Data fusion system and method based on multiple integrals

Abstract

The invention discloses a data fusion system based on multiple integrals. The data fusion system comprises a first data conversion module which represents integral physical data and integrated physical data according to a constitutive relation between integral physical quantity data and integrated physical quantity data; a first band-pass filtering module performs band-pass filtering on an integration result of the integrated physical quantity data, performs frequency alignment on the integrated physical quantity data and the integrated physical quantity data, and performs band-pass filtering on the integrated physical quantity data after frequency alignment; and the first Kalman filtering module performs data fusion based on multi-rate Kalman filtering on the integrated physical quantity data and the integrated physical quantity data after band-pass filtering. According to the invention, the reliability and accuracy of data are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of data fusion, and specifically refers to a data fusion system and method based on multiple integrals. Background Art

[0002] In experiments, single data measurement often has its limitations, which requires sensors for test data to have very high precision. However, it is often difficult to find all sensors that meet the experimental accuracy requirements, especially in more complex tests. Therefore, if the reliability of the experimental results can be improved by fusing the measurement results of other data, it can better meet the high-precision requirements for measurement results in the current complex environment. Summary of the Invention

[0003] The purpose of the present invention is to provide a data fusion system and method based on multiple integrals, which improves the reliability and accuracy of data.

[0004] To achieve this purpose, the data fusion system based on multiple integrals designed by the present invention includes:

[0005] The first data conversion module is used to represent integral physical data and integrated physical data according to the constitutive relationship between integral physical quantity data and integrated physical quantity data;

[0006] The first band-pass filtering module is used to perform band-pass filtering on the integration result of the integrated physical quantity data, align the frequencies of the integral physical quantity data and the integrated physical quantity data, and perform band-pass filtering on the frequency-aligned integral physical quantity data;

[0007] The first Kalman filtering module is used to perform data fusion on the integrated physical quantity data and the integral physical quantity data after band-pass filtering based on multi-rate Kalman filtering.

[0008] Preferably, the physical quantities of the integrated physical quantity data and the integral physical quantity data are selected according to the actual application scenarios, including displacement data, velocity data, acceleration data, force data, temperature data, and pressure data.

[0009] Preferably, the specific method for aligning the sampling frequencies of the integrated physical quantity data and the integral physical quantity data after band-pass filtering is:

[0010] Check and adjust the sampling frequencies of the integrated physical quantity data and the integral physical quantity data, upsample the data with the lower sampling frequency to the same frequency as the other group of data with the higher sampling frequency, and the upsampling is achieved through an interpolation algorithm, including linear interpolation, quadratic interpolation, and cubic interpolation.

[0011] Preferably, the specific steps for performing data fusion on the integrated physical quantity data after band-pass filtering and the integrated physical quantity data based on multi-rate Kalman filtering include:

[0012] The state equation is as follows:

[0013]

[0014]

[0015] In the formula, r(q) is the integrated physical quantity data, is the first derivative of the integrated physical quantity data, e(q) is the observed value of the integrated physical quantity data, i(q) represents the state noise, i~(0,p) where p is the variance of the observed value of the integrated physical quantity data;

[0016] Taking the integrated physical quantity data as the observed value, the following Kalman filter observation equation can be established:

[0017] O(q) = [1 0]R(q) + j(q) (3)

[0018] In the formula, j(q) represents the state noise, j~(0,k) where k is the variance of the observed value of the integrated physical quantity data;

[0019] The discrete form of the above equation can be expressed as:

[0020] R L+1 = AR L + Be L + g L (4)

[0021] z L = MR L + f L (5)

[0022] In the formula: L represents the time step; e L represents the measured integrated physical quantity data, z L represents the measured integrated physical quantity data; g L represents the discrete state noise, f L represents the discrete measurement noise; R L is the displacement state vector of the system at time L, R L+1 is the integrated physical quantity state vector of the system at time (L + 1); A is the first derivative matrix, B is the second derivative matrix, and M is the constant coefficient matrix;

[0023] The state noise covariance matrix C is:

[0024]

[0025] The observation noise covariance matrix D is as follows:

[0026] D = h 5 k / dq (7)

[0027] Where h 1 is the first constant, h 2 is the second constant, h 3 is the third constant, h 4 is the fourth constant, h 5 is the fifth constant; dq represents differentiation; p is the variance of the observed value of the physical quantity to be integrated;

[0028] The specific steps of the multi-rate Kalman filtering process for fusing the physical quantity data to be integrated and the integrated physical quantity data are as follows:

[0029] Initialize the state vector, the state noise covariance matrix, and the observation noise covariance matrix;

[0030] Based on the prediction of the physical quantity data to be integrated, the state prediction formula for the integrated physical quantity data is:

[0031]

[0032] Where represents the state after prediction by the state equation prediction system of the integrated physical quantity data at the current L moment; represents the state before prediction by the state equation prediction system of the integrated physical quantity data at the current L + 1 moment;

[0033] The corresponding covariance matrix prediction formula is:

[0034]

[0035] Where A T is the transpose of the first derivative matrix; represents the state after prediction by the state equation prediction system at the current L moment; represents the covariance matrix of the predicted state; C represents the state noise covariance matrix;

[0036] When the prediction is made t a / t b times, fuse the acceleration and displacement data for observation update, where t a represents the displacement measurement time interval, and t b represents the strain measurement time interval;

[0037]

[0038]

[0039]

[0040] represents the state of the integrated physical quantity data state equation prediction system before prediction at the current L moment; F L represents the predicted measured integrated physical quantity data; M T is the transpose of the constant coefficient matrix; represents the state of the state equation prediction system before prediction at the current L+1 moment; represents the state of the integrated physical quantity data state equation prediction system after prediction at the current L+1 moment; represents the identity matrix; D is the observation noise covariance matrix; represents the state of the state equation prediction system after prediction at the current L+1 moment.

[0041] Preferably, a data fusion system for the strain and displacement of a vibrating beam structure in a suspension tunnel marine engineering test, which includes:

[0042] The second data conversion module is used to represent the strain and displacement data of the vibrating beam structure according to the strain modal shape and modal coordinate superposition displacement;

[0043] The second band-pass filter module is used to perform band-pass filtering on the integration result of the strain data of the vibrating beam structure, upsample the displacement data of the vibrating beam structure to the same frequency as the strain data, and perform band-pass filtering on the upsampled displacement data of the vibrating beam structure;

[0044] The second Kalman filter module is used to perform data fusion based on multi-rate Kalman filtering on the strain data of the vibrating beam structure after band-pass filtering and the displacement data of the vibrating beam structure.

