Method for realizing jacket structure response estimation based on double Kalman filters

Abstract

The invention discloses a method for realizing jacket structure response estimation based on double Kalman filters, which belongs to the technical field of structure health monitoring and comprises the following steps: establishing a finite element model according to jacket structure information to be measured; performing modal analysis on the jacket structure model to obtain modal parameters; establishing a reduced-order modal shape vector and a double-Kalman filter state matrix; establishing a double-Kalman filter observation matrix; and establishing a double-Kalman filtering framework for response estimation of the to-be-observed position of the jacket structure, and outputting a state vector of the jacket structure by taking actual measurement response as input to obtain a strain response time history of the to-be-measured position. By adopting the method, the response time history of the underwater fatigue position of the jacket structure is accurately and quickly estimated by using the reduced order numerical modal information of the jacket structure, combining the multi-type response measured data and considering the influence of the load on the state of the jacket structure at the same time by implementing the Kalman filtering process twice.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a method for realizing pipe frame structural response estimation based on a dual Kalman filter. Background Art

[0002] With the depletion of onshore resource reserves, energy development has expanded to the ocean on a large scale in recent years. Marine engineering structures, such as offshore oil and gas platforms, offshore wind farms and other structures play an important role in the field of energy development and transportation, and jacket foundations have been widely used in offshore fixed structures. However, in long-term service, affected by harsh marine environmental conditions and continuous cyclic loads, including wind loads and wave loads, high periodic strains will occur in key locations. Continuous monitoring of the strain response time history at the fatigue hotspots of the jacket structure is crucial for evaluating the remaining life of the structure.

[0003] Limited by construction conditions and monitoring costs, the sensor network of in-service offshore engineering structures is generally located above water, while fatigue hotspots are generally located underwater. Using known structural information and available measured response data to estimate the response time history of unobserved locations is an important way to achieve fatigue damage analysis of jacket structures.

[0004] Kalman filtering is an optimized recursive data processing method based on probability theory and mathematical statistics. It uses a state space model composed of state equations and observation equations to describe the filter. According to the linear unbiased minimum mean square error estimation criterion, it recursively obtains the optimal estimate of the system state. In the initial setting, the noise covariance value is set to suppress the interference of environmental noise and human operation errors on the estimation results.

[0005] Although relevant technologies have been used for structural response identification, they still have the following defects: using a single type of response cannot fully capture the low-frequency and high-frequency information of the structure, and the existing technology ignores the process of load acting on the structure. Summary of the invention

[0006] The purpose of the present invention is to provide a method for realizing the response estimation of the jacket structure based on the dual Kalman filter, which utilizes the reduced-order numerical modal information of the jacket structure, combines the measured response data of the acceleration and strain sensors, and considers the influence of the load on the system state. By implementing two Kalman filtering processes, the purpose of accurately and quickly estimating the response time history of the underwater fatigue position of the jacket structure is achieved.

[0007] To achieve the above object, the present invention provides a method for estimating the structure response of a jacket based on a dual Kalman filter, the steps comprising:

[0008] S1. Establishing a finite element model according to the structure information of the jacket to be tested;

[0009] S2. Perform modal analysis on the jacket structure model using finite element software to obtain the jacket structure modal parameters;

[0010] S3, establishing a reduced-order modal vibration vector based on the modal parameters of the jacket structure, and establishing a dual Kalman filter state matrix using the jacket structure motion equation;

[0011] S4. Using numerical simulation, obtain the response of the sensor locations to be deployed on the jacket structure, and establish a dual Kalman filter observation matrix based on the relationship between various responses and state vectors;

[0012] S5. A dual Kalman filter framework for estimating the response of the position to be observed of the jacket structure is established, and the measured response is used as input, and the state vector of the jacket structure is output to obtain the strain response time history of the position to be measured.

[0013] Preferably, in step S2, the modal parameters of the jacket structure include frequency, displacement vibration mode and strain vibration mode.

[0014] Preferably, in step S3, a reduced-order modal vibration shape vector is established according to the arrangement position of the sensor and the position of the response to be estimated in combination with the modal parameters, and the displacement vibration shape is φ=[x1,x2,x3,...,x n ], the strain vibration mode is ψ=[y1,y2,y3,...,y n ], where n is the sum of the number of sensors to be deployed and the number of responses to be measured, x n and n are the displacement mode value and strain mode value corresponding to the nth point position respectively.

