Adaptive determination method and device of modal order in structural vibration test and storage medium

Abstract

This application relates to the field of structural dynamics testing and provides an adaptive method, apparatus, and storage medium for determining the modal order in structural vibration testing. The method includes: acquiring complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; extracting modal parameters and synthesizing a fitted frequency response function based on a set initial modal order; calculating two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation; increasing the modal order in a step-by-step manner and repeating the above steps; evaluating the improvement in modal fitting effect based on two consecutive iterative calculations; jointly determining whether the extraction of modal parameters has reached saturation convergence based on the absolute values ​​of the two technical indicators and the corresponding differences in directional increments between adjacent orders; if so, stopping the order increment and outputting the current order as the optimal modal order for accurate identification of modal parameters.

Description

Technical Field

[0001] This application relates to the field of structural dynamics testing, and in particular to an adaptive method, apparatus and storage medium for determining the modal order in structural vibration testing. Background Technology

[0002] Modal analysis is one of the core technologies in structural dynamics. It identifies modal parameters such as the natural frequencies, damping ratios, and mode shapes of a structure by processing data such as frequency response functions obtained from excitation and sensing tests. These parameters are crucial for evaluating the dynamic characteristics of a structure, diagnosing faults, revising models, and predicting responses. In practical engineering applications, curve fitting based on the frequency response function is the mainstream method for modal parameter identification. Its accuracy and reliability largely depend on a key premise: whether the assumed modal order is appropriate.

[0003] Currently, methods for determining modal order mainly rely on human experience and interpretation of criteria. Engineers typically make judgments based on steady-state plots, observing the stability of system poles as the assumed modal order increases. Poles with minimal changes in frequency and damping ratio across multiple consecutive orders are considered stable physical modes. However, this method has the following significant shortcomings in practice: 1) It is highly dependent on the professional experience of the operators; different analysts may choose different orders for the same set of data, leading to subjective and inconsistent identification results; 2) Manually observing the steady-state plot and judging convergence is a tedious and time-consuming process, especially when there are many data channels and dense modes, resulting in low efficiency and difficulty in automating the analysis process; 3) Relying solely on the steady-state plot for judgment sometimes makes it difficult to find a precise balance between underfitting and overfitting, potentially missing true modes or introducing spurious modes. Summary of the Invention

[0004] This application provides an adaptive method, device, and storage medium for determining the modal order in structural vibration testing. By combining two indices and analyzing the incremental difference between adjacent orders, the optimal modal order is determined automatically and accurately, thereby improving the efficiency and objectivity of modal analysis.

[0005] On the one hand, this application provides an adaptive method for determining the modal order in structural vibration testing, the method comprising: Obtain complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; An initial modal order is set, and the measured frequency response function is curve-fitted based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; Two technical indicators for comprehensively evaluating the fitting quality are calculated: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. The modal order is increased in a step-by-step manner, and the modal parameter extraction, curve fitting, and calculation of the two technical indicators are repeated. Based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, the difference of the directional increment between adjacent orders is calculated to evaluate the improvement of the modal fitting effect. Based on the absolute values ​​of the two technical indicators and the corresponding differences in the directional increments of adjacent orders, it is jointly determined whether the extraction of modal parameters has reached a saturated convergence state. If it is determined that the saturation convergence state has been reached, the order increment is stopped, and the current order is output as the optimal modal order for accurate identification of modal parameters.

[0006] On the other hand, this application provides an adaptive determination device for modal order in structural vibration testing, the device comprising: The acquisition module is used to acquire complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; The extraction module is used to set the initial modal order and perform curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; The calculation module is used to calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. The iterative module is used to increase the modal order in a step-by-step manner, and repeatedly perform modal parameter extraction, curve fitting, and calculation of the two technical indicators; The evaluation module is used to calculate the difference of the directional increment between adjacent orders based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, so as to evaluate the improvement of the modal fitting effect. The joint judgment module is used to jointly judge whether the extraction of modal parameters has reached a saturated convergence state based on the absolute values ​​of the two technical indicators and the corresponding difference in the directional increments of adjacent orders. The processing module is used to stop increasing the order if it determines that the saturation convergence state has been reached, and outputs the current order as the optimal mode order for accurate identification of mode parameters.

[0007] 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 adaptive determination method for modal order in the above-described structural vibration test.

[0008] Fourthly, this application provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the technical solution of the adaptive determination method for modal order in the above-described structural vibration test.

[0009] As can be seen from the technical solution provided in this application, on the one hand, by calculating the two complementary technical indicators—the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation—a comprehensive and integrated evaluation of the fitting quality can be achieved. The complex frequency response correlation coefficient measures the consistency between the fitted curve and the measured curve in amplitude and phase from the perspective of morphological similarity, while the normalized least squares complex frequency response deviation quantifies the overall fitting error from the perspective of error energy. The combined use of these two indicators overcomes the potential bias of a single criterion, providing a more sufficient and reliable basis for judging the quality of the fit, thus laying a solid foundation for accurately determining the modal order. On the other hand, by evaluating whether the improvement rate of these two key indicators tends to level off (i.e., the incremental difference approaches zero) as the modal order increases, it is possible to effectively determine whether the fitting process has reached saturation. This allows the method to intelligently distinguish between "still needing improvement." In contrast to the two scenarios of "insignificant improvement," this approach achieves an automatic balance between fitting accuracy and model simplicity. It avoids both underfitting due to premature iteration termination and overfitting due to unlimited increases in the modal order. Thirdly, the entire process integrates initial order setting, iterative fitting, index calculation, difference analysis, convergence judgment, and order output into a coherent automated closed loop. Users only need to provide measured data and set broad initial parameters and thresholds; the method automatically performs the search and judgment until it outputs the optimal modal order. This significantly reduces reliance on operator expertise and manual intervention, freeing analysts from tedious steady-state diagram observation and experience-based judgment. It not only greatly improves the efficiency of modal parameter identification but also effectively enhances the objectivity of the analysis process and the repeatability of the results, providing key technical support for the automation and standardization of structural vibration testing and analysis. In summary, the technical solution of this application, through dual-index combination and adjacent-order incremental difference analysis, achieves automated and accurate determination of the optimal modal order, thereby improving the efficiency and objectivity of modal analysis. Attached Figure Description

[0010] 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.

[0011] Figure 1 This is a flowchart of the adaptive determination method for modal order in structural vibration testing provided in the embodiments of this application; Figure 2 This is a schematic diagram of the structure of the adaptive determination device for modal order in structural vibration testing 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

[0012] 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.

[0013] 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.

[0014] For ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale.

[0015] Currently, methods for determining modal order mainly rely on human experience and interpretation of criteria. Engineers typically make judgments based on steady-state plots, observing the stability of system poles as the assumed modal order increases. Poles with minimal changes in frequency and damping ratio across multiple consecutive orders are considered stable physical modes. However, this method has the following significant shortcomings in practice: 1) It heavily relies on the professional experience of the operators; different analysts may choose different orders for the same set of data, leading to subjective and inconsistent identification results; 2) Manually observing steady-state plots and determining convergence is a tedious and time-consuming process, especially when there are many data channels and dense modes, resulting in low efficiency and difficulty in automating the analysis process; 3) Relying solely on steady-state plots sometimes makes it difficult to find a precise balance between underfitting and overfitting, potentially missing true modes or introducing spurious modes. To improve the automation and objectivity of modal parameter identification, the industry needs a method that can adaptively and accurately determine the optimal modal order to overcome over-reliance on human experience and improve analysis efficiency and consistency of results.

