Structural vibration detection method based on inequality constraint hybrid least square algorithm

Abstract

The invention discloses a structural vibration detection method based on an inequality constraint hybrid least square algorithm in the technical field of structural vibration detection. The method comprises the following steps: S1, system model construction: establishing a linear discrete stochastic system state space model; s2, designing an algorithm: proposing a hybrid least square algorithm with input inequality constraints; s3, solving a system model: applying a proposed inequality constraint hybrid least square algorithm to a discrete system to realize simultaneous optimal estimation of a system state and input; and S4, performing comparison simulation: performing simulation by taking a two-layer shear structure as an example, comparing the state and input estimation of the shear structure under the conditions of no constraint and existence of inequality constraint, and verifying the effectiveness of the method. According to the invention, the hybrid least square algorithm of the input inequality constraint is provided, and the filtering effect is optimized by using part of input information, so that the accuracy of structural vibration detection is improved.

Description

Technical Field

[0001] This invention relates to the field of structural vibration detection technology, and in particular to a method for structural vibration detection. Background Technology

[0002] In the field of building structure vibration monitoring, structures such as high-rise buildings, long-span bridges, and industrial plants often face challenges in directly measuring or accurately acquiring external inputs when subjected to seismic activity, strong wind loads, or dynamic excitations from people or equipment. These external excitations can be considered unknown inputs to the building's dynamic system, with uncertainties in magnitude, direction, and frequency, thus posing a challenge to estimating the structural state (such as inter-story displacement, velocity, and acceleration). Therefore, how to simultaneously estimate the structural vibration state response and unknown external excitations using only limited sensor measurement information is a key issue in current structural health monitoring.

[0003] It is worth noting that unknown inputs in actual building structures often have inherent physical constraints. For example, the peak value of seismic excitation is limited by seismic intensity and site conditions; the magnitude of wind load is affected by wind field energy, topographic features, and building height; and vibrations generated by human activity or mechanical equipment operation also have definite amplitude ranges. These boundary characteristics are all inherent prior information of the structural dynamic system, which can theoretically effectively improve the accuracy and robustness of state estimation and excitation reconstruction.

[0004] However, existing structural vibration detection technologies generally employ unconstrained modeling methods when dealing with unknown external excitations, failing to fully utilize the physical feasible domain information of the excitation. This leads to problems such as increased bias, filter divergence, or instability in estimation results under complex environments. Therefore, existing technologies still have significant shortcomings in incorporating physical boundary constraints into the estimation of unknown inputs, making it difficult to meet the comprehensive requirements of modern building structural health monitoring for real-time performance, stability, and high accuracy. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a structural vibration detection method based on an inequality constraint hybrid least squares algorithm. This method is used to solve the structural vibration detection problem where the external excitation input has physical boundary constraints. It makes full use of the physical boundary constraints of the excitation, treating them as prior information, which can improve the accuracy of structural vibration detection.

[0006] The objective of this invention is achieved as follows: a structural vibration detection method based on an inequality constraint hybrid least squares algorithm, comprising the following steps:

[0007] Step 1) Constructing the system model: Based on the structural kinematic equilibrium equations, establish a state-space dynamic model containing mass, damping, and stiffness parameters. Discretize the model and introduce inequality constraints from external excitation inputs to obtain a linear discrete stochastic system model with input inequality constraints. This model is used to describe the vibration response behavior of the structure under external excitation inputs.

[0008] Step 2) Algorithm design: A hybrid least squares algorithm with input inequality constraints is proposed, which explicitly embeds the input constraint information into the estimation framework to achieve joint estimation of structural vibration state response and external unknown excitation input, and uses the input constraint information to improve the accuracy and stability of the estimation.

[0009] Step 3) Solve the system model: Apply the algorithm proposed in Step 2) to the linear discrete stochastic model established in Step 1), so that the algorithm can simultaneously utilize the state equation, measurement equation and input constraint information to achieve the optimal estimation of the structural vibration state response and the external unknown excitation input, and obtain the structural vibration state (displacement, velocity) response information. Based on this, construct the structural vibration detection characteristic parameters.