[0015] Preferably, the sensor types include strain sensors and acceleration sensors.

[0016] Preferably, in step S3, using the jacket structure motion equation to establish a dual Kalman filter state matrix includes:

[0017] The motion equation of the jacket structure is:

[0018]

[0019] Where, u(t), and Represent the displacement, velocity and acceleration vectors respectively, M, C, K represent the mass matrix, damping matrix and stiffness matrix of the jacket structure respectively, f(t) represents the load, and the matrix S of the specified force position is p The product of and the time vector p(t);

[0020] The continuous time equation of the motion of the jacket structure is projected into the finite-order modal space using u(t)=φz(t), and the mass is normalized to obtain the continuous time decoupled motion equation, which is:

[0021]

[0022] Γ=φ T Cφ

[0023] Ω 2 =φ T Kφ

[0024] Where z(t) represents the displacement in the modal coordinate system, represents the velocity in the modal coordinate system, represents the acceleration in the modal coordinate system;

[0025] Introducing the state vector The motion equation of the jacket structure is obtained, and its expression is:

[0026]

[0027] The obtained jacket structure motion equation is discretized to obtain the state equation:

[0028] x k+1 =Ax k +Bp k

[0029] In the formula, A c represents the state transfer matrix, B c represents the control input matrix, x k+1 represents the state vector of the k+1th step, A and B represent the state transfer matrix and control input matrix of the discretized state space model, respectively, which can be expressed as B=[AI]A c -1 B c , x k represents the state vector at step k.

[0030] Preferably, the step S4 specifically includes:

[0031] Apply load to the jacket structure and obtain the response time history of the locations where strain sensors and acceleration sensors are to be deployed and the locations to be measured;

[0032] The obtained response data of the strain sensor and acceleration sensor positions are fused, and the acceleration is expressed by the motion equation of the jacket structure as follows:

[0033]

[0034] The strain is expressed through the relationship between the strain vibration mode, displacement vibration mode and modal coordinates as follows:

[0035] ε(t)=ψ(φ T φ) -1 φ T u(t)

[0036] Through the relationship between acceleration and strain and the state vector, an observation matrix containing multiple types of responses is established, and the formula is:

[0037] d(t)=G c x(t)+J c p(t)

[0038] In the formula, G c and J c They represent matrices related to structural material parameters and sensor and load locations, respectively;

[0039] Further discretize the observation equation to obtain d k =Gx k +Jp k .

[0040] Preferably, the step S5 specifically includes:

[0041] S51, performing the first double Kalman filtering process to estimate the load;

[0042] Given the input force and the initial expectation and covariance of the jacket structure state vector;

[0043] Make a priori estimate of the input at the current moment based on the initial expectation and covariance of the input;

[0044] Calculate the Kalman gain of the input estimate and use the measurement vector at the current time to make a posteriori estimate of the input;

[0045] S52, performing a second dual Kalman filtering process to estimate the state vector of the jacket structure;

[0046] Taking the posterior estimated value of the input as a known quantity, a priori estimating the state at the current moment based on the state at the previous moment;

[0047] Calculate the Kalman gain of the state estimate and use the measurement vector to correct the prior estimate of the state;

[0048] Repeat the above steps until the number of iterations reaches the response time step;

[0049] S53. The strain response time history of the position to be measured is obtained by using the relationship between the strain and the state vector of the jacket structure, and the strain response time history is compared with the measured strain response time history to perform error analysis.

[0050] Therefore, the present invention adopts the above-mentioned method for realizing the estimation of the structure response of the jacket based on the dual Kalman filter, which has the following beneficial effects:

[0051] (1) Based on the motion equation of the jacket structure, the state matrix is ​​established in combination with numerical modal parameters. In this process, finite-order modes are used to characterize the vibration characteristics of the structure, which reduces the calculation cost and improves the calculation efficiency.

