CN103698071B - The data-driven method of Suo Li course identification is become during drag-line based on monitoring acceleration - Google Patents

Abstract

The present invention proposes a data-driven method for identifying the time-varying cable force history of the cable based on monitoring acceleration, using the efficient unsupervised learning algorithm of complexity tracking, and utilizing the monitoring information of the multi-channel acceleration sensor arranged on the cable , realizing the real-time identification of the cable force time history. The complexity pursuit algorithm can autonomously decompose the acceleration response of the cable into the single-mode response of the cable, and then identify the real-time frequency of the cable through the extremely short-term acceleration information, and calculate the time history of the cable force through the tension string theory. Through the simulation analysis of the cable-stayed bridge combined with the measured cable force and wind speed and the model test of the cable, it is proved that the proposed complexity pursuit algorithm can accurately identify the time-varying cable force history in real time. The invention is a direct and effective time-varying cable force process identification method, which is simple and easy to use, has high cable force identification accuracy, strong timeliness and can realize online real-time identification, and is especially suitable for online evaluation of draglines.

Description

Data-driven method for time-varying cable force history identification based on monitoring acceleration

technical field

The invention relates to a method for identifying the response of a civil engineering structure, in particular to a data-driven method for identifying the time-varying cable force history of a cable based on monitoring acceleration.

Background technique

Cable-stayed bridge is the most widely used bridge type in the world because of its large span, beautiful appearance, and convenient construction. Cable-stayed bridges generally become a landmark building in a region, and are often a transportation hub in a region, which has a vital impact on the political economy of the region.

As the main load-bearing component of the cable-stayed bridge, the cable-stayed cables are composed of high-strength steel wire bundles and PE sheaths. During the service period of stay cables for decades, the coupling of environmental erosion, material aging, long-term effect of load, fatigue effect and mutation effect will inevitably lead to damage accumulation and resistance of structures and systems. Attenuation, so that the ability to resist natural disasters and even normal environmental effects is reduced, and in extreme cases it will cause catastrophic accidents. In order to ensure the normal operation of the bridge structure, the best solution is to carry out regular inspection and maintenance of the stay cables, and it is necessary to conduct a safety assessment based on the inspection results. However, due to the limitations of non-destructive testing methods (magnetic flux leakage testing, X-ray testing, ultrasonic testing, cable force testing based on vibration method, etc.), only a very small part of the cable-stayed cables have been tested during the actual operation of the cable-stayed bridge. In view of the prevalence of cable damage and the high cost of cable repair and replacement, in order to meet the needs of corrosion fatigue assessment of cable-stayed structures under operating conditions, it is urgent to understand the structure of cable-stayed structures during the entire service process. Cable Process Response.

The current cable force test devices include: pressure ring, magnetic flux sensor, fiber grating smart cable, etc., among which the pressure ring and fiber grating smart cable can directly test the cable force history, and are widely installed and applied to new bridges. However, these cable force monitoring sensors are generally expensive, complicated to install (only for new bridges), and more importantly, the durability of the sensors is relatively poor. These inherent shortcomings limit the large-scale application of the above sensors. Since replacing the cable force monitoring sensor is time-consuming, labor-intensive and expensive, it is urgent to develop a time-saving, labor-saving and economical real-time cable force history monitoring method.

Contents of the invention

Based on the above shortcomings, the present invention provides a data-driven method for identifying time-varying cable force history based on multi-channel monitoring acceleration to solve the problem of identifying time-varying cable force history.

The present invention adopts the following technical solution to realize: a data-driven method for identifying the time-varying cable force history of the cable based on monitoring acceleration, the steps are as follows:

Step 1: Arrange 2-3 acceleration sensors in the same plane as the cable to be tested, test the acceleration response of the cable under environmental excitation, and identify the fundamental frequency of the cable and the The highest frequency that can be excited in the time period, the fundamental frequency of the cable is represented by f ₁ , The highest frequency of the cable that can be identified in the monitoring acceleration signal is denoted by _fi , f _i ≈i×f ₁ , where, Indicates the circular frequency of the i-th mode of the cable under the action of the cable force T, μ is the density per unit cable length, and L is the length of the stay cable L;

Step 2: Design a high-pass filter with a cutoff frequency (i-1.5)f ₁ to extract the highest second-order frequencies f _i and f _i-1 appearing in the multi-channel acceleration signal of the cable;

Step 3: Select a window function of 3 seconds, and filter and preprocess the multi-channel acceleration signal in the window function. After preprocessing, the acceleration signal is separated by a complexity-seeking algorithm to obtain a single-mode response signal, and the fast Fourier transform or Calculate the frequency of the single-mode response signal from the power spectrum, and use the tensioned string theory to calculate the time-varying cable force of the cable through the identified frequency;

Step 4: Sliding window function, repeat step 3 for the acceleration signal in the window function, and identify the time-varying cable force history of the cable.