[0016] To address the aforementioned problems in the prior art, this application proposes an adaptive method for determining the modal order in structural vibration testing, the flowchart of which is attached. Figure 1 As shown, it mainly includes steps S1 to S7, which are detailed below: Step S1: Obtain complex data of the measured frequency response function of the structure obtained through excitation and sensing tests.

[0017] In structural dynamics testing, by arranging one or more excitation points (inputs) and multiple response sensors (outputs) on the structure under test, and applying a known excitation signal, such as hammer impact or frequency sweep of a vibrator, a set of frequency response functions (FRFs) can be measured. Each input-output channel corresponds to one FRF. The data processed in this application are complex data of these measured FRFs at discrete sampling points within a specified frequency range. Complex data refers to FRF values ​​at each frequency point that simultaneously contain amplitude (the amplitude reflects the ratio of the response to the excitation amplitude) and phase (the phase reflects the delay of the response relative to the excitation) information, usually expressed in the form of real and imaginary parts, or amplitude and phase angle. The acquired data can be a two-dimensional complex matrix. Its rows correspond to the output degrees of freedom, and its columns correspond to the input degrees of freedom. Each element is a frequency. f The complex FRF value at the specified location. Typically, before entering the processing flow of this method, the raw test data can be preprocessed as necessary, such as averaging, windowing, smoothing, etc., to improve the signal-to-noise ratio.

[0018] Step S2: Set the initial modal order and perform curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function.

[0019] After obtaining the measured FRF data, it is necessary to start searching for the optimal modal order from a reasonable starting point. Setting the initial modal order can be based on simple heuristics, such as observing the number of resonance peaks in the measured FRF amplitude-frequency curve. For a given FRF frequency band with [number of resonance peaks], [further details on this heuristic would be needed]. For structures with obvious resonance peaks, the initial order can be set. ,in, k It is an empirical coefficient (usually) This is used to account for a possible complex mode pair (conjugate pole) corresponding to each resonance peak, as well as possible repeated roots or local modes. A minimum order of not less than 1 is set. As a lower bound, the final initial order is taken as The purpose of step S2 is to quickly start the iteration process and avoid starting with unrealistic orders that are too low or too high.

[0020] As an embodiment of this application, setting the initial modal order can be achieved through steps S2.1 to S2.3, as detailed below.

[0021] Step S2.1: Automatically or manually identify the resonance peaks of the amplitude-frequency curve of the measured frequency response function, and count the number of resonance peaks in the preset frequency band.

[0022] Local maxima (resonance peaks) on the amplitude-frequency curve can be identified using automatic peak detection algorithms (such as finding points where the first derivative is zero and the second derivative is negative). Users can also manually specify or correct these peaks.

[0023] Step S2.2: Multiply the number of resonance peaks obtained from statistics by an amplification factor preset based on experience to obtain an estimated initial order value.

[0024] For example, if five distinct resonance peaks are identified, and the amplification factor is set to 2, then the estimated initial order is 10. This factor is used to account for a physical mode that typically corresponds to a pair of conjugate complex poles (hence the factor ≥ 2), and to allow for possible repeated roots or computational modes.

[0025] Step S2.3: Compare the estimated initial order value with a minimum order value that guarantees the start of the algorithm, and take the larger of the two as the starting order of the iteration.

[0026] Setting a minimum order (e.g., 2 or 4) ensures that the algorithm starts with an order that has basic modeling capabilities, avoiding iterations from completely unreasonable low orders.

[0027] Set the initial ordern Then, curve fitting is performed on the measured frequency response function based on this order. This step involves calling a modal parameter identification algorithm. In one specific implementation, a least-squares-based complex frequency domain fitting algorithm, such as PolyMAX (pLSCF) or the orthogonal polynomial method, can be used. The input to this algorithm is the measured FRF matrix, i.e., the complex data of the measured frequency response function. and the specified modal order n Its internal execution process is as follows: by solving a least-squares problem with model parameters (polynomial coefficients) as variables, the theoretical model is made to optimally approximate the measured data in the least-squares sense. After solving, the algorithm outputs the result corresponding to the current order. n The preliminary estimation of the modal parameters mainly includes the system poles (containing natural frequency and damping ratio information) and residues (related to the mode shape).

[0028] Subsequently, using these extracted modal parameters, a fitted frequency response function can be synthesized based on modal model theory. Synthetic It is a comparison with actual measurement A complex matrix of the same dimension represents the theoretically predicted frequency response function under the current assumed n-order modal model. Thus, we have obtained two core sets of data for subsequent comparisons: the complex data of the measured frequency response function (i.e.,...) ) and the complex data of the fitted frequency response function at the current order (i.e. ).

[0029] As one embodiment of this application, curve fitting of the measured data based on the current modal order is achieved by calling a preset modal parameter identification algorithm module, which is configured to perform the following steps S2.4 to S2.6: Step S2.4: Receive the measured frequency response matrix and the specified modal order.

[0030] Step S2.5: Use a least-squares-based complex frequency domain fitting algorithm to solve for the system poles and residues of the corresponding order.

[0031] For example, the core of this module could be the PolyMAX (pLSCF) algorithm, which stably calculates the system poles by establishing a rational fractional polynomial model and solving the linear least squares problem in the frequency domain.

[0032] Step S2.6: Reconstruct the complete fitted frequency response function matrix using the system poles and residues.

[0033] Based on the principle of modal superposition, using the identified poles and residues, through the formula... (in, s = jw , For the k-th order pole, (The residue matrix) is used to calculate the fitted FRF at all frequency points.

[0034] Step S3: Calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function.

[0035] To establish an objective and comprehensive quantitative standard to replace human observation and automatically evaluate the "goodness" of frequency response function curve fitting, providing a core basis for determining whether to stop increasing the modal order, one existing approach is a single-index criterion method, which uses only the correlation coefficient or only the error deviation for judgment. However, this approach has the drawback that using only the correlation coefficient may be insensitive to amplitude errors, resulting in a "similar appearance but not a true match," while using only the error deviation may ignore phase information and fail to adequately assess the overall consistency of the form. Both are prone to misjudgment or require the use of other complex criteria, making it impossible to form a simple and effective automated rule. Another existing approach relies on manual interpretation of steady-state diagrams, that is, without calculating such global indicators, it completely relies on engineers to observe the steady-state diagrams of frequency and damping ratio changes with the order to judge pole stability. This approach is highly dependent on expert experience, highly subjective, inefficient, and yields inconsistent results, making it completely impossible to automate the process. Therefore, the technical solution adopted in this application is to calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. This solution, by simultaneously introducing the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation—two complementary global indicators from the perspectives of "morphological similarity" and "error level," respectively—constructs a two-dimensional, objective fitting quality evaluation system. This system simulates and surpasses the human brain's comprehensive judgment logic of "good fitting," providing a quantifiable factual basis necessary for the entire method's automatic decision-making.