[0045] Preferably, the specific method for the second data conversion module to represent the strain and displacement data of the vibrating beam structure according to the strain modal shape and modal coordinate superposition displacement is as follows:

[0046] The displacement and strain of the beam longitudinal coordinate of the beam structure at the x position and t moment are respectively represented by the following two formulas:

[0047]

[0048]

[0049] Among them, d(x,t) represents the displacement of the beam longitudinal coordinate at the x position and t moment, ε(x,t) represents the strain of the beam longitudinal coordinate at the x position and t moment, Φ i (x) represents the value of the i-th order displacement modal shape at the x position, Ψ i (x) represents the value of the i-th order strain modal shape at the x position; η i(t) represents the i-th order modal coordinate; N is the number of superposed modal orders; η i (t) represents the i-th order modal coordinate at time t;

[0050] The strain at M strain measurement points uniformly arranged along the longitudinal direction of the beam structure is expressed as:

[0051] {ε(t)} M×1 =Ψ M×N {η(t)} N×1 (15)

[0052] Among them, Ψ M×N represents the 1st to Nth order mode shapes at M sensors; η(t) represents the modal coordinate at time t; {η(t)} N×1 represents the modal coordinates of the 1st to Nth order modes at time t;

[0053] The strain modal coordinate is expressed according to Equation (15) as:

[0054] {η(t)} N×1 =G N×M {ε(t)} M×1 (16)

[0055] Among them, G N×M is the strain weight matrix, Ψ M×N represents the 1st to Nth order mode shapes at M sensors, η(t) represents the modal coordinate at time t, represents the transpose matrix of Ψ M×N ; ε(t) represents the strain of the beam longitudinal coordinate at time t;

[0056] Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates can be obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix, the strain modal coordinates can be directly calculated according to Equation (16);

[0057] According to the assumption of the neutral axis of the beam cross-section, the relationship between the i-th order strain mode shape and the i-th order displacement mode shape is expressed as:

[0058]

[0059] Among them, y(x) is the distance from the neutral axis in the beam height direction at position x, Ψ i (x) is the strain modal function, is the displacement modal function;

[0060] Integrating Equation (17) gives Equation (18), thus constructing the constitutive relationship between the strain mode and the displacement mode;

[0061]

[0062] where x represents the independent variable of displacement; Φ i (x) represents the displacement mode shape function;

[0063] Determine the integration constant according to the boundary conditions;

[0064]

[0065] where L represents the length of the vibrating beam structure;

[0066] After obtaining the displacement mode shapes of the Nth order, the matrix {Φ(x)} of the displacement mode shapes is obtained 1×N as:

[0067] {Φ(x)} 1×N = {Φ 1 (x), Φ 2 (x),..., Φ N (x)} (20)

[0068] Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates are obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix G N×M , the strain modal coordinates are directly calculated according to Equation (16). Finally, using the calculated displacement modal coordinates and displacement mode shapes, the real-time displacement d(x,t) of the beam structure is calculated according to Equation (13), and the real-time strain ε(x,t) of the beam structure is calculated according to Equation (14).

[0069] Preferably, the specific method for the Kalman filter module to perform data fusion on the integration result of the strain data of the band-pass filtered vibrating beam structure and the displacement data based on multi-rate Kalman filtering is:

[0070] Perform data fusion on the strain and displacement data of the band-pass filtered vibrating beam structure, and the state equation is as follows:

[0071]

[0072] In the formula, d(x) represents the dynamic deflection of the vibrating beam structure, represents the rotation angle of the vibrating beam structure, ε(x) is the observed value of the strain of the vibrating beam structure, and α(x) represents the state noise, α~(0,p), where p is the variance of the observed value of the displacement data of the vibrating beam structure;

[0073] Taking the deflection data as the observed value, the following Kalman filter observation equation can be established:

[0074] O(x) = [1 0]D(x) + j(x) (22)

[0075] In the formula, j(x) represents the state noise, j~(0,k), where k is the variance of the observed value of the strain of the vibrating beam structure, and O(x) represents the predicted value function of the displacement;

[0076] The discrete form of the above equation is expressed as:

[0077] D L+1 = AD L + Be L + g L (23)

[0078] z L = MR L + f L (5)

[0079] Where L represents the time step, e L represents the measured strain data, z L represents the measured displacement data, g L represents the discrete state noise, f L represents the discrete measurement noise, D L represents the displacement state vector of the state equation prediction system at time L, D L+1 represents the displacement state vector of the state equation prediction system at time (L + 1), R L is the displacement state vector of the state equation prediction system at time L, A is the first derivative matrix, B is the second derivative matrix, and M is the constant coefficient matrix;

[0080] The state noise covariance C and the observation noise covariance S are respectively:

[0081]

[0082] S = k / dx (25)

[0083] Where h 1 is the first constant, h 2 is the second constant, h 3 is the third constant, h 4 is the fourth constant, h 5 is the fifth constant. In equation (24), h 1 = 1 / 3, h 2 = 1 / 2, h 3 = 1 / 2, h 4 = 1, h 5 = 1; dx represents the differential; p is the variance of the observed value of the physical quantity to be integrated;

[0084] The multi-rate Kalman filtering process for fusing the data to be integrated and the integrated data is:

[0085] Initialization of the state vector and its covariance matrix;

[0086] Based on the prediction of the data to be integrated, the state prediction formula is:

[0087]

[0088] where, represents the displacement state vector predicted by the state equation prediction system at time L; represents the displacement state vector of the state equation prediction system before prediction at time L+1;

[0089] The corresponding covariance matrix prediction formula is:

[0090]

[0091] where, A T is the transpose of the first derivative matrix; C is the state noise covariance; is the state of the state equation prediction system at the current time L; is the covariance matrix of the predicted state;

[0092] After ta / tb times of prediction, the acceleration and displacement data are fused for observation update, where ta and tb represent the displacement and strain measurement time intervals respectively;

[0093]

[0094]

[0095]

[0096] where, z L represents the measured displacement data, M is a constant coefficient matrix, represents the displacement state vector of the state equation prediction system before prediction at the current time L, F L represents the predicted measured displacement data, C is the state noise covariance, M T is the transpose of the constant coefficient matrix, represents the displacement state vector of the state equation prediction system before prediction at the current (L+1) time, represents the displacement state vector of the state equation prediction system before prediction at time (L+1), represents the displacement state vector of the state equation prediction system after prediction at time (L+1), S is the observation noise covariance, I represents the identity matrix, represents the displacement state vector of the state equation prediction system after prediction at the current (L+1) time.