[0010] Step 4) Perform comparative simulation: Taking a two-layer shear structure as an example, perform simulation. Under the two conditions of no input constraints and inequality constraints, compare the estimated results of the structural vibration state response and the unknown external excitation input. Based on the structural vibration detection characteristic parameters, analyze and judge the structural vibration state, thereby realizing the detection of abnormal structural vibration state.

[0011] Furthermore, step 1) specifically involves: based on the following... The equations of motion for the degrees of freedom establish a state-space dynamic model:

[0012]

[0013] in These are the mass, stiffness, and damping matrices, all of which are known. These are displacement, velocity, and acceleration responses, respectively. It is the input position matrix with a value of 1 at the input degrees of freedom and a value of 0 at other positions; This is the input force, which is usually bounded in practical applications. Rephrasing the above equation in state-space form, we define the state vector. The equations of motion are restated in the state space and corresponding The measurement equation for the acceleration measurement is shown below:

[0014]

[0015]

[0016] in This indicates the measured acceleration value; It outputs the position matrix; It measures noise; and These represent the system matrix, input matrix, output matrix, and feedthrough matrix of the continuous state-space model, respectively.

[0017] By using a zero-order hold to discretize the continuous-time system given by the above two equations, and considering the case where there are inequality constraints in the input, the linear discrete state-space model is obtained as follows:

[0018]

[0019] in The state space matrix is ​​the discretized state space matrix; It is process noise, and its covariance matrix is ; Measurement noise The covariance matrix is ; and It is a constraint matrix.

[0020] Furthermore, step 2) specifically involves proposing a mixed least squares algorithm with input inequality constraints, the details of which are as follows:

[0021] First, the specific details of the hybrid least squares algorithm are given:

[0022] Consider random variables and unknown input vector A class of linear measurement models constituted:

[0023]

[0024] in, With a known mean Covariance ; Measurement value At the same time with and Related, and Given a matrix and assuming The column is full, that is ; Let be a random noise vector with zero mean, and its covariance matrix be... and with and Irrelevant; when given hour, and The linear least mean square estimator is:

[0025]

[0026] The expression for gain is , , The corresponding covariance matrix is:

[0027]

[0028] Input contains inequality constraint information The projection method is applied to estimate the unconstrained input values. Projecting onto a constrained polyhedron, solve the following problems.

[0029]

[0030] Solving quadratic programming problems using the efficient set method; finding the corresponding efficient constraints using the efficient set method. of OK and of element That is, converting inequality constraints into valid equality constraints. ;

[0031] Introduce virtual noise into the input of the valid equality constraints. ,Right now

[0032]

[0033] in It is a zero-mean random noise with a covariance of , and measurement noise Unrelated; combining the effective constraint information of the equation with the linear measurement model yields a new measurement model.

[0034]

[0035] in , , , Applying the MLS algorithm to this measurement model yields random parameters. and input The optimal unbiased estimate is as follows:

[0036]

[0037]

[0038] The expression for the gain matrix is:

[0039]

[0040]

[0041] in ;

[0042] The corresponding covariance matrix is

[0043] .

[0044] Furthermore, step 3) specifically involves applying the hybrid least squares algorithm based on inequality constraints proposed in step 2) to the linear discrete stochastic system with excitation input inequality constraints in step 1), thereby achieving optimal estimation of the structural vibration state response and the external unknown excitation input, including the following:

[0045] Step 3.1) State Propagation: Definition and They are respectively in Always and The optimal unbiased estimate, and the corresponding covariance matrices are respectively , , According to the state equation, the prior representation of the state is as follows:

[0046]

[0047] Its covariance matrix is ​​expressed as

[0048]

[0049] in ;

[0050] Step 3.2) Measurement Update: Based on the measurement equation, the ICMLS algorithm is used, with the corresponding initialization conditions as follows: , At any moment The state and unknown input estimation can be easily obtained in the following form:

[0051]

[0052]

[0053] Gain matrix and It is given by the following formula:

[0054]

[0055]

[0056] in ;

[0057] The corresponding covariance matrix is:

[0058]

[0059] in .

