Stay cable force calculation method and device based on time sequence analysis

Abstract

The invention discloses a stay cable force calculation method and device based on time sequence analysis in the technical field of bridge monitoring, and the method comprises the steps: carrying out the interference elimination preprocessing of an original vibration signal of a target stay cable, and obtaining the information of a target effective frequency band; power spectral density analysis is carried out, and final power spectral density estimation of vibration energy concentration is identified; screening significant spectrum peaks, and combining adjacent peaks in the significant spectrum peaks to obtain a candidate peak set; identifying a fundamental frequency candidate value calculated in real time; acquiring a historical reference fundamental frequency; determining an optimal fundamental frequency based on the fundamental frequency candidate value calculated in real time, the historical reference fundamental frequency and a pre-established harmonic verification mechanism; and calculating a cable force coefficient based on the reference cable force of the target stay cable and the corresponding reference fundamental frequency measured in the early stage of bridge formation, and calculating the current cable force according to the cable force coefficient and the optimal fundamental frequency. According to the method, the calculation efficiency is remarkably improved, the statistical value of long-term monitoring data can be fully played, and cable force dynamic calibration and abnormity early warning are realized.

Description

Technical Field

[0001] This invention relates to a method and apparatus for calculating cable force of cable stays based on time series analysis, belonging to the field of bridge monitoring technology. Background Technology

[0002] In the health monitoring system of long-span cable-stayed bridges, the stay cables, as key components for transmitting the load of the main girder, have their cable force state as a core parameter for assessing the safety of the bridge structure. Currently, the vibration frequency method is commonly used in engineering to calculate cable force, based on the string vibration equation. However, in practical applications, this method faces severe challenges: environmental noise (such as wind-induced vibration and traffic load) significantly reduces the signal-to-noise ratio of acceleration signals; traditional spectrum analysis algorithms are susceptible to high-order harmonic interference, leading to misjudgment of the fundamental frequency; and when calculating cable force using high-frequency components, strong noise interference completely obscures temperature-related characteristics, making it impossible to capture the regular changes in cable force with temperature.

[0003] Current methods for fundamental frequency analysis of cable-stayed bridges suffer from three limitations: First, the harmonic separation mechanism is weak; existing peak detection algorithms lack a physical correlation model for frequency clusters, making it impossible to effectively identify energy distribution distortions in the fundamental and harmonic frequencies when local damage occurs in the cable. Second, long-term dynamic monitoring capabilities are lacking; discretization analysis makes it difficult to construct high-resolution cable force time-history curves, resulting in the inability to provide timely warnings for progressive damage such as cable corrosion and sudden wind-induced vibration events. Third, the result verification system is incomplete; the dispersion of single fundamental frequency extraction results is too large, and there is a lack of cross-time period statistical verification methods. These deficiencies make it difficult for existing methods to meet the accuracy requirements of all-weather health monitoring of long-span bridges, necessitating the development of a new computational method that integrates time-series analysis and physical constraints. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and device for calculating the cable force of a cable-stayed bridge based on time-series analysis. The existing technology has core defects such as insufficient accuracy of fundamental frequency identification due to environmental noise interference, weak harmonic separation mechanism that cannot identify damage characteristics, lack of long-term dynamic monitoring capability that makes it difficult to capture temperature correlation, and excessive dispersion of single analysis results.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, this invention discloses a method for calculating the cable force of a stay cable based on time-series analysis, comprising:

[0007] The original vibration signal of the target cable-stayed cable is preprocessed to eliminate interference, thereby obtaining the effective frequency band information of the target.

[0008] Power spectral density analysis is performed on the effective frequency band information of the target to identify the final power spectral density estimate of the vibration energy concentration;

[0009] Significant spectral peaks are screened from the final power spectral density estimate of the vibration energy concentration by combining amplitude and frequency spacing thresholds, and neighboring peaks among the significant spectral peaks are merged to obtain a candidate peak set.

[0010] The fundamental frequency candidate value is identified in real time from the candidate peak set using a harmonic relationship model;

[0011] Obtain historical reference base frequency;

[0012] The optimal fundamental frequency is determined based on real-time calculated candidate fundamental frequencies, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism.

[0013] Based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, the cable force coefficient is calculated, and the current cable force is calculated according to the cable force coefficient and the optimal fundamental frequency.