[0036] In the above embodiments, the full-channel average complex frequency response correlation coefficient is intended to measure the complex data of the fitted curve, i.e., the fitted frequency response function. The complex data of the measured curve, i.e., the measured frequency response function. Overall morphological similarity in the complex domain (i.e., considering both amplitude and phase). The closer the correlation coefficient is to 1, the more consistent the two are in terms of variation trend and phase relationship. Specifically, as an embodiment of this application, the full-channel average complex frequency response correlation coefficient can be achieved through steps S3.1 and S3.2, which are described in detail below.

[0037] Step S3.1: By processing the measured and fitted complex data sequences of each independent input-output channel pair, an intermediate value characterizing the fitting similarity of that channel is obtained.

[0038] Specifically, for the first i The output and the first j One input channel will transmit the measured complex number sequence. and fitted complex sequences Treat it as a vector. Calculate the multiple correlation coefficient for this channel. As an intermediate value. The calculation can be achieved without relying on specific formula names, but through the following process: consider the projection relationship between two complex sequences, the value of which reflects the directional consistency of the two sequences in complex space. A value close to 1... This means that for this specific measurement channel, the fitted model reproduces the amplitude and phase characteristics of the measured response very well.

[0039] Step S3.2: Combine the median values ​​of all channels and obtain the full-channel average complex frequency response correlation coefficient by taking the arithmetic mean, which reflects the consistency of the global fitting shape.

[0040] Since structural testing typically involves multiple measurement points, in order to obtain a single index representing the overall consistency of the fitted morphology, all... The single-channel complex correlation coefficient calculated from each effective input-output channel. Perform the arithmetic mean:

[0041] Corr(n) is the average complex frequency response correlation coefficient across all channels. It overcomes the limitations that may arise from observing only individual channels and reflects the average morphological fit of the model across the entire structural space.

[0042] The technical solutions exemplified in steps S3.1 and S3.2 above use an arithmetic mean, implicitly assuming that the data quality of all channels is equally important. However, in actual testing, the signal-to-noise ratio or response energy at different measurement points may differ significantly, and the fitting evaluation of low-quality channels may interfere with the overall judgment. Therefore, as another embodiment of this application, the average complex frequency response correlation coefficient of all channels can also be: assigning a weighting coefficient to each input-output channel based on the signal-to-noise ratio or energy of the measured data; for each channel, calculating the complex correlation coefficient between its fitting and the measured complex data sequence as the median value of that channel; and weighting the median values ​​of all channels according to their corresponding weighting coefficients to obtain the average complex frequency response correlation coefficient of all channels. Compared to the technical solutions exemplified in steps S3.1 and S3.2, this solution can improve the robustness and representativeness of the overall evaluation index. This is because, when faced with common engineering problems such as partial sensor failure, uneven excitation, or strong local noise, this solution can automatically focus on reliable data, making the full-channel averaging operation more intelligent and the resulting convergence judgment more reliable. This improves the robustness and environmental adaptability of the entire adaptive method and reduces the negative impact of unreliable data on the global judgment.

[0043] In the above embodiments, the full-channel average normalized least squares complex frequency response deviation aims to quantify the overall error energy between the fitted curve and the measured curve. However, in order to make it comparable and avoid being dominated by the absolute amplitude, this application adopts normalization processing. Specifically, as an embodiment of this application, the full-channel average normalized least squares complex frequency response deviation can be achieved through steps S3.3 and S3.4, which are detailed below.

[0044] Step S3.3: For each independent input-output channel pair, calculate a relative value reflecting the local fitting error of that channel based on its fitted and measured complex data sequence.

[0045] For the i-th output and j-th input channels, calculate their normalized least squares bias. The basic idea is: first, calculate the sum of squares of the residuals at all points across the entire frequency range between the fitted curve and the measured curve (i.e., the error energy); then, normalize this error energy to the energy of the fitted curve itself. This yields... It is a dimensionless relative error value; the smaller it is, the smaller the fitting deviation of the channel.

[0046] Step S3.4: Average the relative values ​​calculated for all channels to generate the full-channel average normalized least squares complex frequency response deviation used to quantify the overall fitting error level.

[0047] Similarly, to obtain the global error level, for all channels... Calculate the arithmetic mean:

[0048] LS_Dev(n) is the average normalized least squares complex frequency response deviation across all channels. It objectively reflects the average relative error across the entire structure when the current-order model interprets measured data.

[0049] By simultaneously calculating and focusing on Corr(n) and LS_Dev(n), this application constructs a two-dimensional evaluation system. Using either metric alone may have limitations: a high correlation coefficient may be accompanied by a significant absolute error, and a small-biased curve may exhibit systematic phase bias. Combining the two allows for a more comprehensive and robust assessment of the fitting quality, providing a solid foundation for determining whether the model is "good enough." This is the primary key technology for achieving subsequent automated intelligent judgment.

[0050] Furthermore, considering that when normalizing using the total energy of the fitted sequence itself, if the fitting quality is poor, the energy of the fitted sequence itself may be distorted, leading to an unstable normalization benchmark. Therefore, a better calculation scheme for the full-channel average normalized least squares complex frequency response deviation could be: for each input-output channel, calculate the complex residuals of its fitted and measured complex data sequences at all frequency points; obtain the magnitude sequence of the measured complex data sequence for that channel, and calculate its average or median as the characteristic amplitude of that channel; divide the sum of the squares of the magnitudes of the complex residuals at all frequency points of that channel by the product of the square of the characteristic amplitude and the number of frequency points to obtain the normalized deviation value of that channel; average the normalized deviation values ​​calculated for all channels to generate the full-channel average normalized least squares complex frequency response deviation. This scheme extracts the characteristic amplitude of the measured data as the normalization denominator, and this benchmark is completely independent of the fitting result, avoiding the self-masking problem caused by a poor fitting model. At the same time, dividing by the number of frequency points normalizes the measurement bandwidth, making the results more comparable. In other words, this scheme makes the normalized deviation value more sensitive to the poor fitting state in the early stage of fitting, and can reveal the problem of underfitting earlier and more accurately. At the same time, its normalization benchmark is stable, ensuring the comparability of deviation values ​​between different channels and different tests. This is equivalent to providing a clearer and more consistent "error scale" for subsequent convergence judgment, enhancing the universality and judgment consistency of the algorithm in different scenarios.

[0051] Step S4: Increase the modal order in a step-by-step manner, and repeat the modal parameter extraction, curve fitting, and calculation of the two technical indicators.

[0052] Obtaining the initial order nAfter determining the fitting quality and corresponding metrics, this application enters an iterative search process. The basic logic is: since a single order cannot determine whether it is optimal, higher orders are systematically tried, and the fitting quality is observed how it changes. Increasing the modal order in a step-by-step manner typically involves increasing the current order... n Increasing a fixed step size (usually 1 or 2, representing the addition of a pair or a pole) yields a new hypothesis order. Then, for this new order... Repeat steps S2 and S3, focusing on the core operations: that is, based on the order. Modal parameters were extracted and curves were fitted again, and the corresponding full-channel average complex frequency response correlation coefficient Corr(n') and full-channel average normalized least squares complex frequency response deviation LS_Dev(n') were calculated.

