Spacecraft vibration response resonance point identification detection method

Abstract

The application discloses a spacecraft vibration response resonance point identification detection method and relates to the technical field of spacecraft vibration response, and comprises the following steps: on the basis of obtaining a mixed response signal, a support vector regression model is constructed with an instantaneous phase fluctuation factor and a kurtosis deviation rate factor as inputs, a structure response credibility score value of each frequency point is generated, the mixed response signal under the condition that the acceleration sensor has a self-excitation frequency is used to distinguish structure modal frequencies and the self-resonance frequency of the acceleration sensor, and the frequency points which neither belong to the structure modal frequencies nor the self-resonance frequency of the acceleration sensor are classified as undecided frequency points. The application solves the problem that the self-excitation frequency of the acceleration sensor interferes with structure modal identification, and realizes accurate distinction and labeled output of the structure modal frequencies and the self-resonance frequency of the sensor.

Description

Technical Field

[0001] This invention relates to the field of spacecraft vibration response technology, and more specifically to a method for identifying and detecting resonance points in spacecraft vibration response. Background Technology

[0002] Spacecraft vibration response resonance point identification and detection refers to the process of accurately identifying resonance points of a spacecraft within a specific frequency range by analyzing the vibration response data generated by its structure under external or internal excitations (such as launch loads, attitude adjustments, thermal deformation, etc.) during ground testing or on-orbit operation. These resonance points are the characteristic frequency points where the structural system resonates near that frequency. Existing identification and detection technologies typically involve four main steps: First, vibration signal acquisition, which involves deploying accelerometers or sensor arrays at key parts of the spacecraft structure to obtain multi-channel vibration response data under excitation; second, signal preprocessing, which involves denoising, filtering, and normalizing the acquired data to improve data quality; third, feature extraction and modal identification, which uses Fast Fourier Transform (FFT), power spectral density analysis, wavelet transform, or modal parameter estimation methods to analyze the frequency response of the signal and extract characteristic frequencies, damping ratios, and mode shapes representing the structural resonance behavior; and finally, resonance point determination and result output, which identifies and confirms resonance points based on specific criteria (such as amplitude transitions, modal frequency clustering, etc.) and outputs analysis reports for structural optimization or safety warnings. This entire process places high demands on the robustness of the identification algorithm, the rationality of the sensor layout, and the accuracy of the signal processing strategy, making it a crucial technical means to ensure the reliability of spacecraft structures and the safety of missions.

[0003] The existing technology has the following shortcomings:

[0004] In the process of conducting high-order modal response tests on high-frequency flexible components of spacecraft (such as solar panel hinge segments), it is often necessary to deploy high-sensitivity accelerometers near structural connections to capture local vibration signals. However, under high-frequency excitation conditions, due to the specific structural resonance characteristics of some sensor materials, local resonance phenomena may occur during excitation, forming a so-called "self-excited frequency" response. This response is superimposed on the actual vibration response signal of the structure, resulting in independent peaks with high amplitudes in the frequency spectrum. Because this type of self-excited response has the non-structural characteristic of prominent amplitude originating from the sensor itself, existing spacecraft vibration response resonance point identification and detection technologies cannot accurately distinguish between structural modal frequencies and the accelerometer's own resonance frequencies based on the mixed response signals when the accelerometer has a self-excited frequency. This can easily lead to misidentification of the sensor's self-excited frequency as a high-order resonance point of the spacecraft structure. This problem directly results in false high-order modes in the modal identification results, interfering with the judgment of structural stiffness and mode shape, and potentially causing errors in frequency avoidance design, affecting the accuracy of the overall structural modal safety assessment and design acceptance.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for identifying and detecting resonance points in the vibration response of spacecraft, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for identifying and detecting resonance points in spacecraft vibration response, specifically comprising the following steps:

[0008] S1. By extracting the multi-channel discrete frequency difference of the spectral response signals of different types of accelerometers deployed at multiple structural points, a local peak consistency discrimination factor is constructed to identify whether the accelerometer has a self-excited frequency.

[0009] S2. Based on the identification of the self-excited frequency, wavelet packet decomposition and Hilbert instantaneous feature extraction are performed on the corresponding channel spectrum signal. An interference frequency band index table is constructed by combining the frequency co-occurrence probability of multiple measurement points to determine the mixed response signal of the accelerometer when the self-excited frequency exists.

[0010] S3. Based on the obtained mixed response signal, construct a support vector regression model with instantaneous phase fluctuation factor and kurtosis deviation factor as input, generate the structural response confidence score for each frequency point, distinguish the structural modal frequency and the accelerometer's own resonance frequency according to the mixed response signal under the condition of self-excited frequency of the accelerometer, and classify the frequency points that do not belong to either the structural modal frequency or the accelerometer's own resonance frequency as unresolved frequency points.

[0011] S4. Based on the distinction between the structural modal frequencies and the resonant frequencies of the accelerometer itself, generate and output the corresponding frequency classification label set.

[0012] S5. Dynamically adjust the frequency point identification strategy based on the frequency classification label set, including triggering the neighbor measurement point association verification process under the undecided frequency label, performing frequency point elimination operation under the accelerometer's own resonant frequency label, and performing trust enhancement fitting processing under the structural modal frequency label.

[0013] Preferably, S1 is as follows:

[0014] The spectral response signals collected by different types of accelerometers deployed at multiple structural points are normalized, the discrete frequency main peak set within the main frequency range of each accelerometer channel is extracted, and the amplitude difference of each frequency point among all accelerometer channels is calculated to form a channel difference vector.

[0015] A local peak consistency discrimination factor is constructed based on the channel difference vector. The local peak consistency discrimination factor is composed of the amplitude deviation rate of the frequency point in all acceleration sensor channels and the synergy weight of the peak frequency position. The normalized discrimination value is generated by weighted linear superposition.

[0016] When the local peak consistency discrimination factor is less than the preset trust threshold, and the frequency point has an amplitude response higher than the amplitude deviation identification threshold only in a single acceleration sensor channel, while no frequency point that meets the amplitude response identification condition is detected in the other acceleration sensor channels, it is determined that the acceleration sensor has a self-excited frequency.

[0017] Preferably, S2 specifically includes the following steps:

[0018] S201. Based on the identification of the existence of self-excited frequency, wavelet packet decomposition is performed on the spectral signal of the accelerometer channel with self-excited frequency to obtain multiple frequency sub-band signals; Hilbert transform is performed on each frequency sub-band signal to extract the instantaneous energy value, instantaneous frequency value and instantaneous phase change rate corresponding to each frequency point, and the frequency point is combined with the three instantaneous feature parameters to generate the instantaneous feature matrix of the frequency point.

[0019] S202. Based on the instantaneous feature matrix of the frequency point, calculate the difference between each pair of channels for the instantaneous frequency value of each frequency point in all acceleration sensor channels, and count the number of channels whose difference is less than the frequency synchronization judgment threshold; use the ratio between the counted number of channels and the total number of acceleration sensor channels as the frequency co-occurrence probability value, and construct an interference frequency band index table using the frequency point, instantaneous energy value, instantaneous frequency value and frequency co-occurrence probability value as fields;

[0020] S203. Select the set of frequency points from the interference frequency band index table whose frequency co-occurrence probability value is less than the frequency consistency judgment threshold and whose instantaneous energy value is higher than the energy comparison reference value only in one accelerometer channel, and mark them as the mixed response signal frequency band when the accelerometer has a self-excited frequency.

[0021] Preferably, S202 specifically refers to:

[0022] The instantaneous frequency value corresponding to each frequency point in the instantaneous feature matrix of the frequency point in all acceleration sensor channels is used as the input reference. The instantaneous frequency difference between each pair of channels is calculated according to the channel combination relationship, and a frequency difference array is generated.

[0023] For all instantaneous frequency differences in the frequency difference array, count the number of channel combinations that are less than the frequency synchronization judgment threshold, and divide the counted number by the total number of accelerometer channels to calculate the frequency co-occurrence probability value.

[0024] The instantaneous energy value, instantaneous frequency value, and frequency co-occurrence probability value corresponding to each frequency point are read sequentially to construct a data record unit with a unified field structure, and the data record unit is arranged and combined in order of frequency points to form an interference frequency band index table.

