Bridge cable force identification method based on self-regression power spectrum self-adaptive estimation

Abstract

The invention relates to the technical field of structure health monitoring, in particular to a bridge cable force identification method based on self-regression power spectrum self-adaptive estimation, which comprises the following steps: determining an optimal self-regression model order empirical value; evaluation indexes of the power spectrum of the off-line vibration response data are calculated respectively, weighted summation is carried out on the evaluation indexes to serve as an evaluation function of the power spectrum, and a weight coefficient is optimized and solved; and substituting the optimized and solved weight coefficient into a power spectrum evaluation function, assuming a group of autoregression model orders to respectively calculate an autoregression power spectrum and a corresponding power spectrum evaluation function for vibration response data monitored on line, and predicting an optimal model order suitable for the current vibration data by minimizing the power spectrum evaluation function. Autoregression power spectrum estimation is realized; and picking up a frequency corresponding to a peak value from the power spectrum curve, and realizing cable force identification according to a frequency-cable force calculation formula. According to the invention, effective tracking of the time-varying frequency and the time-varying cable force of the bridge cable is realized.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring technology, and in particular to a method for identifying bridge cable forces based on adaptive estimation of autoregressive power spectrum. Background Technology

[0002] Cable-stayed bridges, with their superior spanning capacity, have become one of the most commonly used bridge types for long-span bridges. As the main load-bearing components of this type of bridge, the health of the cables directly affects the safety of the entire structure. Cable force is a key mechanical indicator reflecting the actual working condition of the cables, and effective testing of cable force is of great significance for the health monitoring and safety assessment of long-span cable-stayed bridges.

[0003] Cable force testing methods include magnetic flux measurement, pressure sensor testing, and vibration methods. Among these, the vibration method is widely used in engineering practice due to its advantages such as simplicity, non-destructive testing, and cost-effectiveness. The basic procedure of this method includes measuring the cable vibration response, identifying the cable's natural frequency, and calculating the cable force based on string vibration theory. Accurately identifying the cable's natural frequency based on its vibration response is a crucial step in ensuring the accuracy of the vibration method for cable force testing.

[0004] To identify the natural frequency of the cable, the acquired time-domain vibration response signal must first be converted to the frequency domain. Then, the frequency values ​​corresponding to the spectral peaks are extracted from the power spectrum or time-frequency spectrum as the estimation result. Currently, this type of spectrum estimation is mostly based on Fourier transform theory. To avoid increased frequency identification errors due to spectral leakage, the vibration signal used for spectrum estimation is usually required to have sufficient data length. However, excessively long data segments weaken the ability to capture time-varying frequency characteristics, thus affecting the effective tracking of time-varying cable forces.

[0005] Power spectrum estimation methods based on autoregressive models can determine frequencies using only short-time vibration data, significantly reducing dependence on data length and effectively improving the ability to track time-varying frequencies. However, the estimation accuracy of this method is highly dependent on the order of the autoregressive model: too low an order leads to underfitting of the power spectrum, making it impossible to display the peak values ​​of the natural frequencies; too high an order causes overfitting, producing spurious frequency peaks in the power spectrum curve. Therefore, the optimal model order must be determined before using the autoregressive model method for spectrum estimation.

[0006] In offline analysis, the model order can usually be determined empirically using power spectrum visualization results. However, when this method is applied to real-time online monitoring data of bridges, the cable force identification process needs to be completely unattended. In this case, how to adaptively determine the order of the autoregressive model is crucial for accurately monitoring cable force changes. Summary of the Invention

[0007] To address this, the present invention provides a bridge cable force identification method based on autoregressive power spectrum adaptive estimation, which overcomes the problems of difficulty in tracking time-varying cable forces and the inability of manual intervention in the identification process to meet online monitoring requirements in the prior art.

[0008] To achieve the above objectives, this invention provides a bridge cable force identification method based on autoregressive power spectrum adaptive estimation, comprising:

[0009] Step S1: Obtain cable vibration response data from the past hour and set the short-time data window length to [value missing]. The vibration response data of 1 hour is divided into equal window lengths. Paragraph; for the first ( Vibration response data of segment ) were analyzed using different autoregressive model orders. and the empirical value of the optimal autoregressive model order The corresponding power spectrum is calculated using the following formula.