[0014] Furthermore, the formula for the target effective frequency band information is:

[0015] ;

[0016] In the formula, x filtered Indicates the target's effective frequency band information. This represents a zero-phase bidirectional filter function. This represents the transfer function of the Butterworth bandpass filter. This represents the signal after removing invalid values ​​from the original acceleration signal x(t);

[0017] ;

[0018] ;

[0019] In the formula, For the center frequency, π is the mathematical constant of a circle. The lower cutoff frequency, The upper cutoff frequency; is the quality factor of the l-th second-order bandpass unit; s is the complex frequency independent variable.

[0020] Further, the step of performing power spectral density analysis on the target effective frequency band information to identify the final power spectral density estimate of the vibration energy concentration includes:

[0021] The target effective frequency band information Divide into K overlapping segments, each segment having an acceleration signal length of... Each acceleration signal segment uses the Hanning window. To reduce spectral leakage, each segment of the acceleration signal x is obtained k The formula for (n) is:

[0022] ;

[0023] ;

[0024] In the formula, D is the inter-segment offset, and N is the number of sampling points per segment;

[0025] Perform a Discrete Fourier Transform on each acceleration signal segment to obtain the spectrum, and calculate the one-sided power spectrum. The formula is:

[0026] ;

[0027] In the formula, The energy normalization factor for the window function. The sampling frequency of the original input signal. This represents the spectrum obtained by performing a discrete Fourier transform on each segment of the acceleration signal;

[0028] The power spectrum of all segments was analyzed using the Welch method. The final power spectral density estimate is obtained by averaging, as shown in the formula:

[0029] ;

[0030] In the formula, S xx (f) represents the final power spectral density estimate.

[0031] Furthermore, the combination of amplitude and frequency spacing thresholds filters significant spectral peaks from the final power spectral density estimate of the vibration energy concentration, and merges neighboring peaks among the significant spectral peaks to obtain a candidate peak set, including:

[0032] Set minimum peak relative height From the final power spectral density estimate, values ​​higher than the maximum amplitude are filtered out and retained. The peak, the formula is:

[0033] ;

[0034] In the formula, Higher than the maximum amplitude The peak, This is the maximum amplitude value;

[0035] The result Sort by frequency in ascending order, if the frequency difference between the two peaks is... Less than the merging threshold Then, redundant peaks are merged, and peaks with larger amplitudes are retained. The formula is as follows:

[0036] ;

[0037] In the formula, The frequency of the (j+1)th peak after sorting by frequency in ascending order. Let j be the frequency of the j-th peak after sorting by frequency in ascending order. This represents the (j+1)th peak after being sorted in ascending order of frequency. This represents the j-th peak after being sorted in ascending order of frequency. To obtain the maximum value;

[0038] Repeat the merging process until there are no more neighboring peaks to merge, thus obtaining a set of candidate peaks.

[0039] Furthermore, the step of identifying the real-time calculated fundamental frequency candidate value from the candidate peak set through the harmonic relationship model includes:

[0040] Select the minimum frequency from the candidate peak set. Maximum amplitude frequency and the second largest amplitude frequency Arrange the smallest frequencies in ascending order of frequency magnitude. Maximum amplitude frequency and the second largest amplitude frequency And form a frequency group F, represented as:

[0041] ;

[0042] Let the base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate values ​​for the fundamental frequency. Represents a positive integer.

[0043] Furthermore, the aforementioned base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate fundamental frequencies, including:

[0044] The formula for generating candidate fundamental frequencies is:

[0045] ;

[0046] In the formula, Candidate fundamental frequency;

[0047] calculate For the corresponding order m+n, the formula for verifying higher-order harmonics is:

[0048] ;

[0049] In the formula, n is an integer. It is a rounding function;

[0050] Error assessment is performed using the following formula:

[0051] ;

[0052] Traversal Find the first one that satisfies of Combine, return immediately The real-time calculated candidate value of the fundamental frequency is obtained.

[0053] Furthermore, obtaining the historical reference base frequency includes:

[0054] Probability density modeling, the formula is:

[0055] ;

[0056] In the formula, Let be the probability density function. A set of fundamental frequency sequences calculated for the obtained historical time period The total number of elements in the fundamental frequency sample set, i∈[1,N], This represents the i-th fundamental frequency sample. The independent variable of the frequency function is... Let h be the Gaussian kernel density function, and h be the bandwidth. , The standard deviation of all fundamental frequency samples;

[0057] Calculate the probability density function In the domain The maximum point on the frequency spectrum is used as the historical reference fundamental frequency, and the formula is:

[0058] ;

[0059] In the formula, As a historical reference frequency, The minimum frequency in the domain, This represents the maximum frequency within the defined domain.

