Structural modal pole screening method, device and storage medium

Abstract

This application relates to the field of structural dynamics testing and provides a method, apparatus, and storage medium for screening structural modal poles. The method includes: acquiring the frequency response function of the structure to be analyzed and identifying an initial set of modal poles accordingly; calculating a baseline fitting quality index for the current pole set based on all poles in the initial set of modal poles; forming a sub-pole set for each pole in the current set of poles, reconstructing the frequency response function based on the sub-pole set, and calculating the change in fitting quality caused by removing the pole; determining whether the change in fitting quality for each pole meets a preset redundancy criterion; if the determination result is that the preset redundancy criterion is met, then candidate poles are removed from the current set of poles, and the resulting set of poles is used as the new current set of poles, and the iteration is returned; otherwise, the iteration is terminated and the current set of poles is output as the screened key modal poles.

Description

Technical Field

[0001] This application relates to the field of structural dynamics testing, and in particular to a method, apparatus and storage medium for screening structural modal poles. Background Technology

[0002] In the design, verification, and health monitoring of engineering structures, obtaining accurate dynamic characteristics is crucial. Structural modal parameters, including frequencies, damping ratios, and mode shapes, are core characteristics of these properties. Typically, the frequency response function of the structure is measured experimentally, and modal parameters are extracted from it using parameter identification algorithms. This process generates a steady-state diagram containing a large number of candidate poles, including both physical poles reflecting the true dynamic characteristics of the structure and mathematical or spurious poles introduced by test noise, nonlinear factors, or algorithm errors.

[0003] Currently, identifying true physical poles from steady-state graphs primarily relies on manual interpretation. Engineers manually select what they deem reliable poles based on criteria such as the "steady-state" property of pole clustering. However, this method is highly dependent on personal experience, resulting in inefficiency, strong subjectivity, and poor consistency. To reduce manual intervention, some automated or semi-automated methods have been proposed, such as preliminary screening based on fixed thresholds like pole distribution density and frequency spacing. However, these methods typically rely on pre-set global thresholds, making it difficult to adapt to complex situations with different structures, test conditions, or signal-to-noise ratios. This can lead to the erroneous retention of redundant poles or the removal of important poles, resulting in a decrease in the accuracy of the final modal model.

[0004] Therefore, existing technologies lack a method that can adaptively and objectively quantify the importance of each pole and automatically, efficiently, and accurately select key modal poles. This has become a major obstacle to improving the automation level and accuracy of structural modal parameter identification. Summary of the Invention

[0005] This application provides a structural modal pole selection method, apparatus, and storage medium. By quantitatively evaluating the impact of each pole on data fitting and automatically iteratively eliminating redundant poles, objective and efficient modal parameter selection is achieved.

[0006] On the one hand, this application provides a structural modal pole selection method, the method comprising: Step S1: Obtain the frequency response function of the structure to be analyzed, and identify the initial set of modal poles based on the frequency response function; Step S2: Based on all poles in the initial modal pole set, reconstruct the frequency response function and calculate the baseline fitting quality index under the current pole set; Step S3: For each pole in the current pole set, perform the following importance evaluation operation: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole; Step S4: Based on the change in fitting quality corresponding to each pole obtained in step S3, identify the candidate pole that has the least impact on the current fitting quality, and determine whether its change meets the preset redundancy standard. Step S5: If the judgment result of step S4 meets the preset redundancy standard, the candidate poles are removed from the current pole set, and the pole set obtained after removal is used as the new current pole set. The process is then returned to step S2 for iteration. If the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered critical modal poles.

[0007] On the other hand, this application provides a structural modal pole screening device, the device comprising: The acquisition module is used to acquire the frequency response function of the structure to be analyzed, and to identify the initial set of modal poles based on the frequency response function; The reconstruction module is used to reconstruct the frequency response function based on all poles in the initial modal pole set, and to calculate the baseline fitting quality index under the current pole set. The evaluation module is used to perform the following importance evaluation operation for each pole in the current pole set: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole; The judgment module is used to identify the candidate poles that have the least impact on the current fitting quality based on the change in fitting quality corresponding to each pole, and to determine whether the change in its change meets the preset redundancy standard. The iteration module is used to remove the candidate poles from the current pole set if the result of judging whether the change amount meets the preset redundancy standard is that the preset redundancy standard is met, and use the pole set obtained after removal as the new current pole set, and return to the reconstruction module for iteration; if the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered key modal poles.

[0008] Thirdly, this application provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the technical solution of the above-described structural modal pole selection method.

[0009] Fourthly, this application provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described structural modal pole selection method.

[0010] As can be seen from the technical solution provided in this application, on the one hand, this application does not rely on the subjective interpretation of the steady-state diagram by engineers or fixed geometric thresholds. Instead, it removes a pole from the current pole set to form a sub-pole set, reconstructs the frequency response function based on the sub-pole set, and calculates the change in fitting quality caused by removing the pole. A calculable quantitative index reflecting the contribution of each pole to the overall data fitting is defined. This quantitative index comes directly from the data itself, providing an objective and unified standard for measuring the importance of poles, thus avoiding inconsistencies and subjective biases caused by manual screening. On the other hand, through a closed-loop process of identifying and judging candidate poles based on changes and iteratively eliminating and returning, this application achieves automatic identification and elimination of redundant poles. This process does not require manual intervention in each step of the decision-making; the system can automatically perform evaluation and judgment. The process of breaking down and updating operations until the termination condition is met not only significantly improves the screening efficiency, but more importantly, for the same set of data, the technical solution of this application produces the same screening results every time it runs, ensuring the consistency and repeatability of the output. Thirdly, the "redundancy standard" used in the technical solution of this application to determine whether the change in value meets the preset redundancy standard can be dynamically adjusted based on the characteristics of the current dataset, rather than a globally fixed value. The iterative process allows the screening benchmark (i.e., the baseline fit quality index) to be dynamically updated as unimportant poles are removed. This means that the evaluation of the remaining poles is carried out under a continuously purified reference system, enabling the screening standard to adapt to the actual distribution and quality of poles in the current dataset, thereby more accurately distinguishing between critical poles and redundant poles, improving screening accuracy, and better adapting to different test objects and data conditions. In summary, the technical solution of this application achieves objective and efficient modal parameter screening by quantitatively evaluating the impact of each pole on data fitting and automatically iteratively removing redundant poles. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the structural modal pole selection method provided in the embodiments of this application; Figure 2This is a schematic diagram of the structural modal pole screening device provided in the embodiments of this application; Figure 3 This is a schematic diagram of the device provided in the embodiments of this application. Detailed Implementation

[0013] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0014] In this specification, adjectives such as "first" and "second" are used only to distinguish one element or action from another, without necessarily requiring or implying any actual such relationship or order. Where circumstances permit, reference to an element or component or step (etc.) should not be construed as being limited to only one of the elements, components, or steps, but may be one or more of the elements, components, or steps, etc.

