A method for realizing the response estimation of jacket structures based on dual Kalman filters

Abstract

The present invention discloses a method for realizing the response estimation of a jacket structure based on a dual Kalman filter, belonging to the technical field of structural health monitoring. The steps include: establishing a finite element model according to the information of the jacket structure to be measured; performing modal analysis on the jacket structure model to obtain modal parameters; establishing a reduced-order modal vibration mode vector and a dual Kalman filter state matrix; establishing a dual Kalman filter observation matrix; establishing a dual Kalman filtering framework for the response estimation of the position to be observed of the jacket structure, using the measured response as the input, outputting the state vector of the jacket structure, and obtaining the strain response time history of the position to be measured. By adopting the above method, the present invention utilizes the reduced-order numerical modal information of the jacket structure, combines multi-type measured response data, and simultaneously considers the influence of the load on the state of the jacket structure, and accurately and quickly estimates the response time history of the underwater fatigue position of the jacket structure through two Kalman filtering processes.

Description

Technical Field

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

[0002] With the depletion of onshore resource reserves, in recent years, energy development has expanded widely to the ocean. Ocean engineering structures, such as offshore oil and gas platforms, offshore wind farms, etc., play an important role in the fields of energy development and transportation, and jacket foundations have been widely used in offshore fixed structures. However, during long-term service, affected by harsh marine environmental conditions and continuous cyclic loads, including wind loads and wave loads, high-cycle strains will occur at key positions. Continuous monitoring of the strain response time history at the fatigue hot spots 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 ocean engineering structures is generally located in the above-water part, while the fatigue hot spots are generally located underwater. Using known structural information and available measured response data to estimate the response time history of unobserved positions is an important way to realize the fatigue damage analysis of jacket structures.

[0004] Kalman filtering is an optimized recursive data processing method based on probability theory and mathematical statistics. The filter is described by a state space model consisting of a state equation and an observation equation. According to the linear unbiased minimum mean square error estimation criterion, the optimal estimate of the system state is obtained recursively. 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 the related technologies have been used for the response identification of structures, there are the following defects: using a single type of response cannot completely capture the low-frequency and high-frequency information of the structure, and the existing technologies ignore the action process of the load on the structure. Summary of the Invention

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

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

[0008] S1. Establish a finite element model according to the information of the to-be-measured jacket structure;

[0009] S2. Use a finite element software to conduct modal analysis on the jacket structure model to obtain the modal parameters of the jacket structure;

[0010] S3. Based on the modal parameters of the jacket structure, establish a reduced-order modal vibration mode vector, and use the motion equation of the jacket structure to establish the state matrix of the dual Kalman filter;

[0011] S4. Use numerical simulation to obtain the responses at the positions where sensors are planned to be installed on the jacket structure, and establish the observation matrix of the dual Kalman filter according to the relationships between various responses and the state vector;

[0012] S5. Establish a dual Kalman filter framework for estimating the responses at the positions to be observed on the jacket structure, use the measured responses as inputs, output the state vector of the jacket structure, and obtain the time history of the strain response at the positions 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, according to the installation positions of the sensors and the positions of the responses to be estimated, combined with the modal parameters, establish a reduced-order modal vibration mode vector. The displacement vibration mode is φ = [x1, x2, x3,..., x n , and the strain vibration mode is ψ = [y1, y2, y3,..., y n , where n is the sum of the number of sensors planned to be installed and the number of responses to be measured, and x n and y n are the displacement vibration mode values and strain vibration mode values corresponding to the nth point position respectively.