[0010]

[0011] In the formula, Spectral line frequency The power spectrum at that location, Sampling frequency, For spectral line frequencies, The imaginary unit, For the order of the autoregressive model, For noise covariance, These are the autoregressive coefficients. Number the autoregressive coefficients;

[0012] Step S2, based on the first Vibration data of segments at different model orders The power spectrum under the given conditions is used to calculate the corresponding evaluation index values. The evaluation indexes include peak significance index, peak resolution, power spectrum entropy, power spectrum smoothness, improved AIC criterion, and improved BIC criterion.

[0013] Step S3: Construct the weighted power spectrum evaluation function using the following formula.

[0014]

[0015] In the formula, For the weighted power spectrum evaluation function, Peak significance index, For peak resolution, For power spectral entropy, For power spectrum smoothness, To improve the AIC criteria, To improve the BIC criteria; , , , and For weighting coefficients, This represents the total number of samples;

[0016] Step S4, with Calculate the weighted power spectrum evaluation function using the initial values ​​of the weighting coefficients, and construct the loss function by combining the empirical values ​​of the optimal autoregressive model:

[0017]

[0018] In the formula, Used to represent a vector composed of weight coefficients. To minimize the weighted power spectrum evaluation function, we provide an approach oriented towards the first... The order-predicted value of the autoregressive model for segment vibration data;

[0019] Step S5: Using the gradient descent method, respectively through the formula...

[0020] , and

[0021] Iterative update of weight coefficient vector In response to Meeting convergence conditions Iteration stopped;

[0022] Among them, superscript Indicates the number of iterations; This is the momentum coefficient, with a value of 0.9; This represents the historical gradient weight, with a value of 0.9. It is a momentum vector, and its initial value is zero; Represents the loss function weight coefficient vector The gradient; The adaptive learning rate; the initial value of the adaptive learning rate. ,

[0023] Step S6: Substitute the solved weight coefficient vector into the weighted power spectrum evaluation function in step S3;

[0024] Step S7, for the vibration response data, assume that the order variation range of the autoregressive model is... Under their respective regression model orders, the power spectrum and the power spectrum evaluation function are calculated based on step S1. Minimize the power spectrum evaluation function to determine the optimal model order suitable for the current vibration response data segment, calculate the power spectrum curve for the corresponding order, and pick the cable natural frequency from the power spectrum curve. ; Subscript For frequency order;

[0025] Step S8, calculate the cable force using the following formula:

[0026]

[0027] In the formula, Indicates storage, Indicates mass per unit length. It is the length of the cable. It is the cross-sectional area of ​​the cable. It is the elastic modulus of the cable. It is the first First frequency.

[0028] Further, in step S1, the empirical value of the optimal autoregressive model The acquisition process includes:

[0029] Step S101: Specify the order of the autoregressive model ;

[0030] Step S102, by analyzing vibration data The autocorrelation function is used to establish the Yule-Walker equation based on the noise covariance and the autoregressive coefficients. The noise covariance and autoregressive coefficients are then solved to calculate the power spectrum. Indicates the length of the data window Sample number within, , Indicates the total number of samples;

[0031] Step S103: Compare the orders of different autoregressive models The power spectrum is used to derive the empirical value of the optimal autoregressive model. .

[0032] Further, it is characterized in that, in step S2,

[0033] The peak significance index is obtained by the following formula:

[0034] ,

[0035] In the formula, This represents the amplitude at the highest peak on the power spectrum curve. The frequency corresponding to the highest peak. and Frequency Nearby frequency band Mean and standard deviation of the intrinsic power spectrum amplitude;

[0036] The peak resolution is obtained by the following formula:

[0037] ,

[0038] In the formula, The frequency difference between the highest peak and its nearest neighbor on the self-power spectrum curve is calculated using the following formula: , The half-power bandwidth frequency is the highest peak on the power spectrum curve. The half-power bandwidth frequency at the nearest peak;

[0039] The power spectral entropy is obtained by the following formula:

[0040] ,

[0041] In the formula, The total number of spectral lines. For the first Each spectral line frequency;

[0042] The power spectrum smoothness is obtained by the following formula:

[0043] ;

[0044] The improved AIC criterion is obtained according to the following formula:

[0045] ;

[0046] The improved BIC criterion is obtained using the following formula:

[0047] .