[0015] For ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale.

[0016] Currently, identifying true physical poles from steady-state graphs primarily relies on manual interpretation. Engineers manually select poles deemed reliable based on criteria such as the "steady-state" nature of pole clustering. However, this method is highly dependent on personal experience, resulting in inefficiency, strong subjectivity, and poor consistency. To reduce manual intervention, some automated or semi-automated methods have been proposed, such as preliminary screening based on fixed thresholds like pole distribution density and frequency intervals. However, these methods typically rely on pre-set global thresholds, making it difficult to adapt to complex situations with different structures, test conditions, or signal-to-noise ratios. They may incorrectly retain redundant poles or remove important ones, leading to a decrease in the accuracy of the final modal model. Therefore, existing technologies lack a method that can adaptively and objectively quantify the importance of each pole and automatically, efficiently, and accurately screen out key modal poles. This has become a major obstacle to improving the automation level and accuracy of structural modal parameter identification.

[0017] To address the aforementioned problems in existing technologies, this application proposes a structural modal pole selection method, which can be applied to the dynamic characteristic testing of engineering structures (e.g., aerospace vehicles, bridges, buildings, and mechanical equipment, etc.). Its flowchart is attached. Figure 1 As shown, it mainly includes steps S1 to S5, which are detailed below: Step S1: Obtain the frequency response function of the structure to be analyzed, and identify the initial set of modal poles based on the frequency response function.

[0018] In structural dynamics testing, the frequency response function is the core data characterizing the dynamic properties of a structure. To ensure that subsequent screening processes are based on high-quality, high signal-to-noise ratio data, it is preferable to preprocess the raw measurement data.

[0019] Specifically, the frequency response function of the structure to be analyzed can be obtained through the following steps S11 to S12: Step S11: Set the target frequency analysis range.

[0020] Here, the target frequency analysis range is the core frequency band that all subsequent analysis operations focus on. It is typically determined by engineers in advance through analysis or estimation based on the physical characteristics of the structure under test (e.g., dimensions, materials, boundary conditions) and the purpose of the test. For example, in modal testing of aerospace, civil engineering, or mechanical equipment, engineers may primarily focus on the first few (e.g., the first 10 or 20) dominant modes excited by the structure under normal operating conditions. The significance of setting this range is to concentrate computational resources and analytical attention on the frequency band where the true physical modes are most likely to occur, thereby eliminating interference from high-frequency noise and low-frequency drift, and establishing a clear and effective "working window" for subsequent processing.

[0021] Step S12: Based on the target frequency analysis range, perform frequency interval filtering on the raw frequency response function measurement data directly acquired from the test equipment to obtain the frequency response function for subsequent steps.

[0022] The raw frequency response function measurement data directly acquired from the testing equipment is typically obtained by a system composed of testing equipment such as exciters, force sensors, and accelerometers, using methods such as hammer impact or exciter frequency sweep. This data is a complex matrix, with rows and columns corresponding to different response and excitation points, containing complete excitation-response amplitude and phase information. However, the raw data inevitably contains irrelevant high-frequency components introduced by electronic noise from the testing system and environmental vibration interference, as well as low-frequency components introduced by sensor zero drift. Specifically, frequency range filtering of the raw frequency response function measurement data directly acquired from the testing equipment based on the target frequency analysis range can be achieved by designing a digital bandpass filter, whose passband range is the target frequency analysis range set in step S11. The frequency response function sequences corresponding to each response point and excitation point in the raw data are processed by this digital bandpass filter. The filtering operation can effectively attenuate or eliminate signal components outside the passband frequency range, thereby retaining the effective dynamic response information related to the structural modes within the target frequency band and significantly improving the signal-to-noise ratio of the data. The purified frequency response function data obtained after this preprocessing is the "frequency response function" mentioned in all subsequent steps of this method, which lays a solid data foundation for high-precision parameter identification and screening.

[0023] After obtaining clean frequency response function data, it is necessary to initially extract a set of candidate modal poles from it. As an embodiment of this application, identifying the initial set of modal poles based on the frequency response function can be achieved through steps S13 and S14, as detailed below: Step S13: Apply the multi-reference least squares complex frequency domain polynomial method or random subspace identification algorithm to the frequency response function to generate a pole steady-state diagram.

[0024] This step is a standard procedure in modal parameter identification, aiming to automatically generate a large number of candidate poles from frequency or time domain data. Multi-reference least squares complex frequency domain polynomial methods (e.g., PolyMAX) and stochastic subspace identification (SSI) algorithms are mature and high-precision parameter identification methods in this field. Taking the PolyMAX method as an example, its basic process is as follows: using the filtered frequency response function data obtained in step S12 as input, a series of complex poles can be calculated at different model orders by constructing and solving a linear least squares problem about the polynomial coefficients. Each complex pole... It contains two key pieces of information: its actual part Related to the damping ratio, the imaginary part Related to the damped natural frequency. A pole steady-state plot is generated by traversing a sequence of model orders from low to high (e.g., from order 2 to 100, with a step size of 2) and plotting all identified poles at each order on a frequency-order coordinate system. In this plot, poles representing the true physical modes remain relatively constant near their natural frequencies, exhibiting vertical "steady pillars" or "clusters" as the model order increases; while mathematical poles and spurious poles, generated by measurement noise, computational errors, or system nonlinearity, will randomly change positions, forming scattered background points. The steady-state plot provides engineers with an important basis for visually identifying physical poles.

[0025] Step S14: Extract complex poles corresponding to the preset maximum modal order from the pole steady-state diagram to form an initial set of modal poles.