[0052] (2) The measured acceleration and measured strain are integrated and used together as the observation vector, which solves the state vector drift phenomenon caused by using only acceleration and can supplement the deficiency of high-frequency structural information caused by using only strain;

[0053] (3) A dual Kalman filter is used to perform filtering twice to estimate the input and state vectors respectively, taking into account the impact of the load on the structural state vector and improving the accuracy of the estimation results.

[0054] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0056] Figure 2 is a flowchart of the implementation of the dual Kalman filtering process in an embodiment of the present invention;

[0057] Figure 3 4 is a comparison diagram of the response estimation result and the actual result in the embodiment of the present invention. DETAILED DESCRIPTION

[0058] Example

[0059] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0060] Reference Figure 1 The present invention provides a method for estimating the structure response of a pipe frame based on a dual Kalman filter, the steps comprising:

[0061] S1. Establish a finite element model based on the structure information of the jacket to be tested, perform structural analysis on it, obtain the stress concentration position of the structure, and use the sea surface and the upper part as the directly observable position of the jacket structure according to the actual operating conditions.

[0062] S2. Use finite element software to perform modal analysis on the jacket structure model to obtain the jacket structure modal parameters, including frequency, displacement vibration mode and strain vibration mode.

[0063] S3. According to the sensor information of the directly observable position and the stress concentration position combined with the modal parameters, the reduced-order modal vibration vector is established. The sensor types include strain sensors and acceleration sensors. The displacement vibration shape is φ=[x1,x2,x3,...,x n ], the strain vibration mode is ψ=[y1,y2,y3,...,y n ], where n is the sum of the number of sensors to be deployed and the number of responses to be measured, x n and n are the displacement mode value and strain mode value corresponding to the nth point position respectively.

[0064] The dual Kalman filter state matrix is ​​established using the jacket structure motion equation. Specifically, the jacket structure motion equation is:

[0065]

[0066] Where, u(t), and Represent the displacement, velocity and acceleration vectors respectively, M, C, K represent the mass matrix, damping matrix and stiffness matrix of the jacket structure respectively, f(t) represents the load, and the matrix S of the specified force position is p The product of and the time vector p(t);

[0067] The continuous time equation of the motion of the jacket structure is projected into the finite-order modal space using u(t)=φz(t), and the mass is normalized to obtain the continuous time decoupled motion equation, which is:

[0068]

[0069] Γ=φ T Cφ

[0070] Ω 2 =φ T Kφ

[0071] Where z(t) represents the displacement in the modal coordinate system, represents the velocity in the modal coordinate system, represents the acceleration in the modal coordinate system;

[0072] Introducing the state vector The motion equation of the jacket structure is obtained, and its expression is:

[0073]

[0074] The obtained motion equation of the jacket structure is discretized to obtain the state equation, which is the state matrix in the dual Kalman filter. The formula is:

[0075] x k+1 =Ax k +Bp k

[0076] In the formula, A c represents the state transfer matrix, B c represents the control input matrix, x k+1 represents the state vector of the k+1th step, A and B represent the state transfer matrix and control input matrix of the discretized state space model, respectively, which can be expressed as B=[AI]A c -1 B c , x k represents the state vector at step k.

[0077] S4. Use numerical simulation to obtain the response of the sensor locations to be deployed on the jacket structure, and establish a dual Kalman filter observation matrix based on the relationship between various responses and state vectors. Specifically include:

[0078] A load is applied to the jacket structure to obtain the response time history of the positions of the strain sensors and acceleration sensors to be arranged and the positions to be measured. In this embodiment, 4 strain gauges and 2 acceleration sensors are arranged, strain gauges are arranged at positions 1 to 4, and acceleration sensors are arranged at positions 5 to 6. The strain time history near the bottom of the jacket structure is estimated, that is, the dimension of the strain and displacement mode vector is 7.

[0079] The obtained response data of the strain sensor and acceleration sensor positions are fused, and the acceleration is expressed by the motion equation of the jacket structure as follows:

[0080]

[0081] The strain is obtained through the relationship between the strain vibration mode, displacement vibration mode and modal coordinates. The displacement vector can be obtained through u(t)=φz(t), where z(t) is the displacement in the modal coordinate system, which can be expressed as z(t)=(φ T φ) -1 φ T u(t).