[0025] Preferably, S3 specifically includes the following steps:

[0026] S301. For each frequency point in the mixed response signal of the accelerometer under the condition of self-excited frequency, extract the instantaneous phase change rate sequence and calculate the standard deviation as the instantaneous phase fluctuation factor. Calculate the kurtosis value of the response amplitude of each frequency point in all accelerometer channels and compare it with the reference kurtosis value corresponding to the structural modal characteristics to obtain the kurtosis deviation rate factor.

[0027] S302. Using the instantaneous phase fluctuation factor and kurtosis deviation factor as input features, construct a support vector regression model, and use structural modal frequencies and the resonant frequency samples of the accelerometer itself for supervised training, establish a mapping function between frequency points and structural response confidence scores, and output the structural response confidence score for each frequency point.

[0028] S303. Set the structural modal confidence threshold and the resonance interference confidence threshold. Classify the frequency points whose structural response confidence score is higher than the structural modal confidence threshold as structural modal frequencies, classify the frequency points whose structural response confidence score is lower than the resonance interference confidence threshold as the accelerometer's own resonance frequency, and classify the frequency points whose structural response confidence score is between the two thresholds as undecided frequency points.

[0029] Preferably, S301 is as follows:

[0030] For the mixed response signal of the accelerometer under the condition of self-excited frequency, the phase values ​​corresponding to multiple sampling times are extracted at each frequency point to form a time-ordered sequence of instantaneous phase change rate. The standard deviation of the instantaneous phase change rate sequence is calculated, and the instantaneous phase fluctuation factor corresponding to the frequency point is output.

[0031] For each frequency point, the corresponding amplitude response set is extracted from all acceleration sensor channels, and kurtosis calculation is performed on the amplitude response set to obtain the amplitude response kurtosis value of the frequency point in all channels.

[0032] The amplitude response kurtosis value corresponding to each frequency point is compared with the reference kurtosis value corresponding to the structural modal features. Based on the comparison difference, the kurtosis deviation rate factor of the frequency point is calculated and used as an input feature in the subsequent frequency point credibility assessment process.

[0033] Preferably, S302 is as follows:

[0034] The instantaneous phase fluctuation factor and kurtosis deviation factor corresponding to each frequency point are combined into a two-dimensional input vector. Normalization is performed through a unified interval mapping to generate an input feature matrix, which serves as the input set for the support vector regression model.

[0035] A training sample set is constructed. The target score value corresponding to the structural modal frequency sample in the training sample set is set as the first value, and the target score value corresponding to the resonant frequency sample of the accelerometer itself in the training sample set is set as the second value. The first value is greater than the second value. The regression mapping learning operation is performed on the support vector regression model through supervised training.

[0036] The normalized input vector of each frequency point is input into the support vector regression model after the regression mapping learning operation to generate the structural response confidence score value corresponding to the frequency point, and the structural response confidence score value is used for subsequent classification and judgment processing of the frequency point.

[0037] Preferably, S4 is as follows:

[0038] Extract the mapping data between frequency points and corresponding classification types from the distinction results between structural modal frequencies and the resonant frequencies of the accelerometer itself;

[0039] For each frequency point, the frequency value and the corresponding classification type are combined according to a preset field format and sorted in ascending order of frequency value to generate a set of frequency classification labels.

[0040] The frequency classification label set is saved as a structured data file and written to a preset storage path for subsequent frequency identification and response analysis.

[0041] Preferably, S5 is as follows:

[0042] For frequency values ​​marked as unresolved frequency points in the frequency classification label set, trigger the neighboring measurement point association test process. Specifically, combine the frequency labels corresponding to the acceleration sensor channels in spatially adjacent locations, perform a consistency test between neighboring measurement points. If there are two or more frequency points labeled as structural modal frequencies and the frequency difference is less than the frequency similarity judgment threshold, then the unresolved frequency point is re-marked as a structural modal frequency.

[0043] For frequency values ​​marked as the sensor's own resonant frequency in the frequency classification label set, the corresponding frequency points and their energy characteristics are removed from the frequency analysis results and are not included in the subsequent structural frequency identification calculation process.

[0044] For the frequency values ​​marked as structural modal frequencies in the frequency classification label set, a response consistency fitting operation is performed based on their amplitude variation trends in multiple acceleration sensor channels. A reliable fitting function is calculated and the confidence score of the corresponding frequency point in the frequency identification result is updated.

[0045] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0046] 1. This invention constructs a multi-channel analysis framework based on the spectral response characteristics of an accelerometer, combining instantaneous feature extraction, co-occurrence probability modeling, statistical factor evaluation, and support vector regression identification mechanisms to achieve accurate analysis of mixed response signals in the presence of self-excited frequencies. This technical solution introduces instantaneous phase fluctuation factors and kurtosis deviation factors as modeling features, effectively characterizing the essential differences in statistical behavior between structural modal responses and the sensor's own resonant responses. Furthermore, a frequency point reliability scoring system is constructed through a supervised-trained support vector regression model, and a three-stage classification strategy is implemented based on the scoring results, enabling accurate differentiation between structural modal frequencies and the accelerometer's own resonant frequencies. Simultaneously, to further improve classification robustness, a neighboring measurement point association verification mechanism, a frequency point elimination process, and a response consistency fitting algorithm are used to dynamically adjust the frequency identification strategy, ensuring that the final frequency identification results have high consistency and reliability.

[0047] 2. This invention achieves effective deconstruction of non-stationary mixed responses by performing wavelet packet decomposition and Hilbert instantaneous feature analysis on the structural response signal. Secondly, the introduction of frequency co-occurrence probability effectively measures the synchronicity of structural responses across multiple channels, providing data support for locating interference frequency bands. Thirdly, the structural response credibility scoring model, combined with statistical deviation factors, improves the ability to identify non-structural pseudo-peaks and reduces the risk of misjudging sensor self-excited responses as higher-order modes. Finally, through frequency label output and classification-driven post-processing strategies, the identification results are ensured to be interpretable, traceable, and practical, which helps to improve the accuracy and automation level of spacecraft modal identification and structural safety assessment. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0049] Figure 1 This is a flowchart illustrating the spacecraft vibration response resonance point identification and detection method of the present invention. Detailed Implementation

[0050] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art.

[0051] This invention provides, for example Figure 1 The spacecraft vibration response resonance point identification and detection method shown includes the following steps:

[0052] S1. By extracting the multi-channel discrete frequency difference of the spectral response signals of different types of accelerometers deployed at multiple structural points, a local peak consistency discrimination factor is constructed to identify whether the accelerometer has a self-excited frequency.

[0053] In this embodiment, S1 specifically refers to:

[0054] The spectral response signals collected by different types of accelerometers deployed at multiple structural points are normalized, the discrete frequency main peak set within the main frequency range of each accelerometer channel is extracted, and the amplitude difference of each frequency point among all accelerometer channels is calculated to form a channel difference vector.

[0055] In the process of identifying and detecting resonance points in spacecraft vibration response, to accurately extract the characteristic response information of accelerometers from multiple structural points, the spectral response signals acquired by each accelerometer channel can be normalized. This normalization process unifies the amplitude differences caused by sensitivity, damping characteristics, signal-to-noise ratio, etc., of different types of accelerometers to a comparable scale. Normalization can be achieved by scaling the spectral amplitude data of each channel to its maximum value, linearly compressing the spectral amplitude to between 0 and 1, facilitating direct comparison of frequency responses from different channels. The dominant frequency range of each accelerometer channel refers to the effective frequency segment containing the main modal response of the structure within the spectrum acquired by that channel. This range is typically defined based on the frequency coverage of the excitation source, the sensor's sensitive frequency band, and the predicted values ​​of the structural modal frequencies. The discrete frequency peak set refers to the set of local extreme frequency points extracted from the spectral curve using a peak detection algorithm within the dominant frequency range, representing the energy concentration areas of each frequency detected by the sensor channel. For each frequency point, its amplitude response is extracted from all accelerometer channels, and the difference between its maximum amplitude and the amplitudes of other channels is calculated. This difference can be quantified using amplitude difference or relative deviation rate, forming a channel amplitude difference sequence corresponding to a frequency point. Combining multiple channel difference sequences at multiple frequencies constitutes a complete channel difference vector. For example, if the normalized amplitudes of the four sensor channels at 120Hz are 0.9, 0.1, 0.08, and 0.12, then there is a significant amplitude deviation between different channels at this frequency point. The channel difference value at this frequency point is recorded as a four-dimensional vector, used to subsequently construct a local peak consistency discriminant factor. This method enables structural response consistency analysis, providing fundamental data support for identifying self-excited frequency interference.

