Bridge static deflection and dynamic deflection real-time separation method and system and storage medium

Abstract

The invention discloses a real-time separation method for static deflection and dynamic deflection of a bridge. The method comprises the following steps: determining an initial value parameter of deflection separation; establishing a correlation model of the temperature signal and the deflection signal through a linear regression mode; predicting the probability distribution of the static deflection and the temperature at the t + 1 moment based on the mean vector and the covariance matrix of the posterior static deflection value and the posterior temperature value at the t moment, and obtaining the mean vector and the covariance matrix of the prior static deflection value and the prior temperature value at the t + 1 moment; calculating a mean vector and a covariance matrix of a posterior static deflection value and a posterior real temperature value at the t + 1 moment by combining a prior prediction result at the t + 1 moment based on the total deflection and the temperature measurement value so as to obtain a corrected static deflection value and a corrected real temperature value at the t + 1 moment, and subtracting the static deflection from the total deflection to obtain a dynamic deflection value; and real-time separation of static deflection and dynamic deflection is realized through iteration. According to the method, the bridge real-time deflection monitoring data is taken as a main object, the information of the temperature change trend is fused in the static deflection separation process through iteration of prior prediction and posterior correction, the separation result basis is sufficient, the algorithm complexity is low, and the engineering practicability is high.

Description

Technical Field

[0001] The present application relates to the field of bridge health monitoring, and in particular to a method for real-time separation of static deflection and dynamic deflection of a bridge. Background Art

[0002] In the bridge health monitoring system, bridge dynamic deflection is an important structural response that reflects the health status of the bridge structure. Since bridge dynamic deflection is a comprehensive effect caused by vehicle load effect and temperature field effect, in order to accurately evaluate the working performance and health status of in-service bridges, it is necessary to separate the deflection caused by vehicle load and the deflection caused by temperature from the bridge dynamic deflection response data.

[0003] At present, there are two major problems that need to be solved in the separation algorithm of static deflection and dynamic deflection. The first is the real-time performance of the algorithm. For the structural intelligent monitoring system that pursues automation and intelligence, the algorithm needs to have real-time functions and low complexity to meet the needs of real-time analysis of the monitoring system; the second is the robustness of the algorithm. Most separation algorithms only use the information of the deflection signal to separate static deflection and dynamic deflection, and fail to make full use of the static deflection information hidden in the temperature signal, which makes the separation of static deflection susceptible to abnormal fluctuations and noise of the deflection sensor. Summary of the invention

[0004] In view of the problems existing in the prior art, the present application proposes a real-time separation method for static deflection and dynamic deflection of a bridge, which can separate dynamic deflection and static deflection for a single bridge deflection sensor in real time and accurately.

[0005] Compared with the prior art, this application can separate the static deflection and dynamic deflection of the bridge in real time and accurately, and can make full use of the information implied by the temperature signal to enhance the robustness of the algorithm. Specifically, it includes the following steps:

[0006] Step 1, determine the initial value parameters of deflection separation; establish a correlation model between temperature signal and deflection signal by linear regression;

[0007] Step 2, based on the mean vector and covariance matrix of the posterior static deflection value and the posterior temperature value at time t, the probability distribution of the static deflection and the temperature at time t+1 is predicted to obtain the mean vector and covariance matrix of the prior static deflection value and the prior temperature value at time t+1;

[0008] Step 3, based on the total deflection and temperature measurement values, combined with the results of the prior prediction at time t+1, calculate the mean vector and covariance matrix of the posterior static deflection value and the posterior true temperature value at time t+1, and then obtain the corrected static deflection value and true temperature value at time t+1, and subtract the static deflection from the total deflection to obtain the dynamic deflection value;

[0009] Step 4: Realize the real-time separation of static deflection and dynamic deflection through iteration. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 A flow chart of a method for separating static deflection and dynamic deflection of a bridge provided in an embodiment of the present application;

[0011] Figure 2 It is a comparison diagram of the static deflection separated in real time and the original signal in the embodiment.

[0012] Figure 3 is the dynamic deflection of real-time separation in the embodiment. DETAILED DESCRIPTION

[0013] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings.

[0014] Step 1 (corresponding to part S1 in the flow chart), collect the total deflection signal including static deflection and dynamic deflection, and collect the temperature signal of the same frequency in the same period (which can also be obtained through simulation);

[0015] In the absence of temperature signal data of the same frequency in the same period, and based on the previous experience of the sensor, when the deflection data changes approximately sinusoidally in a day, it can be assumed that the temperature changes sinusoidally in a day. The sampling points on a sinusoidal curve with an amplitude of 1 and a period of 24h can be used instead of the measured temperature data.