The present invention also has the following technical features:

1. The time-varying frequency of the cable should be identified through the multi-channel acceleration signal, and then the time-varying cable force history of the cable should be identified.

2. Perform high-pass filter preprocessing on the multi-channel acceleration signal to extract the highest second-order frequency that can be excited by the cable.

3. Using the complexity-seeking processing algorithm, the multi-modal response in the sliding window is decomposed into a single-mode response, and the frequency resolution of the frequency resolution Δf≤0.025HZ is used to accurately identify the frequency of the single-mode response, using the tensioned string theory Calculate the time-varying cable force history.

The present invention is based on mature acceleration sensor testing technology. Compared with other types of cable force monitoring sensors currently developed, the acceleration sensor used in the present invention is mature and reliable, with high test accuracy, low price, and convenient sensor installation and replacement, thus making the present invention The time-varying cable force history identification system proposed by the invention has extremely high reliability and durability. The present invention monitors acceleration information and calculates cable force by identifying time-varying frequency. The method is simple and easy to use, has high cable force identification accuracy, strong timeliness, and can realize online real-time identification. The method of the present invention has strong robustness and reliability, and is especially suitable for Online assessment for Lasso.

Description of drawings

Figure 1 is a schematic diagram of the smart cable fabrication structure of the Benchmark bridge and the location of the C8 cable;

Figure 2 is the measured wind speed and cable force time history curve of the Benchmark bridge (the test time is 1:00-2:00 AM on January 17, 2008, and the selected cable force to be identified is in the red frame);

Fig. 3 is the time-history graph of the acceleration of the cable of the Benchmark bridge (the start time is 1:40 AM on January 17, 2008);

Fig. 4 is the 10-second acceleration power spectrum diagram of the eighth point channel of the C8 cable;

Fig. 5 is the frequency multiplication characteristic diagram of C8 cable;

Fig. 6 is the time-course curve and its power spectrum after the 3-second acceleration filtering of the eighth-point channel and the quarter-point channel of the C8 cable;

Fig. 7 is the single-mode response time-history curve and its power spectrum obtained by complexity pursuit;

Fig. 8 is the time-varying frequency diagram of the identified C8 cable;

Fig. 9 is a comparison chart of the algorithm identification C8 cable force of the present invention and the measured cable force;

Figure 10 is a schematic diagram of the time-varying cable force history identification test device for the cable;

Figure 11 is a power spectrum diagram of S#1 test acceleration for 10 seconds;

Figure 12 is a diagram of the multiplier frequency relationship of the test cable

Fig. 13 is the time-history curve and its power spectrum after the 3-second acceleration filtering of the test cable S#1 and S#3 sensors;

Fig. 14 is the single-mode response time-history curve and its power spectrum diagram obtained by complexity pursuit;

Fig. 15 is the time-varying frequency diagram of the test cable identified;

Fig. 16 is a diagram of comparison working condition 1 between the cable force of the algorithm identification test of the present invention and the measured cable force;

Fig. 17 is a comparison working condition 2 of the algorithm identification test cable force of the present invention and the measured cable force.

Detailed ways

The specific embodiment of the present invention is described by combining the simulation analysis of the cable-stayed bridge with the measured cable force and the measured wind speed and the model test of the cables.

For a stay cable with small sag (the length is L, the cross-sectional area is A, and the Young's modulus is E), the lateral vibration motion equation of the out-of-plane i-th mode can be expressed as

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, m _i =μL/2 represents the weight per unit cable length, μ represents the density per unit cable length; ζ _i is the i-th order modal damping ratio; α _i =i ² π ² T/2L, β _ik =EAπ ⁴ i ² k ² ／8L ³ ; F _i (t) is external excitation; Indicates the circular frequency of the i-th mode of the cable under the action of the cable force T, and the unit of ω _i is rad/s. The calculation formula of the cable shows that there is a multiplier relationship between the circular frequency of each order of the cable and the fundamental frequency, that is, ω _i ≈i×ω ₁ ; at the same time, the circular frequency ω _i of each order of the cable is between the cable force T There is a direct mapping relationship. According to the tensioned string theory, the cable force T can be expressed as

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The core of the data-driven method for identifying the time-varying cable force history of the cable based on the monitoring acceleration of the present invention is the identification algorithm of the time-varying modal circular frequency ω _i . According to the modal superposition theory, the displacement vector x(t)=[x ₁ (t),…,x _n (t)] ^T of the environmental excitation pull-down cable can be expressed as

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Phi;q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&DoubleLeftRightArrow;</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&Phi;</span>}}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula, Indicates the mode shape matrix, q(t)=[q ₁ (t),...,q _n (t)] ^T is the mode response vector, the i-th mode shape (the i-th column of the Φ matrix) and the mode The responses are denoted as φ _i and q _i (t), respectively. The decomposition calculation of the above displacement vector is realized by the blind element separation algorithm, so that represents the modal response vector estimate, Represents the estimated value of the mode shape vector, and the complexity of the y _i (t) signal is defined as