[0060] Furthermore, the determination of the optimal fundamental frequency based on real-time calculated candidate fundamental frequency values, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism includes:

[0061] Establish a harmonic verification mechanism, the formula is as follows:

[0062] ;

[0063] In the formula, The candidate values ​​for the fundamental frequency are calculated in real time. As a historical reference frequency, Verify the calculated values ​​for harmonics;

[0064] If the verification fails, the optimal fundamental frequency is searched within a range of ±5%, using the following formula:

[0065] ;

[0066] ;

[0067] In the formula, To be the optimal fundamental frequency, These are the weighted smoothing coefficients. The average of all fundamental frequency estimates. This is the adjusted candidate optimal fundamental frequency. It is a vector consisting of all actual harmonic frequencies. A vector consisting of the order indices of the harmonics. As the independent variable, It is the Euclidean norm.

[0068] Further, the calculation of the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target stay cable measured in the early stage of bridge completion, and the calculation of the current cable force based on the cable force coefficient and the optimal fundamental frequency, includes:

[0069] Reference cable forces measured in the early stages of bridge completion and corresponding reference fundamental frequency The cable tension coefficient C is calculated using the following formula:

[0070] ;

[0071] Based on the optimal fundamental frequency Calculate the current cable force The formula is:

[0072] .

[0073] Secondly, the present invention also discloses a cable force calculation device based on time-series analysis, comprising:

[0074] The preprocessing module is used to perform interference removal preprocessing on the original vibration signal of the target cable-stayed cable to obtain the effective frequency band information of the target;

[0075] The analysis module is used to perform power spectral density analysis on the effective frequency band information of the target and identify the final power spectral density estimate of the vibration energy concentration.

[0076] The detection and merging module is used to filter significant spectral peaks from the final power spectral density estimate of the vibration energy set by combining amplitude and frequency spacing thresholds, and merge neighboring peaks among the significant spectral peaks to obtain a candidate peak set.

[0077] The fundamental frequency solution module is used to identify real-time calculated candidate fundamental frequencies from the candidate peak set using a harmonic relationship model.

[0078] The estimation calculation module is used to obtain the historical reference fundamental frequency;

[0079] The dynamic fundamental frequency verification module is used to determine the optimal fundamental frequency based on real-time calculated fundamental frequency candidate values, historical reference fundamental frequencies, and pre-established harmonic verification mechanisms.

[0080] The cable force calculation module is used to calculate the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, and to calculate the current cable force based on the cable force coefficient and the optimal fundamental frequency.

[0081] The beneficial effects achieved by this invention are as follows:

[0082] The method provided by this invention establishes a harmonic model by intelligently selecting three key characteristic frequencies—the minimum frequency, the maximum amplitude frequency, and the second-largest amplitude frequency—and optimizes the fundamental frequency solution path, significantly improving computational efficiency compared to full-frequency calculation. It utilizes time-varying fundamental frequency data accumulated over a long period by a health monitoring system, extracting the probabilistic dominant frequency through kernel density estimation, overcoming random errors in single measurements, and fully leveraging the statistical value of long-term monitoring data. Using a stable fundamental frequency as a benchmark, it verifies the harmonic compliance of real-time data or historical records online, achieving dynamic cable force calibration and anomaly early warning, accurately reflecting the evolution trend of the structural state. Attached Figure Description

[0083] Figure 1 This is a flowchart illustrating a method for calculating cable force based on time-series analysis provided by the present invention.

[0084] Figure 2 This is a time history curve of the vibration acceleration of a cable-stayed bridge throughout the day in Example 2.

[0085] Figure 3 The image shows the 10-minute vibration acceleration time history curve of a cable-stayed bridge in Example 2.

[0086] Figure 4 This is a power spectral density distribution diagram of the cable-stayed bridge in Example 2.

[0087] Figure 5 In Example 2 Significant frequency plot when = 0.05.

[0088] Figure 6The graph shows the fundamental frequency result calculated in Example 2.

[0089] Figure 7 The fundamental frequency time history curve in Example 2

[0090] Figure 8 The kernel density estimation curve in Example 2.

[0091] Figure 9 The power spectral density map after accurate identification in Example 2

[0092] Figure 10 The final fundamental frequency time history curve of the stay cable in Example 2.