[0097] A data fusion method based on multiple integrals, comprising the following steps:

[0098] Represent the integral physical data and the integrand physical data according to the constitutive relationship between the integral physical quantity data and the integrand physical quantity data;

[0099] Perform band-pass filtering on the integration result of the integrand physical quantity data, align the frequencies of the integral physical quantity data and the integrand physical quantity data, and perform band-pass filtering on the integral physical quantity data after frequency alignment;

[0100] Perform data fusion based on multi-rate Kalman filtering on the integrand physical quantity data and the integral physical quantity data after band-pass filtering.

[0101] A data fusion method for strain and displacement of a vibrating beam structure in a suspended tunnel marine engineering test, comprising the following steps:

[0102] Represent the strain and displacement data of the vibrating beam structure according to the superposition of the strain modal shape and the modal coordinates of displacement;

[0103] Perform band-pass filtering on the integration result of the strain data of the vibrating beam structure, upsample the displacement data of the vibrating beam structure to the same frequency as the strain data, and perform band-pass filtering on the upsampled displacement data of the vibrating beam structure;

[0104] Perform data fusion based on multi-rate Kalman filtering on the strain data of the vibrating beam structure and the displacement data of the vibrating beam structure after band-pass filtering.

[0105] A computer program product, comprising a computer program, characterized in that the steps of the above method are implemented when the computer program is executed by a processor.

[0106] Advantages of the present invention:

[0107] The present invention is applicable to two data fusion methods in structural and marine engineering tests, can fuse data with the same sampling frequency and different sampling frequencies, and can also fuse data with a multiple integral relationship between data. The principle is simple and convenient, easy to apply and popularize, has a wide application range, can play a good role in most structural and marine engineering tests, has a short implementation time, high use efficiency, is stable and reliable, can make the test model reach the target data state after implementation, and can improve the reliability and accuracy of the data. Description of the drawings

[0108] Figure 1 It is a schematic structural diagram of the present invention;

[0109] Figure 2 It is a flow chart of the present invention;

[0110] Figure 3It is a diagram of a data fusion calculation method;

[0111] Figure 4 It is a schematic diagram of a suspension tunnel;

[0112] Figure 5 It is a diagram of the displacement result calculated from strain;

[0113] Figure 6 It is a diagram of the data fusion result. Detailed implementation manners

[0114] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0115] Embodiment 1

[0116] A data fusion system based on multiple integrals, as Figure 1 shown, which includes:

[0117] The first data conversion module is used to represent the integral physical data and the integrand physical data according to the constitutive relationship between the integral physical quantity data and the integrand physical quantity data. This design can accurately perform conversion according to the constitutive relationship between the integral physical quantity data and the integrand physical quantity data to ensure the accuracy and consistency of the data. Only by ensuring the accuracy and consistency of the data can subsequent data processing and analysis be carried out;

[0118] The first band-pass filtering module is used to perform band-pass filtering on the integral result of the integrand physical quantity data (the filtering range of the band-pass filtering is determined according to the frequency characteristics of the integrand physical quantity data and the integral physical quantity data. Band-pass filtering only allows waves in a specific frequency band to pass through while shielding other frequency bands. The purpose is to avoid data drift during the integration of the integrand physical quantity data, mainly to avoid incremental drift), align the frequencies of the integral physical quantity data and the integrand physical quantity data, and perform band-pass filtering on the frequency-aligned integral physical quantity data. This design can effectively remove noise and interference signals;

[0119] The first Kalman filtering module is used to perform data fusion based on multi-rate Kalman filtering on the integrand physical quantity data and the integral physical quantity data after band-pass filtering (Kalman filtering is a method widely used in data processing. This method estimates data by continuously predicting and correcting in the time domain. Generally, the sampling frequencies of different physical quantities and different measurements are different. For this, a multi-rate Kalman filter can be used to fuse the integrand physical quantity data and the integral physical quantity data at different sampling rates to improve the estimation of the integral data signal). This design can achieve real-time and dynamic fusion of the integrand physical quantity data and the integral physical quantity data, and improve the accuracy and reliability of the data.

[0120] In the above technical solution, the physical quantities of the integrated physical quantity data and the integrated physical quantity are selected according to the actual application scenario, including displacement data, velocity data, acceleration data, force data, temperature data, and pressure data; the above design can improve the practicability and reliability of data fusion.

[0121] In the above technical solution, the specific method for aligning the sampling frequencies of the integrated physical quantity data after band-pass filtering and the integrated physical quantity data is as follows:

[0122] Check and adjust the sampling frequencies of the integrated physical quantity data and the integrated physical quantity data, and upsample the data with the lower sampling frequency to the same frequency as the other set of data with the higher sampling frequency (ensuring that the sampling frequencies of the integrated physical quantity data and the integrated physical quantity data are aligned). The upsampling is achieved through an interpolation algorithm, including linear interpolation, quadratic interpolation, and cubic interpolation; the above improves the quality of data fusion and enhances the flexibility of data processing.

[0123] In the above technical solution, the specific steps for performing data fusion on the integrated physical quantity data after band-pass filtering and the integrated physical quantity data based on multi-rate Kalman filtering include:

[0124] The state equation is as follows:

[0125]

[0126]

[0127] In the formula, r(q) is the integrated physical quantity data, is the first derivative of the integrated physical quantity data, e(q) is the observed value of the integrated physical quantity data, i(q) represents the state noise, i~(0,p) where p is the variance of the observed value of the integrated physical quantity data;

[0128] Taking the integrated physical quantity data as the observed value, the following Kalman filter observation equation can be established:

[0129] O(q)=[1 0]R(q)+j(q) (3)

[0130] In the formula, j(q) represents the state noise, j~(0,k) where k is the variance of the observed value of the integrated physical quantity data.

