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

Abstract

The application discloses a bridge static deflection and dynamic deflection real-time separation method, system and storage medium, and comprises the following contents: initial value parameters of deflection separation are determined; a correlation model of temperature signals and deflection signals is established in a linear regression manner; posteriori static deflection values, mean vectors and covariance matrices of posteriori temperature values at t time are used to predict probability distributions of static deflection and temperature at t+1 time, so that mean vectors and covariance matrices of a priori static deflection value and a priori temperature value at t+1 time are obtained; based on total deflection and temperature measurement values, the results of a priori prediction at t+1 time are combined to calculate mean vectors and covariance matrices of posteriori static deflection values and posteriori real temperature values at t+1 time, and then corrected static deflection values and real temperature values at t+1 time are obtained; and total deflection is subtracted from the static deflection to obtain dynamic deflection values; and the real-time separation of the static deflection and the dynamic deflection is realized through iteration. The application takes bridge real-time deflection monitoring data as the main object, and through iteration of a priori prediction and posteriori correction, information of temperature change trends is fused in the static deflection separation process, the separation result is sufficient, the algorithm complexity is low, and the engineering practicability is strong.

Description

TECHNICAL FIELD

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

[0002] In a bridge health monitoring system, the bridge dynamic deflection is an important structural response reflecting the health state of the bridge structure. Since the bridge dynamic deflection is a comprehensive effect caused by both vehicle load effect and temperature field effect, in order to accurately evaluate the working performance and health state of the in-service bridge, the deflection caused by the vehicle load and the deflection caused by the temperature effect need to be separated from the bridge dynamic deflection response data.

[0003] At present, there are two problems to be solved in the separation algorithm of static deflection and dynamic deflection. One is the real-time of the algorithm. For the structure intelligent monitoring system pursuing automation and intelligence, the algorithm needs to have the function of real-time and low complexity to meet the real-time analysis demand of the monitoring system. The other is the robustness of the algorithm. Most separation algorithms only use the information of the deflection signal to separate the static deflection and the dynamic deflection, and fail to fully utilize the hidden static deflection information in the temperature signal, which makes the separation of the static deflection easily affected by the abnormal fluctuation and noise of the deflection sensor. SUMMARY

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

[0005] Compared with the prior art, the present application can real-time and accurately separate the bridge static deflection and dynamic deflection, and fully utilize the information hidden in the temperature signal to enhance the robustness of the algorithm. Specifically, the following steps are included:

[0006] Step 1, determining the initial value parameters of deflection separation; a correlation model of the temperature signal and the deflection signal is established by means of linear regression;

[0007] Step 2, based on the mean vector and the 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 the 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 value, combining the prior prediction result at time t+1, the mean vector and the covariance matrix of the posterior static deflection value and the posterior real temperature value at time t+1 are calculated, and then the corrected static deflection value and the real temperature value at time t+1 are obtained. The dynamic deflection value is obtained by subtracting the static deflection from the total deflection;

[0009] Step 4, real-time separation of static deflection and dynamic deflection is achieved by iteration. BRIEF DESCRIPTION OF DRAWINGS

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

[0011] Figure 2 A comparison chart of the real-time separated static deflection and the original signal according to an embodiment of the present application.

[0012] Figure 3 The real-time separated dynamic deflection according to an embodiment of the present application. DETAILED DESCRIPTION

[0013] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be described in further detail below with reference to the drawings;

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

[0015] When there is no relevant data of the temperature signal of the same frequency in the same period, and based on the past experience of the sensor, the deflection data is approximately sinusoidal in a day, it is assumed that the temperature in a day is sinusoidal, and the sampling points on the sinusoidal curve with an amplitude of 1 and a period of 24h are used to replace the actually measured temperature data;

[0016] Step 2 (corresponding to S2 part in the flow chart), initial value determination;

[0017] Determine the covariance matrix Q of the temperature and the change amount of the temperature-induced deflection process, is the average value of the change amount of the temperature in a unit time, is the average value of the change amount of the temperature-induced deflection in a unit time, The value is determined by experience without basis; as shown in the following formula:

[0018]

[0019] Determine the covariance matrix R of the temperature and the observation deviation of the temperature-induced deflection, is the mean error of the measurement of the temperature sensor, is the average amplitude of the vehicle-induced deflection, The value is determined by experience without basis; as shown in the following formula:

[0020]

[0021] Determine the posterior temperature value mean at the initial time Posterior static deflection value mean The temperature value at the initial moment and the total deflection value at the initial moment are taken respectively to constitute the posterior temperature value and the posterior static deflection value mean vector X0 at the initial moment:

[0022]