[0093] Figure 11 The time history curve of the cable force in Example 2 is shown. Detailed Implementation

[0094] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0095] Example 1, as Figure 1 As shown, this invention discloses a method for calculating the cable force of a stay cable based on time series analysis, including:

[0096] The original vibration signal of the target cable-stayed cable is preprocessed to eliminate interference, thereby obtaining the effective frequency band information of the target.

[0097] Power spectral density analysis is performed on the effective frequency band information of the target to identify the final power spectral density estimate of the vibration energy concentration;

[0098] Significant spectral peaks are screened from the final power spectral density estimate of the vibration energy concentration by combining amplitude and frequency spacing thresholds, and neighboring peaks among the significant spectral peaks are merged to obtain a candidate peak set.

[0099] The fundamental frequency candidate value is identified in real time from the candidate peak set using a harmonic relationship model;

[0100] Obtain historical reference base frequency;

[0101] The optimal fundamental frequency is determined based on real-time calculated candidate fundamental frequencies, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism.

[0102] Based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, the cable force coefficient is calculated, and the current cable force is calculated according to the cable force coefficient and the optimal fundamental frequency.

[0103] Cable vibration signal preprocessing methods include:

[0104] Based on the characteristic that the fundamental frequency of cable-stayed bridge vibration is within 0.1~5Hz, the original acceleration signal... Preprocessing is performed. First, invalid values ​​in the signal are eliminated:

[0105] ;

[0106] Subsequently, a Butterworth bandpass filter was used for frequency band extraction, and its transfer function is:

[0107] ;

[0108] In the formula, For the center frequency, π is the mathematical constant of a circle. The lower cutoff frequency, The upper cutoff frequency; is the quality factor of the l-th second-order bandpass unit; s is the complex frequency independent variable.

[0109] Finally, phase filtering is performed ( To avoid signal distortion, the final output signal is preprocessed.

[0110] ;

[0111] In the formula, x filtered Indicates the target's effective frequency band information. This represents a zero-phase bidirectional filter function. This represents the transfer function of the Butterworth bandpass filter. This represents the signal after removing invalid values ​​from the original acceleration signal x(t).

[0112] The step of performing power spectral density analysis on the target effective frequency band information to identify the final power spectral density estimate of the vibration energy concentration includes:

[0113] The target effective frequency band information Divide into K overlapping segments, each segment having an acceleration signal length of... Each acceleration signal segment uses the Hanning window. To reduce spectral leakage, each segment of the acceleration signal x is obtained k The formula for (n) is:

[0114] ;

[0115] ;

[0116] In the formula, D is the inter-segment offset, which is generally 50%, and N is the number of sampling points per segment;

[0117] Perform a Discrete Fourier Transform (DFT) on each acceleration signal segment to obtain the spectrum, and calculate the one-sided power spectrum. The formula is:

[0118] ;

[0119] In the formula, The energy normalization factor for the window function. The sampling frequency of the original input signal. This represents the spectrum obtained by performing a discrete Fourier transform on each segment of the acceleration signal;

[0120] The power spectrum of all segments was analyzed using the Welch method. Averaging yields the final power spectral density (PSD) estimate, as shown in the formula:

[0121] ;

[0122] In the formula, S xx (f) represents the final power spectral density estimate.

[0123] The combination of amplitude and frequency spacing thresholds filters significant spectral peaks from the final power spectral density estimate of the vibration energy concentration, and merges neighboring peaks among the significant spectral peaks to obtain a candidate peak set, including:

[0124] After power spectral density (PSD) analysis, the spectrum S of the cable-stayed bridge vibration signal... xx (f) may contain multiple peaks, including both true fundamental and harmonic components, as well as noise or interference peaks. To accurately extract the effective frequency components, a dual-threshold peak detection and merging strategy is employed.

[0125] Set minimum peak relative height From the final power spectral density estimate, values ​​higher than the maximum amplitude are filtered out and retained. The peak, the formula is:

[0126] ;

[0127] In the formula, Higher than the maximum amplitude The peak, For the maximum amplitude, ;

[0128] Minimum peak spacing constraint: Adjacent peaks must be spaced at least... To prevent dense noise peaks from affecting the detection.

[0129] Because noise or spectral leakage can cause multiple adjacent peaks for the same frequency component, redundant peaks need to be merged. The resulting... Sort by frequency in ascending order, if the frequency difference between the two peaks is... Less than the merging threshold Then, redundant peaks are merged, and peaks with larger amplitudes are retained. The formula is as follows:

[0130] ;

[0131] In the formula, The frequency of the (j+1)th peak after sorting by frequency in ascending order. Let j be the frequency of the j-th peak after sorting by frequency in ascending order. This represents the (j+1)th peak after being sorted in ascending order of frequency. This represents the j-th peak after being sorted in ascending order of frequency. To obtain the maximum value;

[0132] Repeat the merging process until there are no more neighboring peaks to merge, thus obtaining a set of candidate peaks.