[0056] A local peak consistency discrimination factor is constructed based on the channel difference vector. The local peak consistency discrimination factor is composed of the amplitude deviation rate of the frequency point in all acceleration sensor channels and the synergy weight of the peak frequency position. The normalized discrimination value is generated by weighted linear superposition.

[0057] In the process of identifying and detecting resonance points in spacecraft vibration response, to accurately identify whether accelerometers exhibit consistent characteristics caused by structural response at specific frequency points, a local peak consistency discriminant factor can be constructed based on the channel difference vector. The channel difference vector records the spectral amplitude differences of each frequency point across different accelerometer channels, serving as a crucial basis for measuring the consistency of responses from different sensors. When constructing the local peak consistency discriminant factor, firstly, the amplitude deviation rate of the frequency point across all accelerometer channels needs to be calculated. The amplitude deviation rate represents the relative deviation of a single channel's amplitude from the average or maximum amplitude of all channels, and is a quantitative indicator reflecting the differences in channel response consistency. Secondly, the peak frequency position synergy needs to be calculated, referring to whether the frequency point is simultaneously at a local peak in different channels. If a frequency point only exhibits a peak in a single channel without a corresponding peak in other channels, the synergy is poor; conversely, it is strong. These two quantitative parameters reflect the degree of channel synergy at the amplitude level and the structural response characteristic level, respectively. To comprehensively describe the consistency of these two parameters, a weighted linear superposition of amplitude deviation rate and frequency position synergy can be performed by setting a weighting factor. The weighting value can be empirically set based on sensor type, channel spacing, or stability observed in historical data. The resulting value represents the consistency discrimination strength of that frequency point under the current channel layout. To facilitate subsequent identification processing, this discrimination strength needs to be normalized, varying between 0 and 1. The closer the normalized discrimination value is to 1, the more consistent the channel response; the closer it is to 0, the more likely there is an abnormal response in a single channel, thus providing a basis for identifying self-excited frequency conditions. This method of constructing the discrimination factor can effectively suppress unstructured response interference caused by local resonance of the equipment, and is a key technical means to improve the accuracy of high-order mode identification.

[0058] When the local peak consistency discrimination factor is less than the preset trust threshold, and the frequency point has an amplitude response higher than the amplitude deviation identification threshold only in a single acceleration sensor channel, while no frequency point that meets the amplitude response identification condition is detected in the other acceleration sensor channels, it is determined that the acceleration sensor has a self-excited frequency.

[0059] In the process of identifying and detecting resonance points in spacecraft vibration response, to determine whether a particular accelerometer has a self-excited frequency, the numerical result of the local peak consistency discrimination factor can be used. Specifically, after extracting the local peak consistency discrimination factor for each frequency point, if the factor is lower than a preset trust threshold, it indicates that the frequency point does not have a good consistent response across multiple sensor channels, suggesting a possible abnormal response. Furthermore, if the frequency point only shows an amplitude response in one accelerometer channel, and the amplitude is greater than the amplitude deviation identification threshold, while other sensor channels do not meet the amplitude response identification condition at the same frequency point, it can be determined that the high response at that frequency point is not caused by overall structural excitation, but may be due to local resonance behavior of the sensor in that channel under high-frequency excitation, i.e., the sensor's own self-excited frequency response. This judgment is made because true structural resonance should produce an approximate response pattern at multiple spatially distributed measurement points, while local resonance of the sensor itself can only produce a prominent response at a single measurement point with significant amplitude differences. Therefore, this judgment logic can effectively distinguish between structural resonance and sensor resonance.

[0060] The preset trust threshold is an empirical or statistical boundary value set based on the numerical distribution characteristics of the local peak consistency discrimination factor. It is used to distinguish frequency points with strong and poor structural consistency. It is generally derived through comparative training with a large amount of historical modal test data, or it can be combined with a model prediction based on typical structural distributions. The amplitude deviation identification threshold is a definitional value used to quantitatively judge whether the frequency response of a certain channel is abnormally prominent. It is usually set based on the sensitivity parameters of different types of accelerometers, the geometric distance between the measuring point and the excitation source, and the damping characteristics of the structure. This ensures that it does not excessively exclude effective information or excessively broaden the identification range of abnormal responses under real structural response conditions. The frequency response identification condition is a basic judgment criterion used to eliminate invalid frequency points that have no response. It is achieved by setting a minimum response threshold, which helps to build a stable response identification system. Through the combination of these parameter settings and the construction of discrimination rules, a rigorous and robust self-excited frequency identification mechanism can be formed, improving the accuracy and reliability of high-order modal identification.

[0061] S2. Based on the identification of the self-excited frequency, wavelet packet decomposition and Hilbert instantaneous feature extraction are performed on the corresponding channel spectrum signal. An interference frequency band index table is constructed by combining the frequency co-occurrence probability of multiple measurement points to determine the mixed response signal of the accelerometer when the self-excited frequency exists.

[0062] In this embodiment, S2 specifically includes the following steps:

[0063] S201. Based on the identification of the existence of self-excited frequency, wavelet packet decomposition is performed on the spectral signal of the accelerometer channel with self-excited frequency to obtain multiple frequency sub-band signals; Hilbert transform is performed on each frequency sub-band signal to extract the instantaneous energy value, instantaneous frequency value and instantaneous phase change rate corresponding to each frequency point, and the frequency point is combined with the three instantaneous feature parameters to generate the instantaneous feature matrix of the frequency point.

[0064] Given the identification of self-excited frequencies, multi-scale decomposition of the accelerometer channel spectrum signal exhibiting these frequencies is necessary. This is achieved by first inputting the accelerometer channel spectrum signal into a wavelet packet decomposition process. A wavelet packet function with a fixed number of levels is used to divide the original signal into multiple frequency sub-bands, ensuring that each sub-band has non-overlapping coverage and consistent resolution. Subsequently, each frequency sub-band signal undergoes Hilbert transform processing to construct an analytical signal for extracting instantaneous features. At each frequency point, the instantaneous energy value, instantaneous frequency value, and instantaneous phase change rate are extracted based on the magnitude and derivative information of the transformed complex signal. For each frequency point, the original frequency index is used as the key, and the three instantaneous feature values ​​are used as corresponding fields. All records are combined sequentially according to the frequency point sorting method to generate a frequency point instantaneous feature matrix, which serves as the data foundation for subsequent modeling input.

[0065] Wavelet packet decomposition is a method for frequency localization analysis of input signals at multiple scales. Compared to ordinary wavelet transform, it has equal resolution in both high and low frequency ranges, making it suitable for capturing fine-grained frequency component changes in higher-order modes. Wavelet packet decomposition divides the signal into multiple frequency sub-bands through full-band reconstruction, ensuring that each sub-band represents a local response within a specific frequency range, which is beneficial for subsequent feature extraction. Hilbert transform is a complex transform technique for constructing analytic signals from real signals, which can be used to extract the instantaneous characteristics of signals at the microscopic scale in real time. Through Hilbert transform, the instantaneous frequency change trajectory, phase derivative information, and energy intensity of the signal at each moment can be obtained, enabling the capture of non-steady-state characteristics of vibration signals. The instantaneous energy value reflects the response intensity at the current frequency point, the instantaneous frequency value reveals local frequency shift characteristics, and the instantaneous phase change rate is used to determine frequency jumps and fluctuation trends. The combination of these three can comprehensively characterize the dynamic response features of each frequency point.

[0066] S202. Based on the instantaneous feature matrix of the frequency point, calculate the difference between each pair of channels for the instantaneous frequency value of each frequency point in all acceleration sensor channels, and count the number of channels whose difference is less than the frequency synchronization judgment threshold; use the ratio between the counted number of channels and the total number of acceleration sensor channels as the frequency co-occurrence probability value, and construct an interference frequency band index table using the frequency point, instantaneous energy value, instantaneous frequency value and frequency co-occurrence probability value as fields;

[0067] S203. Select the set of frequency points from the interference frequency band index table whose frequency co-occurrence probability value is less than the frequency consistency judgment threshold and whose instantaneous energy value is higher than the energy comparison reference value only in one accelerometer channel, and mark them as the mixed response signal frequency band when the accelerometer has a self-excited frequency.