[0016] Step 2 (corresponding to part S2 in the flow chart), the initial value is determined.

[0017] Determine the covariance matrix Q of the temperature and temperature-induced deflection process changes, is the average value of the temperature change per unit time, is the average value of the change in temperature-induced deflection per unit time, In the absence of a basis, the value can be obtained based on experience. As shown in the following formula:

[0018]

[0019] Determine the covariance matrix R of the temperature and temperature-induced deflection observation deviations, is the mean error of the temperature sensor measurement, is the average amplitude of vehicle-induced deflection, In the absence of a basis, the value can be obtained based on experience. As shown in the following formula:

[0020]

[0021] Determine the mean of the posterior temperature values ​​at the initial moment Mean a posteriori static deflection value The temperature value at the initial moment and the total deflection value at the initial moment can be taken respectively. The mean vector X0 of the posterior temperature value and the posterior static deflection value at the initial moment is formed

[0022]

[0023] Determine the covariance matrix P0 of the a posteriori temperature value and the a posteriori static deflection value at the initial moment. P0 can be taken as a second-order unit matrix

[0024]

[0025] Step 3 (corresponding to S3 in the flowchart), a linear regression model is established with a known total deflection signal of the sensor as the dependent variable and the temperature signal in the same time as the independent variable. This period of time is not included in the real-time cleaning process. Assuming the slope of the obtained model is k and the intercept is b, the linear change factors of using the posterior static deflection value and posterior temperature value at time t to predict the prior static deflection value and prior temperature value at time t+1 are as follows:

[0026]

[0027] Step 4 (corresponding to S4 in the flowchart), a priori prediction module. Based on the mean vector and covariance matrix of the a posteriori static deflection value and the a posteriori true temperature value at time t, the probability distribution of the static deflection and the true temperature at time t+1 is predicted to obtain the mean vector and covariance matrix of the a priori static deflection value and the a priori temperature value at time t+1.

[0028] The mean vector of the prior static deflection value and the prior temperature value at time t+1 The following formula can be used for calculation:

[0029]

[0030] X t It is the mean vector of the a posteriori static deflection value and the a posteriori temperature value at time t, which is determined by X0 in S2 at the initial moment; A and B are calculated in S3 and are linearly changing elements.

[0031] The covariance matrix of the prior static deflection value and the prior temperature value at time t+1 The following formula can be used for calculation:

[0032]

[0033] P t is the covariance matrix of the posterior static deflection value and the posterior temperature value at time t, which is determined by P0 in S2 at the initial time; Q is the covariance matrix of the temperature and temperature-induced deflection process change, which is determined in S2.

[0034] Step 5 (corresponding to S5 in the flowchart). First, the Kalman gain is calculated based on the covariance matrix of the prior static deflection value and the prior temperature value at time t+1; then, the mean vector and covariance matrix of the posterior static deflection value and the posterior temperature value at time t+1 are calculated based on the Kalman gain, the total deflection value and the temperature value observed at time t+1, and the mean vector and covariance matrix of the prior static deflection value and the prior true temperature value at time t+1 calculated in S4.

[0035] Kalman gain K at time t+1 t+1 The following formula can be used for calculation:

[0036]

[0037] is the covariance matrix of the prior static deflection value and the prior temperature value at time t+1, which is determined in S4; R is the covariance matrix of the temperature and temperature-induced deflection observation deviation, which is determined in S2.

[0038] The mean vector X of the a posteriori static deflection value and the a posteriori temperature value at time t+1 t+1 The following formula can be used for calculation:

[0039]

[0040] is the mean matrix of the prior static deflection value and the prior temperature value at time t+1, which is determined in S4; Z t+1 It is a vector consisting of the total deflection value and temperature value observed at time t+1.

[0041]

[0042] signal t+1 is the total deflection value observed at time t+1; T t+1 The temperature value observed at time t+1. The covariance matrix P of the posterior static deflection value and the posterior temperature value at time t+1 t+1 The following formula can be used for calculation:

[0043]

[0044] I is the second-order identity matrix; It is the covariance matrix of the prior static deflection value and the prior temperature value at time t+1.