[0133] The process of identifying real-time calculated fundamental frequency candidate values ​​from the candidate peak set using a harmonic relationship model includes:

[0134] In the vibration analysis of cable-stayed bridges, the fundamental frequency can be accurately identified from multiple peak frequencies using a harmonic relationship model. This method is based on the physical property that the vibration frequency of a cable-stayed bridge must satisfy an integer multiple harmonic relationship (i.e., (where n is the harmonic order).

[0135] Select the minimum frequency from the candidate peak set. Maximum amplitude frequency and the second largest amplitude frequency Arrange the smallest frequencies in ascending order of frequency magnitude. Maximum amplitude frequency and the second largest amplitude frequency And form a frequency group F, represented as:

[0136] ;

[0137] Let the base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate values ​​for the fundamental frequency. Represents a positive integer.

[0138] The base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate fundamental frequencies, including:

[0139] The formula for generating candidate fundamental frequencies is:

[0140] ;

[0141] In the formula, Candidate fundamental frequency;

[0142] calculate The corresponding order m+n is used to verify higher-order harmonics. The corresponding order (m+n) is given by the formula:

[0143] ;

[0144] In the formula, n is an integer. It is a rounding function;

[0145] Error assessment is performed using the following formula:

[0146] ;

[0147] Traversal Find the first full Sufficient Combine, return immediately The real-time calculated candidate value of the fundamental frequency is obtained.

[0148] A set of fundamental frequency sequences calculated from historical time periods Constructing a fundamental frequency sample set and using kernel density estimation to determine the optimal reference fundamental frequency, the step of obtaining historical reference fundamental frequencies includes:

[0149] Probability density modeling, the formula is:

[0150]

[0151] In the formula, Let be the probability density function. A set of fundamental frequency sequences calculated for the obtained historical time period The total number of elements in the fundamental frequency sample set, i∈[1,N], This represents the i-th fundamental frequency sample. The independent variable of the frequency function is... Let h be the Gaussian kernel density function, and h be the bandwidth. , The standard deviation of all fundamental frequency samples;

[0152] The Gaussian kernel density function is expressed as:

[0153] ;

[0154] Calculate the probability density function In the domain The maximum point on the frequency spectrum is used as the historical reference fundamental frequency, and the formula is:

[0155] ;

[0156] In the formula, As a historical reference frequency, The minimum frequency in the domain, This represents the maximum frequency within the defined domain.

[0157] The determination of the optimal fundamental frequency based on real-time calculated candidate fundamental frequency values, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism includes:

[0158] Establish a harmonic verification mechanism, the formula is as follows:

[0159] ;

[0160] In the formula, The candidate values ​​for the fundamental frequency are calculated in real time. As a historical reference frequency, Verify the calculated values ​​for harmonics;

[0161] If the verification fails, the optimal fundamental frequency is searched within a range of ±5%, using the following formula:

[0162] ;

[0163] ;

[0164] In the formula, To be the optimal fundamental frequency, These are the weighted smoothing coefficients. The average of all fundamental frequency estimates. This is the adjusted candidate optimal fundamental frequency. It is a vector consisting of all actual harmonic frequencies. A vector consisting of the order indices of the harmonics. As the independent variable, It is the Euclidean norm.

[0165] The process of calculating the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, and calculating the current cable force based on the cable force coefficient and the optimal fundamental frequency, includes:

[0166] Based on string vibration theory, a dynamic cable force monitoring model is established, using reference cable forces measured in the early stages of bridge completion. and corresponding reference fundamental frequency The cable tension coefficient C is calculated using the following formula:

[0167] ;

[0168] Reference base frequency Calculated using initial cable tension monitoring data from the health monitoring system .

[0169] Based on the optimal fundamental frequency Calculate the current cable force The formula is:

[0170] .

[0171] Example 2, based on the same inventive concept as Example 1, provides a method for calculating cable force based on time-series analysis, including: cable vibration signal preprocessing, power spectral density analysis, dual-threshold peak detection and merging, solving the fundamental frequency using a harmonic relationship model, calculating the reference fundamental frequency using kernel density estimation, dynamic fundamental frequency verification, and cable force calculation.

