A low-level test data driven method for predicting high-level response of structure vibration

Abstract

This invention discloses a method for predicting high-level structural vibration responses driven by low-level experimental data, primarily addressing the technical problems of high cost and risk in existing high-level experiments, as well as the complexity and time-consuming computation of traditional simulation modeling. The method includes the following steps: Step 1: Design and conduct multiple low-level vibration experiments to obtain low-level excitation data and low-level experimental data; Step 2: Preprocess the low-level excitation data and low-level experimental data; Step 3: Construct a mapping relationship model and establish an optimization objective function; Step 4: Optimize the mapping relationship matrix; Step 5: Use the optimized mapping relationship matrix to calculate the dynamic response data of the structure to be predicted under high-level vibration experiments. This invention effectively overcomes the dependence of high-level experiments on high-cost, high-risk physical experiments and complex, detailed simulations.

Description

Technical Field

[0001] This invention relates to a method for predicting structural vibration response, specifically a method for predicting high-level structural vibration response driven by low-level experimental data. Background Technology

[0002] In the fields of aerospace, aviation, and energy equipment, the performance and safety requirements for structures under extreme dynamic load environments are extremely stringent. High-level vibration testing plays a crucial role in engineering applications as an important means of evaluating the ultimate bearing capacity of structures, identifying potential failure modes, and verifying design safety margins.

[0003] High-volume vibration tests face a dual challenge: on the one hand, they require high-thrust, high-performance excitation equipment, leading to high testing costs; on the other hand, they may cause damage or destruction to the specimens, accompanied by high safety risks. To reduce the direct reliance on high-volume vibration tests, numerical simulation methods based on physical models (such as finite element analysis) are widely used for test prediction and design optimization.

[0004] However, this method has significant limitations in practical applications: First, the construction process of high-fidelity simulation models is complex and requires specialized knowledge, making it prone to human error; second, large-scale calculations consume substantial computational resources and time, limiting the iterative efficiency of engineering design. Therefore, there is an urgent need for a high-volume response prediction technology that can effectively avoid or significantly reduce high-cost physical experiments and complex, time-consuming high-fidelity simulation calculations. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problems of high cost and high risk of existing high-scale experiments, as well as the complexity and long computation time of traditional simulation modeling, and to provide a method for predicting high-scale structural vibration response driven by low-scale experimental data.

[0006] To achieve the above objectives, the technical solution provided by this invention is as follows: A method for predicting high-level responses to structural vibrations driven by low-level experimental data, characterized by the following steps: Step 1: Design and conduct multiple low-level vibration tests for the structure to be predicted, collect low-level excitation data, and collect dynamic response data of the structure under various low-level vibration conditions through preset measuring points on the structure to be predicted, as low-level test data. Step 2: Perform unified standardization preprocessing on low-level excitation data and low-level test data under various low-level vibrations to ensure that the two types of data are consistent in the frequency dimension. Step 3: Obtain the power spectral density matrix of the measurement point response based on the processed low-level excitation data and low-level experimental data. and excitation input power spectral density matrix And construct the following power spectral density matrix of the measurement point response. With the excitation input power spectral density matrix Mapping relationship model between them:

[0007] In the formula: The mapping relationship matrix, , For the degrees of freedom of the measuring point, For the degree of freedom of motivation; For frequency; Simultaneously, the following optimization objective function is constructed to constrain the solution of the mapping relation matrix:

[0008] In the formula: Denotes the Frobenius norm; The number of low-volume trials, ; For the first The power spectral density matrix of the measurement point response corresponding to the second-lowest vibration test. For the first The excitation input power spectral density matrix corresponding to the second lowest level vibration test; Step 4: Minimize the objective function constructed in Step 3 using an optimization algorithm. The goal is to minimize the difference between the predicted and measured values ​​until the convergence condition is met, thereby obtaining the optimized mapping matrix. Step 5: Use the mapping matrix obtained in Step 4 to calculate the dynamic response data of the structure to be predicted under high-level vibration test, so as to realize the dynamic response prediction of the structure under high-level vibration test.

[0009] Furthermore, in step 1, accelerometers or strain gauges are set up at different selected locations on the structure to be predicted as measuring points, and dynamic response data of the structure to be predicted under various low-level vibrations are collected by the accelerometers or strain gauges.

[0010] Furthermore, the unified standardization preprocessing described in step 2 specifically includes: Interpolation alignment processing is performed on low-level excitation data and low-level test data under various low-level vibrations to unify them onto the same frequency axis, so that the low-level excitation data and low-level test data under various low-level vibrations are consistent in the frequency dimension.

[0011] Furthermore, in step 4, the optimization algorithm is either a gradient descent algorithm or an adaptive optimization algorithm.

[0012] 5. The method for predicting high-level structural vibration response driven by low-level experimental data according to claim 4, characterized in that: The adaptive optimization algorithm is either the Adam algorithm or the RMSprop algorithm.

[0013] Furthermore, in step 4, the convergence condition is the optimization objective function. The number of iterations drops to the set threshold, or the maximum number of iterations reaches the set limit.