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; log</span>}\frac{\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; log</span>}\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula, and Represents the variance matrix of n×n long-term predictors and short-term predictors, and The matrix elements of are expressed as

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\\ \stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

long-term forecast and the short-term forecast The calculation formula is

$\begin{array}{cc}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In the present invention, ${\mathrm{\&lambda;}}_S=2^{-1/h_{\mathrm{the\; s}}}=1/2,{\mathrm{\&lambda;}}_S=2^{-1/h_L}=2^{-1/900000,}$ h _L ＞＞ h _S , and The matrix can be calculated by fast convolution algorithm. If the signal y _i (t) is an ideal single-mode response signal, the signal complexity function value F(y _i ) is the largest, so it is only necessary to find the extreme value of the signal complexity function F(y _i ), and the optimal response signal y _i (t) can accurately describe the reconstruction value of the modal response vector.

The process of finding the extreme value of the complexity function F(y _i ) can be realized by the classic gradient optimization algorithm, and the differential of the complexity function F(y _i ) with respect to w _i can be expressed as

${<span\; class="notranslate">\; \&dtri;</span>}_{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

when When F=0, the complexity function F(y _i ) can reach the optimal point, the above formula can be rewritten as

${<span\; class="notranslate">\; \&dtri;</span>}_{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The above formula is transformed into a generalized eigenvalue problem, so w _i is The eigenvector of , the eigenvalue is γ _i =V _i ／U _i . After obtaining w _i , the reconstructed single-mode response vector can be obtained by formula (3) The above is obtained by optimizing the signal complexity function F(y _i ) and monitoring the displacement response vector x(t) as a single-mode response q(t)=[q ₁ (t),...,q _n (t)] ^T The process is called the complexity pursuit algorithm. The acceleration response and velocity response can be calculated in the same way.

For a single-mode response signal q(t)=[q ₁ (t),…,q _n (t)] ^T , since only the frequency component of the control mode is dominant in each modal response, only the separation The obtained q(t)=[q ₁ (t),...,q _n (t)] ^T is performed by fast Fourier transform (FFT) or power spectrum analysis to obtain the modal frequency of the signal, through the formula ( 2) The relationship between the cable force and the frequency of the cable is shown, and the cable force is obtained.

For the single-mode response signal q _i (t), the frequency resolution Δf is the reciprocal of the selected window function time τ Δf=1/τ, and the cable force calculation formula with an error term is

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&PlusMinus;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;\&Delta;f</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{{\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&PlusMinus;</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;\&Delta;f</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;\&Delta;f</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\\ <span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&PlusMinus;</span>\frac{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&mu;L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>\frac{{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;f</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, Approximately equal to the fundamental frequency of the cable , the magnitude of the error term depends on Δf/i. It can be seen from formula (9) that for a window function with a relatively short time length, as long as the identification frequency order of the cable (generally i>10) is relatively high, a high frequency resolution can also be achieved.

Example 1:

The Benchmark cable-stayed bridge (C8 cable-stayed cables in Figure 1) is composed of 139 5mm steel wires, the cable length L=100.95m, the cross-sectional area A=2.73×10 ^-3 m ² , and the density per unit length is μ=21.43kg /m. In 2006, the C8 stay cable was replaced with an intelligent cable during the cable replacement project, which can monitor the cable force history in real time.

Step 1: The algorithm of the present invention needs to use the acceleration sensor information of 2 or at most 3 channels to identify the force of the cable, and calculate the wind speed (Fig. 2 (a)) and the force of the cable (Fig. 2 ( b) Acceleration responses at L/8 and L/4 positions under action. The power spectrum analysis (Figure 4) of the 10-second acceleration time history of the L/8 channel of the C8 cable (Figure 3) shows that the highest order frequency excited by the C8 cable is the 30th order, and it can be seen that the frequency between the cable frequencies There is a clear frequency doubling relationship (Figure 5).

Step 2: Design a high-pass filter, the cutoff frequency is approximately equal to (30-1.5)f ₁ ≈38Hz, and filter out the 29th and 30th order frequency components;

Step 3: Select a window function of 3 seconds, apply the filter designed in step 2 to filter the acceleration curve in the window function, the acceleration time history curve and power spectrum of the L/8 and L/4 channels after filtering are shown in Figure 6 . The complexity pursuit algorithm is used to process the filtered acceleration time-history curves of L/8 and L/4 channels, and the single-mode response signal is separated, and its power spectrum is calculated (Fig. 7). The frequencies of the dominant modes and the cable forces are calculated using tensioned string theory.