[0131] The discrete form of the above equation can be expressed as:

[0132] R L+1 =AR L +Be L +g L (4)

[0133] z L =MRL +f L (5)

[0134] In the formula: L represents the time step; e L represents the measured data of the physical quantity to be integrated, z L represents the measured data of the integrated physical quantity; g L represents the discrete state noise, f L represents the discrete measurement noise; R L is the displacement state vector of the system at time L, R L+1 is the integrated physical quantity state vector of the system at time (L + 1); A is the first derivative matrix, B is the second derivative matrix, and M is the constant coefficient matrix;

[0135] The state noise covariance matrix C is:

[0136]

[0137] The observation noise covariance matrix D is:

[0138] D = h 5 k / dq (7)

[0139] In the formula, h 1 is the first constant, h 2 is the second constant, h 3 is the third constant, h 4 is the fourth constant, h 5 is the fifth constant; dq represents the differential; p is the variance of the observed value of the physical quantity data to be integrated;

[0140] The specific steps of the multi-rate Kalman filtering process for fusing the physical quantity data to be integrated and the integrated physical quantity data are as follows:

[0141] Initialize the state vector, and initialize the state noise covariance matrix and the observation noise covariance matrix;

[0142] Based on the prediction of the physical quantity data to be integrated, the state prediction formula for the integrated physical quantity data is:

[0143]

[0144] In the formula, represents the predicted state of the integrated physical quantity data state equation for the system at the current time L after prediction; represents the state of the integrated physical quantity data state equation for the system at the current time L + 1 before prediction;

[0145] The corresponding covariance matrix prediction formula is:

[0146]

[0147] In the formula, A T is the transpose of the first derivative matrix; represents the state of the state equation prediction system after prediction at the current L moment; represents the covariance matrix of the predicted state; C represents the state noise covariance matrix;

[0148] When performing t a / t b times of prediction, the acceleration and displacement data are fused for observation update, where t a represents the displacement measurement time interval, and t b represents the strain measurement time interval;

[0149]

[0150]

[0151]

[0152] represents the state of the integrated physical quantity data state equation prediction system before prediction at the current L moment; F L represents the predicted measured integrated physical quantity data; M T is the transpose of the constant coefficient matrix; represents the state of the state equation prediction system before prediction at the current L + 1 moment; represents the state of the integrated physical quantity data state equation prediction system after prediction at the current L + 1 moment; I represents the identity matrix; D is the observation noise covariance matrix; represents the state of the state equation prediction system after prediction at the current L + 1 moment; The above design improves the accuracy and reliability of data fusion.

[0153] In the above technical solution, a data fusion system for the strain and displacement of a vibrating beam structure in a suspended tunnel marine engineering test includes:

[0154] The second data conversion module is used to represent the strain and displacement data of the vibrating beam structure according to the strain modal shape (the mode is the inherent vibration characteristic of the structural system, the free vibration of the linear system is decomposed and coupled into N orthogonal single-degree-of-freedom vibration systems, corresponding to the N modes of the system, and each mode has a specific natural frequency, damping ratio and modal shape) and the modal coordinate superposition displacement;

[0155] The second band-pass filtering module is used to perform band-pass filtering on the integration result of the strain data of the vibrating beam structure, upsample the displacement data of the vibrating beam structure to the same frequency as the strain data, and perform band-pass filtering on the upsampled displacement data of the vibrating beam structure;

[0156] The second Kalman filter module is used to perform data fusion on the strain data of the vibrating beam structure after band-pass filtering and the displacement data of the vibrating beam structure based on multi-rate Kalman filtering.

[0157] In the above technical solution, the specific method for the second data conversion module to represent the strain and displacement data of the vibrating beam structure according to the strain modal shape and modal coordinate superposition displacement is as follows:

[0158] The displacement and strain of the beam longitudinal coordinate of the beam structure at the x position at the t moment are respectively represented by the following two formulas:

[0159]

[0160]

[0161] Among them, d(x,t) represents the displacement of the beam longitudinal coordinate at the x position at the t moment, ε(x,t) represents the strain of the beam longitudinal coordinate at the x position at the t moment, Φ i (x) represents the value of the i-th order displacement modal shape at the x position, Ψ i (x) represents the value of the i-th order strain modal shape at the x position; η i (t) represents the i-th order modal coordinate; N is the number of superposed modal orders; η i (t) represents the i-th order modal coordinate at the t moment;

[0162] The strain at M strain measurement points uniformly arranged along the longitudinal direction of the beam structure is expressed as:

[0163] {ε(t)} M×1 =Ψ M×N {η(t)} N×1 (15)

[0164] Among them, Ψ M×N represents the 1st to Nth order modal shapes at M sensors; η(t) represents the modal coordinate at the t moment; {η(t)} N×1 represents the modal coordinates from the 1st order to the Nth order at the t moment;

[0165] The strain modal coordinate is expressed according to formula (15) as:

[0166] {η(t)} N×1 =G N×M {ε(t)} M×1 (16)

[0167] Among them, G N×M is the strain weight matrix, Ψ M×N represents the 1st to Nth order modal shapes at M sensors, η(t) represents the modal coordinate at the t moment, denotes Ψ M×N is the transposed matrix of, and ε(t) represents the strain of the beam longitudinal coordinate at time t;

[0168] Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates can be obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix, the strain modal coordinates can be directly calculated according to Equation (16);

[0169] According to the assumption of the neutral axis of the beam cross-section, the relationship between the i-th order strain modal shape and the i-th order displacement modal shape is expressed as:

[0170]

[0171] where y(x) is the distance from the position x to the neutral axis in the beam height direction, and Ψ i (x) is the strain modal function, is the displacement modal function; here, the constitutive relationship between the strain mode and the displacement mode is established;

[0172] Integrating Equation (17) gives Equation (18), thus constructing the constitutive relationship between the strain mode and the displacement mode;

[0173]

[0174] where x represents the independent variable of the displacement; Φ i (x) represents the displacement modal shape function;

[0175] The integration constants are determined according to the boundary conditions; the support settlement is not considered;

[0176]

[0177] where L represents the length of the vibrating beam structure;

[0178] After obtaining the displacement modal shapes of N orders, the matrix {Φ(x)} of the displacement modal shapes 1×N is:

[0179] {Φ(x)} 1×N ={Φ 1 (x), Φ 2 (x),..., Φ N (x)} (20)

[0180] Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates are obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix G N×MAfter that, the strain modal coordinates are directly calculated according to Equation (16). Finally, using the calculated displacement modal coordinates and displacement modal vibration modes, the real-time displacement d(x,t) of the beam structure is calculated according to Equation (13), and the real-time strain ε(x,t) of the beam structure is calculated according to Equation (14).