[0068] To accurately identify the frequency bands of the mixed response signals generated by the accelerometer under self-excited frequency conditions, a filtering operation needs to be performed on the interference frequency band index table. First, each frequency point record in the interference frequency band index table is traversed one by one, and a threshold judgment is applied to the frequency co-occurrence probability value corresponding to each frequency point. When the frequency co-occurrence probability value of a frequency point is less than the frequency consistency judgment threshold, it indicates that the vibration response at that frequency point does not exhibit frequency synchronization among multiple accelerometer channels, suggesting inconsistent origins. Subsequently, the instantaneous energy values ​​of that frequency point are compared across all accelerometer channels. If only one channel has an instantaneous energy value greater than the energy comparison benchmark, while all other channels are lower than the benchmark, it indicates that the frequency point may be a local resonance signal caused by the sensor itself in that channel. Through this dual-condition filtering operation, unstructured, inconsistent, and strongly localized vibration features can be clustered and identified in the frequency dimension. The sets of frequency points that meet the conditions are logically aggregated and marked as the mixed response signal frequency bands of the accelerometer under self-excited frequency conditions. For example, at a frequency point around 245 Hz, if the instantaneous energy in channel A is significantly higher than the set threshold, and the co-occurrence probability is much lower than the set lower limit, it can be identified as a mixed response signal frequency band.

[0069] The frequency co-occurrence probability value is calculated based on the instantaneous frequency synchronization between different sensor channels. It is used to measure whether a frequency point belongs to the modal component of the consistent response of multiple channels. The frequency consistency judgment threshold is a numerical boundary set manually or adaptively, usually based on the system's measurement point layout density and structural response characteristics. When the frequency co-occurrence probability value is less than this threshold, it means that the response lacks cross-channel consistency and has potential unstructured characteristics. The energy comparison benchmark value is a quantitative reference for determining whether there is abnormal energy concentration in local channels. It can be obtained through statistical results of historical test data or percentile extraction of current test data. This benchmark value helps identify response behavior with abnormally prominent energy in a single channel. The logical basis for combining the frequency co-occurrence probability value and the energy comparison benchmark value for screening is that the true structural response has inter-channel synchronization and relatively balanced energy, while sensor self-excitation interference usually manifests as energy concentration in individual channels and lack of consistency, thus possessing good separability and determinability.

[0070] In this embodiment, S202 specifically refers to:

[0071] The instantaneous frequency value corresponding to each frequency point in the instantaneous feature matrix of the frequency point in all acceleration sensor channels is used as the input reference. The instantaneous frequency difference between each pair of channels is calculated according to the channel combination relationship, and a frequency difference array is generated.

[0072] To evaluate whether each frequency point exhibits consistent response characteristics across different accelerometer channels, the instantaneous frequency value corresponding to each frequency point in the instantaneous feature matrix is ​​used as the input benchmark. Based on the channel combination relationship, instantaneous frequency difference calculations are performed on each pair of channels. Specifically, for a given frequency point, the instantaneous frequency value corresponding to that frequency point is extracted from all accelerometer channels, constructing a frequency value vector of equal length. Then, difference calculations are performed on the values ​​between each pair of channels in this frequency value vector, and the results are stored sequentially as a frequency difference array according to the channel combination order. Taking a four-accelerometer channel as an example, for a given frequency point, its instantaneous frequency values ​​in the four channels are f1, f2, f3, and f4, then six sets of difference calculations need to be performed on the combined pairs: f1 minus f2, f1 minus f3, f1 minus f4, f2 minus f3, f2 minus f4, and f3 minus f4. All differences are generated into a six-bit array according to the original channel combination order for subsequent co-occurrence statistics. This process can be implemented in parallel through matrix operations, improving the efficiency of batch computation and ensuring high resolution of response judgments.

[0073] The instantaneous feature matrix of a frequency point is a three-dimensional structured dataset, where each frequency point corresponds to the instantaneous frequency values ​​of multiple channels. This structure is used to capture the response consistency at the same frequency point under a multi-sensor deployment. The instantaneous frequency value represents the local frequency response of the signal at that frequency point and is an important indicator for determining whether structural resonance exists. By calculating the difference between each pair of channels, the frequency response differences of different channels at that frequency point can be quantified. The frequency difference array is a centralized representation of this difference. The smaller the difference, the stronger the synchronicity between channels; the larger the difference, the more divergent the response, which can be used to determine whether the frequency point belongs to a local specific response. This method has high robustness in multi-channel vibration signal analysis, can effectively identify abnormal response modes caused by sensor self-excitation, and provides a quantitative basis for constructing a frequency co-occurrence probability index.

[0074] For all instantaneous frequency differences in the frequency difference array, count the number of channel combinations that are less than the frequency synchronization judgment threshold, and divide the counted number by the total number of accelerometer channels to calculate the frequency co-occurrence probability value.

[0075] To further analyze the response consistency of frequency points across multiple accelerometer channels, a statistical judgment operation needs to be performed on all instantaneous frequency differences in the frequency difference array corresponding to each frequency point. Specifically, a frequency synchronization judgment threshold is first set to measure the degree of synchronization between the responses of two channels. Then, the frequency difference array is iterated sequentially, counting the number of frequency differences less than the frequency synchronization judgment threshold. For example, if six channel combinations are formed from four sensor channels, and four of these combinations have instantaneous frequency differences less than the frequency synchronization judgment threshold, the count is four. Next, the count is divided by the total number of sensor channels to obtain a normalized frequency co-occurrence probability value, which represents the degree to which the frequency point remains synchronized across multiple channels. This calculation process can be performed collaboratively using logical comparisons and vector operations to ensure the efficiency and accuracy of the analysis.

[0076] The frequency synchronization judgment threshold is a boundary used to assess whether the instantaneous frequency response difference is within an acceptable range. It is typically determined based on statistical analysis of historical test data or calibration data. The setting of this threshold directly affects the sensitivity of the co-occurrence probability and the stringency of the judgment criteria. The frequency co-occurrence probability value is a normalized numerical indicator used to describe the degree of response consistency of the same frequency point across different channels. Counting the number of channel combinations with values ​​less than the judgment threshold reflects the structural propagation consistency of that frequency point, while the participation of the total number of channels ensures a uniform scale of the calculation results. The introduction of this probability value helps maintain higher resolution of structural intrinsic features when there are local sensor anomalous responses and provides a quantitative basis for subsequent identification of interfering frequency bands.

[0077] The instantaneous energy value, instantaneous frequency value, and frequency co-occurrence probability value corresponding to each frequency point are read sequentially to construct a data record unit with a unified field structure, and the data record unit is arranged and combined in order of frequency points to form an interference frequency band index table.

[0078] To establish comprehensive characteristic information for each frequency point, the instantaneous energy value, instantaneous frequency value, and frequency co-occurrence probability value corresponding to each frequency point need to be uniformly collected. This can be achieved by iterating through the frequency points using structured programming, reading the three key parameter values ​​for each point, and writing these three parameters into a standard-format data record unit in a unified field order. Each record unit represents all the analytical characteristics of a frequency point. For example, within the 100 to 300 Hz range, frequency points are divided into intervals of 0.5 Hz. The three parameters extracted for each frequency point are 1.6, 245.5, and 0.32, forming a structured record unit containing these three fields. Next, these record units are arranged sequentially according to the frequency points from low to high, and logical combinations are achieved using arrays or list containers to ultimately generate an interference frequency band index table. This index table reflects the energy changes, frequency synchronization levels, and potential interference probabilities of all frequency points in the entire test channel, serving as the foundation for subsequent frequency band identification and interference screening.

[0079] The instantaneous energy value represents the response intensity of a frequency point in the current subband, serving as a quantitative indicator of the actual strength of the structure's response to excitation. The instantaneous frequency value represents the instantaneous center frequency of that frequency point in the time domain, a characteristic parameter for measuring spectral drift. The frequency co-occurrence probability value is used to evaluate the consistency of the response of that frequency point across different channels; the closer the probability is to a certain value, the stronger the consistency. A data recording unit is the smallest unit of information organized in a unified field order, facilitating indexing and computation. The unified field structure ensures data comparability and batch processing capabilities between recording units, while the frequency-point order ensures the orderliness of the index table, aiding subsequent algorithms in range retrieval, boundary judgment, and interference cluster identification. Therefore, the interference frequency band index table is not only a data integration structure but also a data mapping tool with the ability to express interference information.