[0053] This iterative process simulates the process of engineers manually increasing the order of the steady-state plot hypothesis, but the key difference is that each iteration automatically generates quantitative, global fit quality assessment data (Corr and LS_Dev), rather than relying solely on qualitative observations of pole stability. These index values, arranged in order of order, constitute the "data trend line" for subsequent intelligent analysis.

[0054] Step S5: Based on the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response obtained from two consecutive iterations, calculate the difference of the directional increment between adjacent orders to evaluate the improvement of the modal fitting effect.

[0055] Simply focusing on the "static" level of fitting quality at each order (the absolute values ​​of Corr(n) and LS_Dev(n)) is insufficient. In engineering practice, a common challenge is whether to continue increasing the order after the fitting metrics reach a certain "good" value. In other words, how to dynamically and intelligently determine whether the fitting process has reached a saturation point—that is, whether the improvement brought by further increasing model complexity is negligible—and thus avoid meaningless overfitting calculations has always been a concern in the industry. One existing technical solution is the static threshold method, which sets fixed target thresholds only for the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation in the above embodiment. For example, the full-channel average complex frequency response correlation coefficient > 0.95 and the full-channel average normalized least squares complex frequency response deviation < 0.05, stopping when these values ​​are reached. However, this approach cannot distinguish between barely meeting the target and fully saturated states. For complex structures, the fit may still have significant room for improvement after reaching a fixed threshold, leading to underfitting. Conversely, simple structures may easily meet the target, but further computation offers no benefit, resulting in wasted computational resources and a lack of marginal benefit analysis capabilities. Another existing approach is to preset a maximum order, i.e., to pre-set a sufficiently large safety order upper limit and forcibly stop iterations at this point. This approach is actually very blind and inefficient. For simple models, it will cause a lot of overfitting computations, while for complex models, the preset upper limit may still be insufficient, completely lacking adaptability.

[0056] In view of the shortcomings of the prior art, this application introduces dynamic trend analysis. Specifically, based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, the difference in directional increments between adjacent orders is calculated to evaluate the improvement in modal fitting. This approach no longer merely focuses on "what level" of the fitting quality is now, but rather intelligently focuses on "how fast the improvement is as the order increases." When the increment difference approaches zero, it indicates that the "marginal improvement effect" of increasing the order has tended to disappear, and the fitting has entered a plateau. This makes... Figure 1 The example method possesses the ability to sense saturation, thus achieving a dynamic and adaptive balance between fitting accuracy and model efficiency. This is the core intelligent logic for achieving adaptive determinism rather than blind iteration or pre-set termination, crucial for avoiding overfitting and improving computational efficiency. Calculating the difference in directional increments between adjacent orders is central to this analysis. Specifically: For the correlation coefficient of the average complex frequency response across all channels, calculate This reflects the improvement in global morphological similarity as the order increases from n-1 to n.

[0057] For the average normalized least squares complex frequency response deviation of the entire channel, calculate This reflects the reduction in global error resulting from increasing the order.

[0058] These directional incremental differences are essentially the first derivative or marginal benefit of the fit quality as a function of model complexity. They are used to evaluate the improvement in modal fit: like It is a significantly positive value and If the result is a significant positive value, it indicates that increasing the order n brings about a significant improvement in the fitting quality, and the improvement is obvious, so further exploration is warranted.

[0059] like and If all these values ​​become very small (close to zero), it means that the improvement from further increasing the order is negligible, and the fitting effect has entered a plateau or saturation region. At this point, further increasing the order is likely to waste computational resources trying to fit random noise in the data, leading to overfitting.

[0060] Through this step, the method of this application obtains key dynamic information for determining when to stop iterating, thereby possessing the potential ability to distinguish between "necessary improvement" and "overfitting".

[0061] Step S6: Based on the absolute values ​​of the two technical indicators and the corresponding differences in directional increments between adjacent orders, jointly determine whether the extraction of modal parameters has reached a saturated convergence state.

[0062] To integrate static fitting quality benchmarks with dynamic improvement trend information, forming an executable and unambiguous automated convergence determination rule to ultimately replace manual decision-making, this application uses the absolute values ​​of two technical indicators and their corresponding adjacent order directional increment differences to jointly determine whether the extraction of modal parameters has reached saturation convergence. Step S6 essentially defines the determination logic that "jointly" integrates static benchmarks and dynamic trends. It requires that both conditions be met simultaneously: "fitting quality is good enough" (meaning the absolute value meets the standard) and "fitting has no significant improvement" (meaning the increment difference approaches zero) for convergence to be determined. This ensures that the optimal order of the output simultaneously meets both accuracy requirements and efficiency, representing an optimized and robust engineering decision. Step S6 guides all the aforementioned calculations and analyses to a crucial step of a clear and reliable technical action (stopping iteration and outputting), because joint judgment implies the simultaneous satisfaction of multiple conditions, simulating the comprehensive considerations an experienced engineer would make when observing the steady-state plot and the fitting curve.

[0063] As an embodiment of this application, the joint determination of whether the extraction of modal parameters has reached saturation convergence state based on the absolute values ​​of two technical indicators and their corresponding adjacent order directional increment differences can be achieved through the following steps S6.1 to S6.4, which are detailed below: Step S6.1: Perform the first qualification judgment: check whether the correlation coefficient of the full-channel average complex frequency response under the current order meets the preset standard for characterizing high similarity.

[0064] Step S6.1 ensures that the model's morphology is highly consistent with the measured data. For example, a standard can be set as follows: ( For example, the first preset threshold. =0.95 or higher), which is a "precision" threshold.

[0065] Step S6.2: Perform the second qualification judgment: check whether the average normalized least squares complex frequency response deviation of the full channel under the current order meets the maximum allowable error limit.

[0066] Step S6.2 ensures that the overall error level of the model has been controlled within an engineering-acceptable range. For example, an error limit can be set. ( For example, a second preset threshold. =0.05 or lower), which is an "error" threshold.

[0067] Step S6.3: Perform convergence determination: Check whether the difference between the adjacent order directional increments of the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response has stabilized, i.e., its change is below a small threshold indicating that the improvement is negligible.

[0068] Step S6.3 ensures that the fitting quality has stabilized, and further increasing the order yields minimal benefit. For example, a small threshold can be set. ,Require and Here, For a local minimum, for example, =0.001.

[0069] Step S6.4: When the first qualification judgment, the second qualification judgment, and the convergence judgment are all passed simultaneously, a preliminary signal indicating that the convergence state has been reached is generated.

[0070] The multi-condition joint judgment process exemplified in steps S6.1 to S6.4 above defines a "good" model as one that is sufficiently accurate at the absolute level (first and second qualification judgments) and has no significant improvement in marginal benefits (convergence judgment). Only when all three conditions are met can the extraction of modal parameters be considered to have reached saturated convergence. At this point, the current order n is considered a candidate "optimal order" that achieves a good balance between accuracy and efficiency.