[0045] Step 6 (corresponding to part S6 in the flowchart), iterate from Step 4 to Step 5. Based on the posterior static deflection value, the mean vector, and the covariance matrix of the posterior temperature value at time t + 1 obtained in Step 5, calculate the prior static deflection value, the mean vector, and the covariance matrix of the prior temperature value at time t + 2, and then obtain the Kalman gain, the posterior static deflection value, the mean vector, and the covariance matrix of the posterior temperature value at time t + 2.

[0046] And so on, the obtained posterior static deflection value is the separated static deflection time series. That is, the sequence of static deflection S t is a set of vectors X obtained during the iteration process t (0 < t < n, where n is the total number of separated time points), the sequence formed by the first element of each vector.

[0047] The dynamic deflection sequence D t is obtained by subtracting the static deflection at the corresponding time from the total deflection sequence signal t . It can be determined by the following formula:

[0048] D t = signal t - S t , (0 < t < n)

[0049] According to the above steps, the real-time separation of static deflection and dynamic deflection is achieved.

[0050] The following provides an example of separating dynamic deflection and static deflection from the total deflection acquisition data of a certain bridge in one day by the above method.

Claims

1. A real-time separation method for static deflection and dynamic deflection of a bridge, characterized in that: The steps include: S1, collect the total deflection signal including static deflection and dynamic deflection, and collect the temperature signal of the same frequency in the same period (which can also be obtained through simulation); S2, initial value determination. Determine the covariance matrix of the temperature and temperature-induced deflection process changes. Its value can generally be based on experience, taking the diagonal matrix composed of the average value of the temperature change in unit time and the average value of the temperature-induced deflection change in unit time; determine the covariance matrix of the temperature and temperature-induced deflection observation deviations. Its value can generally be based on experience, taking the diagonal matrix composed of the measurement error of the temperature sensor and the average amplitude of the vehicle-induced deflection; determine the mean vector and covariance matrix of the posterior temperature value and the posterior static deflection value at the initial moment. The mean vector can be taken as a two-dimensional column vector composed of the observed temperature value at the initial moment and the total deflection value at the initial moment, and the covariance matrix can be taken as a second-order unit matrix. S3, a correlation model between temperature signal and deflection signal is established by linear regression. According to the slope and intercept of the linear model, the linear change factors of the prior static deflection value and the prior temperature value at time t are obtained by using the posterior static deflection value and the posterior temperature value at time t to predict the prior static deflection value and the prior temperature value at time t+1. S4, a priori prediction module. Based on the mean vector and covariance matrix of the a priori static deflection prediction value and the a priori true temperature prediction value at time t, the probability distribution of the static deflection and the true temperature at time t+1 is predicted to obtain the mean vector and covariance matrix of the a priori static deflection prediction value and the a priori temperature prediction value at time t+1. S5, a posteriori correction module. First, the Kalman gain is calculated based on the covariance matrix of the prior static deflection prediction value and the prior true temperature prediction value at time t+1; then, the mean vector and covariance matrix of the a posteriori static deflection value and the posterior temperature prediction value at time t+1 are calculated based on the Kalman gain, the total deflection value and temperature value observed at time t+1, and the mean vector and covariance matrix of the a priori static deflection value and the prior true temperature value at time t+1 calculated in S4. S6, iterates steps S4 to S5. By the mean vector and covariance matrix of the a posteriori static deflection value and the a posteriori temperature value at the t+1 moment obtained in the S5 step, the mean vector and covariance matrix of the a priori static deflection value and the a priori temperature value at the t+2 moment are calculated, and then the Kalman gain, the mean vector and covariance matrix of the a posteriori static deflection value and the a posteriori temperature value at the t+2 moment are obtained; and by the same analogy, the a posteriori static deflection value obtained is the separated static deflection time series, and the dynamic deflection is obtained by deducting the static deflection at the current moment from the total deflection at the current moment, thereby realizing the real-time separation of the static deflection and the dynamic deflection at the t+2 moment and the subsequent moments.

2. The method for real-time separation of static deflection and dynamic deflection according to claim 1, characterized in that: The initial value in step S2 is determined as follows: Determine the covariance matrix Q of the temperature and static deflection process changes, is the average value of the temperature change per unit time, is the average value of the change in static deflection per unit time, In the absence of a basis, the value can be obtained based on experience. As shown in the following formula: Determine the covariance matrix R of temperature and static deflection observation deviations, is the measurement error of the temperature sensor, is the average amplitude of vehicle-induced deflection, In the absence of a basis, the value can be obtained based on experience. As shown in the following formula: Determine the mean of the posterior temperature values ​​at the initial time Mean a posteriori static deflection value The temperature value at the initial moment and the total deflection value at the initial moment can be taken respectively. The mean vector X0 of the posterior temperature value and the posterior static deflection value at the initial moment is formed Determine the covariance matrix P0 of the a posteriori temperature value and the a posteriori static deflection value at the initial moment. P0 can be taken as a second-order unit matrix .