[0080] S3. Based on the obtained mixed response signal, construct a support vector regression model with instantaneous phase fluctuation factor and kurtosis deviation factor as input, generate the structural response confidence score for each frequency point, distinguish the structural modal frequency and the accelerometer's own resonance frequency according to the mixed response signal under the condition of self-excited frequency of the accelerometer, and classify the frequency points that do not belong to either the structural modal frequency or the accelerometer's own resonance frequency as unresolved frequency points.

[0081] In this embodiment, S3 specifically includes the following steps:

[0082] S301. For each frequency point in the mixed response signal of the accelerometer under the condition of self-excited frequency, extract the instantaneous phase change rate sequence and calculate the standard deviation as the instantaneous phase fluctuation factor. Calculate the kurtosis value of the response amplitude of each frequency point in all accelerometer channels and compare it with the reference kurtosis value corresponding to the structural modal characteristics to obtain the kurtosis deviation rate factor.

[0083] S302. Using the instantaneous phase fluctuation factor and kurtosis deviation factor as input features, construct a support vector regression model, and use structural modal frequencies and the resonant frequency samples of the accelerometer itself for supervised training, establish a mapping function between frequency points and structural response confidence scores, and output the structural response confidence score for each frequency point.

[0084] S303. Set the structural modal confidence threshold and the resonance interference confidence threshold. Classify the frequency points whose structural response confidence score is higher than the structural modal confidence threshold as structural modal frequencies, classify the frequency points whose structural response confidence score is lower than the resonance interference confidence threshold as the accelerometer's own resonance frequency, and classify the frequency points whose structural response confidence score is between the two thresholds as undecided frequency points.

[0085] Using the structural response confidence score as input, two predefined thresholds are introduced as classification boundaries for structural modal frequencies and the accelerometer's own resonant frequencies, respectively. First, a structural modal confidence threshold is set to identify the critical point where the score reaches the confidence level of the structural response features. When the score corresponding to a frequency point is higher than this structural modal confidence threshold, the frequency point is determined to belong to the structural modal frequency. Second, a resonance interference confidence threshold is set to characterize the criterion for determining whether the score value is lower than the upper limit of the sensor's resonance features. When the score value of a frequency point is lower than this resonance interference confidence threshold, the frequency point is classified as the accelerometer's own resonant frequency. When the score value falls within the range between the two thresholds, it indicates that the frequency point has ambiguity in its feature representation and lacks a clear classification basis; therefore, it is marked as an undecided frequency point and enters the subsequent classification mechanism for further processing.

[0086] The structural modal confidence threshold and the resonance interference confidence threshold, serving as two classification thresholds, are fixed values ​​set based on response distribution analysis using the model training sample set. The structural modal confidence threshold is typically determined based on the lower quartile or minimum confidence boundary of all structural modal sample scores, ensuring sufficient stability of frequencies classified as structural modal frequencies at the feature level. The resonance interference confidence threshold is generally set based on the upper boundary of resonance sample scores, ensuring the exclusion of misclassification due to model fluctuations. The interval between the two thresholds is used to cover the uncertain region of discrimination, identify boundary frequency points, and facilitate further judgment in subsequent steps using neighboring measurement point information or joint indicators. This dual-threshold structure achieves robust control over frequency point classification results, enhancing the model's discrimination accuracy and anti-interference capability under complex mixed response signals.

[0087] In this embodiment, S301 specifically refers to:

[0088] For the mixed response signal of the accelerometer under the condition of self-excited frequency, the phase values ​​corresponding to multiple sampling times are extracted at each frequency point to form a time-ordered sequence of instantaneous phase change rate. The standard deviation of the instantaneous phase change rate sequence is calculated, and the instantaneous phase fluctuation factor corresponding to the frequency point is output.

[0089] When analyzing the hybrid response signal of an accelerometer with a self-excited frequency, it is necessary to extract the instantaneous phase values ​​corresponding to multiple sampling times at each frequency point and construct a time-ordered sequence of instantaneous phase change rates. This operation can extract phase information from the analytic signal after Hilbert transform, then calculate the phase difference between adjacent sampling points according to the sampling time order, and construct a sequence of change rates from the continuous phase differences. To obtain a robust measure of volatility, the standard deviation of this sequence needs to be calculated to reflect the degree of phase perturbation at the current frequency point in the time dimension. If the standard deviation of the phase volatility at a certain frequency point is significantly large, it may mean that its phase evolution is unstable, further indicating that the frequency point may be affected by unstructured local resonance factors, thus providing a basis for subsequent classification judgment. For example, at a frequency of 1000Hz, if the phase change rates at 10 consecutive moments are 0.02, 0.01, 0.03, 0.12, 0.15, 0.10, 0.09, 0.11, 0.13, and 0.14 respectively, their standard deviation can be calculated as a stable volatility index, which can be used as the instantaneous phase volatility factor corresponding to that frequency point.

[0090] In this process, the frequency point represents the location of the frequency domain component being analyzed, and the instantaneous phase value represents the phase characteristic of each sampling point in the time series corresponding to that frequency point. The instantaneous phase change rate sequence is composed of the phase increments between every pair of sampling points, representing the rate fluctuation of phase change over a short period of time. The standard deviation is used to quantify the fluctuation range of the entire sequence, i.e., whether the phase change of a certain frequency point is concentrated and stable across multiple sampling times. The instantaneous phase volatility factor is represented by the standard deviation value; a larger value indicates more severe fluctuations, while a smaller value indicates more stable phase evolution. This factor can be effectively used to distinguish between structural modal frequencies and the resonant frequencies of the accelerometer itself: the former usually manifests as relatively stable phase evolution across multiple channels, while the latter may manifest as abnormally severe phase perturbations in an isolated channel, thus providing clear input for subsequent machine learning models.

[0091] For each frequency point, the corresponding amplitude response set is extracted from all acceleration sensor channels, and kurtosis calculation is performed on the amplitude response set to obtain the amplitude response kurtosis value of the frequency point in all channels.

[0092] For each frequency point, the corresponding amplitude response value can be extracted from all accelerometer channels, constructing an amplitude response set composed of amplitudes from multiple channels. This amplitude response set is then used as input data to perform kurtosis calculation. Kurtosis represents the sharpness of the data distribution, reflecting the amplitude distribution characteristics of a frequency point across multiple channels. By statistically analyzing the concentration and tail thickness of the amplitude response set, it can be determined whether there is abnormal amplitude behavior at that frequency point that deviates from the normal structural response. For example, if the amplitude responses of a frequency point in 10 channels are 0.2, 0.3, 0.25, 0.28, 2.1, 0.27, 0.26, 0.29, 0.3, and 0.31, the kurtosis value will significantly increase due to the relatively large value of 2.1, indicating that a certain channel has an abnormal resonant response at that frequency point. Such kurtosis indices help identify potential unstructured resonance features in the accelerometer response.

[0093] Kurtosis calculation is based on statistical characteristics and is typically evaluated as the ratio of the fourth-order center moment to the standard deviation. The amplitude response set consists of the amplitude of each frequency point across all accelerometer channels, exhibiting typical spatial distribution characteristics. A high kurtosis value usually indicates a prominent response intensity at that frequency point in a few channels, while the response is stable in most channels; this non-uniform pattern may originate from local resonances in the accelerometer's own material. Low kurtosis values ​​indicate more consistent channel responses, with the frequency point response pattern closely resembling typical structural modal frequency characteristics. Using the kurtosis value of each frequency point in subsequent calculations of the kurtosis deviation factor can assist support vector regression models in distinguishing between structural modal frequencies and the accelerometer's own resonant frequencies, ensuring the accuracy of frequency point classification.

[0094] The amplitude response kurtosis value corresponding to each frequency point is compared with the reference kurtosis value corresponding to the structural modal features. Based on the comparison difference, the kurtosis deviation rate factor of the frequency point is calculated and used as an input feature in the subsequent frequency point credibility assessment process.