[0071] As another embodiment of this application, the joint judgment of whether the extraction of modal parameters has reached saturation convergence state based on the absolute values ​​of two technical indicators and their corresponding adjacent order directional increment differences can also be achieved through a phased progressive judgment process, namely: First stage - rapid screening: check whether the correlation coefficient of the full channel average complex frequency response under the current order is greater than the first threshold, and whether the deviation of the full channel average normalized least squares complex frequency response is less than the second threshold. If not, it is directly judged as not converged and the iteration continues. If yes, it enters the second stage; Second stage - fine judgment: calculate the adjacent order directional increment differences of the two technical indicators (i.e., the correlation coefficient of the full channel average complex frequency response and the deviation of the full channel average normalized least squares complex frequency response); check whether the correlation coefficient of the full channel average complex frequency response is greater than the third threshold higher than the first threshold, and whether the deviation of the full channel average normalized least squares complex frequency response is less than the fourth threshold lower than the second threshold; at the same time, check whether the absolute values ​​of the two adjacent order directional increment differences are both less than a convergence threshold; when all the conditions of the second stage are met at the same time, a preliminary signal indicating that the convergence state has been reached is generated. Compared to the flat structure of multiple conditions being judged "simultaneously" in the examples of steps S6.1 to S6.4 above, this scheme is actually a phased and progressive judgment process. The first stage sets a relatively lenient threshold for rapid screening, which can eliminate a large number of obviously non-converged iterations in advance, greatly reducing unnecessary fine calculations. In the fine judgment stage, stricter thresholds are used (e.g., higher correlation coefficient requirements, lower bias requirements). This reflects the dynamic idea that "as the fitting deepens, the requirements should be continuously improved," so that the final convergence criterion not only looks at trend stability, but also requires to achieve higher absolute quality, thus potentially obtaining better fitting results than the original scheme. Therefore, without sacrificing the accuracy of the final judgment, this scheme significantly improves the overall algorithm's running efficiency (reducing the amount of computation) through process optimization. At the same time, the phased criteria make the convergence logic more hierarchical and engineering-logical, easier to understand and adjust.

[0072] Furthermore, to prevent premature termination caused by accidental random fluctuations in the data leading to a single iteration coincidentally meeting the conditions, this application may introduce a robustness enhancement mechanism. After generating the initial signal, the following steps are performed to verify the stability of the convergence state, including steps S6.5 and S6.6: Step S6.5: Maintain the incremental iteration of the modal order and continue to execute the multi-condition joint decision process.

[0073] The multi-condition joint determination process that is continuously executed here is the process exemplified in steps S6.1 to S6.4 above. It should be noted that after the initial signal is generated, it does not stop immediately, but continues to increment the order step by step, and observes whether the conditions can still be met in subsequent iterations.

[0074] Step S6.6: Record the number of times the initial signal is generated in each iteration, and when the number reaches the preset threshold of continuous stable number of times, finally confirm that the saturation convergence state has been reached.

[0075] For example, a threshold of K=5 consecutive stable iterations can be set. Convergence is only confirmed if, after the initial signal is generated, the next K iterations (corresponding to orders n+1, n+2, ..., n+K) also generate an initial signal. This ensures the reliability and robustness of the convergence state, effectively avoiding misjudgments caused by single-point fluctuations.

[0076] The technical solutions exemplified in steps S6.5 and S6.6 above introduce a delayed confirmation mechanism—a threshold for the number of consecutive stable iterations—to prevent the convergence from stopping immediately upon meeting the condition only once. Instead, it requires the convergence signal to appear continuously throughout a series of iterations. This significantly improves the robustness and anti-interference capability of the convergence determination, ensuring that the determined "optimal order" is based on a stable and reliable fitting platform, rather than a random fluctuation point, thereby greatly improving the reliability and accuracy of the final modal parameter identification results.

[0077] As another embodiment of this application, after generating the initial signal, an adaptive verification mechanism is also included. Specifically, after generating the initial signal, a required number of consecutive verifications, M, is dynamically determined based on the current correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response. The higher the fitting quality (higher correlation coefficient, lower deviation), the smaller the value of M can be. The process continues iterating and monitoring, and only when the initial signal can be generated in the next M consecutive iterations is the saturation convergence state finally confirmed. In this adaptive mechanism, the number of consecutive verifications, M, is no longer a fixed value, but a variable dynamically adjusted according to the current fitting quality. When the indicator shows a very good fit, the system has more "confidence" and can reduce the number of verifications to terminate quickly. When the indicator just barely meets the target, more caution is needed, and the number of verifications is increased. This mimics the flexibility of human expert judgment. In other words, this adaptive mechanism is an intelligent control strategy with "perception-decision" capabilities. It avoids the shortcomings of the "one-size-fits-all" strategy and can minimize unnecessary iterative calculations while ensuring the reliability of the results. As a result, it achieves better overall performance in terms of "computational efficiency and result reliability" than the fixed-number mechanism.

[0078] Step S7: If it is determined that the saturation convergence state has been reached, stop increasing the order and output the current order as the optimal mode order for accurate identification of mode parameters.

[0079] After the above joint judgment and stability verification, if it is finally confirmed that the saturation convergence state has been reached, the iterative search process terminates. The order increment stops, and the current order n that satisfies the convergence condition is officially output as the optimal mode order.

[0080] This optimal modal order is a key output that can be directly used to guide subsequent accurate modal parameter identification. For example, based on this optimal order, a final, high-precision modal parameter extraction algorithm (e.g., PolyMAX combined with least squares frequency domain method (LSFD) for residue estimation) can be run to obtain a reliable set of natural frequencies, damping ratios, and mode shapes based on the optimal complexity model. Thus, this application completes a fully automated process from raw test data to determining model complexity, laying a solid foundation for obtaining accurate modal parameters.

[0081] To enable those skilled in the art to accurately understand and implement this method, the following provides a more in-depth explanation of the specific calculation methods for the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation. For the full-channel average complex frequency response correlation coefficient, the calculation of its single-channel intermediate value (i.e., the complex correlation coefficient) can be achieved through the following steps S3.1a to S3.1d. The purpose is to obtain a scalar value that sensitively reflects the amplitude consistency of two complex sequences: Step S3.1a: Multiply and sum the conjugates of the fitted complex sequences of the input-output channels and the measured complex sequences.

[0082] This operation is mathematically equivalent to calculating the complex inner product of two complex sequences. The fitted sequence... With the measured sequence conjugate Multiply each element and then sum them up. This result is a complex number whose magnitude reflects the intensity of the "projection" of the two sequences in the complex domain.

[0083] Step S3.1b: Perform modulo squaring on the summation result to obtain a numerical value that reflects the projection relationship between the sequences.

[0084] Squaring the complex inner product obtained in the previous step after taking its modulus, we get... This step eliminates the phase of the complex inner product, resulting in a pure real number that represents the "energy" of the linear correlation between the fitted sequence and the measured sequence.

[0085] Step S3.1c: Calculate the sum of the energies of the fitted sequence and the measured sequence respectively.

[0086] Calculate the energy of the fitted sequence itself and the energy of the measured sequence itself These two values ​​represent the total energy of the fitted model and the measured data, respectively.

[0087] Step S3.1d: Scale the value reflecting the projection relationship between sequences with the product of the two energy sums to output an intermediate value between 0 and 1.

[0088] Finally, the multiple correlation coefficient of this channel is calculated as follows: .

[0089] The closer this value is to 1, the higher the amplitude-phase fit consistency of the channel. From a signal processing perspective, this formula calculates the coherence coefficients of two complex signals in the frequency domain after removing their respective DC components (e.g., processed). It considers both amplitude and phase information, making it a powerful tool for evaluating morphological similarity.