[0023] The covariance matrix P0 of the posterior temperature value and the posterior static deflection value at the initial moment is determined, and P0 is taken as a second-order unit matrix

[0024]

[0025] Step 3 (corresponding to the S3 part in the flow chart), a linear regression model is established with a total deflection signal known by the sensor as the dependent variable and a temperature signal in the same period as the independent variable; the period does not include the real-time cleaning process, and the obtained model slope is k and the intercept is b, and the linear change elements for predicting the prior static deflection value and the prior temperature value at t+1 moment using the posterior static deflection value and the posterior temperature value at t moment are as follows:

[0026]

[0027] Step 4 (corresponding to the S4 part in the flow chart), the prior prediction module, based on the mean vector and the covariance matrix of the posterior static deflection value and the posterior real temperature value at t moment, predicts the probability distribution of the static deflection and the real temperature at t+1 moment, and obtains the mean vector and the covariance matrix of the prior static deflection value and the prior temperature value at t+1 moment;

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

[0029]

[0030] X t The mean vector of the posterior static deflection value and the posterior temperature value at t moment is determined by X0 in S2 at the initial moment; A and B are calculated in S3 and are linear change elements;

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

[0032]

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

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

[0035] The Kalman gain K at the t+1 moment t+1 is calculated by the following formula:

[0036]

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

[0038] The mean vector X of the posterior static deflection value and the posterior temperature value at the t+1 moment t+1 is calculated by the following formula:

[0039]

[0040] The mean vector of the prior static deflection value and the prior temperature value at the t+1 moment is determined in S4; Z t+1 is a vector composed of the total deflection value and the temperature value observed at the t+1 moment;

[0041]

[0042] signal t+1 The total deflection value observed at the t+1 moment; T t+1 The temperature value observed at the t+1 moment;

[0043] The covariance matrix P of the posterior static deflection value and the posterior temperature value at the t+1 moment t+1 is calculated by the following formula:

[0044]

[0045] I is a second-order unit matrix; The covariance matrix of the prior static deflection value and the prior temperature value at the t+1 moment;

[0046] Step 6 (corresponding to the S6 part in the flow chart), iteration is performed on steps 4 to 5; the mean vector and covariance matrix of the prior static deflection value and prior temperature value at t+2 time are calculated from the mean vector and covariance matrix of the posterior static deflection value and posterior temperature value at t+1 time obtained in step 5, and then the Kalman gain, the mean vector and covariance matrix of the posterior static deflection value and posterior temperature value at t+2 time are obtained;

[0047] By analogy, the obtained posterior static deflection value is the separated static deflection time sequence, i.e., the static deflection S t The sequence of each vector is a sequence composed of the first element of each vector in the group of vectors X t obtained in the iteration process, wherein 0<t<n, n is the total number of separated time points;

[0048] The dynamic deflection sequence D t is obtained by subtracting the static deflection at the corresponding time from the total deflection sequence signal t , i.e., determined by the following formula:

[0049] D t = signal t -S t , (0<t<n)

[0050] According to the above steps, the real-time separation of static deflection and dynamic deflection is realized.

Claims

1. A method for real-time separation of static and dynamic deflection of a bridge, characterized in that, Includes the following steps: S1, Collect the total deflection signal including static deflection and dynamic deflection, and collect the temperature signal of the same frequency within the same time period; S2, Initial values ​​are determined. The covariance matrix of the temperature and temperature-induced deflection process changes is determined by taking a diagonal matrix composed of the average temperature change per unit time and the average temperature-induced deflection change per unit time. The covariance matrix of the temperature and temperature-induced deflection observation deviations is determined by taking a diagonal matrix composed of the measurement error of the temperature sensor and the average amplitude of the vehicle-induced deflection. The mean vector and covariance matrix of the posterior temperature value and posterior static deflection value at the initial time are determined. The mean vector is taken as a two-dimensional column vector composed of the observed temperature value at the initial time and the total deflection value at the initial time. The covariance matrix is ​​taken as a second-order identity matrix. S3. A correlation model between temperature and deflection signals is established through linear regression. Based on the slope and intercept of the linear model, the linear variation elements of the prior static deflection and prior temperature values ​​at time t+1 are obtained using the posterior static deflection and posterior temperature values ​​at time t. S4, the prior prediction module, based on the mean vector and covariance matrix of the posterior static deflection prediction value and the posterior true temperature prediction value at time t, predicts the probability distribution of static deflection and true temperature at time t+1, and obtains the mean vector and covariance matrix of the prior static deflection prediction value and the prior temperature prediction value at time t+1. S5, the posterior correction module, first calculates the Kalman gain based on the covariance matrix of the prior static deflection prediction value and the prior true temperature prediction value at time t+1; then, 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 prior static deflection value and the prior true temperature value at time t+1 calculated in S4, it calculates the mean vector and covariance matrix of the posterior static deflection value and the posterior temperature prediction value at time t+1. S6. Iterate through steps S4 to S5. Using the mean vector and covariance matrix of the posterior static deflection value and posterior temperature value obtained in step S5 at time t+1, calculate the mean vector and covariance matrix of the prior static deflection value and prior temperature value at time t+2, and then obtain the Kalman gain, the mean vector and covariance matrix of the posterior static deflection value and posterior temperature value at time t+2; and so on. The obtained posterior static deflection value is the separated static deflection time series. The dynamic deflection is obtained by subtracting the static deflection at the current time from the total deflection at the current time, thereby realizing the real-time separation of static deflection and dynamic deflection at time t+2 and subsequent times.