[0181] In the above technical solution, the specific method for the Kalman filter module to perform data fusion of the integration result of the strain data of the vibration beam structure after band-pass filtering and the displacement data based on multi-rate Kalman filtering is as follows:

[0182] Perform data fusion on the strain and displacement data of the vibration beam structure after band-pass filtering. The state equation is as follows:

[0183]

[0184] In the formula, d(x) represents the dynamic deflection of the vibration beam structure, represents the rotation angle of the vibration beam structure, ε(x) is the observed value of the strain of the vibration beam structure, and α(x) represents the state noise, α~(0,p), where p is the variance of the observed value of the displacement data of the vibration beam structure;

[0185] Taking the deflection data as the observed value, the following Kalman filter observation equation can be established:

[0186] O(x) = [1 0]D(x) + j(x) (22)

[0187] In the formula, j(x) represents the state noise, j~(0,k), where k is the variance of the observed value of the strain of the vibration beam structure, and O(x) represents the predicted value function of the displacement;

[0188] The discrete form of the above equation is expressed as:

[0189] D L+1 = AD L + Be L + g L (23)

[0190] z L = MR L + f L (5)

[0191] Among them, L represents the time step, e L represents the measured strain data, z L represents the measured displacement data, g L represents the discrete state noise, f L represents the discrete measurement noise, D L represents the displacement state vector of the state equation prediction system at the L-th moment, D L+1Denote the displacement state vector of the state equation prediction system at time (L+1), R L is the displacement state vector of the state equation prediction system at time L, A is the first derivative matrix, B is the second derivative matrix, and M is the constant coefficient matrix;

[0192] The state noise covariance C and the observation noise covariance S are respectively:

[0193]

[0194] S = k / dx (25)

[0195] where, h 1 is the first constant, h 2 is the second constant, h 3 is the third constant, h 4 is the fourth constant, h 5 is the fifth constant. In equation (25), h 1 = 1 / 3, h 2 = 1 / 2, h 3 = 1 / 2, h 4 = 1, h 5 = 1; dx represents the differential; p is the variance of the observed value of the physical quantity to be integrated;

[0196] The multi-rate Kalman filtering process for fusing the data to be integrated and the integrated data is as follows:

[0197] Initialize the state vector and its covariance matrix;

[0198] Based on the prediction of the data to be integrated, the state prediction formula is:

[0199]

[0200] where, represents the predicted displacement state vector of the state equation prediction system at time L; represents the displacement state vector of the state equation prediction system before prediction at time L+1;

[0201] The corresponding covariance matrix prediction formula is:

[0202]

[0203] where, A T is the transpose of the first derivative matrix; C is the state noise covariance; is the state of the state equation prediction system at the current time L; is the covariance matrix of the predicted state;

[0204] After ta / tb times of prediction, the acceleration and displacement data are fused for observation update, where ta and tb represent the time intervals of displacement and strain measurements respectively;

[0205]

[0206]

[0207]

[0208] Among them, z L represents the measured displacement data, M is a constant coefficient matrix, represents the displacement state vector of the state equation prediction system before prediction at the current L moment, F L represents the predicted measured displacement data, C is the state noise covariance, M T is the transpose of the constant coefficient matrix, represents the displacement state vector of the state equation prediction system before prediction at the current (L + 1) moment, represents the displacement state vector of the state equation prediction system before prediction at the (L + 1) moment, represents the displacement state vector of the state equation prediction system after prediction at the (L + 1) moment, S is the observation noise covariance, I represents the identity matrix, represents the displacement state vector of the state equation prediction system after prediction at the current (L + 1) moment; The above design enables the test model to reach the target data state, improving the reliability and accuracy of the data.

[0209] Example 2

[0210] A data fusion method based on multiple integrals, as Figure 2 shown,

[0211] The specific method of data fusion includes the following steps:

[0212] Express the integral physical data and the integrand physical data according to the constitutive relationship between the integral physical quantity data and the integrand physical quantity data;

[0213] Perform band-pass filtering on the integral result of the integrand physical quantity data, align the frequencies of the integral physical quantity data and the integrand physical quantity data, and perform band-pass filtering on the integral physical quantity data after frequency alignment;

[0214] Perform data fusion based on multi-rate Kalman filtering on the integrand physical quantity data and the integral physical quantity data after band-pass filtering.

[0215] Example 3

[0216] In an ocean engineering experiment with a suspended tunnel as the research object, the influence of the side wall distance on the dynamic response of the suspended tunnel (simplified into a vibrating beam structure) is studied. The calculation can be carried out according to the Figure 3 flow chart shown below.

[0217] Step 1: Determine that the physical quantities required for fusion are strain ε and displacement d (strain ε corresponds to the data of the physical quantity to be integrated, and displacement d corresponds to the integrated physical quantity data), as Figure 4 shown; the real-time displacement and strain of the vibrating beam structure can be expressed according to the superposition of modal coordinates of displacement and strain modal shapes (modal is the inherent vibration characteristic of the structural system. The free vibration of a linear system is decomposed and coupled into N orthogonal single-degree-of-freedom vibration systems, corresponding to the N modes of the system, and each mode has a specific natural frequency, damping ratio, and modal shape). Therefore, the displacement and strain of the beam longitudinal coordinate at position x and time t can be expressed by the following two equations respectively:

[0218]

[0219]

[0220] In Equations (13) and (14): d(x,t) represents the displacement of the beam longitudinal coordinate at position x and time t, ε(x,t) represents the strain of the beam longitudinal coordinate at position x and time t, Φ i (x) represents the value of the i-th order displacement modal shape at position x, Ψ i (x) represents the value of the i-th order strain modal shape at position x; η i (t) represents the i-th order modal coordinate; N is the number of modal orders to be superimposed; η i (t) represents the i-th order modal coordinate at time t; according to Equation (13), the real-time deflection curve (i.e., displacement d) of the beam structure can be obtained through the displacement modal shape and the corresponding modal coordinates;

[0221] Step 2: If M strain sensors are uniformly arranged along the longitudinal direction of the beam structure during the dynamic deflection monitoring of the beam, the strain at the M strain measurement points can be expressed by the following equation:

[0222] {ε(t)} M×1 = Ψ M×N {η(t)} N×1 (15)

[0223] where Ψ M×N represents the modal shapes of the 1st to Nth orders at the M sensors; η(t) represents the modal coordinate at time t; {η(t)} N×1 represents the modal coordinates of the 1st to Nth orders at time t;