[0090] The calculation of the single-channel relative value (i.e., normalized deviation) of the full-channel average normalized least squares complex frequency response deviation aims to obtain a robust index that is insensitive to amplitude and focuses on the relative magnitude of the fitting error. This is specifically implemented as shown in steps S3.3a to S3.3d below: Step S3.3a: Calculate the complex residuals of the fitted complex sequence and the measured complex sequence at each frequency sampling point of the input-output channel point by point.

[0091] For each frequency point f ,calculate This complex residual contains information about both magnitude and phase errors.

[0092] Step S3.3b: Sum the squared magnitudes of the complex residuals at all frequency points to obtain the total fitting error energy of the input-output channels.

[0093] calculate This is the error objective function in the classical least squares sense, which quantifies the overall deviation between the fitted value and the measured value over the entire frequency band.

[0094] Step S3.3c: Calculate the total energy of the complex sequence fitted to the channel itself.

[0095] calculate As mentioned above.

[0096] Step S3.3d: Divide the total fitting error energy by the total energy of the fitted sequence itself to obtain the relative value. The normalized bias of this channel is:

[0097] The smaller this value, the smaller the fitting bias of that channel. Normalization is a key aspect of this application; it eliminates the differences in absolute error energy between different channels caused by variations in excitation magnitude and transmission path gain, allowing errors from different measurement points to be compared and averaged on a fair scale. This ensures that the full-channel average normalized least squares complex frequency response bias LS_Dev(n) truly reflects the relative level of the model error, rather than being dominated by the absolute amplitude of the data.

[0098] After outputting the optimal modal order, the following result visualization steps S7.1 and S7.2 are also included: Step S7.1: Based on all the identification results corresponding to the optimal modal order, automatically generate a steady-state diagram showing the change of frequency and damping ratio with the assumed order.

[0099] The system automatically plots a scatter plot showing the frequency and damping ratio of all identified poles as a function of order throughout the entire iteration process, from the initial order to the optimal order (or slightly higher).

[0100] Step S7.2: On the steady-state diagram, apply stability criteria to automatically filter and highlight stable poles that meet physical meaning. Stability criteria include the fluctuation range limits of frequency and damping ratio under multiple consecutive assumed orders.

[0101] After obtaining the optimal modal order, in order to automatically and objectively filter out physically stable modes from all the poles identified at that order, replacing the traditional screening process that relies entirely on manual observation and experience, the above embodiment can automatically filter and highlight physically stable poles using stability criteria as described above. This can be achieved by: traversing all poles identified at the optimal modal order; for each pole, checking whether the relative fluctuation of its frequency value is less than a first stability tolerance and whether the relative fluctuation of its damping ratio value is less than a second stability tolerance in the identification results of the current order and several consecutive increasing orders; and displaying poles that simultaneously meet the requirements of the relative fluctuation tolerance of frequency value and the relative fluctuation tolerance of damping ratio value on the steady-state diagram in a way that distinguishes them from unstable poles. For example, solid circles represent stable poles, and hollow dots or crosses represent unstable poles. The above solution transforms engineering experience (e.g., stable poles should exhibit small frequency and damping ratio fluctuations across successive orders) into specific, automatically executable computer instructions, such as traversal, tolerance checking, and differential display. This automates the final crucial step in modal parameter identification—stable mode selection—not only freeing up analysts but also ensuring the objectivity and traceability of the screening process, thus achieving closed-loop automation of the entire process "from data to final reliable modal parameters."

[0102] As another embodiment of this application, the application of the stability criterion in the above embodiment to automatically filter and highlight stable poles that conform to physical meaning can also be as follows: based on all poles identified in the entire iteration process from the initial order to the optimal order, cluster analysis is performed in the frequency-damping ratio coordinate system; clusters with density higher than a preset threshold and the standard deviation of frequency and damping ratio of poles within the cluster is less than the corresponding tolerance are identified as stable pole clusters; the center point or the point with the highest density of each stable pole cluster is highlighted on the steady-state diagram as a stable pole that conforms to physical meaning. Compared to the longitudinal trajectory tracking based on "the current order and several consecutive previous orders" in the aforementioned embodiments, this scheme transforms into lateral spatial clustering analysis based on all historical data. It solves the special problem that trajectory tracking methods may face—trajectory tracking methods are sensitive to the continuity of pole order and may fail to track when modes are dense or poles cross. In contrast, clustering analysis does not depend on the order of poles changing with order, but only focuses on their final distribution in the parameter space, thus avoiding tracking errors. This shows that clustering methods can more robustly identify the real physical mode clusters, are not sensitive to occasional pole jumps or order changes during iteration, and can directly provide parameter estimates (cluster centers) of stable modes. The results may be more stable and accurate than simply selecting poles of a certain order.

[0103] To ensure the quality of the input data, an optional but beneficial preprocessing step can be introduced between steps S1 and S2. This preprocessing involves: after acquiring the complex data of the measured frequency response function of the structure obtained through excitation and sensing tests, and before setting the initial modal order, the following data purification and enhancement steps are included: applying a smoothing filter to the original complex frequency response data to suppress high-frequency random noise introduced during the measurement process; scanning the data sequence to identify and repair abnormal amplitude or phase jump points caused by test interference, ensuring that the data quality meets the requirements for subsequent fitting. For example, outliers can be identified using statistical methods and replaced with interpolated neighboring points.

[0104] It should be noted that, Figure 1 The example method operates entirely within an automated control loop, configured to automatically execute steps S1 through S7 without human input of the final order or intervention in convergence decisions. Furthermore, in each iteration, it calculates and utilizes only two core metrics—the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation—for convergence decisions, without relying on calculated mode shapes, modal confidence criteria, or other derived parameters, thereby minimizing computational overhead. This makes the method efficient and focused.

[0105] To implement the delayed confirmation concept mentioned in the foregoing embodiments, a set of explicit operational steps is designed to control the iteration, monitoring, and reset logic, making it a runnable algorithm module. The stability verification step for the convergence state is enhanced by a delayed confirmation mechanism. This mechanism is configured to perform the following operations: after the initial signal is generated for the first time, final confirmation is not triggered immediately, but the iteration process is forced to continue for at least a number of rounds determined by a consecutive stability threshold. During the forced iteration rounds, the output of the multi-condition joint decision process is continuously monitored. Final confirmation is only completed when it is detected that an initial signal is generated each time in the iteration rounds determined by the consecutive stability threshold; otherwise, the recorded number of times the initial signal is generated is reset, and the iteration continues. This mechanism acts like a "de-jitter" filter, ensuring that the optimal mode order of the final output is not based on a single accidental fitting fluctuation, but on a continuous, stable, high-quality fitting platform, thus making the adaptive determination method of this application both intelligent and highly reliable.