[0026] After generating the pole steady-state plot, traditional methods require engineers to manually interpret and select stable poles, which introduces subjectivity and inefficiency. This application employs an inclusive strategy to construct the starting point for the automatic selection process. The preset maximum modal order is a sufficiently high value to ensure that the model built by the algorithm at this order can cover (or even overestimate) all possible real modes. Complex poles corresponding to the preset maximum modal order are extracted from the pole steady-state plot to form an initial set of modal poles. Specifically, this can be achieved by reading all data points present in the pole steady-state plot at the highest preset model order (e.g., order 100). Each point corresponds to an identified complex pole. All these poles are collected to form an initial candidate set P = { , , ..., This set is a "complete set," which almost necessarily contains all real physical poles, but also contains a large number of redundant mathematical poles and noisy poles. The value of this application lies in the fact that subsequent steps can automatically and objectively filter out the truly critical parts from this initial set, which is a mixture of both.

[0027] Step S2: Based on all poles in the initial set of modal poles, reconstruct the frequency response function and calculate the baseline fitting quality index under the current set of poles.

[0028] After obtaining the initial pole set, an evaluation benchmark needs to be established. This benchmark is used to measure the overall fitting effect of all current poles on the original test data, and serves as a reference for subsequently evaluating the importance of individual poles. As an embodiment of this application, the frequency response function is reconstructed based on all poles in the initial modal pole set, and the baseline fitting quality index under the current pole set is calculated through steps S21 to S23, as detailed below: Step S21: Based on the current set of poles, use the frequency domain least squares method to solve for the residues corresponding to each pole in order to reconstruct the frequency response function and obtain the reconstructed frequency response function.

[0029] This step is the core technology for achieving data fitting and model reconstruction. Frequency domain least squares is a classic method in structural dynamics for modal parameter fitting. Its technical principle is: in the frequency domain, assume the structure's frequency response function matrix... It can be determined by a set of known complex poles { } (and its conjugate) and the residue matrix to be found { The term is approximated by the upper and lower residual terms {LR, UR} used to compensate for the residual effects of low and high frequencies. Based on the current pole set, the residues corresponding to each pole are solved using the frequency domain least squares method. Specifically, the process involves taking the value λ of each pole in the current pole set P. i As a known constant, it is substituted into the theoretical expression of the frequency response function to construct a function for all residues R. i The system of linear equations for the residuals LR and UR is used. The optimal residues and residuals are solved by minimizing the L2 error of the reconstructed frequency response function (i.e., the calculated value of the theoretical expression) and the frequency response function obtained in step S1 (i.e., the measured value) at all frequency points and all pairs of response and excitation points. This process is a standard linear least squares problem. When solving for the residues corresponding to each pole using the frequency domain least squares method, the upper and lower residuals used to compensate for low-frequency quality effects and high-frequency stiffness effects are also solved simultaneously. Here, low-frequency quality effects are usually caused by the non-ideal characteristics of the accelerometer in the low-frequency range, while high-frequency stiffness effects may be related to the sensor's mounting stiffness or the local stiffness of the structure. Introducing upper and lower residuals that are inversely and directly proportional to the frequency for compensation can significantly improve the fitting accuracy of the theoretical model to the measured data in the mid-frequency range (i.e., the modal density region), which is key to obtaining accurate reconstruction.

[0030] To improve the numerical stability of the solution, especially when the normal equations are ill-conditioned due to dense poles or poor test data conditions, it is preferable to use a singular value decomposition (SVD) algorithm to solve the normal equations in the frequency domain least squares method, thereby numerically and stably determining the residues corresponding to each pole. SVD is a robust matrix factorization algorithm that effectively handles ill-conditioned or rank-deficient linear systems. By ignoring unstable solution components corresponding to minimal singular values, it obtains numerically stable and physically reasonable residue solutions, thus ensuring the robustness of the entire reconstruction and evaluation process.

[0031] Step S22: Calculate the average correlation between the reconstructed frequency response function and the frequency response function obtained in step S1 on multiple pairs of response points and excitation points, and use it as the first fitting quality index.

[0032] After obtaining the reconstructed frequency response function, it is necessary to quantify its consistency with the original data from the perspective of "waveform similarity". The average correlation between the reconstructed frequency response function and the frequency response function obtained in step S1 is calculated across multiple response point and excitation point pairs. Specifically, for each response point i and excitation point j pair, the reconstructed frequency response function curve is calculated. Comparison with measured frequency response function curve Multiple correlation coefficient within the target frequency range The complex correlation coefficient reflects the consistency of two complex curves in amplitude and phase; the closer its value is to 1, the more similar the fitted waveform is to the measured waveform. Then, the correlation coefficient is calculated for all valid measurement point pairs (i, j). Calculating the arithmetic mean yields the average correlation. This metric is sensitive to the overall shape and phase matching of the curve, and can effectively identify mode shape errors or phase shifts caused by missing poles.

[0033] Step S23: Calculate the average least squares deviation between the reconstructed frequency response function and the frequency response function obtained in step S1 on multiple pairs of response points and excitation points, and use it as the second fitting quality index.

[0034] In addition to waveform similarity, quantification from the perspective of "amplitude error" is also necessary. The average least squares deviation between the reconstructed frequency response function and the frequency response function obtained in step S1 is calculated across multiple response and excitation point pairs. Specifically, for each measurement point pair (i, j), the average least squares deviation is calculated at all discrete frequency points. Above, the sum of the squares of the differences between the reconstructed values ​​and the measured values, i.e. Then, this error is normalized by dividing by the total number of frequency points to obtain the mean square deviation of the measurement point pair. Finally, for all measurement point pairs... Calculate the arithmetic mean, which yields the mean least squares deviation. This metric directly reflects the error level of the overall magnitude fitting of the model. Average correlation. and mean least squares deviation Together, they constitute the baseline fit quality index under the current set of poles. , These provide a multi-dimensional and precise quantitative benchmark for subsequent assessment of the importance of individual poles.

[0035] Step S3: For each pole in the current pole set, perform the following importance evaluation operation: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole.