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention constructs six power spectrum evaluation indicators such as the peak significance index, optimizes the solution of weight coefficients by using machine learning algorithms, obtains the power spectrum evaluation function by weighted summation, and adaptively determines the optimal autoregressive model order by minimizing the power spectrum evaluation function, thereby realizing adaptive estimation of the power spectrum of vibration response. Taking advantage of the fact that this power spectrum estimation method only requires short-time data, it can effectively track the time-varying frequency and time-varying cable force of bridge cables. Attached Figure Description

[0049] Figure 1 This is a graph showing the variation of the power spectrum evaluation function with the order of the autoregressive model in an embodiment of the present invention;

[0050] Figure 2This is a graph showing the power spectrum estimation results of an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0052] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0053] An embodiment of the present invention provides a bridge cable force identification method based on autoregressive power spectrum adaptive estimation, comprising:

[0054] Step S1: Obtain cable vibration response data from the past hour and set the short-time data window length to [value missing]. The vibration response data of 1 hour is divided into equal window lengths. Paragraph; for the first ( Vibration response data of segment ) were analyzed using different autoregressive model orders. and the empirical value of the optimal autoregressive model order The corresponding power spectrum is calculated using the following formula.

[0055]

[0056] In the formula, Spectral line frequency The power spectrum at that location, Sampling frequency, For spectral line frequencies, The imaginary unit, For the order of the autoregressive model, For noise covariance, These are the autoregressive coefficients. Number the autoregressive coefficients;

[0057] Step S2, based on the first Vibration data of segments at different model orders The power spectrum under the given conditions is used to calculate the corresponding evaluation index values. The evaluation indexes include peak significance index, peak resolution, power spectrum entropy, power spectrum smoothness, improved AIC criterion, and improved BIC criterion.

[0058] Step S3: Construct the weighted power spectrum evaluation function using the following formula.

[0059]

[0060] In the formula, For the weighted power spectrum evaluation function, Peak significance index, For peak resolution, For power spectral entropy, For power spectrum smoothness, To improve the AIC criteria, To improve the BIC criteria; , , , and The weighting coefficients are predicted using the following machine learning algorithm. This represents the total number of samples;

[0061] Step S4, with Calculate the weighted power spectrum evaluation function using the initial values ​​of the weighting coefficients, and construct the loss function by combining the empirical values ​​of the optimal autoregressive model:

[0062]

[0063] In the formula, Used to represent a vector composed of weight coefficients. To minimize the weighted power spectrum evaluation function, we provide an approach oriented towards the first... The order-predicted value of the autoregressive model for segment vibration data;

[0064] Step S5: Using the gradient descent method, respectively through the formula...

[0065] , and

[0066] Iterative update of weight coefficient vector In response to Meeting convergence conditions Iteration stopped;

[0067] Among them, superscript Indicates the number of iterations; This is the momentum coefficient, with a value of 0.9; This represents the historical gradient weight, with a value of 0.9. It is a momentum vector, and its initial value is zero; Represents the loss function weight coefficient vector The gradient; The adaptive learning rate; the initial value of the adaptive learning rate. ,

[0068] Step S6: Substitute the solved weight coefficient vector into the weighted power spectrum evaluation function in step S3;

[0069] Step S7, for the vibration response data, assume that the order variation range of the autoregressive model is... Under their respective regression model orders, the power spectrum and the power spectrum evaluation function are calculated based on step S1. Minimize the power spectrum evaluation function to determine the optimal model order suitable for the current vibration response data segment, calculate the power spectrum curve for the corresponding order, and pick the cable natural frequency from the power spectrum curve. ; Subscript For frequency order;

[0070] Step S8, calculate the cable force using the following formula:

[0071]

[0072] In the formula, Indicates storage, Indicates mass per unit length. It is the length of the cable. It is the cross-sectional area of ​​the cable. It is the elastic modulus of the cable. It is the first First frequency.

[0073] Specifically, in step S1, the empirical value of the optimal autoregressive model The acquisition process includes:

[0074] Step S101: Specify the order of the autoregressive model ;

[0075] Step S102, by analyzing vibration data The autocorrelation function is used to establish the Yule-Walker equation based on the noise covariance and the autoregressive coefficients. The noise covariance and autoregressive coefficients are then solved to calculate the power spectrum. Indicates the length of the data window Sample number within, , Indicates the total number of samples;

[0076] Step S103: Compare the orders of different autoregressive models The power spectrum is used to derive the empirical value of the optimal autoregressive model. .