[0106] In another embodiment of this application, the step of verifying the stability of the convergence state can be further enhanced in efficiency through a predictive early termination mechanism. This mechanism is configured to perform the following operations: during the continuous generation of the initial signal, the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response are fitted in real time as a function of the number of iterations. If the fitted curves show that the predicted values ​​of these two indicators in subsequent iterations have entered the stable band defined by preset upper and lower limits, and the slope of the curves is close to zero, then even if the preset number of consecutive stable iterations has not been reached, the saturated convergence state is confirmed in advance. The above mechanism includes real-time curve fitting and judgment based on predicted values. That is, it no longer only looks at whether there has been continuous success in the past, but predicts the future trend of the indicators through a mathematical model and makes decisions based on the predictions. Essentially, the goal of this mechanism is to terminate the iteration as early and safely as possible under sufficiently reliable conditions. Therefore, it overcomes the redundant iterations that may be caused by the fixed delay mechanism in the last few iterations, and can make optimal decisions based on the actual situation of the fitting process, demonstrating optimization capabilities in the time dimension and raising the intelligence and economy of the adaptive determination method to a new level.

[0107] From the above Figure 1The adaptive method for determining modal order in the example structural vibration test demonstrates that, on the one hand, by calculating the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation—two complementary technical indicators—a comprehensive evaluation of the fitting quality can be achieved. The complex frequency response correlation coefficient measures the consistency between the fitted curve and the measured curve in amplitude and phase from the perspective of morphological similarity, while the normalized least squares complex frequency response deviation quantifies the overall fitting error from the perspective of error energy. Using these two indicators together overcomes the potential bias of a single criterion, providing a more sufficient and reliable basis for judging the quality of the fit, thus laying a solid foundation for accurately determining the modal order. On the other hand, by evaluating whether the improvement rate of these two key indicators tends to level off (i.e., the incremental difference approaches zero) as the modal order increases, it is possible to effectively determine whether the fitting process has reached saturation. This allows the method to intelligently distinguish between… The method automatically balances fitting accuracy and model simplicity by considering two scenarios: "still needs improvement" and "improvement is no longer significant." This avoids both underfitting due to premature iteration termination and overfitting due to unlimited increases in the modal order. Thirdly, the entire process integrates initial order setting, iterative fitting, index calculation, difference analysis, convergence judgment, and order output into a coherent automated closed loop. Users only need to provide measured data and set broad initial parameters and thresholds; the method automatically performs the search and judgment until it outputs the optimal modal order. This significantly reduces reliance on operator expertise and manual intervention, freeing analysts from tedious steady-state diagram observation and experience-based judgment. It not only greatly improves the efficiency of modal parameter identification but also effectively enhances the objectivity of the analysis process and the repeatability of the results, providing key technical support for the automation and standardization of structural vibration testing and analysis. In summary, the technical solution of this application, through dual-index combination and adjacent-order incremental difference analysis, achieves automated and accurate determination of the optimal modal order, thereby improving the efficiency and objectivity of modal analysis.

[0108] Please see the appendix Figure 2 This application provides an adaptive determination device for modal order in structural vibration testing. The device includes an acquisition module 201, an extraction module 202, a calculation module 203, an iteration module 204, an evaluation module 205, a joint judgment module 206, and a processing module 207, which are described in detail below: The acquisition module 201 is used to acquire complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; Extraction module 202 is used to set the initial modal order and perform curve fitting on the measured frequency response function based on the initial modal order in order to extract modal parameters and synthesize the fitted frequency response function; The calculation module 203 is used to calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, which are calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. Iteration module 204 is used to increase the modal order in a step-by-step manner, repeatedly performing modal parameter extraction, curve fitting, and calculation of two technical indicators; Evaluation module 205 is used to calculate the difference of directional increment between adjacent orders based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, so as to evaluate the improvement of the modal fitting effect. The joint judgment module 206 is used to jointly judge whether the extraction of modal parameters has reached the saturation convergence state based on the absolute values ​​of two technical indicators and the corresponding adjacent order directional increment differences. The processing module 207 is used to stop increasing the order if it is determined that the saturation convergence state has been reached, and output the current order as the optimal mode order for accurate identification of mode parameters.

[0109] From the above Figure 2As demonstrated by the adaptive modal order determination device in the example structural vibration test, on the one hand, by calculating the two complementary technical indicators—the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation—a comprehensive and integrated evaluation of the fitting quality can be achieved. The complex frequency response correlation coefficient measures the consistency between the fitted curve and the measured curve in amplitude and phase from the perspective of morphological similarity, while the normalized least squares complex frequency response deviation quantifies the overall fitting error from the perspective of error energy. Using these two indicators in combination overcomes the potential bias of a single criterion, providing a more sufficient and reliable basis for judging the quality of the fit, thus laying a solid foundation for accurately determining the modal order. On the other hand, by evaluating whether the improvement rate of these two key indicators tends to level off (i.e., the incremental difference approaches zero) as the modal order increases, it is possible to effectively determine whether the fitting process has reached saturation. This allows the method to intelligently distinguish between… The method automatically balances fitting accuracy and model simplicity by considering two scenarios: "still needs improvement" and "improvement is no longer significant." This avoids both underfitting due to premature iteration termination and overfitting due to unlimited increases in the modal order. Thirdly, the entire process integrates initial order setting, iterative fitting, index calculation, difference analysis, convergence judgment, and order output into a coherent automated closed loop. Users only need to provide measured data and set broad initial parameters and thresholds; the method automatically performs the search and judgment until it outputs the optimal modal order. This significantly reduces reliance on operator expertise and manual intervention, freeing analysts from tedious steady-state diagram observation and experience-based judgment. It not only greatly improves the efficiency of modal parameter identification but also effectively enhances the objectivity of the analysis process and the repeatability of the results, providing key technical support for the automation and standardization of structural vibration testing and analysis. In summary, the technical solution of this application, through dual-index combination and adjacent-order incremental difference analysis, achieves automated and accurate determination of the optimal modal order, thereby improving the efficiency and objectivity of modal analysis.

[0110] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. For example... Figure 3 As 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 an adaptive method for determining modal orders in structural vibration testing. When the processor 30 executes the computer program 32, it implements the steps in the above-described embodiment of the adaptive method for determining modal orders in structural vibration testing, for example... Figure 1 Steps S1 to S7 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 2The functions of the acquisition module 201, extraction module 202, calculation module 203, iteration module 204, evaluation module 205, joint judgment module 206, and processing module 207 are shown.

[0111] For example, the computer program 32 for the adaptive determination method of modal order in structural vibration testing mainly includes: acquiring complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; setting an initial modal order and performing curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; calculating two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function; and increasing the modal order in a step-by-step manner. The modal order is determined by repeatedly performing modal parameter extraction, curve fitting, and calculation of two technical indicators. Based on the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response obtained from two consecutive iterations, the difference in directional increments between adjacent orders is calculated to evaluate the improvement in modal fitting performance. Based on the absolute values ​​of the two technical indicators and their corresponding differences in directional increments between adjacent orders, it is jointly determined whether the modal parameter extraction has reached saturation convergence. If saturation convergence has been reached, the order increment is stopped, and the current order is output as the optimal modal order for accurate modal parameter identification. The computer program 32 can be divided into one or more modules / units, which are stored in memory 31 and executed by 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 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, extraction module 202, calculation module 203, iteration module 204, evaluation module 205, joint judgment module 206, and processing module 207 (a module in the virtual device). The specific functions of each module are as follows: Acquisition module 201 is used to acquire the complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; extraction module 202 is used to set the initial modal order and perform curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; calculation module 203 is used to calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function, and the full-channel... The module includes: an average normalized least squares complex frequency response deviation; an iteration module 204, used to increase the modal order in a step-by-step manner, repeatedly performing modal parameter extraction, curve fitting, and calculation of two technical indicators; an evaluation module 205, used to calculate the difference in directional increments between adjacent orders based on the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response obtained from two consecutive iterations, in order to evaluate the improvement of the modal fitting effect; a joint judgment module 206, used to jointly judge whether the extraction of modal parameters has reached a saturated convergence state based on the absolute values ​​of the two technical indicators and their corresponding differences in directional increments between adjacent orders; and a processing module 207, used to stop the order increment if the saturated convergence state has been reached, and output the current order as the optimal modal order for accurate identification of modal parameters.