[0036] Existing technologies (e.g., manual interpretation of steady-state plots or screening based on fixed geometric rules) lack an objective and quantifiable standard to accurately assess the true contribution of each candidate pole to the accuracy of the final modal model. This makes the screening process reliant on experience, unable to distinguish between "redundant poles" that have a negligible impact on the fitting results and crucial "critical poles." For example, the manual experience-based approach, where engineers visually examine the steady-state plot and select poles based on the density and stability of the cluster, is highly subjective, inefficient, and prone to inconsistencies in conclusions reached by different operators or even the same operator at different times. The fixed threshold-based screening approach, which sets fixed thresholds such as frequency intervals and damping ratio ranges, and removes poles that do not meet the thresholds, also has significant drawbacks. It cannot adapt to the dynamic characteristics of pole distribution under different structures and test signal-to-noise ratios, and may mistakenly delete "marginal" true poles that contribute to a specific model, or retain mathematical poles that appear to meet the thresholds but have a very small actual contribution. Therefore, the technical solution of this application is to perform the following importance assessment operation for each pole in the current pole set: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole. This solution assigns a direct and quantitative importance score to each pole through the operation of "removing the pole and calculating the change in fitting quality." This importance score (i.e., the change in fitting quality) directly reflects the degree to which the existence of the pole affects the overall data fitting accuracy, transforming the subjective "whether it appears stable" into the objective "how much fitting error it contributes," thus providing a unified and fair basis for comparison and judgment.

[0037] Specifically, for each pole in the current set of poles, the following importance evaluation operation is performed: For the current set of poles P = { , ,…, The k-th pole in} Perform the following sub-steps: 1) Remove the pole from the current set of poles to form a sub-set of poles.

[0038] That is, construct a new set of poles. This set represents the assumption that there are no poles. The situation at that time.

[0039] 2) Reconstruct the frequency response function based on the sub-pole set.

[0040] This operation is exactly the same as the reconstruction principle in step S2, but the set of poles used is... Based on the current set of poles (here, the set of sub-poles). The frequency response function is reconstructed by solving for the residues corresponding to each pole using the frequency domain least squares method. Similarly, in this solution process, the upper and lower residual terms are solved simultaneously, and singular value decomposition can be preferred to ensure numerical stability.

[0041] 3) Calculate the change in fit quality caused by removing the pole.

[0042] Specifically, the change in fitting quality caused by removing the poles can be calculated through steps S31 to S34, as detailed below: Step S31: Calculate the average correlation between the reconstructed frequency response function after removing the k-th pole and the frequency response function obtained in step S1. .

[0043] This step is similar in principle to step S22, but the calculation object is based on the sub-pole set. Reconstructed frequency response function The average correlation between it and the original data was obtained. .

[0044] Step S32: Calculate the average correlation relative to the baseline average correlation. The amount of decrease .

[0045] This calculates the degradation of the correlation metric. Baseline average correlation. It is the optimal value that includes all poles. It is a non-negative value; the larger the value, the more likely the pole has been removed. The more severe the deterioration of the model waveform similarity, the more important that pole is for maintaining the accuracy of the model waveform.

[0046] Step S33: Calculate the average least squares deviation between the reconstructed frequency response function after removing the k-th pole and the frequency response function obtained in step S1. .

[0047] This step is similar in principle to step S23, and the calculation is based on... The average least squares deviation corresponding to the reconstructed model .

[0048] Step S34: Calculate the mean least squares deviation relative to the baseline mean least squares deviation The increase .

[0049] This calculates the increment of the error index. Similarly, even though it is a non-negative value, the larger the value, the more the removal of the pole causes the model's magnitude error to increase, thus implying that the pole is more critical to controlling the model's magnitude error.

[0050] Among them, the change in fitting quality is from and Common representation. This two-dimensional vector ( , It accurately and quantitatively describes the poles. The "cost" of removing a pole from the model is as follows: the smaller the change, the smaller the contribution of the pole to the overall model fit, and the lower its importance; conversely, the larger the change, the more critical the pole. In this way, each pole obtains an "importance ID card" calculated based on objective data, completely replacing subjective experience judgment.

[0051] To improve evaluation efficiency, especially when the initial pole set is large, this step supports parallel computation. Step S3 performs importance evaluation operations, including parallel computation, simultaneously performing operations such as forming sub-pole sets, reconstruction, and calculating the change in fit quality for multiple poles in the current pole set. Since the evaluation operations for each pole are independent, multi-core processors or computing clusters can be used to evaluate different poles. By assigning computation to different computation threads or processes for simultaneous processing, the overall evaluation time is significantly shortened, enabling this method to efficiently process large datasets with complex structures and hundreds or thousands of candidate poles.

[0052] Step S4: Based on the change in fitting quality corresponding to each pole obtained in step S3, identify the candidate pole that has the least impact on the current fitting quality, and determine whether its change meets the preset redundancy standard.

[0053] After obtaining a quantitative evaluation of each pole, how can we automate and rationally make decisions—that is, "which one to remove first?" and "when to stop removing poles?"? Existing methods lack an adaptive and logical decision-making process. For example, attempting to remove poles in an arbitrary order, i.e., removing them one by one according to frequency and observing the overall error change, is inefficient and may cause the model to deteriorate rapidly by removing a practically important pole first, interfering with subsequent judgments. To address this, the technical solution adopted in this application is: based on the change in fitting quality corresponding to each pole obtained in step S3, identify the candidate poles that have the least impact on the current fitting quality, and determine whether their change in fitting quality meets a preset redundancy criterion. This scheme, on the one hand, identifies candidate poles that have the least impact on the current fit quality, ensuring that each iteration starts by attempting to eliminate the "least important" and "safest" poles in the current set. This "easy-to-difficult" strategy minimizes the risk of irreversible damage to the model due to the accidental removal of important poles, ensuring the robustness of the selection process. On the other hand, the redundancy criterion for judging whether the change in the pole meets the preset redundancy criteria can be a threshold that is dynamically adjusted based on data characteristics or iteration stage. This differs from a fixed threshold, allowing the system to flexibly decide "whether it is redundant" based on the overall quality of the current pole set. For example, in the early stages of iteration, the criteria can be relatively lenient to quickly eliminate a large number of obviously redundant poles; in the later stages of iteration, the criteria can be tightened for fine-tuning. This dynamism makes the selection process more intelligent and adaptable to more complex data situations.