[0224] The strain modal coordinate can be expressed according to Equation (15) as:

[0225] {η(t)} N×1 = G N×M {ε(t)} M×1 (16)

[0226] In Equation (16), G N×M is the strain weight matrix, Ψ M×N represents the 1st to Nth order mode shapes at M sensors, η(t) represents the modal coordinate at time t, represents the transpose matrix of Ψ M×N ε(t) represents the strain of the beam longitudinal coordinate at time t; Since the displacement mode and the strain mode have the same modal coordinate, the displacement modal coordinate can be obtained by calculating the strain modal coordinate; After obtaining the strain weight matrix, the strain modal coordinate can be directly calculated according to Equation (16);

[0227] Step 3: According to the assumption of the neutral axis of the beam cross-section, the relationship between the i-th order strain mode shape and the i-th order displacement mode shape can be expressed as:

[0228]

[0229] where y(x) is the distance from the neutral axis in the beam height direction at position x, Ψ i (x) is the strain mode function, is the displacement mode function; Equation (17) establishes the constitutive relationship between the strain mode and the displacement mode;

[0230] Integrating Equation (17) gives Equation (18), thus constructing the constitutive relationship between the strain mode and the displacement mode.

[0231]

[0232] where x represents the independent variable of displacement; Φ i (x) represents the displacement mode shape function;

[0233] Step 4: Determine the integration constants according to the boundary conditions, without considering the support settlement:

[0234]

[0235] where L represents the length of the vibrating beam structure;

[0236] After obtaining the displacement mode shapes of N orders, the displacement mode shapes can be written in the following matrix form:

[0237] {Φ(x)} 1×N = {Φ 1 (x), Φ 2 (x),..., ΦN (x)} (20)

[0238] Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates can be obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix G N×M the strain modal coordinates can be directly calculated according to Equation (16). Finally, using the calculated displacement modal coordinates and displacement modal eigenvectors, the real-time deflection curve d(x,t) of the beam structure can be calculated according to Equation (13).

[0239] Step Five: To avoid the low-frequency drift phenomenon of the strain gauges, the integration result needs to be band-pass filtered. At the same time, the displacement measurement result is upsampled to the same frequency as the strain gauge measurement. The displacement measurement result also needs to be band-pass filtered, and the filtering range is the same as the integration result to reduce the influence outside the filtering range.

[0240] Step Six: Perform multi-rate Kalman filtering on the filtered strain data and displacement data. The specific steps are as follows:

[0241] Generally speaking, the sampling frequency of the strain gauge is higher than the frame rate of the video, that is, the sampling rate of the strain is higher than the sampling rate of the deflection measurement. In this regard, a multi-rate Kalman filter can be used to fuse the strain and deflection at different sampling rates to improve the estimation of the deflection signal. This method fuses the low-sampling-rate deflection data and the high-sampling-rate strain data. The state equation is as follows:

[0242]

[0243] In the formula, d(x) represents the dynamic deflection of the vibrating beam structure, represents the rotation angle of the vibrating beam structure, ε(x) is the observed value of the strain of the vibrating beam structure, and α(x) represents the state noise, α~(0,p), where p is the variance of the observed value of the displacement data of the vibrating beam structure;

[0244] Taking the deflection data as the observed value, the following Kalman filter observation equation can be established:

[0245] O(x) = [1 0]D(x) + j(x) (22)

[0246] In the formula, j(x) represents the state noise, j~(0,k), where k is the variance of the observed value of the strain of the vibrating beam structure, and O(x) represents the predicted value function of the displacement;

[0247] The discrete form of the above equation can be expressed as:

[0248] D L+1 = AD L + Be L + gL (23)

[0249] z L = MR L + f L (4)

[0250] where L represents the time step, e L represents the measured strain data, z L represents the measured displacement data, g L represents the discrete state noise, f L represents the discrete measurement noise, D L represents the displacement state vector of the state equation prediction system at time step L, D L+1 represents the displacement state vector of the state equation prediction system at time step (L + 1), R L is the displacement state vector of the state equation prediction system at time step L, A is the first derivative matrix, B is the second derivative matrix, and M is a constant coefficient matrix;

[0251] The state noise covariance is C, and the observation noise covariance is S, respectively:

[0252]

[0253] S = k / dx (25)

[0254] where h 1 is the first constant, h 2 is the second constant, h 3 is the third constant, h 4 is the fourth constant, h 5 is the fifth constant. In equation (24), h 1 = 1 / 3, h 2 = 1 / 2, h 3 = 1 / 2, h 4 = 1, h 5 = 1; dx represents the differential; p is the variance of the observed value of the physical quantity to be integrated;

[0255] The multi-rate Kalman filtering process for fusing the physical quantity data to be integrated and the integrated physical quantity data is as Figure 3 shown, and the specific steps are:

[0256] 1. Initialization of the state vector and its covariance matrix (equations (1), (6), and (7))

[0257] 2. Prediction based on the physical quantity data to be integrated. The state prediction formula is:

[0258]

[0259] where, Denotes the displacement state vector predicted by the state equation prediction system at time L; Denotes the displacement state vector before prediction by the state equation prediction system at time L+1;

[0260] The corresponding covariance matrix prediction formula is:

[0261]

[0262] Where, A T Is the transpose of the first derivative matrix; C is the state noise covariance; Is the state of the state equation prediction system at the current time L; Is the covariance matrix of the predicted state;

[0263] 3. When making t a / t b times of predictions, fuse the acceleration and displacement data for observation update, where t a , t b Represent the displacement and strain measurement time intervals respectively.

[0264]

[0265]

[0266]

[0267] Where, z L Represents the measured displacement data, M is a constant coefficient matrix, Represents the displacement state vector before prediction by the state equation prediction system at the current time L, F L Represents the predicted measured displacement data, C is the state noise covariance, M T Is the transpose of the constant coefficient matrix, Represents the displacement state vector before prediction by the state equation prediction system at the current (L+1) time, Represents the displacement state vector before prediction by the state equation prediction system at time (L+1), Represents the displacement state vector after prediction by the state equation prediction system at time (L+1), S is the observation noise covariance, I represents the identity matrix, Represents the displacement state vector after prediction by the state equation prediction system at the current (L+1) time;

[0268] Step Six: The data of the integrated physical quantity is identified. The accuracy of the integrated physical quantity data is determined by the normalized root mean square error (NRSME). This index judges the measurement error as a whole, and its formula is as follows

[0269]

[0270] Wherein: and d i respectively represent the estimated value and the true value at the i-th step; n represents the number of data points; the final calculation result is as Figure 5 and Figure 6 shown.