[0172] The aforementioned cable vibration signal preprocessing includes: taking the time history curve of the vibration acceleration of a cable-stayed bridge throughout the day as an example, such as... Figure 2 As shown, the sampling frequency is 50Hz.

[0173] The target cable vibration signal is preprocessed to eliminate interference and retain effective frequency band information. The cable vibration acceleration is divided into 10-minute acceleration data segments, and invalid values ​​are processed (invalid values ​​are replaced with 0) and bandpass filtering is applied for noise reduction. =0.1Hz, =5Hz), the 10-minute vibration acceleration time history curve of the cable-stayed bridge is as follows: Figure 3 As shown.

[0174] The power spectral density analysis includes: calculating the signal power spectral density using the Welch method, identifying the frequency band characteristics where vibration energy is concentrated, and the power spectral density distribution of the actual bridge's cable-stayed cables is as follows. Figure 4 As shown.

[0175] The aforementioned dual-threshold peak detection and merging includes: after power spectral density analysis, the spectrum of the cable-stayed bridge vibration signal. It may contain multiple peaks, including real fundamental and harmonic components, as well as noise or interference peaks. In order to accurately extract the effective frequency components, a dual-threshold peak detection and merging strategy is adopted.

[0176] Perform dual-threshold peak detection and merging to identify significant spectral peaks and their corresponding frequencies, and define frequency merging thresholds. Merge adjacent peaks to avoid duplicate counting.

[0177] The harmonic relationship model for solving the fundamental frequency includes: based on the physical characteristic that the vibration frequency of a cable-stayed bridge must satisfy an integer multiple harmonic relationship, i.e. , where n is the harmonic order, and the fundamental frequency can be accurately identified from multiple peak frequencies through the harmonic relationship model.

[0178] In this embodiment, the fundamental frequency is generated. Simulated signals with different response frequencies of 0.8Hz are used to derive and verify the minimum frequency. Maximum amplitude frequency Second maximum amplitude frequency A calculation model for the harmonic relationship between them.

[0179] like Figure 5 As shown, take =0.05, the calculated fundamental frequency result is as follows Figure 6 As shown, Figure 6 (a)-(i) in the text correspond to respectively Figure 5 The fundamental frequency identification results of each analog signal in (a)-(i) of the present invention under the method of the present invention, except for Figure 6 In the case described in (e), the fundamental frequency for other operating conditions can be effectively calculated, and the power spectral density is expressed in units of [unit missing]. .

[0180] The kernel density estimation calculation of the reference fundamental frequency includes: calculating the reference fundamental frequency based on historical fundamental frequency data using a kernel density estimation method. In this embodiment, the vibration data of the actual bridge cable-stayed bridge is divided into 10-minute intervals to obtain 144 sets of acceleration data. The fundamental frequency of the cable-stayed bridge is calculated according to the method in the previous step. The fundamental frequency time history curve and the corresponding kernel density estimation curve are shown below. Figure 7 and Figure 8 As can be seen, in the actual bridge data, due to noise interference, it is difficult to calculate the fundamental frequency using only the harmonic relationship model. However, through time series data analysis, the reference fundamental frequency of the cable-stayed bridge can be obtained. =0.702Hz.

[0181] The dynamic fundamental frequency verification includes: comparing the candidate fundamental frequency value with the reference fundamental frequency, verifying the reliability of the candidate fundamental frequency value through harmonic matching, and using the reference fundamental frequency. Using the center frequency, the fundamental frequency data of the cable-stayed bridge at various times were checked and calculated. Figure 4 Even the fundamental frequency, which was not very obvious in the original text, can be accurately identified, such as... Figure 9 After dynamic verification calculations, the final fundamental frequency time history curve of the cable-stayed bridge is as follows: Figure 10 The fundamental frequency shows a clear trend of change with temperature, which is consistent with the actual change law of bridge structure.

[0182] The cable force calculation includes: based on the verification results of the fundamental frequency candidate value, calculating the cable force value of the stay cable using the string vibration theory formula. In this embodiment, the cable force is based on the completed bridge cable force F = 3257 kN. =0.703Hz, calculated cable tension coefficient K=6590.33kN / Hz 2 The time history curve of the cable force on that day is calculated as follows: Figure 11 The maximum cable force on that day was 3360.77 kN, the minimum cable force was 3134.90 kN, and the cable force deviation was -3.6% to 3.1%.