[0095] To calculate the kurtosis deviation factor at a frequency point, the kurtosis value of the amplitude response across all accelerometer channels at each frequency point needs to be compared point-by-point with a pre-established reference kurtosis value under structural modal characteristics. The reference kurtosis value can be obtained by statistically analyzing the amplitude responses of multiple known structural modal frequencies in historical tests, forming a standard kurtosis curve or database. In the actual calculation process, the degree of kurtosis deviation is obtained by calculating the ratio of the difference between the current kurtosis value of a frequency point and the corresponding reference kurtosis value. For example, if the kurtosis value of a certain frequency point is 4.8, and the corresponding reference kurtosis value is 2.5, the deviation ratio is calculated using a normalization method to obtain the kurtosis deviation factor for that frequency point. This factor reflects the degree of deviation of the amplitude response shape at the frequency point from the structural modal frequency, thus being used to assess the likelihood that it belongs to the structural response or sensor resonance response.

[0096] The kurtosis deviation factor is a nonlinear input feature constructed based on differences in distribution characteristics, possessing high discriminative power and universality. The amplitude response kurtosis value characterizes the sharpness of the response distribution of a frequency point in the spatial dimension, while the reference kurtosis value represents the typical response pattern under the structural mode. The comparison of differences is completed by calculating the relative deviation rate, avoiding misjudgments due to absolute value shifts caused by differences in the testing environment. This factor serves as a key discriminant indicator in the subsequent frequency point confidence scoring, and is jointly input with the instantaneous phase fluctuation factor into the support vector regression model to drive the mode attribution identification of frequency points. Utilizing the kurtosis deviation factor helps to eliminate local resonance points that are abruptly enhanced only in a few sensor channels, improving the accuracy and stability of identifying structural modal frequencies.

[0097] In this embodiment, S302 specifically refers to:

[0098] The instantaneous phase fluctuation factor and kurtosis deviation factor corresponding to each frequency point are combined into a two-dimensional input vector. Normalization is performed through a unified interval mapping to generate an input feature matrix, which serves as the input set for the support vector regression model.

[0099] To construct the input set for a support vector regression model, the instantaneous phase variability factor and kurtosis factor at each frequency point need to be combined to form a two-dimensional input vector. After combination, to ensure that each feature dimension has a uniform numerical scale during model learning, the two-dimensional input vector needs to be normalized. Normalization can use a minimum-maximum interval linear mapping method to map all factor values ​​to a fixed range, such as between 0 and 1, thereby eliminating the imbalance caused by differences in factor numerical dimensions during model training. Taking a certain frequency point as an example, if its instantaneous phase variability factor is 0.13 and its kurtosis factor is 0.28, after normalization, it may be mapped to 0.52 and 0.76, combined into a two-dimensional input vector [0.52, 0.76], thus forming a row-arranged input feature matrix across all frequency points. This matrix structure can be directly used as the input dataset for the support vector regression model for regression learning.

[0100] The instantaneous phase variability factor represents the drastic phase change of a frequency point in the time domain, while the kurtosis factor reflects the degree of deviation of a frequency point from the spatial response distribution. The two-dimensional input vector formed by these factors comprehensively characterizes the unstructured response properties of the frequency point. During normalization, interval mapping not only improves the model's convergence efficiency but also effectively avoids overfitting or neglecting a particular dimension. The input feature matrix, by retaining the feature combinations for each frequency point, ensures that the model has sufficient discriminative ability to learn the nonlinear mapping relationship between frequency points and structural response confidence scores during training. This feature matrix serves as the fundamental input for determining whether each frequency point belongs to a structural modal frequency or a sensor resonant frequency in subsequent training and prediction.

[0101] A training sample set is constructed. The target score value corresponding to the structural modal frequency sample in the training sample set is set as the first value, and the target score value corresponding to the resonant frequency sample of the accelerometer itself in the training sample set is set as the second value. The first value is greater than the second value. The regression mapping learning operation is performed on the support vector regression model through supervised training.

[0102] To implement supervised training of the support vector regression model, a training sample set containing known frequency labels needs to be constructed. In this set, each sample consists of a two-dimensional input vector and a corresponding target score. The input vector comprises the instantaneous phase variability factor and kurtosis factor of the frequency point. For structural modal frequency samples, a higher target score is set, indicating that the frequency point is more likely to originate from the true structural response; conversely, for accelerometer self-resonance frequency samples, a lower target score is set, representing that the frequency point is more likely to belong to sensor interference. In practice, the frequency point classification can be determined through manual calibration, experimental data labeling, or historical modal experimental results. After constructing the training sample set, it is input into the support vector regression model for training, allowing the model to learn the nonlinear mapping relationship between input features and confidence scores.

[0103] The target score corresponding to the structural modal frequency samples guides the model to identify high-confidence structural response points and is typically set to a value close to the upper limit, such as 1. The target score corresponding to the accelerometer's own resonant frequency samples reflects the lower limit of confidence for non-structural source resonances and is typically set to 0. The relative relationship between the first and second values ​​forms an ordered gradient in the model's score interval, ensuring that the model output is interpretable on a numerical scale. The support vector regression model achieves the mapping ability from feature vectors to structural response confidence scores by minimizing the error between the predicted score and the target score. This supervised learning process significantly improves the model's accuracy in classifying new frequency points and is the core foundation for subsequent frequency point differentiation processing.

[0104] The normalized input vector of each frequency point is input into the support vector regression model after the regression mapping learning operation to generate the structural response confidence score value corresponding to the frequency point, and the structural response confidence score value is used for subsequent classification and judgment processing of the frequency point.

[0105] The normalized input vector for each frequency point is fed into a support vector regression model that has already completed regression mapping learning, sequentially obtaining the structural response confidence score corresponding to that frequency point under the current input feature conditions. The input vector is formed by combining the instantaneous phase fluctuation factor and the kurtosis deviation factor in a fixed order, and enters the support vector regression model after unified normalization mapping. The model predicts the probability that a frequency point belongs to a structural modal feature in the response signal through the nonlinear mapping relationship established during the training phase. The closer the score is to the structural modal target value set during training, the more likely the frequency point belongs to the intrinsic structural response; conversely, the closer the score is to the sensor resonance target value, the lower its probability. For example, if the input vector of a certain frequency point obtains a score of 0.92 in the model output, while the target score value for the structural modal frequency sample in the model is set to 1.0 and the target score value for the sensor resonance frequency sample is set to 0.0, then this frequency point can be judged as a highly reliable structural modal frequency.

[0106] The structural response confidence score is essentially a quantitative indicator assigned to the frequency response signal attribute in the support vector regression model. This indicator predicts the frequency response classification by considering the input features of a nonlinear distribution. The instantaneous phase variability factor characterizes the phase stability of the frequency point, and the kurtosis factor reflects the sharpness of the signal amplitude in its statistical distribution. Together, they constitute the key descriptive variables of the input feature space. The support vector regression model determines the support vector boundary based on the training sample set and establishes a mapping function so that the input features can be accurately mapped to a value within the scoring interval. The score not only provides a quantitative result of the frequency point attribute but also directly serves as the basis for subsequent frequency point classification processing, forming the foundation for effectively distinguishing the structural modal frequency from the resonant frequency of the accelerometer itself.

[0107] S4. Based on the distinction between the structural modal frequencies and the resonant frequencies of the accelerometer itself, generate and output the corresponding frequency classification label set.

[0108] In this embodiment, S4 specifically refers to:

[0109] Extract the mapping data between frequency points and corresponding classification types from the distinction results between structural modal frequencies and the resonant frequencies of the accelerometer itself;

[0110] Based on the distinction between structural modal frequencies and the sensor's own resonant frequencies, mapping data between frequency points and corresponding classification types is extracted. Specifically, this involves assigning category labels to each frequency point based on the previously completed frequency confidence scoring and classification operations. In the structural response confidence scoring results, each frequency point is known to correspond to one of three categories: structural modal frequency, sensor's own resonant frequency, or undetermined frequency point. The extraction operation involves pairing the value of each frequency point with its classification result, forming a set of data pairs containing both frequency value and category name. This mapping data can be automatically obtained programmatically. For example, during the frequency classification process, each frequency point and its classification result can be synchronously written into a cached data structure, then uniformly read and output. Alternatively, label values ​​can be generated by logically judging the confidence scoring results and preset thresholds, and then the frequency values ​​and labels can be combined through a traversal method to form structured data. In this process, "frequency point" refers to the characteristic frequency position determined in the spectrum analysis, "classification type" refers to the three frequency state labels determined based on the confidence scoring rules, and "mapping data" refers to the data entity formed by combining the former two in a one-to-one correspondence, which can be used for subsequent output and recognition. The core technical means of this operation are the explicit definition of data pairing and structured storage rules and the automation of classification information extraction.