[0077] Specifically, in step S2,

[0078] The peak significance index is obtained by the following formula:

[0079] ,

[0080] In the formula, This represents the amplitude at the highest peak on the power spectrum curve. The frequency corresponding to the highest peak. and Frequency Nearby frequency band Mean and standard deviation of the intrinsic power spectrum amplitude;

[0081] The peak resolution is obtained by the following formula:

[0082] ,

[0083] In the formula, The frequency difference between the highest peak and its nearest neighbor on the self-power spectrum curve is calculated using the following formula: , The half-power bandwidth frequency is the highest peak on the power spectrum curve. The half-power bandwidth frequency at the nearest peak;

[0084] The power spectral entropy is obtained by the following formula:

[0085] ,

[0086] In the formula, The total number of spectral lines. For the first Each spectral line frequency;

[0087] The power spectrum smoothness is obtained by the following formula:

[0088] ;

[0089] The improved AIC criterion is obtained according to the following formula:

[0090] ;

[0091] The improved BIC criterion is obtained using the following formula:

[0092] .

[0093] Example 1

[0094] Taking a long-span cable-stayed bridge for both road and rail use as an example, its monitoring system deployed accelerometers on one of the bridge's stay cables to test the cable's vibration response data. The accelerometers used a frequency of 20Hz. The mass per unit length of this stay cable is... =155.8 The cable length is =296.011m, cable cross-sectional area is =0.01828 The elastic modulus of the cable is MPa.

[0095] Step S1: Select 1 hour of existing cable vibration response data and set the short-time data window length to [value missing]. =30s, divide the vibration response data into equal window lengths. Paragraph; for the first ( Vibration response data of segment ) were analyzed using different autoregressive model orders. Estimate its power spectrum ;

[0096] Comparison of different orders of autoregressive models The power spectrum diagram below is used to obtain the optimal autoregressive model empirical value corresponding to the vibration response data of each segment. .

[0097] Step S2, based on the first obtained in step S1 Vibration data of segments at different model orders The power spectrum under each condition was calculated to determine its peak significance index. Peak resolution Power spectral entropy Power spectrum smoothness Improve AIC criteria Improve BIC Criteria ;

[0098] Using the vibration data of the first segment in the model order Taking the power spectrum at 75 as an example, its peak significance index is: Peak resolution value Power spectral entropy Power spectrum smoothness Improve AIC guidelines Improve the BIC criteria to ;

[0099] Step S3: Combine the evaluation index values ​​of each power spectrum obtained in step S2 to construct a weighted power spectrum evaluation function. ;

[0100] Taking the calculated values ​​of each evaluation index in step S2 as an example, the constructed power spectrum evaluation function is as follows:

[0101]

[0102] The machine learning prediction algorithm for the weight coefficients is as follows:

[0103] Step S4, with As the initial values ​​of the weighting coefficients, the power spectrum of each vibration data segment under different autoregressive model orders is used to calculate the evaluation function under the current weighting coefficients according to the power spectrum evaluation function. And by minimizing the evaluation function Give the first Autoregressive model order predicted values ​​of segment vibration data Combining the empirically optimal autoregressive model order from step S1 Construct the loss function ;

[0104] Step S5: Iteratively update the weight coefficient vector using the gradient descent method. ,until Meeting convergence conditions The iteration stops, and the optimized weight coefficient vector is output. Iteration termination condition Weighting coefficients , , , and The predicted values ​​are 0.0005, 0.9120, 0.0830, 0.0032 and 0.0013, respectively.

[0105] Step S6: Substitute the predicted weight coefficients obtained from the optimization solution into the power spectrum evaluation function, and the specific expression of the power spectrum evaluation function is given as follows:

[0106] ;

[0107] Step S7: For the vibration response data segment monitored online, taking the data from 00:01:30 to 00:60 on February 5, 2015 as an example, assuming the order of the autoregressive model... The range of variation is In their respective regression model orders Next, calculate the power spectrum, and then calculate the power spectrum evaluation function. The power spectrum minimization evaluation function is shown in [link to function]. Figure 1 The optimal model order for the current vibration response data segment is determined to be 47. The power spectrum curve for this order is given below. Figure 2 And pick out the natural frequency of the cable from the power spectrum curve. ;

[0108] Step S8 according to formula The physical parameters of the cable =155.8kg =296.011m、 =0.01828m2, Substituting MPa into the formula, and taking the 16th frequency as an example, the cable force value is calculated. .