[0271] Example 4

[0272] A computer program product, comprising a computer program, characterized in that when the computer program is executed by a processor, it implements the steps of the method described in Example 2.

[0273] Contents not described in detail in this specification belong to the prior art well-known to those skilled in the art.

Claims

1. A data fusion system based on multiple integration, characterized in that: It includes: The first data conversion module is used to represent the integrated physical data and the integrated physical data according to the constitutive relationship between the integrated physical quantity data and the integrated physical quantity data; The first bandpass filtering module is used to perform bandpass filtering on the integration result of the integrated physical quantity data, align the frequency of the integrated physical quantity data with the integrated physical quantity data, and perform bandpass filtering on the frequency-aligned integrated physical quantity data; The first Kalman filter module is used to perform data fusion based on multi-rate Kalman filtering on the integrated physical quantity data and the integrated physical quantity data after bandpass filtering.

2. The data fusion system based on multiple integration according to claim 1, characterized in that: The physical quantities of the integrated physical quantity data and the integrated physical quantity data are selected according to actual application scenarios, including displacement data, velocity data, acceleration data, force data, temperature data, and pressure data.

3. The data fusion system based on multiple integration according to claim 1, characterized in that: The specific method of aligning the sampling frequency of the integrated physical quantity data after bandpass filtering with the integrated physical quantity data is: Check and adjust the sampling frequencies of the integrated physical quantity data and the integrated physical quantity data, and upsample the data with a lower sampling frequency to the same frequency as another set of data with a higher sampling frequency. The upsampling is achieved through an interpolation algorithm, including linear interpolation, quadratic interpolation, and cubic interpolation.

4. The data fusion system based on multiple integration according to claim 1, characterized in that: The specific steps of performing data fusion based on multi-rate Kalman filtering on the integrated physical quantity data after bandpass filtering and the integrated physical quantity data include: The state equation is as follows: In the formula, r(q) is the integrated physical quantity data, is the first-order derivative of the integrated physical quantity data, e(q) is the observed value of the integrated physical quantity data, i(q) represents the state noise, i~(0,p) where p is the variance of the observed value of the integrated physical quantity data; Taking the integrated physical quantity data as the observation value, the following Kalman filter observation equation can be established: O(q)=[1 0]R(q)+j(q) (3) In the formula, j(q) represents the state noise, j~(0,k) where k is the variance of the observation value of the integrated physical quantity data; The discrete form of the above equation can be expressed as: R L+1 =AR L +Be L +g L (4) z L =MR L +f L (5) Where: L represents the time step; e L Represents the measured integrated physical quantity data, z L Represents the measured integrated physical quantity data; g L represents the discrete state noise, f L represents the discrete measurement noise; R L is the displacement state vector of the system at time L, R L+1 is the integrated physical quantity state vector of the system at time (L+1); A is the first-order derivative matrix, B is the second-order derivative matrix, and M is the constant coefficient matrix; The state noise covariance matrix C is: The observation noise covariance matrix D is: D=h5k / dq (7) In the formula, h1 is the first constant, h2 is the second constant, h3 is the third constant, h4 is the fourth constant, and h5 is the fifth constant; dq represents differential; p is the variance of the observed value of the integrated physical quantity data; The specific steps of the multi-rate Kalman filter process for fusing the integrated physical quantity data and the integrated physical quantity data are: Initialize the state vector, initialize the state noise covariance matrix and the observation noise covariance matrix; Based on the prediction of the integrated physical quantity data, the state prediction formula of the integrated physical quantity data is: In the formula, Indicates the state of the system predicted by the state equation of the integrated physical quantity data at the current time L; Indicates the state of the system predicted by the integrated physical quantity data state equation before the current L+1 moment prediction; The corresponding covariance matrix prediction formula is: In the formula, A T is the transpose of the first-order derivative matrix; It represents the state of the system predicted by the state equation at the current time L; represents the covariance matrix of the predicted state; C represents the state noise covariance matrix; When t a / t b After the prediction, the acceleration and displacement data are integrated for observation update, t a represents the displacement measurement time interval, t b represents the strain measurement time interval; Indicates the state of the system predicted by the integrated physical quantity data state equation before the current time L; F L Indicates the predicted measured integrated physical quantity data; M T is the transpose of the constant coefficient matrix; It represents the state of the state equation prediction system before the current L+1 time prediction; represents the state of the system predicted by the integrated physical quantity data state equation at the current L+1 moment; I represents the unit matrix; D is the observation noise covariance matrix; It represents the state predicted by the state equation at the current time L+1.

5. A data fusion system for strain and displacement of a vibrating beam structure in a suspended tunnel marine engineering test, characterized in that: It includes: The second data conversion module is used to represent the strain and displacement data of the vibration beam structure according to the strain mode shape and the modal coordinate superimposed displacement; The second bandpass filtering module is used to perform bandpass filtering on the integral result of the strain data of the vibration beam structure, upsample the displacement data of the vibration beam structure to the same frequency as the strain data, and perform bandpass filtering on the upsampled displacement data of the vibration beam structure; The second Kalman filter module is used to perform data fusion based on multi-rate Kalman filtering on the strain data of the vibration beam structure after bandpass filtering and the displacement data of the vibration beam structure.