[0111] For each frequency point, the frequency value and the corresponding classification type are combined according to a preset field format and sorted in ascending order of frequency value to generate a set of frequency classification labels.

[0112] For each frequency point, the frequency value and corresponding classification type are combined according to a preset field format and arranged in ascending order of frequency value to generate a frequency classification label set. Specifically, this involves encapsulating the paired frequency values ​​and classification types in the discrimination results using a standardized format, integrating them into a unified data record unit. The preset field format refers to a data structure template predefined by the system, typically including two main fields: a frequency field and a classification type field. The frequency field records the numerical value of the frequency point, and the classification type field records the corresponding classification label, such as structural modal frequency, sensor resonant frequency, or unresolved frequency point. The combination method can be implemented using structures or key-value pairs to ensure the correlation between each frequency point and its classification label. After combination, all data record units are sorted in ascending order of frequency value. The sorting can use quicksort or stablesort algorithms to generate a frequency classification label set with continuity and readability. This set is an important foundation for subsequent data output and structural state identification, ensuring the integrity, standardization, and logical consistency of the data presentation. The key technologies of the entire process lie in the unified format data encapsulation, the ascending order sorting mechanism, and the orderly construction strategy of the label set.

[0113] The frequency classification label set is saved as a structured data file and written to a preset storage path for subsequent frequency identification and response analysis.

[0114] For each frequency point, the frequency value and its corresponding classification type are combined according to a preset field format and arranged in ascending order of frequency value to generate a frequency classification label set. Specifically, after a frequency point has been classified as a structural modal frequency, sensor resonant frequency, or undecided frequency point, a fixed format is used to combine and encapsulate the value of each frequency point with its classification type to achieve unified data management and structured storage. The preset field format refers to a predefined data organization form, usually using a binary tuple or table structure. The field order and data type must be consistent. The frequency field is numeric, and the classification field is enumerated or string, ensuring standardized data format and strong readability. After combination, sorting can be performed programmatically to ensure that all frequency points are arranged in ascending order of value, thereby improving the search efficiency and processing consistency of the frequency label set. In the implementation process, arrays, dictionaries, or database tables can be used as containers, and standard ascending sorting functions can be called to sort the frequency fields while retaining the corresponding classification information. The final output is saved as a frequency classification label set, suitable for subsequent structural state identification and frequency filtering processing.

[0115] S5. Dynamically adjust the frequency point identification strategy based on the frequency classification label set, including triggering the neighbor measurement point association verification process under the undecided frequency label, performing frequency point elimination operation under the accelerometer's own resonant frequency label, and performing trust enhancement fitting processing under the structural modal frequency label.

[0116] In this embodiment, S5 specifically refers to:

[0117] For frequency values ​​marked as unresolved frequency points in the frequency classification label set, trigger the neighboring measurement point association test process. Specifically, combine the frequency labels corresponding to the acceleration sensor channels in spatially adjacent locations, perform a consistency test between neighboring measurement points. If there are two or more frequency points labeled as structural modal frequencies and the frequency difference is less than the frequency similarity judgment threshold, then the unresolved frequency point is re-marked as a structural modal frequency.

[0118] When performing the neighboring measurement point association test on frequency values ​​marked as unresolved frequency points in the frequency classification label set, the first step is to determine the set of spatially adjacent channels corresponding to each unresolved frequency point based on the physical deployment location of the accelerometer. This is typically done based on the sensor installation topology or coordinate distance thresholds. Subsequently, the frequency values ​​already marked as structural modal frequencies in the adjacent channels are filtered. Frequency points whose frequency difference with the current unresolved frequency point is lower than the frequency similarity judgment threshold are considered valid reference points. When the number of valid reference points reaches two or more, the frequency point is considered to exhibit cross-measurement point co-occurrence characteristics in space and can be identified as a potential structural modal response frequency. Therefore, the frequency point originally marked as unresolved is updated to a structural modal frequency label. This process enhances the accuracy of identifying frequency points that are easily misjudged, such as boundary modes and weak response modes, and improves the adaptability of the frequency identification algorithm to complex structural response scenarios. In this process, the "frequency similarity judgment threshold" is used to control the acceptable deviation between frequency points. It is usually set by the historical structural frequency stability distribution or the measured error range, while the determination of the set of adjacent measurement points needs to be adapted and adjusted in combination with the actual sensor layout density and local structural features.

[0119] For frequency values ​​marked as the sensor's own resonant frequency in the frequency classification label set, the corresponding frequency points and their energy characteristics are removed from the frequency analysis results and are not included in the subsequent structural frequency identification calculation process.

[0120] When processing frequency values ​​labeled as the resonant frequencies of the accelerometer itself in the frequency classification label set, it is necessary to locate the corresponding data record units in the frequency analysis results, including all feature information such as frequency value, instantaneous energy, instantaneous frequency, and phase. By constructing filtering logic, data exclusion operations are performed on frequency points labeled as the resonant frequencies of the accelerometer itself. Specifically, this can be achieved through conditional filtering and index deletion mechanisms to remove these frequency points from the spectral dataset, feature matrix, or frequency index table, ensuring that they are no longer used as input for structural modal frequency extraction, modeling, or fitting analysis. The core purpose of this processing method is to eliminate non-structural response frequency components caused by the sensor's own resonant devices, avoiding confusion with true structural modal characteristics and improving the purity and robustness of the frequency identification process. During this process, it is necessary to ensure that the exclusion operation does not affect the calculation of the structural response confidence score of other frequency points, and to avoid mistakenly deleting similar frequency points through a precise frequency value matching mechanism. Simultaneously, an error tolerance range can be set to control the accuracy of the exclusion.

[0121] For the frequency values ​​marked as structural modal frequencies in the frequency classification label set, a response consistency fitting operation is performed based on their amplitude variation trends in multiple acceleration sensor channels. A reliable fitting function is calculated and the confidence score of the corresponding frequency point in the frequency identification result is updated.

[0122] When processing frequency values ​​labeled as structural modal frequencies in the frequency classification label set, it is necessary to extract the amplitude response data corresponding to the frequency value from all accelerometer channels and construct an amplitude variation trend sequence with spatial location as a reference. Response consistency fitting operations are performed on these channel amplitude data using methods such as least squares fitting, polynomial curve fitting, or spline interpolation. The fitting results generate a frequency response function to describe the spatial distribution characteristics of the frequency point on the structure. Further, based on the fitting residuals, trend consistency measures, or correlation coefficients between the fitted function and the original channel data, a confidence score for the frequency point in structural modal identification is calculated to update the frequency identification results. This process enhances the stability of structural modal frequency judgment, especially in the presence of noise interference or single-point abnormal fluctuations, helping to suppress local biases using global trends, thereby improving the reliability and completeness of the frequency identification results. All calculations must maintain a one-to-one correspondence between frequency points and their positions in each channel to ensure that the fitting operation has physical spatial interpretability.

[0123] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions according to the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless (e.g., infrared, wireless, microwave, etc.) means. A computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. Available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. Semiconductor media can be solid-state drives.

[0124] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0125] 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.

[0126] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the embodiments described above are merely illustrative; for instance, the division of 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 system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0127] 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.

[0128] In addition, 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.