[0109] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0110] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A bridge cable force identification method based on autoregressive power spectrum adaptive estimation, characterized in that, include: Step S1: Obtain cable vibration response data for the past 1 hour and set the short-time data window length to [value missing]. The vibration response data of 1 hour is divided into equal window lengths. Paragraph; for the first ( Vibration response data of segment ) were analyzed using different autoregressive model orders. and the empirical value of the optimal autoregressive model order The corresponding power spectrum is calculated using the following formula. ， In the formula, Spectral line frequency The power spectrum at that location, Sampling frequency, For spectral line frequencies, The imaginary unit, For the order of the autoregressive model, For noise covariance, These are the autoregressive coefficients. Number the autoregressive coefficients; Step S2, based on the first Vibration data of segments at different model orders The power spectrum under the given conditions is used to calculate the corresponding evaluation index values. The evaluation indexes include peak significance index, peak resolution, power spectrum entropy, power spectrum smoothness, improved AIC criterion, and improved BIC criterion. Step S3: Construct the weighted power spectrum evaluation function using the following formula. ， In the formula, For the weighted power spectrum evaluation function, Peak significance index, For peak resolution, For power spectral entropy, For power spectrum smoothness, To improve the AIC criteria, To improve the BIC criteria; , , , and For weighting coefficients, This represents the total number of samples; Step S4, with Calculate the weighted power spectrum evaluation function using the initial values ​​of the weighting coefficients, and construct the loss function by combining the empirical values ​​of the optimal autoregressive model: ， In the formula, Used to represent a vector composed of weight coefficients. To minimize the weighted power spectrum evaluation function, we provide an approach oriented towards the first... The order-predicted value of the autoregressive model for segment vibration data; Step S5: Using the gradient descent method, respectively through the formula... , and Iterative update of weight coefficient vector ,At Meeting convergence conditions Iteration stopped; Among them, superscript Indicates the number of iterations; This is the momentum coefficient, with a value of 0.9; This represents the historical gradient weight, with a value of 0.

9. It is a momentum vector, and its initial value is zero; Represents the loss function weight coefficient vector The gradient; The adaptive learning rate; the initial value of the adaptive learning rate. , ; Step S6: Substitute the solved weight coefficient vector into the weighted power spectrum evaluation function in step S3; Step S7, for the vibration response data, assume that the order variation range of the autoregressive model is... Under their respective regression model orders, the power spectrum and the power spectrum evaluation function are calculated based on step S1. Minimize the power spectrum evaluation function to determine the optimal model order suitable for the current vibration response data segment, calculate the power spectrum curve for the corresponding order, and pick the cable natural frequency from the power spectrum curve. ; Subscript For frequency order; Step S8, calculate the cable force using the following formula: ， In the formula, Indicates storage, Indicates mass per unit length. It is the length of the cable. It is the cross-sectional area of ​​the cable. It is the elastic modulus of the cable. It is the first First frequency.

2. The bridge cable force identification method based on autoregressive power spectrum adaptive estimation according to claim 1, characterized in that, In step S1, the empirical value of the optimal autoregressive model The acquisition process includes: Step S101: Specify the order of the autoregressive model ; Step S102, by analyzing vibration data The autocorrelation function is used to establish the Yule-Walker equation based on the noise covariance and the autoregressive coefficients. The noise covariance and autoregressive coefficients are then solved to calculate the power spectrum. Indicates the length of the data window Sample number within, , Indicates the total number of samples; Step S103: Compare the orders of different autoregressive models The power spectrum is used to derive the empirical value of the optimal autoregressive model. .

3. The bridge cable force identification method based on autoregressive power spectrum adaptive estimation according to claim 1, characterized in that, In step S2, The peak significance index is obtained by the following formula: ， In the formula, This represents the amplitude at the highest peak on the power spectrum curve. The frequency corresponding to the highest peak. and Frequency Nearby frequency band Mean and standard deviation of the intrinsic power spectrum amplitude; The peak resolution is obtained by the following formula: ， In the formula, The frequency difference between the highest peak and its nearest neighbor on the self-power spectrum curve is calculated using the following formula: , The half-power bandwidth frequency is the highest point on the power spectrum curve. The half-power bandwidth frequency at the nearest peak; The power spectral entropy is obtained by the following formula: ， In the formula, The total number of spectral lines. For the first Each spectral line frequency; The power spectrum smoothness is obtained by the following formula: ； The improved AIC criterion is obtained according to the following formula: ； The improved BIC criterion is obtained using the following formula: 。

Images