[0054] To achieve this goal, the two-dimensional changes corresponding to each pole need to be synthesized into a comparable scalar. Specifically, identifying the candidate poles that have the least impact on the current fit quality can be achieved through steps S41 and S42, as detailed below: Step S41: For each pole in the current set of poles, calculate its corresponding Δρ -k and Δe -k We perform a weighted summation to obtain a comprehensive importance evaluation value.

[0055] Here, the weighted summation operation normalizes two indices with different dimensions and physical meanings and then performs a linear combination. For example, we can first combine all... and Normalization was performed separately to eliminate differences in magnitude, and then different weighting coefficients were assigned according to the actual engineering requirements. and (For example, if more attention is paid to waveform consistency, then assume) ), calculate the comprehensive value This comprehensive importance evaluation value This reflects the overall cost of removing that pole.

[0056] Step S42: Select the pole with the smallest comprehensive importance evaluation value as the candidate pole.

[0057] After calculating all poles Then, through simple numerical comparison, it can be found The pole with the smallest value. This pole means that removing it would have the smallest overall negative impact on the model fit quality in the current set, and is therefore marked as the most likely redundant term in this iteration, i.e., a candidate pole. This method simplifies multidimensional judgment to a reliable scalar comparison, making it easy for the program to execute automatically.

[0058] In the above embodiments, determining whether the change in value meets a preset redundancy criterion is the final threshold for deciding whether to remove the candidate pole. The purpose is to set an objective importance threshold; only poles below this threshold are considered redundant. A specific criterion is: judging candidate poles... Is it less than the first threshold, and its Is it less than the second threshold? This is an AND operation. That is, only if the candidate pole is less than the second threshold... and Only when both thresholds are less than their corresponding thresholds (first threshold, second threshold) is the removal of a pole considered to have an "acceptable" or "insignificant" impact on the model, thus meeting the redundancy criterion and allowing for safe removal. If any change exceeds its threshold, it indicates that removing the pole would cause an unacceptable degradation in some aspect of the model's quality, therefore failing to meet the redundancy criterion and should be retained.

[0059] The setting of the first and second thresholds in the above embodiments is crucial. Using fixed thresholds may not be suitable for the characteristics of different datasets. Therefore, this application provides an adaptive dynamic setting method, namely, the setting of the first and second thresholds, including steps S91 and S92, as described below: Step S91: After initially executing steps S1 to S4, obtain the corresponding values ​​for all poles. and Statistical distribution.

[0060] Specifically, in the first iteration, after evaluating all initial poles, all the collected data are... Values ​​and All These values ​​constitute two sets of data samples, reflecting the distribution of the influence of each pole on waveform correlation and amplitude error under the current dataset.

[0061] Step S92: Based on the statistical distribution, dynamically set the first threshold and the second threshold so that the threshold can distinguish the change corresponding to the outlier poles that are significantly deviated from the main group in the statistical distribution.

[0062] This step is the core of intelligently setting thresholds based on the inherent characteristics of the data. For example, it can calculate... Sample mean and standard deviation Then set the first threshold to ,in, It is a coefficient selected based on experience (e.g., =1.5 or =2.0). Similarly, calculate mean and standard deviation Set the second threshold to , This is a coefficient selected based on experience. This threshold setting method, based on "mean plus a certain number of standard deviations," is a common technique in statistics for identifying outliers. It considers poles whose changes are significantly greater than the mainstream pole group as important "outliers," and uses their corresponding changes as a threshold reference. This threshold setting is data-driven and adaptive, automatically adapting to differences in importance distribution under different test objects and data with different signal-to-noise ratios, thus making the redundancy standard more scientific and universally applicable.

[0063] Step S5: If the judgment result of step S4 meets the preset redundancy standard, then remove the candidate poles from the current pole set and use the pole set obtained after removal as the new current pole set, and return to step S2 for iteration; if the preset redundancy standard is not met, then terminate the iteration and output the current pole set as the filtered critical modal poles.

[0064] Step S5 implements the iterative loop and termination control of the method, serving as the execution engine for automated screening. Its logic is as follows: it starts by attempting to eliminate the least important poles and verifies whether the quality of the model after elimination remains within an acceptable range. If so, the pole is confirmed as redundant and formally eliminated, and this process continues among the remaining poles; if not, it indicates that the remaining poles are sufficiently important, and the screening is complete.

[0065] Before the iteration begins, to record a complete screening history for analysis and traceability, the following initialization can be performed: Before the first execution of step S2, a dynamic result record table is initialized, and each time candidate poles are removed in step S5, the parameters of the removed poles and their corresponding changes in fit quality are added to the dynamic result record table in real time. The dynamic result record table supports real-time querying and tracing of the screening history during the iteration process. This table records the frequency, damping ratio, and other parameters of the poles removed in each iteration. and These values ​​form a complete "filter log," greatly enhancing the transparency and analyzability of the process.

[0066] If the judgment result of step S4 is that the preset redundancy standard is met, then the following elimination and update operations from step S41 to step S43 are performed: Step S41: Remove candidate poles from the current set of poles.

[0067] Step S42: After removing candidate poles and before returning to step S2, the following steps are also included: Step S51: Update the baseline fitting quality index by setting the fitting quality index corresponding to the set of remaining poles after removing candidate poles as the new baseline fitting quality index.

[0068] After removing redundant poles, a complete reconstruction needs to be performed again based on the remaining pole set (i.e., returning to step S2), to calculate the new average correlation and average least squares bias, and to replace the old ones with them. and This ensures that the evaluation benchmark for each iteration is based on the state of the current optimal model, making the assessment of the importance of the remaining poles increasingly accurate.

[0069] Step S43: Using the set of poles obtained after removal as the new current set of poles, return to step S2 for iteration.

[0070] During the iteration process, to avoid performing extensive calculations in the later stages of screening just to remove poles with negligible contributions, a convergence check can be introduced to terminate the iteration early and improve efficiency. The iteration process in step S5 also includes a convergence check step: Step S52: Monitor the sum of changes in the fitting quality of the removed candidate poles over multiple consecutive iterations; Step S53: If the sum of changes in fitting quality is lower than a convergence threshold, terminate the iteration early and output the current pole set. This approach is based on the fact that if the sum of the importance (measured by "change in fitting quality") of several recently removed poles is already very small (e.g., below the convergence threshold), it provides a strong signal that even the least important poles in the remaining pole set are negligible in importance. Continuing the iteration in this situation, even if one or two more poles are removed, will only result in a negligible improvement in model quality, which is counterproductive. In other words, the algorithm considers it to have reached a "convergence point with diminishing returns," and the cost-effectiveness of continuing the calculation is very low. Therefore, terminating the iteration early is reasonable and efficient. For example, if three poles are removed consecutively ( + If the sum is less than a very small value (e.g., 0.001), it indicates that the contribution of subsequent poles is negligible, and the iteration can be stopped early. The current result is output, which is a highly concise set with key poles intact and redundant poles fully removed.