Step 4: Slide the time window of 3 seconds point by point, repeat step 3, filter the acceleration signal in the sliding window, separate the single-mode response signal, and identify the frequency through Fourier transform or power spectrum analysis, so as to obtain the frequency variation with time curve (Figure 8), and then the cable force time history curve (Figure 9).

The time-history curve of the monitored cable force is in good agreement with the time-history curve of the identified cable force, which verifies the accuracy of the algorithm proposed in the present invention.

Example 2:

The length of the test cable is 14.02m, the diameter is 1.5cm, and the mass per unit length is 1.33kg/m. One section of the test cable is fixed, and the other end uses a threaded rod to adjust the stretching length of the cable, thereby adjusting the size of the cable force. At the same time, a dynamometer is arranged at the end of the test cable to monitor the change of the cable force time history. The test cable uses 2 A fan is used as an external excitation to generate vibration.

Step 1: Lay out acceleration sensors S#1-S#3 at L/4, L/2 and 3/4L respectively to test the out-of-plane response. The sampling frequency is 200Hz. The geometric dimensions of the test device and sensor layout are shown in Figure 8. The power spectrum analysis is performed on the 10-second acceleration time history of the test cable S#1 sensor (Fig. 11). The highest order frequency excited by the test cable is the 14th order. At the same time, it can be seen that there is an obvious difference between the test cable frequencies. Doubling frequency relationship (Fig. 12);

Step 2: Design a high-pass filter, the cutoff frequency is approximately equal to (14-1.5)f ₁ ≈28Hz, which can filter out the 13th and 14th order frequency components;

Step 3: Select a window function of 3 seconds, and apply the filter designed in step 2 to filter the acceleration curve in the window function. After filtering, the acceleration time history curve and power spectrum of sensors S#1 and S#3 are shown in Figure 13 . The complexity pursuit algorithm is used to process the acceleration time-history curves of the filtered S#1 and S#3 sensors, and the single-mode response signal is separated, and its power spectrum is calculated (Fig. The frequencies of the dominant modes and the cable forces are calculated using tensioned string theory.

Step 4: Slide the time window of 3 seconds point by point, and repeat step 3 to obtain the curve of frequency changing with time (Figure 15), and then obtain the time history curve of cable force (Figure 16-17). The time-history curves of the monitored cable force and the identified cable force time-history curves of the two working conditions of the test cable are in good agreement, which verifies the accuracy of the algorithm proposed by the present invention from the perspective of experiments.

Claims (4)

1. A data-driven method based on the time-varying cable force history identification of the dragline of monitoring acceleration, characterized in that, the steps are as follows: Step 1: Arrange 2-3 acceleration sensors in the same plane as the cable to be tested, test the acceleration response of the cable under environmental excitation, and identify the fundamental frequency of the cable and the time through the acceleration signal within 10 seconds of one channel The highest frequency that can be excited in the segment, the fundamental frequency of the cable is represented by f ₁ , The highest frequency of the cable that can be identified in the monitoring acceleration signal is denoted by _fi , f _i ≈i×f ₁ , where, Indicates the circular frequency of the i-th mode of the cable under the action of the cable force T, μ is the density per unit cable length, and L is the length of the cable; Step 2: Design a high-pass filter with a cutoff frequency (i-1.5)f ₁ to extract the highest second-order frequencies f _i and f _i-1 appearing in the multi-channel acceleration signal of the cable; Step 3: Select a window function of 3 seconds, and filter and preprocess the multi-channel acceleration signal in the window function. After preprocessing, the acceleration signal is separated by a complexity-seeking algorithm to obtain a single-mode response signal, and the fast Fourier transform or Calculate the frequency of the single-mode response signal from the power spectrum, and use the tensioned string theory to calculate the time-varying cable force of the cable through the identified frequency; Step 4: Sliding window function, repeat step 3 for the acceleration signal in the window function, and identify the time-varying cable force history of the cable. 2. The data-driven method for identifying the time-varying cable force history of the cable based on monitoring acceleration according to claim 1, characterized in that: the time-varying frequency of the cable should be identified through multi-channel acceleration signals, and then the time-varying frequency of the cable should be identified. The course of variable cable force. 3. The data-driven method for identifying the time-varying cable force history of the cable based on monitoring acceleration according to claim 1, characterized in that: the multi-channel acceleration signal is preprocessed by high-pass filtering to extract the highest value that the cable can be excited from. 2nd order frequency. 4. The data-driven method for identifying the time-varying cable force history of the cable based on the monitoring acceleration according to claim 1, characterized in that: using the complexity pursuit processing algorithm, the multimodal response in the sliding window is decomposed into single-mode State response, frequency resolution Δf≤0.025HZ The frequency resolution of the frequency resolution can accurately identify the frequency of the single mode response, and use the tension string theory to calculate the time-varying cable force history.