[0082] The strain vector is obtained by ε(t)=ψz(t). The strain vector is transformed to further obtain the formula:

[0083] ε(t)=ψ(φ T φ) -1 φ T u(t)

[0084] In order to reflect the layout position of the sensor, a selection matrix is ​​introduced in the input vector. The selection matrix is ​​a diagonal matrix, and its elements are 1 or 0. The element at the degree of freedom corresponding to the layout position of the sensor is 1, otherwise it is 0.

[0085] Considering the general form of the measurement vector, the measurement vector is expressed in the following form:

[0086]

[0087] Where S d , S v , S a The matrices represent the displacement (strain), velocity, and acceleration measurement positions, respectively. In this example, strain gauges are arranged at positions 1 to 4, and acceleration sensors are arranged at positions 5 to 6. Then S d =[1,1,1,1,0,0,0],S v =[0,0,0,0,0,0,0], S a =[0,0,0,0,1,1,0].

[0088] Through the relationship between acceleration and strain and the state vector, an observation matrix containing multiple types of responses is established, and the formula is:

[0089] d(t)=G c x(t)+J c p(t)

[0090] In the formula, G c and J c They represent matrices related to structural material parameters and sensor and load locations, respectively;

[0091] Further discretize the observation equation to obtain d k =Gx k +Jp k , which is the observation matrix in the Kalman filter.

[0092] S5. A dual Kalman filter framework for estimating the response of the position to be observed of the jacket structure is established, and the measured response is used as input, and the state vector of the jacket structure is output to obtain the strain response time history of the position to be measured.

[0093] Reference Figure 3 , a double Kalman filtering process is implemented to obtain the strain time history of the fatigue position of the jacket structure.

[0094] S51, performing the first double Kalman filtering process to estimate the load;

[0095] First, given the initial expectation of the input and covariance and the initial expectation of the system state vector and covariance

[0096] Secondly, the input at the current moment is estimated a priori based on the initial expectation and covariance of the input And update the error covariance Among them, Q p is the process noise covariance of the calibration input force.

[0097] Calculate the Kalman gain of the input estimate Where R is the covariance of the measurement noise, J is the direct feedthrough matrix, and the measured vector is used to calculate the a posteriori estimate of the input And update the error covariance Where, d k represents the observation vector, and G represents the output influence matrix.

[0098] S52, performing a second dual Kalman filtering process to estimate the state vector of the jacket structure;

[0099] The posterior estimated value of the above input is used as a known quantity, and the current state is estimated based on the state of the previous moment. Error covariance of updated state Among them, Q x To calibrate the noise covariance of the state vector process, A and B represent the state transfer matrix and control input matrix of the discretized state space model, respectively, which can be expressed as B=[AI]A c -1 B c .

[0100] Calculate the Kalman gain for the state estimate Combined with the measurement vector, the prior estimate of the state is corrected and the error covariance of the state is updated I represents the identity matrix.

[0101] Repeat the above steps until the number of iterations reaches the response time step. In each iteration, the measured response is used as the known quantity to predict the state vector as the input of the Kalman filter process.

[0102] S53, using the relationship between strain and the state vector of the jacket structure to obtain the strain response time history of the position to be measured, and compare it with the measured strain response time history to perform error analysis, refer to Figure 3 , which is a comparison chart of the estimated response time course of 60 to 70 seconds and the actual time course.

[0103] Therefore, the present invention adopts the above-mentioned method for realizing the response estimation of the jacket structure based on the dual Kalman filter, utilizes the reduced-order numerical modal information of the jacket structure, combines multiple types of response measured data, and considers the influence of the load on the jacket structure state. By implementing two Kalman filtering processes, the purpose of accurately and quickly estimating the response time history of the underwater fatigue position of the jacket structure is achieved.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for estimating the structure response of a pipe frame based on a dual Kalman filter, characterized in that the steps include: S1. Establishing a finite element model according to the structure information of the jacket to be tested; S2. Perform modal analysis on the jacket structure model using finite element software to obtain the jacket structure modal parameters; S3, establishing a reduced-order modal vibration vector based on the modal parameters of the jacket structure, and establishing a dual Kalman filter state matrix using the jacket structure motion equation; S4. Using numerical simulation, obtain the response of the sensor locations to be deployed on the jacket structure, and establish a dual Kalman filter observation matrix based on the relationship between various responses and state vectors; S5. A dual Kalman filter framework for estimating the response of the position to be observed of the jacket structure is established, and the measured response is used as input, and the state vector of the jacket structure is output to obtain the strain response time history of the position to be measured.

2. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 1, characterized in that: In step S2, the modal parameters of the jacket structure include frequency, displacement vibration mode and strain vibration mode.

3. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 2, characterized in that: In step S3, the reduced-order modal vibration vector is established according to the arrangement position of the sensor and the position of the response to be estimated in combination with the modal parameters, and the displacement vibration shape is φ=[x1,x2,x3,...,x n ], the strain vibration mode is ψ=[y1,y2,y3,...,y n ], where n is the sum of the number of sensors to be deployed and the number of responses to be measured, x n and n are the displacement mode value and strain mode value corresponding to the nth point position respectively.

4. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 3, characterized in that: The sensor types include strain sensors and acceleration sensors.

5. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 4, characterized in that: The step S3 uses the jacket structure motion equation to establish the dual Kalman filter state matrix, including: The motion equation of the jacket structure is: Where, u(t), and ü(t) represent displacement, velocity and acceleration vectors respectively, M, C, K represent the mass matrix, damping matrix and stiffness matrix of the jacket structure respectively, f(t) represents the load, and the matrix S of the specified force position is p The product of and the time vector p(t); The continuous time equation of the motion of the jacket structure is projected into the finite-order modal space using u(t)=φz(t), and the mass is normalized to obtain the continuous time decoupled motion equation, which is: C=φ T Cφ Oh 2 =φ T Kφ Where z(t) represents the displacement in the modal coordinate system, represents the velocity in the modal coordinate system, represents the acceleration in the modal coordinate system; Introducing the state vector The motion equation of the jacket structure is obtained, and its expression is: The obtained jacket structure motion equation is discretized to obtain the state equation: x k+1 =Ax k +Bp k In the formula, A c represents the state transfer matrix, B c represents the control input matrix, x k+1 represents the state vector of the k+1th step, A and B represent the state transfer matrix and control input matrix of the discretized state space model, respectively, which can be expressed as B=[AI]A c -1 B c , x k represents the state vector at step k.

6. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 5, characterized in that: The step S4 specifically includes: Apply load to the jacket structure and obtain the response time history of the locations where strain sensors and acceleration sensors are to be deployed and the locations to be measured; The obtained response data of the strain sensor and acceleration sensor positions are fused, and the acceleration is expressed by the motion equation of the jacket structure as follows: The strain is expressed through the relationship between the strain vibration mode, displacement vibration mode and modal coordinates as follows: ε(t)=ψ(φ T f) -1 f T u(t) Through the relationship between acceleration and strain and the state vector, an observation matrix containing multiple types of responses is established, and the formula is: d(t)=G c x(t)+J c p(t) In the formula, G c and J c They represent matrices related to structural material parameters and sensor and load locations respectively; Further discretize the observation equation to obtain d k =Gx k +Jp k .

7. The method for realizing the estimation of the structure response of a pipe frame based on a dual Kalman filter according to claim 6, characterized in that: The step S5 specifically includes: S51, performing the first double Kalman filtering process to estimate the load; Given the input force and the initial expectation and covariance of the jacket structure state vector; Make a priori estimate of the input at the current moment based on the initial expectation and covariance of the input; Calculate the Kalman gain of the input estimate and use the measurement vector at the current time to make a posteriori estimate of the input; S52, performing a second dual Kalman filtering process to estimate the state vector of the jacket structure; Taking the posterior estimated value of the input as a known quantity, a priori estimating the state at the current moment based on the state at the previous moment; Calculate the Kalman gain of the state estimate and use the measurement vector to correct the prior estimate of the state; Repeat the above steps until the number of iterations reaches the response time step; S53. The strain response time history of the position to be measured is obtained by using the relationship between the strain and the state vector of the jacket structure, and the strain response time history is compared with the measured strain response time history to perform error analysis.

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