[0071] If the preset redundancy criteria are not met, the iteration is terminated, and the current set of poles is output as the selected critical modal poles.

[0072] When the variation of the identified "least important pole" still exceeds the redundancy criterion, it proves that all poles in the current set have a non-negligible contribution to the model, and the screening process naturally terminates. The pole set output at this time is the critical modal pole obtained through an automated and quantitative evaluation process.

[0073] After step S5 iteration terminates and the filtered set of critical modal poles is output, the automated process of this method has completed the core screening task. However, in order to obtain complete modal parameters that can be directly used for engineering analysis and to verify the reliability of the screening results, the following post-processing and verification steps are usually included.

[0074] After outputting the current set of poles as the filtered critical mode poles, the following is also included: Step S54: Based on the key modal poles, the residues corresponding to each pole are finally determined by the frequency domain least squares method to complete the full set identification of structural modal parameters.

[0075] This step is crucial for obtaining the final, usable modal model. During the screening process, the residues obtained each time the frequency response function is reconstructed are based on the then-current set of temporary poles, and may be updated during iterations. Once the final set of key poles is determined, a final, precise parameter fitting is performed using this set as a fixed foundation. Based on the key modal poles, the residues corresponding to each pole are finally determined using the frequency domain least squares method. Specifically, the key modal pole set output in step S5 is used as the known and fixed pole values. The frequency domain least squares method is applied again, and based on these poles, a final, and most precise global fitting is performed on the frequency response function obtained in step S1. This fitting will solve for the residue matrix corresponding to each key pole. This matrix contains key information describing the amplitude and direction of each modal mode. Combining the known poles (including frequency and damping ratio information) and the finally determined residues constitutes the complete set of structural modal parameters, including the frequency, damping ratio, and mode shape of each mode. Thus, this method achieves the entire automated processing flow from raw test data to a clean set of key modal parameters.

[0076] To ensure that the selected poles not only fit the data used for screening well, but also represent the true physical properties of the structure, and to avoid overfitting to the data of a specific test, independent model validation can be performed: After outputting the filtered key modal poles in step S5, the following modal model verification steps are also included, detailed in steps S141 and S142: Step S141: Construct a complete structural modal model based on the key modal poles and their final determined residues.

[0077] Using the key poles and their final residues obtained in step S54, a parameterized theoretical frequency response function model, i.e., a structural modal model, can be constructed. This model mathematically fully characterizes the structural dynamics described by these selected poles.

[0078] Step S142: On a different set of test frequency response functions than those used in step S1, evaluate the prediction accuracy of the structural modal model. If the accuracy meets the standard, confirm the effectiveness of the key modal poles.

[0079] This is a crucial step in verifying the physical meaning and generalization ability of the screening results. Another set of test frequency response functions should come from independent test data of the same structure at different times or under different excitation levels / locations. The modal model constructed in step S141 is used to predict the frequency response function on this new set of data that was not involved in the screening process, and the fitting error (such as average correlation and average deviation) between the predicted results and the measured data is calculated. If the accuracy meets the standards, for example, the average correlation between the prediction and the measured data is higher than 0.9, and the average deviation is lower than a certain engineering acceptable threshold, it strongly proves that the model constructed from the selected key poles can not only "interpret" the data used to train it, but also "predict" new observation data. This indicates that these poles capture the intrinsic, repeatable physical and dynamic characteristics of the structure, rather than random noise or phenomena specific to a particular test, thus confirming the effectiveness of the key modal poles. This verification step greatly enhances the reliability and engineering practical value of the method's output results.

[0080] From the above Figure 1As can be seen from the example of the structural modal pole selection method, on the one hand, this application does not rely on the subjective interpretation of the steady-state diagram by engineers or fixed geometric thresholds. Instead, it removes a pole from the current pole set to form a sub-pole set, reconstructs the frequency response function based on the sub-pole set, and calculates the change in fitting quality caused by removing the pole. A calculable quantitative index reflecting the contribution of each pole to the overall data fitting is defined. This quantitative index is directly derived from the data itself, providing an objective and unified standard for measuring the importance of poles, thus avoiding inconsistencies and subjective biases caused by manual selection. On the other hand, through a closed-loop process of identifying and judging candidate poles based on changes and iteratively eliminating and returning, this application achieves automatic identification and elimination of redundant poles. This process does not require manual intervention in each step of the decision-making; the system can automatically perform evaluation and judgment. The process of breaking down and updating operations until the termination condition is met not only significantly improves the screening efficiency, but more importantly, for the same set of data, the technical solution of this application produces the same screening results every time it runs, ensuring the consistency and repeatability of the output. Thirdly, the "redundancy standard" used in the technical solution of this application to determine whether the change in value meets the preset redundancy standard can be dynamically adjusted based on the characteristics of the current dataset, rather than a globally fixed value. The iterative process allows the screening benchmark (i.e., the baseline fit quality index) to be dynamically updated as unimportant poles are removed. This means that the evaluation of the remaining poles is carried out under a continuously purified reference system, enabling the screening standard to adapt to the actual distribution and quality of poles in the current dataset, thereby more accurately distinguishing between critical poles and redundant poles, improving screening accuracy, and better adapting to different test objects and data conditions. In summary, the technical solution of this application achieves objective and efficient modal parameter screening by quantitatively evaluating the impact of each pole on data fitting and automatically iteratively removing redundant poles.