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

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

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

[0018]

[0019] In the formula, u(t), and represent the displacement, velocity, and acceleration vectors respectively, M, C, and K represent the mass matrix, damping matrix, and stiffness matrix of the jacket structure respectively, f(t) represents the load, which is represented by the product of the matrix S p at the specified force position and the time history vector p(t);

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

[0021]

[0022] \(\Gamma=\varphi\) T \(C\varphi\)

[0023] \(\Omega\) 2 \(=\varphi\) T \(K\varphi\)

[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] Introduce the state vector to obtain the motion equation of the jacket structure, and its expression is:

[0026]

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

[0028] \(x\) k+1 \(=Ax\) k \(+Bp\) k

[0029] where \(A\) c represents the state transition matrix, \(B\) c represents the control input matrix, \(x\) k+1 represents the state vector at the \((k + 1)\)-th step. \(A\) and \(B\) respectively represent the state transition matrix and the control input matrix of the discretized state space model, and can be expressed as \(B=[A - I]A\) c -1 \(B\) c and \(x\) k represents the state vector at the \(k\)-th step.

[0030] Preferably, the specific steps in step S4 include:

[0031] Apply loads to the jacket structure to obtain the response time histories at the positions where strain sensors and acceleration sensors are to be arranged and the positions to be measured;

[0032] Fuse the response data at the positions of the obtained strain sensors and acceleration sensors. The acceleration is expressed by the motion equation of the jacket structure as:

[0033]

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

[0035] ε(t) = ψ(φ T φ) -1 φ T u(t)

[0036] An observation matrix containing multiple types of responses is established through the relationships between acceleration, strain and the state vector, and the formula is:

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

[0038] Where G c and J c represent matrices related to structural material parameters and sensor and load positions respectively;

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

[0040] Preferably, the step S5 specifically includes:

[0041] S51. Conduct the first dual Kalman filtering process to estimate the load;

[0042] Given the initial expectations and covariances of the input force and the jacket structure state vector;

[0043] Perform a prior estimate of the current input based on the given initial expectations and covariances;

[0044] Calculate the Kalman gain of the input estimate and perform a posterior estimate of the input using the measurement vector at the current time;

[0045] S52. Conduct the second dual Kalman filtering process to estimate the state vector of the jacket structure;

[0046] Take the posterior estimate value of the input as a known quantity and perform a prior estimate of the current state based on the state at the previous time;

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

[0048] Repeat the above steps until the number of iteration steps reaches the response time history step size;

[0049] S53. Use the relationship between strain and the state vector of the jacket structure to obtain the strain response time history at the position to be measured, and compare it with the measured strain response time history for error analysis.

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

[0051] (1) Based on the motion equation of the jacket structure, a state matrix is established by combining numerical modal parameters. In this process, the vibration characteristics of the structure are characterized by a finite number of modes, reducing the computational cost and improving the computational efficiency;

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

[0053] (3) The dual Kalman filter is used for two-stage filtering to estimate the input and the state vector respectively, considering the influence of the load on the state vector of the structure and improving the accuracy of the estimation result.

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is the flowchart of the method of the embodiment of the present invention;

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

[0057] Figure 3 is the comparison diagram of the response estimation result and the true result in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] Embodiment

[0059] To make the objectives, 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 with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention.

[0060] Referring to Figure 1 , the present invention provides a method for realizing the response estimation of a jacket structure based on a dual Kalman filter, and the steps include:

[0061] S1. Establish a finite element model according to the information of the jacket structure to be measured, perform structural analysis on it, obtain the stress concentration positions of the structure, and take the ocean water surface and the upper part as the directly observable positions 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 modal parameters of the jacket structure, including frequency, displacement mode shape, and strain mode shape.

[0063] S3. Based on the sensor information at directly observable positions and the stress concentration positions, combined with the modal parameters, establish a reduced-order modal mode shape vector. The sensor types include strain sensors and acceleration sensors. The displacement mode shape is φ = [x1, x2, x3,..., x n , and the strain mode shape 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, and x n and y n are the displacement mode shape values and strain mode shape values corresponding to the nth point position, respectively.