[0129] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for identifying a resonance point of a spacecraft vibration response, the method comprising: Specifically comprising the following steps: ​ S1, by the spectrum response signal of multiple structure point layout different type acceleration sensor multi-channel discrete frequency difference extraction, construct local peak consistency discriminant factor, identify whether there is self-excitation frequency situation of acceleration sensor; S2, on the basis of identifying the existence of self-excitation frequency, wavelet packet decomposition and Hilbert instantaneous feature extraction are performed on the corresponding channel spectrum signal, and an interference frequency band index table is constructed combining the frequency co-occurrence probability of multiple measuring points to determine the mixed response signal of the acceleration sensor under the condition of self-excitation frequency; S3, on the basis of obtaining the mixed response signal, a support vector regression model is constructed with the instantaneous phase fluctuation factor and the kurtosis deviation rate factor as input, and the structural response credibility score value of each frequency point is generated, the structural modal frequency and the acceleration sensor self-resonance frequency are distinguished according to the mixed response signal of the acceleration sensor under the condition of self-excitation frequency, and the frequency points which do not belong to the structural modal frequency and the acceleration sensor self-resonance frequency are classified as undecided frequency points; S4, based on the distinction result between the structural modal frequency and the acceleration sensor self-resonance frequency, the corresponding frequency classification label set is generated and output; S5, according to the frequency classification label set, the dynamic regulation and control of frequency point identification strategy is performed, including triggering the adjacent measuring point association verification process under the undecided frequency label, performing frequency point elimination operation under the acceleration sensor self-resonance frequency label, and performing trust enhancement fitting processing under the structural modal frequency label.

2. The method of claim 1, wherein: S1 specifically: The spectrum response signals collected by the different types of acceleration sensors arranged at multiple structure points are normalized, the discrete frequency main peak set within the main frequency range of each acceleration sensor channel is extracted, and the amplitude difference of each frequency point between all acceleration sensor channels is calculated to form a channel difference vector; Based on the channel difference vector, a local peak consistency discriminant factor is constructed, which is composed of amplitude deviation rate and peak frequency position cooperativity weight of frequency points in all acceleration sensor channels, and a normalized discriminant value is generated by weighted linear superposition; When the local peak consistency discriminant factor is less than the preset trust threshold, and the frequency point only exists in a single acceleration sensor channel with amplitude response higher than the amplitude deviation recognition threshold, and no frequency point reaching the amplitude response recognition condition is detected in the remaining acceleration sensor channels, it is judged that the acceleration sensor has self-excitation frequency.

3. The method of claim 1, wherein: S2 specifically includes the following steps: S201, on the basis of identifying the existence of self-excitation frequency, the wavelet packet decomposition processing is performed on the spectrum signal of the acceleration sensor channel with self-excitation frequency, and a plurality of frequency sub-band signals are obtained; Hilbert transform processing is performed on each frequency sub-band signal, the instantaneous energy value, instantaneous frequency value and instantaneous phase change rate of each frequency point are extracted, and the frequency point and the three instantaneous feature parameters are combined to generate a frequency point instantaneous feature matrix; S202, based on the frequency point instantaneous feature matrix, the instantaneous frequency values of each frequency point in all acceleration sensor channels are calculated for the difference between each other, and the number of channels with a difference value less than a frequency synchronization judgment threshold is counted; the ratio between the number of channels counted and the total number of acceleration sensor channels is taken as the frequency co-occurrence probability value, and the frequency point, the instantaneous energy value, the instantaneous frequency value and the frequency co-occurrence probability value are taken as fields to construct an interference frequency band index table; S203, from the interference frequency band index table, a frequency co-occurrence probability value less than a frequency consistency judgment threshold and a frequency point set with only one acceleration sensor channel with an instantaneous energy value higher than an energy comparison reference value are selected, and marked as a mixed response signal frequency band under the condition of acceleration sensor self-excitation frequency.

4. The method of claim 3, wherein: S202 specifically includes: The instantaneous frequency values of each frequency point in the frequency point instantaneous feature matrix corresponding to all acceleration sensor channels are taken as input references, the instantaneous frequency difference value calculation operation between each other is performed according to the channel combination relationship, and a frequency difference value array is generated; For all instantaneous frequency difference values in the frequency difference value array, the number of channel combinations less than the frequency synchronization judgment threshold is counted, and the statistical number is divided by the total number of acceleration sensor channels to calculate the frequency co-occurrence probability value; The instantaneous energy value, the instantaneous frequency value and the frequency co-occurrence probability value corresponding to each frequency point are read in turn to construct a data record unit containing a unified field structure, and the interference frequency band index table is formed by arranging and combining the frequency points in order.

5. The method of claim 1, wherein: S3 specifically includes the following steps: S301, for each frequency point in the mixed response signal under the condition of acceleration sensor self-excitation frequency, the instantaneous phase fluctuation rate sequence is extracted and the standard deviation is calculated as the instantaneous phase fluctuation factor, the kurtosis value of the response amplitude of each frequency point in all acceleration sensor channels is counted, and compared with the reference kurtosis value corresponding to the structural modal characteristic to obtain the kurtosis deviation rate factor; S302, the instantaneous phase fluctuation factor and the kurtosis deviation rate factor are taken as input features to construct a support vector regression model, and the model is supervised trained using structural modal frequency and acceleration sensor self-resonance frequency samples to establish a mapping function between frequency points and structural response credibility score values, and the structural response credibility score values of each frequency point are output; S303, set the structural modal credibility threshold and the resonance interference credibility threshold, classify the frequency points with structural response credibility score values higher than the structural modal credibility threshold as structural modal frequencies, the frequency points with structural response credibility score values lower than the resonance interference credibility threshold as acceleration sensor self-resonance frequencies, and the frequency points with structural response credibility score values between the two thresholds as undecided frequency points.

6. The method of claim 5, wherein: S301 specifically includes: For the mixed response signal under the condition of acceleration sensor self-excitation frequency, the phase values corresponding to multiple sampling times at each frequency point are extracted to form a time-ordered instantaneous phase fluctuation rate sequence, and the standard deviation of the instantaneous phase fluctuation rate sequence is calculated to output the instantaneous phase fluctuation factor corresponding to the frequency point; For each frequency point, a corresponding amplitude response set is extracted from all acceleration sensor channels, a kurtosis calculation operation is performed on the amplitude response set, and a kurtosis value of the amplitude response of the frequency point in all channels is obtained; The kurtosis value corresponding to each frequency point is compared with the reference kurtosis value corresponding to the structural modal characteristic, and a kurtosis deviation rate factor of the frequency point is calculated based on the comparison difference and used as an input feature for subsequent frequency point credibility evaluation.

7. The method of claim 5, wherein: S302 specifically comprises: The instantaneous phase fluctuation factor corresponding to each frequency point is combined with the kurtosis deviation rate factor to form a two-dimensional input vector, normalization processing is performed through unified interval mapping, an input feature matrix is generated, and the input feature matrix is used as an input set of a support vector regression model; A training sample set is constructed, the target score value corresponding to the structural modal frequency sample in the training sample set is set as a first value, the target score value corresponding to the self-resonance frequency sample of the acceleration sensor in the training sample set is set as a second value, the first value is greater than the second value, and a regression mapping learning operation is performed on the support vector regression model through a supervised training manner; The normalized input vector of each frequency point is input into the support vector regression model after the regression mapping learning operation, a structural response credibility score value corresponding to the frequency point is generated, and the structural response credibility score value is used for subsequent classification judgment processing of the frequency point.

8. The method of claim 1, wherein: S4 specifically comprises: Mapping data of the frequency point and the corresponding classification type are extracted from the distinction result between the structural modal frequency and the self-resonance frequency of the acceleration sensor; For each frequency point, the frequency value and the corresponding classification type are combined according to a preset field format, and arranged in ascending order of the frequency value to generate a frequency classification label set; The frequency classification label set is saved as a structured data file, and the file is written into a preset storage path for subsequent frequency identification and response analysis processes.

9. The method of claim 1, wherein: S5 specifically comprises: For the frequency value of the frequency point marked as a pending frequency point in the frequency classification label set, a neighbor point association verification process is triggered, specifically comprising: performing consistency verification between neighbor points according to the frequency labels corresponding to the acceleration sensor channels in the spatially adjacent positions, if there are two or more frequency points with structural modal frequency labels and the frequency difference is less than a frequency similarity judgment threshold, the pending frequency point is re-marked as a structural modal frequency; For the frequency value marked as a sensor self-resonance frequency in the frequency classification label set, the corresponding frequency point and its energy feature are excluded from the frequency analysis result and do not participate in the subsequent structural frequency identification calculation process; For the frequency value marked as a structural modal frequency in the frequency classification label set, a response consistency fitting operation is performed according to the amplitude variation trend in multiple acceleration sensor channels, a credible fitting function is calculated, and the confidence score of the corresponding frequency point in the frequency identification result is updated.

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