[0112] 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.

[0113] 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.

[0114] 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.

[0115] 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.

[0116] 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.

[0117] 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.

[0118] 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.

[0119] 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.

[0120] 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.

[0121] 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 adaptive determination method of modal order in structural vibration testing 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: acquiring complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; setting an initial modal order and performing curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; calculating two technical indicators for comprehensively evaluating the fitting quality: calculation based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. The algorithm calculates the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation. It then incrementally increases the modal order, repeatedly performing modal parameter extraction, curve fitting, and the calculation of the two technical indicators. Based on the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation obtained from two consecutive iterations, it calculates the difference in directional increments between adjacent orders to evaluate the improvement in modal fitting performance. Based on the absolute values ​​of the two technical indicators and their corresponding differences in directional increments between adjacent orders, it jointly determines whether the modal parameter extraction has reached saturation convergence. If saturation convergence has been reached, the order increment is stopped, and the current order is output as the optimal modal order for accurate modal parameter identification. 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.

[0122] 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. An adaptive method for determining the modal order in structural vibration testing, characterized in that, The method includes: Obtain complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; An initial modal order is set, and the measured frequency response function is curve-fitted based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; Two technical indicators for comprehensively evaluating the fitting quality are calculated: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. The modal order is increased in a step-by-step manner, and the modal parameter extraction, curve fitting, and calculation of the two technical indicators are repeated. Based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, the difference of the directional increment between adjacent orders is calculated to evaluate the improvement of the modal fitting effect. Based on the absolute values ​​of the two technical indicators and the corresponding differences in the directional increments of adjacent orders, it is jointly determined whether the extraction of modal parameters has reached a saturated convergence state. If it is determined that the saturation convergence state has been reached, the order increment is stopped, and the current order is output as the optimal modal order for accurate identification of modal parameters.

2. The adaptive determination method for modal order in structural vibration testing according to claim 1, characterized in that, The full-channel average complex frequency response correlation coefficient is calculated as follows: By processing the measured and fitted complex data sequences of each independent input-output channel pair, an intermediate value characterizing the similarity of the input-output channel fit is obtained. By combining the intermediate values ​​of all channels and taking the arithmetic mean, the average complex frequency response correlation coefficient of all channels, which reflects the consistency of the global fitting shape, is obtained.

3. The adaptive determination method for modal order in structural vibration testing according to claim 1, characterized in that, The full-channel average normalized least squares complex frequency response deviation is calculated as follows: For each independent input-output channel pair, a relative value reflecting the local fitting error of the input-output channel is calculated based on the fitted and measured complex data sequence. The relative values ​​calculated for all channels are averaged to generate the full-channel average normalized least squares complex frequency response deviation used to quantify the overall fitting error level.

4. The adaptive determination method for modal order in structural vibration testing according to claim 1, characterized in that, The method of jointly determining whether the extraction of modal parameters has reached saturation convergence based on the absolute values ​​of the two technical indicators and the corresponding differences in directional increments between adjacent orders includes: Perform the first qualification judgment: check whether the correlation coefficient of the full-channel average complex frequency response at the current order meets the preset standard for characterizing high similarity; Perform the second qualification test: check whether the average normalized least squares complex frequency response deviation of the entire channel at the current order meets the maximum allowable error limit; Convergence determination: Check whether the difference between adjacent order directional increments of the correlation coefficient of the full-channel average complex frequency response and the deviation of the full-channel average normalized least squares complex frequency response has stabilized, i.e., its change is below a small threshold indicating that the improvement is negligible. When the first qualification determination, the second qualification determination, and the convergence determination are all passed simultaneously, a preliminary signal indicating that the convergence state has been reached is generated.

5. The adaptive determination method for modal order in structural vibration testing according to claim 4, characterized in that, After generating the initial signal, the following steps are performed to verify the stability of the convergence state: Maintain the incremental iteration of modal order and continuously execute the multi-condition joint decision-making process; The number of times the initial signal is generated in each iteration is recorded, and when the number reaches a preset threshold for continuous stable number of times, the saturation convergence state is finally confirmed.

6. The adaptive determination method for modal order in structural vibration testing according to claim 1, characterized in that, After outputting the optimal modal order, the following result visualization steps are also included: Based on all the identification results corresponding to the optimal modal order, a steady-state diagram of frequency and damping ratio as a function of the assumed order is automatically generated. On the steady-state diagram, stability criteria are applied to automatically filter and highlight stable poles that conform to physical meaning. The stability criteria include the fluctuation range limits of frequency and damping ratio under multiple consecutive assumed orders.

7. The adaptive determination method for modal order in structural vibration testing according to claim 6, characterized in that, The application stability criterion automatically filters and highlights stable poles that conform to physical meaning, including: Iterate through all poles identified at the optimal modal order; For each pole, check whether the relative fluctuation of its frequency value is less than the first stability tolerance and whether the relative fluctuation of its damping ratio value is less than the second stability tolerance in the identification results of the current order and the previous consecutive increasing orders. The poles that simultaneously satisfy the relative fluctuation requirements of the frequency value and the relative fluctuation tolerance requirements of the damping ratio are displayed on the steady-state diagram in a manner distinct from unstable poles.

8. An adaptive device for determining the modal order in structural vibration testing, characterized in that, The device includes: The acquisition module is used to acquire complex data of the measured frequency response function of the structure obtained through excitation and sensing tests; The extraction module is used to set the initial modal order and perform curve fitting on the measured frequency response function based on the initial modal order to extract modal parameters and synthesize the fitted frequency response function; The calculation module is used to calculate two technical indicators for comprehensively evaluating the fitting quality: the full-channel average complex frequency response correlation coefficient and the full-channel average normalized least squares complex frequency response deviation, calculated based on the complex data of the measured frequency response function and the complex data of the fitted frequency response function. The iterative module is used to increase the modal order in a step-by-step manner, and repeatedly perform modal parameter extraction, curve fitting, and calculation of the two technical indicators; The evaluation module is used to calculate the difference of the directional increment between adjacent orders based on the correlation coefficient of the full-channel average complex frequency response obtained from two consecutive iterations and the deviation of the full-channel average normalized least squares complex frequency response, so as to evaluate the improvement of the modal fitting effect. The joint judgment module is used to jointly judge whether the extraction of modal parameters has reached a saturated convergence state based on the absolute values ​​of the two technical indicators and the corresponding difference in the directional increments of adjacent orders. The processing module is used to stop increasing the order if it determines that the saturation convergence state has been reached, and outputs the current order as the optimal mode order for accurate identification of mode parameters.

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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