[0183] Example 3, based on the same inventive concept as Example 1, provides a cable-stayed bridge force calculation device based on time-series analysis, comprising:

[0184] The preprocessing module is used to perform interference removal preprocessing on the original vibration signal of the target cable-stayed cable to obtain the effective frequency band information of the target;

[0185] The analysis module is used to perform power spectral density analysis on the effective frequency band information of the target and identify the final power spectral density estimate of the vibration energy concentration.

[0186] The detection and merging module is used to filter significant spectral peaks from the final power spectral density estimate of the vibration energy set by combining amplitude and frequency spacing thresholds, and merge neighboring peaks among the significant spectral peaks to obtain a candidate peak set.

[0187] The fundamental frequency solution module is used to identify real-time calculated candidate fundamental frequencies from the candidate peak set using a harmonic relationship model.

[0188] The estimation calculation module is used to obtain the historical reference fundamental frequency;

[0189] The dynamic fundamental frequency verification module is used to determine the optimal fundamental frequency based on real-time calculated fundamental frequency candidate values, historical reference fundamental frequencies, and pre-established harmonic verification mechanisms.

[0190] The cable force calculation module is used to calculate the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, and to calculate the current cable force based on the cable force coefficient and the optimal fundamental frequency.

[0191] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0192] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0193] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0194] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0195] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for calculating the cable force of a stay cable based on time series analysis, characterized in that, include: The original vibration signal of the target cable is preprocessed to eliminate interference, thereby obtaining the effective frequency band information of the target. Power spectral density analysis is performed on the effective frequency band information of the target to identify the final power spectral density estimate of the vibration energy concentration; Significant spectral peaks are screened from the final power spectral density estimate of the vibration energy concentration by combining amplitude and frequency spacing thresholds, and neighboring peaks among the significant spectral peaks are merged to obtain a candidate peak set. The fundamental frequency candidate value is identified in real time from the candidate peak set using a harmonic relationship model; Obtain historical reference base frequency; The optimal fundamental frequency is determined based on real-time calculated candidate fundamental frequencies, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism. Based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, the cable force coefficient is calculated, and the current cable force is calculated according to the cable force coefficient and the optimal fundamental frequency.

2. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The formula for the target effective frequency band information is: ； In the formula, x filtered Indicates the target's effective frequency band information. This represents a zero-phase bidirectional filter function. This represents the transfer function of the Butterworth bandpass filter. This represents the signal after removing invalid values ​​from the original acceleration signal x(t); ； ； In the formula, For the center frequency, π is the mathematical constant of a circle. The lower cutoff frequency, This is the upper cutoff frequency; is the quality factor of the l-th second-order bandpass unit; s is the complex frequency independent variable.

3. The method for calculating cable force based on time-series analysis according to claim 2, characterized in that, The step of performing power spectral density analysis on the target effective frequency band information to identify the final power spectral density estimate of the vibration energy concentration includes: The target effective frequency band information Divide into K overlapping segments, each segment having an acceleration signal length of... Each acceleration signal segment uses the Hanning window. To reduce spectral leakage, each segment of the acceleration signal x is obtained k The formula for (n) is: ； ； In the formula, D is the inter-segment offset, and N is the number of sampling points per segment; Perform a Discrete Fourier Transform on each acceleration signal segment to obtain the spectrum, and calculate the one-sided power spectrum. The formula is: ； In the formula, The energy normalization factor for the window function. The sampling frequency of the original input signal. This represents the spectrum obtained by performing a discrete Fourier transform on each segment of the acceleration signal; The power spectrum of all segments was analyzed using the Welch method. The final power spectral density estimate is obtained by averaging, as shown in the formula: ； In the formula, S xx (f) denotes the final power spectral density estimate.

4. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The combination of amplitude and frequency spacing thresholds filters significant spectral peaks from the final power spectral density estimate of the vibration energy concentration, and merges neighboring peaks among the significant spectral peaks to obtain a candidate peak set, including: Set minimum peak relative height From the final power spectral density estimate, values ​​higher than the maximum amplitude are filtered out and retained. The peak, the formula is: ； In the formula, Higher than the maximum amplitude The peak, This is the maximum amplitude value; The result Sort by frequency in ascending order, if the frequency difference between the two peaks is... Less than the merging threshold Then, redundant peaks are merged, and peaks with larger amplitudes are retained. The formula is: ； In the formula, The frequency of the (j+1)th peak after sorting by frequency in ascending order. Let j be the frequency of the j-th peak after sorting by frequency in ascending order. This represents the (j+1)th peak after being sorted in ascending order of frequency. This refers to the j-th peak after being sorted in ascending order of frequency. To obtain the maximum value; Repeat the merging process until there are no more neighboring peaks to merge, thus obtaining a set of candidate peaks.

5. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The process of identifying real-time calculated fundamental frequency candidate values ​​from the candidate peak set using a harmonic relationship model includes: Select the minimum frequency from the candidate peak set. Maximum amplitude frequency and the second largest amplitude frequency Arrange the smallest frequencies in ascending order of frequency magnitude. Maximum amplitude frequency and the second largest amplitude frequency And form a frequency group F, represented as: ； Let the base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate values ​​for the fundamental frequency. Represents a positive integer.

6. The method for calculating cable force based on time-series analysis according to claim 5, characterized in that, The base frequency satisfy , m is the harmonic order, obtained by traversing Harmonic matching search is performed to obtain real-time calculated candidate fundamental frequencies, including: The formula for generating candidate fundamental frequencies is: ； In the formula, Candidate fundamental frequency; calculate For the corresponding order m+n, the formula for verifying higher-order harmonics is: ； In the formula, n is an integer. It is a rounding function; Error assessment is performed using the following formula: ； Traversal Find the first one that satisfies of Combine, return immediately The real-time calculated candidate value of the fundamental frequency is obtained.

7. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The acquisition of the historical reference base frequency includes: Probability density modeling, the formula is: ； In the formula, Let be the probability density function. A set of fundamental frequency sequences calculated for the obtained historical time period The total number of elements in the fundamental frequency sample set, i∈[1,N], This represents the i-th fundamental frequency sample. The independent variable of the frequency function is... Let h be the Gaussian kernel density function, and h be the bandwidth. , The standard deviation of all fundamental frequency samples; Calculate the probability density function In the domain The maximum point on the frequency spectrum is used as the historical reference fundamental frequency, and the formula is: ； In the formula, As a historical reference frequency, The minimum frequency in the domain, This represents the maximum frequency within the defined domain.

8. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The determination of the optimal fundamental frequency based on real-time calculated candidate fundamental frequency values, historical reference fundamental frequencies, and a pre-established harmonic verification mechanism includes: Establish a harmonic verification mechanism, the formula is as follows: ； In the formula, The candidate values ​​for the fundamental frequency are calculated in real time. As a historical reference frequency, Verify the calculated values ​​for harmonics; If the verification fails, the optimal fundamental frequency is searched within a range of ±5%, using the following formula: ； ； In the formula, To be the optimal fundamental frequency, These are the weighted smoothing coefficients. The average of all fundamental frequency estimates. This is the adjusted candidate optimal fundamental frequency. It is a vector consisting of all actual harmonic frequencies. A vector consisting of the order indices of the harmonics. As the independent variable, It is the Euclidean norm.

9. The method for calculating cable force based on time-series analysis according to claim 1, characterized in that, The process of calculating the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, and calculating the current cable force based on the cable force coefficient and the optimal fundamental frequency, includes: Reference cable forces measured in the early stages of bridge completion and corresponding reference fundamental frequency The cable tension coefficient C is calculated using the following formula: ； Based on the optimal fundamental frequency Calculate the current cable force The formula is: 。 10. A cable-stayed bridge force calculation device based on time-series analysis, characterized in that, include: The preprocessing module is used to perform interference removal preprocessing on the original vibration signal of the target cable-stayed cable to obtain the effective frequency band information of the target; The analysis module is used to perform power spectral density analysis on the effective frequency band information of the target and identify the final power spectral density estimate of the vibration energy concentration. The detection and merging module is used to filter significant spectral peaks from the final power spectral density estimate of the vibration energy set by combining amplitude and frequency spacing thresholds, and merge neighboring peaks among the significant spectral peaks to obtain a candidate peak set. The fundamental frequency solution module is used to identify real-time calculated candidate fundamental frequencies from the candidate peak set using a harmonic relationship model. The estimation calculation module is used to obtain the historical reference fundamental frequency; The dynamic fundamental frequency verification module is used to determine the optimal fundamental frequency based on real-time calculated fundamental frequency candidate values, historical reference fundamental frequencies, and pre-established harmonic verification mechanisms. The cable force calculation module is used to calculate the cable force coefficient based on the reference cable force and corresponding reference fundamental frequency of the target cable measured in the early stage of bridge completion, and to calculate the current cable force based on the cable force coefficient and the optimal fundamental frequency.

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