[0064] Use the motion equation of the jacket structure to establish the state matrix of the dual Kalman filter. Specifically, the motion equation of the jacket structure is:

[0065]

[0066] In the formula, u(t), and represent the displacement, velocity, and acceleration vectors respectively. M, C, and K represent the mass matrix, damping matrix, and stiffness matrix of the jacket structure, and f(t) represents the load, which is expressed as the product of the matrix S p at the specified force position and the time history vector p(t);

[0067] Project the continuous-time equation of the jacket structure motion into the finite-order modal space using u(t) = φz(t) and perform mass normalization to obtain the continuous-time decoupled motion equation. The formula is:

[0068]

[0069] Γ = φ T Cφ

[0070] Ω 2 = φ T Kφ

[0071] In the formula, 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] Introduce the state vector to obtain the motion equation of the jacket structure, and its expression is:

[0073]

[0074] The 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 transition matrix, B c represents the control input matrix, x k+1 represents the state vector at the (k + 1)-th step. A and B respectively represent the state transition matrix and the control input matrix of the discretized state space model, and can be expressed as B = [A - I]A c -1 B c , x k represents the state vector at the k-th step.

[0077] S4. Use numerical simulation to obtain the responses at the positions where sensors are to be arranged on the jacket structure, and establish the observation matrix of the dual Kalman filter according to the relationships between various responses and the state vector. Specifically, it includes:

[0078] Apply loads to the jacket structure to obtain the response time histories at the positions where strain sensors and acceleration sensors are to be arranged and the positions to be measured. In this embodiment, 4 strain gauges and 2 acceleration sensors are set. The strain gauges are arranged at positions 1 - 4, and the acceleration sensors are arranged at positions 5 - 6. Estimate the strain time history near the bottom of the jacket structure, that is, the dimension of the strain and displacement mode vectors is 7.

[0079] Fuse the response data at the positions of the obtained strain sensors and acceleration sensors. The acceleration is expressed through the motion equation of the jacket structure as:

[0080]

[0081] The strain is obtained through the relationship between the strain mode, displacement mode and modal coordinates. The displacement vector can be obtained by u(t) = φz(t), where z(t) is the displacement in the modal coordinate system and 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). Transform the strain vector to further obtain the formula:

[0083] ε(t) = ψ(φ T φ) -1 φ T u(t)

[0084] To reflect the layout positions of the sensors, a selection matrix is introduced into the input vector. The selection matrix is a diagonal matrix, and its elements are 1 or 0. The elements at the degrees of freedom corresponding to the layout positions of the sensors are 1, and the others are 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 respectively represent the matrices of the displacement (strain), velocity, and acceleration measurement positions. 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] Based on the relationships between acceleration, strain, and the state vector, an observation matrix containing multiple types of responses is established. The formula is:

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

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

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

[0092] S5. Establish a dual Kalman filter framework for estimating the responses at the positions to be observed of the jacket structure. Using the measured responses as the input, the state vector of the jacket structure is output, and the strain response time history at the positions to be measured is obtained.

[0093] Refer to Figure 3 to implement the dual Kalman filter process and obtain the strain time history at the fatigue positions of the jacket structure.

[0094] S51. Conduct the first dual Kalman filter process to estimate the load;

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

[0096] Secondly, perform a priori estimation of the current input based on the input initial expectation and covariance and update the error covariance where Q p is the process noise covariance for calibrating the input force.

[0097] Calculate the Kalman gain of the input estimation where R is the covariance of the measurement noise, J represents the direct feedthrough matrix, and use the measurement vector to calculate the posterior estimation value of the input and update the error covariance In the formula, d k represents the observation vector, and G represents the output influence matrix.

[0098] S52. Perform the second dual Kalman filtering process to estimate the state vector of the jacket structure;

[0099] Take the above posterior estimation value of the input as a known quantity, and estimate the current state based on the state of the previous moment Update the error covariance of the state where Q x is the noise covariance for calibrating the state vector process, A and B respectively represent the state transition matrix and control input matrix of the discretized state space model, and can be expressed as B = [A - I]A c -1 B c .

[0100] Calculate the Kalman gain of the state estimation and combine the measurement vector to correct the prior estimation of the state and update the error covariance of the state I represents the identity matrix.

[0101] Repeat the above steps until the number of iteration steps reaches the response time history step length. Among them, in each iteration, the measured response is used as a known quantity to predict the state vector as the input of the Kalman filtering process.