[0014] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention collects the input excitation signal (such as acceleration spectrum) and output response signal (such as acceleration, displacement, strain) of a structure in a low-level vibration test, constructs a mapping relationship model between the two, and uses the constructed mapping relationship model to directly calculate and output the response data of the structure under the corresponding high-level working conditions by inputting high-level excitation data, thereby effectively breaking through the dependence on high-cost, high-risk physical tests and complex and detailed simulations; 2. Significantly reduced risk and cost: This invention relies only on safe, low-cost, and easily obtainable low-level test data to predict high-level responses, avoiding the high cost and specimen damage risk of conducting high-level tests; 3. Significantly improves prediction efficiency: It adopts a direct data-driven prediction path, eliminating the need to build complex and sophisticated high-fidelity simulation models, thus significantly improving prediction efficiency; 4. Practicality and ease of use: It provides a practical solution for high-level vibration response prediction that is easy to implement in engineering and can be easily integrated into existing test analysis processes. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating an embodiment of the present invention; Figure 2 This is a schematic diagram of the sensor layout in an embodiment of the present invention; Figure 3 The image shows a comparison of the predicted and measured RMS values ​​of the acceleration response power spectral density in the X direction of sensor A3, the Y direction of sensor A7, the Y direction of sensor A20, and the Z direction of sensor A29 in three high-level tests at -6dB, -3dB, and full-scale 0dB in this embodiment of the invention. (a) is sensor A3, (b) is sensor A7, (c) is sensor A20, and (d) is sensor A29. Figure 4 This refers to the average relative prediction error of the acceleration response in the X, Y, and Z directions of all 36 sensors in the three high-level tests (-6dB, -3dB, and full-scale 0dB) in this embodiment of the invention. Detailed Implementation

[0016] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0017] like Figure 1 As shown, this embodiment provides a method for predicting high-level structural vibration responses driven by low-level experimental data, including the following steps: Step 1: Conduct random low-level vibration tests on the cabin structure to obtain frequency domain data of the structural dynamic response under low-level vibration conditions; specifically: Accelerometers are deployed on the cabin structure to extract the structural acceleration response. The locations of the acceleration sensors are as follows: Figure 2 As shown, a total of 36 accelerometers (A1 to A36) are arranged. Each sensor collects the acceleration response in the X, Y, and Z directions at the measurement point. The bottom of the structure is mounted on a vibration table, and the vibration table applies acceleration excitation in the Y direction. The excitation frequency is... The frequency range was 0–2000 Hz. The experiment considered eight different random vibration test levels: -21 dB, -18 dB, -15 dB, -12 dB, -9 dB, -6 dB, -3 dB, and full-scale 0 dB. The RMS value of the acceleration excitation corresponding to 0 dB was 20 g. The tests at the -21 dB, -18 dB, -15 dB, and -12 dB levels were designed as low-level tests. These low-level tests were conducted to obtain acceleration power spectral density data at various measuring points on the structure, i.e., dynamic response data, which served as the low-level test data.

[0018] Step 2: Perform unified standardization preprocessing on the low-level excitation data and the dynamic response data under various low-level vibrations to ensure consistency between the two types of data in the frequency dimension. Specifically: For low-level excitation data and dynamic response data collected in step 1, interpolation is performed at 1Hz intervals within the frequency range of 1~2000Hz. This ensures that the frequency sampling points of each excitation and response data are completely matched within the 1~2000Hz range, and the frequency interval between adjacent sampling points is uniformly 1Hz. This achieves alignment of excitation and response data of different levels on the same frequency axis, providing a data foundation for the subsequent construction and solution of the excitation-response relationship matrix.

[0019] Step 3: Obtain the power spectral density matrix of the measurement point response based on the processed low-level excitation data and dynamic response data. and excitation input power spectral density matrix And construct the power spectral density matrix of the measurement point response. With the excitation input power spectral density matrix A mapping relationship model between them is established, and then an optimization objective function is built based on low-scale experimental data to solve the relationship matrix; specifically: At each order of magnitude, the low-order test data from each measuring point on the module structure are combined to form the power spectral density matrix of the measuring point response. ,matrix There are 108 rows in total, corresponding to 36 measurement points on the structure. Each measurement point outputs the response of 3 degrees of freedom (X, Y, Z), for a total of 108 response data points, in a matrix. There are a total of 2000 columns, with 2000 frequency points for each response. Each order of magnitude of experiment uses only a single stimulus. The excitation input power spectral density matrix and response matrix are obtained from low-level excitation data. and excitation input power spectral density matrix The relationships between them are represented by the relation matrix. The description is expressed as:

[0020] in, It is a 108-row, 1-column vector representing the mapping relationship between structural excitation and the response at each measuring point.

