specific details. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0204] Although the present application has been described in connection with specific embodiments of the present application, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other memory architectures (such as dynamic RAM (DRAM)) can be used with the embodiments discussed.

[0205] Embodiments of the present application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of the present application shall be included within the protection scope of the present application.

Claims

1. A method for identifying dynamic loads of an uncertain structure, characterized in that, Including: Obtain an uncertainty structure model and determine the random structure parameters of the uncertainty structure model; Determine the load function to be identified of the uncertainty structure model according to the random structure parameters; Determine the measured response of the uncertainty structure, and according to the measured response and the load function to be identified, determine the linear relationship between the load to be identified and the measured response; Determine the sub-domain of the sample space composed of the random structure parameters and its corresponding assigned probability, and according to the assigned probability, the linear relationship and the measured response, determine the distribution of the load to be identified.

2. The method according to claim 1, characterized in that The step of determining the load function to be identified of the uncertainty structure model according to the random structure parameters includes: According to the random structure parameters, determine the basis coefficients and orthogonal polynomial basis functions under the random structure parameters; Use the basis coefficients and orthogonal polynomial basis functions to determine the load function to be identified; The load function to be identified is expressed as: Among them, Θ represents the first structural parameter, N c represents the order of the selected polynomial fitting, c jn (Θ) represents the basis coefficient under the first structural parameter, T n (t) represents the nth-order orthogonal polynomial basis function.

3. The method according to claim 2, wherein The linear relationship between the load to be identified and the measured response is expressed as: where h ij (Θ,t) represents the impulse response function corresponding to the first structural parameter, represents the response at the corresponding position of the deterministic structure under the action of the basis function; After determining the linear relationship between the first load function to be identified and the first measured response according to the first measured response and the impulse response function, it includes: Discretize the linear relationship in the time domain to determine the relationship between the total measured response and the total basis coefficients: Y = R(Θ)C f (Θ), Among them, is the total base coefficient corresponding to m f unknown loads, and R(Θ) represents a polynomial.

4. The method according to claim 1, characterized in that, Determine the sub-domain of the sample space composed of the random structure parameters and its corresponding assigned probability, and according to the assigned probability, the linear relationship and the measured response, determine the distribution of the load to be identified, including: Determine the preliminary probability density function of the load to be identified according to the load function to be identified and the Dirac δ function; Determine the sample space composed of the random structure parameters, divide the sample space using the generalized F deviation to form multiple representative points, and determine the Thiessen polygon unit corresponding to each representative point as the sub-domain of the sample space; Approximate the assigned probability corresponding to each sub-domain using each representative point; Determine the probability density function of the load to be identified according to the assigned probability of the sub-domain and the preliminary probability density function; Determine the distribution of the load to be identified according to the probability density function of the load to be identified.

5. The method according to claim 4, characterized in that, After dividing the sample space of the random structure parameters using the generalized F deviation to form multiple representative points and determining the Thiessen polygon unit corresponding to each representative point as the sub-domain of the sample space, it further includes: Determine the marginal cumulative distribution function of the random structure parameters; Determine the empirical marginal cumulative distribution function affected by the assigned probability of the sub-domain; According to the marginal cumulative distribution function and the empirical marginal cumulative distribution function, determine the division accuracy of the sample space.

6. The method according to claim 5, characterized in that, After determining the probability density function of the load to be identified according to the assigned probability of the sub-domain and the preliminary probability density function, it further includes: Use kernel density estimation to determine the smoothing coefficient; Smooth the Dirac δ function using a continuous Gaussian function and the smoothing coefficient to determine the smoothed probability density function.

7. A dynamic load identification device for an uncertainty structure, characterized in that Including: An acquisition module for acquiring an uncertainty structure model and determining the random structure parameters of the uncertainty structure model; A load function module to be identified, which is used to determine the load function to be identified of the uncertain structure model according to the random structure parameters; A linear relationship module, which is used to determine the measured response of the uncertain structure, and determine the linear relationship between the load to be identified and the measured response according to the measured response, the impulse response function and the load function to be identified; A load distribution module, which is used to determine the subdomain of the sample space composed of the random structure parameters and its corresponding assigned probability, and determine the distribution of the load to be identified according to the assigned probability, the linear relationship and the measured response.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable by the processor, wherein the processor implements the method according to any one of claims 1 to 6 when executing the computer program.

9. A non-transitory computer-readable storage medium, which stores computer instructions for causing a computer to execute the method according to any one of claims 1 to 6.

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