[0102] S53. Use the relationship between the strain and the state vector of the jacket structure to obtain the strain response time history at the position to be measured, compare it with the measured strain response time history, and perform error analysis. Refer to Figure 3 , which is the comparison diagram of the estimated response time history and the true time history from 60 to 70 s.

[0103] Therefore, the present invention adopts the above method for realizing the response estimation of the jacket structure based on the dual Kalman filter. By using the reduced-order numerical modal information of the jacket structure, combining with the measured data of various types of responses, and considering the influence of the load on the state of the jacket structure, through the implementation of 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 solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for realizing the response estimation of a jacket structure based on a dual Kalman filter, characterized in that the steps Including: S1. Establish a finite element model according to the structural information of the jacket to be measured; S2. Perform modal analysis on the jacket structural model using finite element software to obtain the modal parameters of the jacket structure; S3. Establish a reduced-order modal eigenvector based on the modal parameters of the jacket structure, and use the motion equation of the jacket structure to establish the state matrix of the dual Kalman filter; S4. Use numerical simulation to obtain the responses at the positions where sensors are to be arranged on the jacket structure, and establish the observation matrix of the dual Kalman filter according to the relationship between various responses and the state vector; S5. Establish a dual Kalman filtering framework for estimating the responses at the positions to be observed of the jacket structure, use the measured responses as input, output the state vector of the jacket structure, and obtain the strain response time history at the position to be measured; Specifically including: S51. Conduct the first dual Kalman filtering process to estimate the load; Given the initial expectations and covariances of the input force and the state vector of the jacket structure; Perform a priori estimation of the current input according to the given initial expectations and covariances; Calculate the Kalman gain of the input estimation, and perform a posteriori estimation of the input using the measurement vector at the current moment; S52. Conduct the second dual Kalman filtering process to estimate the state vector of the jacket structure; Take the a posteriori estimated value of the input as a known quantity, and perform a priori estimation of the current state based on the state at the previous moment; Calculate the Kalman gain of the state estimation, and use the measurement vector to correct the a priori estimation of the state; Repeat the above steps until the number of iteration steps reaches the response time history step size; S53. Use the relationship between the strain and the state vector of the jacket structure to obtain the strain response time history at the position to be measured, and compare it with the measured strain response time history for error analysis.

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

3. A method for realizing the response estimation of a jacket structure based on a dual Kalman filter according to claim 2, characterized in that: In step S3, a reduced-order modal shape vector is established based on the layout positions of the sensors and the positions of the responses to be estimated in combination with the modal parameters. The displacement mode shape is φ = [x1, x2, x3,..., x n , and the strain mode shape 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, and x n and y n are the displacement mode shape value and the strain mode shape value corresponding to the position of the nth point, respectively.

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

5. A method for realizing the response estimation of a jacket structure based on a dual Kalman filter according to claim 4, characterized in that, In step S3, using the motion equation of the jacket structure to establish the state matrix of the dual Kalman filter includes: The motion equation of the jacket structure is: where \(u(t)\), and represent displacement, velocity, and acceleration vectors respectively, \(M\), \(C\), and \(K\) represent the mass matrix, damping matrix, and stiffness matrix of the jacket structure respectively, \(f(t)\) represents the load, which is expressed as the product of the matrix \(S\) p at the specified force position and the time history vector \(p(t)\); Project the continuous-time equation of the jacket structure motion into a finite-order modal space using u(t) = φz(t) and perform mass normalization to obtain the continuous-time decoupled motion equation, and the formula is: Γ = φ T Cφ Ω 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; Introduce the state vector Obtain the motion equation of the jacket structure, and its expression is as follows: Discretize the obtained motion equation of the jacket structure to obtain the state equation: x k+1 = Ax k + Bp k where, A c represents the state transition matrix, B c represents the control input matrix, x k+1 represents the state vector at the (k + 1)-th step. A and B respectively represent the state transition matrix and the control input matrix of the discretized state space model, and can be expressed as x k represents the state vector at the k-th step.

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

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