3. The real-time separation method of static deflection and dynamic deflection of a bridge according to claim 1 is characterized in that: In step S3, a correlation model between the temperature signal and the deflection signal is established by linear regression, and a matrix expression is established as follows: A linear regression model is established with a known total deflection signal of the sensor as the dependent variable and a temperature signal in the same time as the independent variable. This period of time is not included in the real-time cleaning process. Assuming the slope of the obtained model is k and the intercept is b, the linear change factors of using the posterior static deflection value and posterior temperature value at time t to predict the prior static deflection value and prior temperature value at time t+1 are as follows: 。 4. The real-time separation method of static deflection and dynamic deflection of a bridge according to claim 1 is characterized in that: In step S4, based on the mean vector and covariance matrix of the posterior static deflection value and the posterior temperature value at time t, the mean vector and covariance matrix of the prior static deflection value and the prior temperature value at time t+1 are obtained. The specific process is as follows: The mean vector of the prior static deflection value and the prior temperature value at time t+1 The following formula can be used for calculation: X t It is the mean vector of the a posteriori static deflection value and the a posteriori temperature value at time t, which is determined by X0 in S2 at the initial moment; A and B are calculated in S3 and are linearly changing elements. The covariance matrix of the prior static deflection value and the prior temperature value at time t+1 The following formula can be used for calculation: P t is the covariance matrix of the a posteriori static deflection prediction value and the a posteriori temperature prediction value at time t, which is determined by P0 in S2 at the initial time; represents the transposed matrix of A; Q is the covariance matrix of the temperature and temperature-induced deflection process changes, which is determined in S2.

5. The real-time separation method of static deflection and dynamic deflection of a bridge according to claim 1 is characterized in that: In step S5, firstly, the Kalman gain is calculated based on the covariance matrix of the prior static deflection value and the prior temperature value at time t+1; then, the mean vector and covariance matrix of the posterior static deflection value and the posterior temperature value at time t+1 are calculated based on the Kalman gain, the total deflection value and the temperature value observed at time t+1, and the mean vector and covariance matrix of the prior static deflection value and the prior temperature value at time t+1 calculated in S4. The specific process is as follows: Kalman gain K at time t+1 t+1 The following formula can be used for calculation: is the covariance matrix of the prior static deflection value and the prior temperature value at time t+1, which is determined in S4; R is the covariance matrix of the temperature and temperature-induced deflection observation deviation, which is determined in S2. The mean vector X of the a posteriori static deflection value and the a posteriori temperature value at time t+1 t+1 The following formula can be used for calculation: is the mean matrix of the prior static deflection value and the prior temperature value at time t+1, which is determined in S4; Z t+1 It is a vector consisting of the total deflection value and temperature value observed at time t+1. signal t+1 is the total deflection value observed at time t+1; T t+1 is the temperature value observed at time t+1. The covariance matrix P of the a posteriori static deflection value and the a posteriori temperature value at time t+1 t+1 The following formula can be used for calculation: I is the second-order identity matrix; It is the covariance matrix of the prior static deflection prediction value and the prior temperature prediction value at time t+1.

6. The real-time separation method of static deflection and dynamic deflection of a bridge according to claim 1 is characterized in that: In step S6, steps S4 to S5 are iterated. The mean vector and covariance matrix of the a priori static deflection value and the a priori temperature value at time t+1 obtained in step S5 are used to calculate the mean vector and covariance matrix of the a priori static deflection value and the a priori temperature value at time t+2, and then the Kalman gain, the mean vector and covariance matrix of the a priori static deflection value and the a priori temperature value at time t+2 are obtained. By analogy, the obtained posterior static deflection prediction value is the separated static deflection time series, i.e., the static deflection S t The sequence of t is a set of vectors X obtained during the iterative process t (where 0 < t < n and n is the total number of separated time points), which is the sequence formed by the first element of each vector Dynamic deflection sequence D t From the total deflection sequence signal t Subtract the static deflection at the corresponding moment to get. It can be determined by the following formula: D t =signal t -S t ,(0<t<n) According to the above steps, the real-time separation of static deflection and dynamic deflection is achieved.

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