[0021] To obtain the optimal To accurately represent the mapping relationship between structural excitation and the response at each measuring point, it is necessary to define an objective function that measures the error between the predicted response and the actual response. The excitation and response data from four sets of low-level experiments (-21dB, -18dB, -15dB, and -12dB levels) are expressed as follows: The objective function, taking into account all low-level experimental data, is:

[0022] In the formula: Denotes the Frobenius norm; The number of low-volume trials, ; For the first The power spectral density matrix of the measurement point response corresponding to the second-lowest vibration test. For the first The excitation input power spectral density matrix corresponding to the second lowest level vibration test; By minimizing this objective function, the optimal value can be obtained. To obtain the mapping relationship between stimulus and response.

[0023] Step 4: Solve the relation matrix using the gradient descent method; specifically: Minimize the objective function obtained in step 3 using the Adam algorithm. The initial learning rate was set to 0.01, and a total of 2000 iterations were performed to optimize and obtain the mapping matrix. .

[0024] Step 5: Predict the dynamic response of high-order experimental structures based on the mapping relationship matrix; specifically: Based on the mapping matrix obtained in step 4 and high-level excitation of experimental design ( Calculate the response matrix for high-order-level tests (corresponding to three high-order-level test stimuli: -6dB, -3dB, and full-scale 0dB). ( (Corresponding to three high-order-of-magnitude test response matrices: -6dB, -3dB, and full-scale 0dB). The response matrix contains the acceleration response power spectral density data for each measurement point.

[0025] To compare and verify the accuracy of the invention, four sets of acceleration responses at different measurement points were randomly selected: the acceleration responses in the X direction of sensor A3, the Y direction of sensor A7, the Y direction of sensor A20, and the Z direction of sensor A29. The root mean square (RMS) values ​​of the predicted and measured acceleration response power spectral densities at three high-order-level tests (-6dB, -3dB, and full-scale 0dB) were compared. Figure 3 As shown in the figure, the comparison demonstrates that the predicted results of this invention for three high-scale experiments agree well with the measured values. Furthermore, Figure 4 The average relative prediction error of acceleration response in the X, Y, and Z directions was shown for all 36 sensor measurement points in three high-level tests: -6dB, -3dB, and full-scale 0dB. The average prediction error of each high-level test was controlled within 10%, which verifies that the invention has good prediction accuracy.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for predicting high-level structural vibration responses driven by low-level experimental data, characterized in that, Includes the following steps: Step 1: Design and conduct multiple low-level vibration tests for the structure to be predicted, collect low-level excitation data, and collect dynamic response data of the structure under various low-level vibration conditions through preset measuring points on the structure to be predicted, as low-level test data. Step 2: Perform unified standardization preprocessing on low-level excitation data and low-level test data under various low-level vibrations to ensure that the two types of data are consistent in the frequency dimension. Step 3: Obtain the power spectral density matrix of the measurement point response based on the preprocessed low-level excitation data and low-level experimental data. and excitation input power spectral density matrix And construct the following power spectral density matrix of the measurement point response. With the excitation input power spectral density matrix Mapping relationship model between them: ； In the formula: is a mapping relationship matrix, , is the degree of freedom of the measurement point, is the degree of freedom of the excitation; is the frequency; Simultaneously, the following optimization objective function is constructed. Constrain the above mapping matrix Solving for: ； In the formula: Denotes the Frobenius norm; The number of low-level vibration tests. ; For the first The power spectral density matrix of the measurement point response corresponding to the second-lowest vibration test. For the first The excitation input power spectral density matrix corresponding to the second lowest level vibration test; Step 4: Minimize the objective function constructed in Step 3 using an optimization algorithm. The goal is to minimize the difference between the predicted and measured values ​​until the convergence condition is met, thereby obtaining the optimized mapping matrix. Step 5: Use the mapping matrix obtained in Step 4 to calculate the dynamic response data of the structure to be predicted under high-level vibration test, so as to realize the dynamic response prediction of the structure under high-level vibration test.

2. The method for predicting high-level structural vibration responses driven by low-level experimental data according to claim 1, characterized in that: In step 1, accelerometers or strain gauges are set up at different selected locations on the structure to be predicted as measuring points, and dynamic response data of the structure to be predicted under various low-level vibrations are collected by the accelerometers or strain gauges.

3. The method for predicting high-level structural vibration responses driven by low-level experimental data according to claim 2, characterized in that, The unified standardization preprocessing mentioned in step 2 specifically includes: Interpolation alignment processing is performed on low-level excitation data and low-level test data under various low-level vibrations to unify them onto the same frequency axis, so that the low-level excitation data and low-level test data under various low-level vibrations are consistent in the frequency dimension.

4. A method for predicting high-level structural vibration responses driven by low-level experimental data according to any one of claims 1-3, characterized in that: In step 4, the optimization algorithm is either gradient descent or adaptive optimization.

5. The method for predicting high-level structural vibration response driven by low-level experimental data according to claim 4, characterized in that: The adaptive optimization algorithm is either the Adam algorithm or the RMSprop algorithm.

6. The method for predicting high-level structural vibration responses driven by low-level experimental data according to claim 5, characterized in that: In step 4, the convergence condition is the optimization objective function. The number of iterations drops to the set threshold, or the maximum number of iterations reaches the set limit.

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