6. The data fusion system for strain and displacement of a vibration beam structure in a floating tunnel marine engineering test according to claim 5 is characterized by: The specific method of the second data conversion module expressing the strain and displacement data of the vibration beam structure according to the strain mode shape and the modal coordinate superposition displacement is: The displacement and strain of the beam ordinate of the beam structure at the x position at time t are expressed by the following two equations: Among them, d(x,t) represents the displacement of the beam's ordinate at the x position at time t, ε(x,t) represents the strain of the beam's ordinate at the x position at time t, and Φ i (x) represents the value of the i-th displacement mode at position x, Ψ i (x) represents the value of the i-th order strain mode shape at position x; η i (t) represents the i-th order modal coordinate; N is the number of superimposed modal orders; η i (t) represents the modal coordinates of the i-th order at time t; The strain at M strain test points evenly arranged along the longitudinal direction of the beam structure is expressed as: {ε(t)} M×1 =Ψ M×N {η(t)} N×1 (15) Among them, M×N represents the 1st to Nth order vibration modes at M sensors; η(t) represents the modal coordinates at time t; {η(t)} N×1 Represents the modal coordinates from the first to the Nth order mode at time t; The strain modal coordinates are expressed according to formula (15): {η(t)} N×1 =G N×M {ε(t)} M×1 (16) Among them, G N×M is the strain weight matrix, Ψ M×N represents the 1st to Nth order vibration modes at M sensors, η(t) represents the modal coordinates at time t, Indicates Ψ M×N The transposed matrix of , ε(t) represents the strain of the beam ordinate at time t; Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates are obtained by calculating the strain modal coordinates. After obtaining the strain weight matrix, the strain modal coordinates can be directly calculated according to formula (16); According to the assumption of the neutral axis of the beam section, the relationship between the i-th order strain mode vibration mode and the i-th order displacement mode vibration mode is expressed as: Where y(x) is the distance from the neutral axis to the x position in the beam height direction, Ψ i (x) is the strain mode function, is the displacement mode function; Integrating equation (17) yields equation (18), thus constructing the constitutive relationship between the strain mode and the displacement mode; Among them, x represents the independent variable of displacement; Φ i (x) represents the displacement vibration mode function; Determine the integration constant based on the boundary conditions; Wherein, L represents the length of the vibration beam structure; After obtaining the N-order displacement mode vibration shape, the matrix of displacement mode vibration shape {Φ(x)} 1×N for: {Φ(x)} 1×N ={Φ1(x),Φ2(x),...,Φ N (x)} (20) Since the displacement mode and the strain mode have the same modal coordinates, the displacement modal coordinates are obtained by calculating the strain modal coordinates. N×M After that, the strain modal coordinates are directly calculated according to formula (16). Finally, using the calculated displacement modal coordinates and displacement modal vibration mode, the real-time displacement d(x, t) of the beam structure is calculated according to formula (13), and the real-time strain ε(x, t) of the beam structure is calculated according to formula (14).

7. The data fusion system for strain and displacement of a vibration beam structure in a floating tunnel marine engineering test according to claim 6 is characterized by: The specific method of the Kalman filter module to perform data fusion based on multi-rate Kalman filtering on the integral result of the strain data of the vibration beam structure after bandpass filtering and the displacement data is as follows: The strain and displacement data of the vibration beam structure after bandpass filtering are fused, and the state equation is as follows: In the formula, d(x) represents the dynamic deflection of the vibrating beam structure, represents the rotation angle of the vibration beam structure, ε(x) is the observed value of the strain of the vibration beam structure, α(x) represents the state noise, α~(0,p), where p is the variance of the displacement data observed value of the vibration beam structure; Taking the deflection data as the observation value, the following Kalman filter observation equation can be established: O(x)=[1 0]D(x)+j(x) (22) In the formula, j(x) represents the state noise, j~(0,k) where k is the variance of the observed value of the strain of the vibration beam structure, and O(x) represents the predicted value function of the displacement; The discrete form of the above equation is expressed as: D L+1 =AD L +BeL+g L (23) z L =MR L +f L (5) Where L represents the time step, e L represents the measured strain data, z L Represents the measured displacement data, g L represents the discrete state noise, f L represents the discrete measurement noise, D L represents the displacement state vector of the state equation predicting the system at time L, D L+1 Represents the displacement state vector of the state equation predicting the system at time (L+1), R L is the displacement state vector of the state equation predicting the system at time L, A is the first-order derivative matrix, B is the second-order derivative matrix, and M is the constant coefficient matrix; The state noise covariance C and observation noise covariance S are: S=k / dx (25) Wherein, h1 is the first constant, h2 is the second constant, h3 is the third constant, h4 is the fourth constant, and h5 is the fifth constant. In formula (24), h1=1 / 3, h2=1 / 2, h3=1 / 2, h4=1, and h5=1; dx represents differential; and p is the variance of the observed value of the integrated physical quantity data; The multi-rate Kalman filter process of fusing the integrated data and the integral data is: Initialize the state vector and its covariance matrix; Based on the prediction of the integrated data, the state prediction formula is: in, It represents the displacement state vector of the state equation prediction system after prediction at time L; Represents the displacement state vector of the state equation prediction system before the prediction at time L+1; The corresponding covariance matrix prediction formula is: Among them, A T is the transpose of the first-order derivative matrix; C is the state noise covariance; Predict the state of the system at the current time L for the state equation; is the covariance matrix of the predicted state; After ta / tb predictions are made, the acceleration and displacement data are fused for observation update, where ta and tb represent the displacement and strain measurement time intervals, respectively; Among them, z L represents the measured displacement data, M is a constant coefficient matrix, represents the displacement state vector of the state equation prediction system before the current time L, F L represents the predicted measured displacement data, C is the state noise covariance, M T is the transpose of the constant coefficient matrix, represents the displacement state vector of the state equation prediction system before the current (L+1) time. represents the displacement state vector of the state equation prediction system before the prediction at time (L+1), represents the displacement state vector of the state equation prediction system after prediction at time (L+1), S is the observation noise covariance, I represents the unit matrix, Represents the displacement state vector predicted by the state equation prediction system at the current (L+1) time.

8. A data fusion method based on multiple integration, characterized in that: It follows the steps: The integral physical data and the integrated physical data are expressed according to the constitutive relationship between the integral physical quantity data and the integrated physical quantity data; Performing bandpass filtering on the integration result of the integrated physical quantity data, performing frequency alignment on the integrated physical quantity data and the integrated physical quantity data, and performing bandpass filtering on the frequency-aligned integrated physical quantity data; The integrated physical quantity data after bandpass filtering and the integrated physical quantity data are fused based on multi-rate Kalman filtering.

9. A method for data fusion of strain and displacement of a vibrating beam structure in a suspended tunnel marine engineering test, characterized in that: It follows the steps: The strain and displacement data of the vibration beam structure are expressed according to the strain mode shape and the modal coordinate superimposed displacement; performing bandpass filtering on the integral result of the strain data of the vibration beam structure, upsampling the displacement data of the vibration beam structure to the same frequency as the strain data, and performing bandpass filtering on the upsampled displacement data of the vibration beam structure; The strain data of the vibration beam structure after bandpass filtering and the displacement data of the vibration beam structure are fused based on multi-rate Kalman filtering.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method described in claim 9 are implemented.

Images