[0081] Please see the appendix Figure 2 This application provides a structural modal pole screening device, which includes an acquisition module 201, a reconstruction module 202, an evaluation module 203, a judgment module 204, and an iteration module 205, as detailed below: The acquisition module 201 is used to acquire the frequency response function of the structure to be analyzed and to identify the initial set of modal poles based on the frequency response function; The reconstruction module 202 is used to reconstruct the frequency response function based on all poles in the initial set of modal poles and to calculate the baseline fitting quality index under the current set of poles. Evaluation module 203 is used to perform the following importance evaluation operation for each pole in the current pole set: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole; The judgment module 204 is used to identify the candidate poles that have the least impact on the current fitting quality based on the change in fitting quality corresponding to each pole, and to determine whether the change in its change meets the preset redundancy standard. The iteration module 205 is used to remove candidate poles from the current pole set if the result of judging whether the change meets the preset redundancy standard is that the preset redundancy standard is met, and to use the pole set obtained after removal as the new current pole set, and return to the reconstruction module for iteration; if the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered key modal poles.

[0082] From the above Figure 2 As can be seen from the example of the structural modal pole screening device, on the one hand, this application does not rely on the subjective interpretation of the steady-state diagram by engineers or fixed geometric thresholds. Instead, it removes a pole from the current pole set to form a sub-pole set, reconstructs the frequency response function based on the sub-pole set, and calculates the change in fitting quality caused by removing the pole. A calculable quantitative index reflecting the contribution of each pole to the overall data fitting is defined. This quantitative index is directly derived from the data itself, providing an objective and unified standard for measuring the importance of poles, thus avoiding inconsistencies and subjective biases caused by manual screening. On the other hand, through a closed-loop process of identifying and judging candidate poles based on changes and iteratively eliminating and returning, this application achieves automatic identification and elimination of redundant poles. This process does not require manual intervention in each step of the decision-making; the system can automatically perform evaluation and judgment. The process of breaking down and updating operations until the termination condition is met not only significantly improves the screening efficiency, but more importantly, for the same set of data, the technical solution of this application produces the same screening results every time it runs, ensuring the consistency and repeatability of the output. Thirdly, the "redundancy standard" used in the technical solution of this application to determine whether the change in value meets the preset redundancy standard can be dynamically adjusted based on the characteristics of the current dataset, rather than a globally fixed value. The iterative process allows the screening benchmark (i.e., the baseline fit quality index) to be dynamically updated as unimportant poles are removed. This means that the evaluation of the remaining poles is carried out under a continuously purified reference system, enabling the screening standard to adapt to the actual distribution and quality of poles in the current dataset, thereby more accurately distinguishing between critical poles and redundant poles, improving screening accuracy, and better adapting to different test objects and data conditions. In summary, the technical solution of this application achieves objective and efficient modal parameter screening by quantitatively evaluating the impact of each pole on data fitting and automatically iteratively removing redundant poles.

[0083] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. For example... Figure 3As shown, the electronic device 3 in this embodiment mainly includes: a processor 30, a memory 31, and a computer program 32 stored in the memory 31 and executable on the processor 30, such as a program for a structural modal pole selection method. When the processor 30 executes the computer program 32, it implements the steps described in the above-described structural modal pole selection method embodiment, for example... Figure 1 Steps S1 to S5 are shown. Alternatively, when processor 30 executes computer program 32, it implements the functions of each module / unit in the above-described device embodiments, for example... Figure 2 The functions of the acquisition module 201, reconstruction module 202, evaluation module 203, judgment module 204, and iteration module 205 are shown.

[0084] For example, the computer program 32 of the structural modal pole selection method mainly includes: obtaining the frequency response function of the structure to be analyzed, and identifying an initial set of modal poles based on the frequency response function; reconstructing the frequency response function based on all poles in the initial set of modal poles, and calculating the baseline fitting quality index under the current set of poles; for each pole in the current set of poles, performing the following importance evaluation operation: removing the pole from the current set of poles to form a sub-pole set, reconstructing the frequency response function based on the sub-pole set, and calculating the importance index resulting from removing the pole. The fitting quality change is determined by the following steps: Based on the fitting quality change of each pole obtained in step S3, the candidate pole with the least impact on the current fitting quality is identified, and it is determined whether its change meets the preset redundancy standard. If the determination result of step S4 is that the preset redundancy standard is met, the candidate pole is removed from the current pole set, and the pole set obtained after removal is used as the new current pole set, returning to step S2 for iteration. If the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered key modal pole. The computer program 32 can be divided into one or more modules / units, which are stored in the memory 31 and executed by the processor 30 to complete this application. One or more modules / units can be a series of computer program instruction segments capable of performing specific functions, which are used to describe the execution process of the computer program 32 in the electronic device 3. For example, computer program 32 can be divided into the functions of acquisition module 201, reconstruction module 202, evaluation module 203, judgment module 204, and iteration module 205 (a module in the virtual device). The specific functions of each module are as follows: Acquisition module 201 is used to acquire the frequency response function of the structure to be analyzed and identify the initial set of modal poles based on the frequency response function; Reconstruction module 202 is used to reconstruct the frequency response function based on all poles in the initial set of modal poles and calculate the baseline fitting quality index under the current set of poles; Evaluation module 203 is used to perform the following importance evaluation operation for each pole in the current set of poles: remove the pole from the current set of poles to form a sub-pole set. The process involves several steps: First, the frequency response function is reconstructed based on the set of sub-poles, and the change in fitting quality caused by removing a pole is calculated. Second, a judgment module 204 identifies candidate poles with the least impact on the current fitting quality based on the change in fitting quality corresponding to each pole, and determines whether their change satisfies a preset redundancy criterion. Third, an iteration module 205 removes candidate poles from the current pole set if the result of judging whether their change satisfies the preset redundancy criterion is met, and uses the resulting set of poles as the new current pole set, returning to the reconstruction module for iteration. If the preset redundancy criterion is not met, the iteration is terminated, and the current pole set is output as the filtered key modal poles.

[0085] Electronic device 3 may include, but is not limited to, processor 30 and memory 31. Those skilled in the art will understand that... Figure 3 This is merely an example of electronic device 3 and does not constitute a limitation on electronic device 3. It may include more or fewer components than shown, or combine certain components, or different components. For example, electronic device may also include input / output devices, network access devices, buses, etc.

[0086] The processor 30 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0087] The memory 31 can be an internal storage unit of the electronic device 3, such as a hard disk or RAM. The memory 31 can also be an external storage device of the electronic device 3, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory 31 can include both internal and external storage units of the electronic device 3. The memory 31 is used to store computer programs and other programs and data required by the electronic device. The memory 31 can also be used to temporarily store data that has been output or will be output.