2. The method for real-time separation of static and dynamic deflection according to claim 1, characterized in that, The initial value is determined in step S2 as follows: Determine the covariance matrix Q of the changes in temperature and static deflection. It is the average value of the temperature change per unit time. This represents the average change in static deflection per unit time. When no basis is available, values ​​are determined based on experience, as shown in the following formula: Determine the covariance matrix R of the temperature and static deflection observation biases. This represents the measurement error of the temperature sensor. The average amplitude of the vehicle-induced deflection. When no basis is available, values ​​are determined based on experience, as shown in the following formula: Determine the mean posterior temperature value at the initial time. Posterior static deflection mean The initial temperature value and the initial total deflection value are taken respectively to construct the posterior temperature value and the posterior static deflection value mean vector X0 at the initial time: Determine the covariance matrix P0 of the posterior temperature and posterior static deflection values ​​at the initial time, where P0 is taken as a second-order identity matrix:

3. The method for real-time separation of static and dynamic deflection of bridges according to claim 1, characterized in that, In step S3, a correlation model between the temperature signal and the deflection signal is established using linear regression, and the matrix expression is established as follows: Using the total deflection signal known from the sensor as the dependent variable and the temperature signal within the same time period as the independent variable, a linear regression model is established. This time period is not included in the real-time cleaning process. Let the slope of the obtained model be k and the intercept be b. The linear change factors for predicting the prior static deflection and prior temperature values ​​at time t+1 using the posterior static deflection and posterior temperature values ​​at time t are as follows:

4. The method for real-time separation of static and dynamic deflection of bridges according to claim 2, characterized in that, In step S4, based on the mean vector and covariance matrix of the posterior static deflection value and posterior temperature value at time t, the mean vector and covariance matrix of the prior static deflection value and prior temperature value at time t+1 are obtained. The specific process is as follows: The mean vector of the prior static deflection and prior temperature values ​​at time t+1 Calculate using the following formula: X t Let X be the mean vector of the posterior static deflection and posterior temperature values ​​at time t, which is determined by X0 in S2 at the initial time; A and B are calculated in S3 and are linearly varying elements. The covariance matrix of the prior static deflection and prior temperature values ​​at time t+1 Calculate using the following formula: P t The covariance matrix of the posterior static deflection prediction and the posterior temperature prediction at time t is determined by P0 in S2 at the initial time. Let A be the transpose matrix; Q is the covariance matrix of the temperature and temperature-induced deflection process changes, which is determined in S2.

5. The method for real-time separation of static and dynamic deflection of bridges according to claim 1, characterized in that, In step S5, the Kalman gain is first calculated based on the covariance matrix of the prior static deflection and temperature values ​​at time t+1. Then, based on the Kalman gain, the total deflection and temperature values ​​observed at time t+1, and the mean vector and covariance matrix of the prior static deflection and temperature values ​​at time t+1 calculated in S4, the mean vector and covariance matrix of the posterior static deflection and temperature values ​​at time t+1 are calculated. The specific process is as follows: Kalman gain K at time t+1 t+1 Calculate using the following formula: R 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 deviations, which is determined in S2. The mean vector X of the posterior static deflection and posterior temperature values ​​at time t+1 t+1 Calculate using the following formula: The mean matrix of the prior static deflection and prior temperature values ​​at time t+1 is determined in S4; Z t+1 This is a vector consisting of the total deflection and temperature values ​​observed at time t+1. signal t+1 T represents the total deflection value observed at time t+1; t+1 The temperature value observed at time t+1; The covariance matrix P of the posterior static deflection and posterior temperature values ​​at time t+1 t+1 Calculate using the following formula: I is a second-order identity matrix; Let be the covariance matrix of the prior static deflection prediction and the prior temperature prediction at time t+1.

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

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