[0088] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed. That is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above-described device can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0089] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0090] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0091] In the embodiments provided in this application, it should be understood that the disclosed devices / electronic devices and methods can be implemented in other ways. For example, the device / electronic device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0092] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0093] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0094] If integrated modules / units are implemented as software functional units and sold or used as independent products, they can be stored in a storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program for the structural modal pole screening method can be stored in a storage medium. When executed by a processor, this computer program can implement the steps of the various method embodiments described above, namely, obtaining the frequency response function of the structure to be analyzed and identifying an initial set of modal poles based on the frequency response function; reconstructing the frequency response function based on all poles in the initial set of modal poles and calculating the baseline fitting quality index under the current set of poles; and performing the following importance evaluation operation for each pole in the current set of poles: from the current set of poles... The process involves removing a pole to form a sub-pole set, reconstructing the frequency response function based on this sub-pole set, and calculating the change in fitting quality caused by removing the pole. Based on the changes in fitting quality for each pole obtained in step S3, candidate poles with the least impact on the current fitting quality are identified, and their changes are assessed to determine if they meet a preset redundancy criterion. If the result of step S4 indicates that the preset redundancy criterion is met, the candidate pole is removed from the current pole set, and the resulting set of poles is used as the new current pole set. The process then returns to step S2 for iteration. If the preset redundancy criterion is not met, the iteration terminates, and the current pole set is output as the selected key modal poles. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate form. Storage media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the contents of storage media can be appropriately added to or removed according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, storage media may not include electrical carrier signals and telecommunication signals.

[0095] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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 of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application. The specific embodiments described above further illustrate the purpose, technical solutions, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the protection scope of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A structural modal pole selection method, characterized in that, The method includes: Step S1: Obtain the frequency response function of the structure to be analyzed, and identify the initial set of modal poles based on the frequency response function; Step S2: Based on all poles in the initial modal pole set, reconstruct the frequency response function and calculate the baseline fitting quality index under the current pole set; Step S3: For each pole in the current pole set, perform the following importance evaluation operation: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole; Step S4: Based on the change in fitting quality corresponding to each pole obtained in step S3, identify the candidate pole that has the least impact on the current fitting quality, and determine whether its change meets the preset redundancy standard. Step S5: If the judgment result of step S4 meets the preset redundancy standard, the candidate poles are removed from the current pole set, and the pole set obtained after removal is used as the new current pole set. The process is then returned to step S2 for iteration. If the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered critical modal poles.

2. The structural modal pole selection method according to claim 1, characterized in that, The process of reconstructing the frequency response function based on all poles in the initial modal pole set and calculating the baseline fitting quality index under the current pole set includes: Step S21: Based on the current set of poles, use the frequency domain least squares method to solve for the residues corresponding to each pole, so as to reconstruct the frequency response function and obtain the reconstructed frequency response function; Step S22: Calculate the average correlation between the reconstructed frequency response function and the frequency response function obtained in step S1 on multiple pairs of response points and excitation points, and use it as the first fitting quality index; Step S23: Calculate the average least squares deviation between the reconstructed frequency response function and the frequency response function obtained in step S1 on multiple pairs of response points and excitation points, and use it as the second fitting quality index.

3. The structural modal pole selection method according to claim 1, characterized in that, The importance assessment operation performed in step S3 includes using parallel computing to simultaneously perform the operations of forming a sub-pole set, reconstructing, and calculating the change in fitting quality for multiple poles in the current pole set.

4. The structural modal pole selection method according to claim 1, characterized in that, Before the first execution of step S2, a dynamic result record table is initialized, and each time step S5 is executed to remove candidate poles, the parameters of the removed poles and their corresponding changes in fitting quality are added to the dynamic result record table in real time. The dynamic result record table supports real-time querying and tracing of the filtering history during the iteration process.

5. The structural modal pole selection method according to claim 1, characterized in that, In step S5, if it is determined that the preset redundancy standard is met, then after removing the candidate poles and before returning to step S2, the method further includes: updating the baseline fitting quality index, and setting the fitting quality index corresponding to the set of remaining poles after removing the candidate poles as the new baseline fitting quality index. Step S5 also includes the following convergence determination step: Step S52: Monitor the sum of the changes in fitting quality of the candidate poles that have been eliminated in multiple consecutive iterations; Step S53: If the sum of the changes in the fitting quality is lower than a convergence threshold, the iteration is terminated early, and the current set of poles is output.

6. The structural modal pole selection method according to claim 1, characterized in that, After outputting the filtered critical modal poles in step S5, the following modal model verification steps are also included: Step S141: Based on the key modal poles and their final determined residues, construct a complete structural modal model; Step S142: Evaluate the prediction accuracy of the structural modal model on a different set of test frequency response functions than those used in step S1. If the accuracy meets the standard, the validity of the key modal poles is confirmed.

7. The structural modal pole selection method according to claim 1, characterized in that, The reconstruction of the frequency response function based on all poles in the initial set of modal poles includes: solving the normal equations in the frequency domain least squares method using a singular value decomposition algorithm to numerically and stably determine the residues corresponding to each pole.

8. A structural modal pole selection device, characterized in that, The device includes: The acquisition module is used to acquire the frequency response function of the structure to be analyzed, and to identify the initial set of modal poles based on the frequency response function; The reconstruction module is used to reconstruct the frequency response function based on all poles in the initial modal pole set, and to calculate the baseline fitting quality index under the current pole set. The evaluation module is used to perform the following importance evaluation operation for each pole in the current pole set: remove the pole from the current pole set to form a sub-pole set, reconstruct the frequency response function based on the sub-pole set, and calculate the change in fitting quality caused by removing the pole; The judgment module is used to identify the candidate poles that have the least impact on the current fitting quality based on the change in fitting quality corresponding to each pole, and to determine whether the change in its change meets the preset redundancy standard. The iteration module is used to remove the candidate poles from the current pole set if the result of judging whether the change amount meets the preset redundancy standard is that the preset redundancy standard is met, and use the pole set obtained after removal as the new current pole set, and return to the reconstruction module for iteration; if the preset redundancy standard is not met, the iteration is terminated, and the current pole set is output as the filtered key modal poles.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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