[0060] Further, step 4) specifically involves: using a two-layer shear structure to verify the effectiveness of the proposed method, with the input excitation applied to the first degree of freedom; and measuring the values. The simulated acceleration response includes two degrees of freedom; considering both unconstrained input and input with inequality constraints, the obtained structural vibration state response is compared with the excitation input estimate.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0062] (1) This invention makes full use of the physical boundary of the excitation input and introduces inequality constraints in the hybrid least squares estimation framework. It directly integrates physical prior information such as the peak ground motion limit, wind load range and equipment disturbance amplitude into the solution process, so that the unknown input estimation is more in line with the actual physical law, significantly reduces the deviation and distortion caused by unconstrained solution, and improves the estimation accuracy.

[0063] (2) The present invention effectively suppresses the effects of noise amplification and model uncertainty. Even under complex working conditions such as strong noise, abnormal measurement or limited excitation, it can still maintain stable filtering performance and realize reliable synchronous estimation of structural vibration state response and external excitation input.

[0064] (3) This invention maintains the characteristics of simple calculation structure and easy recursion of the hybrid least squares method. While increasing constraints, it does not significantly increase the computational complexity. It can be directly embedded into the building structure health monitoring system to realize real-time online detection of structural vibration and meet the requirements of engineering applications for high real-time performance and low computational burden. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0066] Figure 1 This is a flowchart of the structural vibration detection method in this invention.

[0067] Figure 2This is a schematic diagram of the two-layer shear structure used in this invention.

[0068] Figure 3 This is a comparison chart of input excitation estimation in this invention.

[0069] Figure 4 This is a comparison diagram of the dynamic response estimation for the first degree of freedom in this invention.

[0070] Figure 5 This is a comparison diagram of the dynamic response estimation for the second degree of freedom in this invention.

[0071] Figure 6 This is a comparison chart of dynamic response estimation errors in this invention.

[0072] Figure 7 This is a comparison chart of input excitation estimation errors in this invention. Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] like Figure 1 As shown, this invention is a structural vibration detection method based on an inequality-constrained hybrid least squares algorithm, comprising the following steps:

[0075] Step 1) System model construction;

[0076] Based on the following The state-space dynamic model is established by the equations of motion of the structure with degrees of freedom:

[0077]

[0078] in These are the mass, stiffness, and damping matrices, all of which are known. These are displacement, velocity, and acceleration responses, respectively. It is the input position matrix with a value of 1 at the input degrees of freedom and a value of 0 at other positions; This refers to the input force. In practical applications, this input force is usually bounded; for example, the loads on a structure, such as earthquakes, wind, and pressure, are all subject to limitations. Relating the above equation in state-space form, we define the state vector. The equations of motion are restated in the state space and corresponding The measurement equation for the acceleration measurement is shown below:

[0079]

[0080]

[0081] in This indicates the measured acceleration value; It outputs the position matrix; It measures noise. and Let represent the system matrix, input matrix, output matrix, and feedthrough matrix of the continuous state-space model, respectively. To achieve the estimator in discrete time, a zero-order hold is used to discretize the continuous-time system given by the above two equations, with a sampling time of 0.005 s. Furthermore, this invention considers the case where there are inequality constraints in the input, resulting in a linear discrete state-space model as follows:

[0082]

[0083] in The state space matrix is ​​the discretized state space matrix; It is process noise, and its covariance matrix is ; Measurement noise The covariance matrix is ; and These are constraint matrices, which are definite and known.

[0084] The purpose of this invention is to design an algorithm for linear discrete system models with inequality constraints on the external excitation input, to achieve joint estimation of the structural vibration state response and the external unknown excitation input, obtain the structural vibration state response and excitation input information, and construct structural vibration detection characteristic parameters for detecting abnormal vibration.

[0085] Step 2) Design the algorithm;

[0086] A mixed least squares algorithm with input inequality constraints is proposed. The specific details of the mixed least squares algorithm are first presented:

[0087] Consider random variables and unknown input vector A class of linear measurement models constituted:

[0088]

[0089] in With a known mean Covariance ; Measurement value At the same time with and Related, and Given a matrix and assuming The column is full, that is ; Let be a random noise vector with zero mean, and its covariance matrix be... and with and Irrelevant. When given hour, and The linear least mean square estimator is:

[0090]

[0091] The expression for gain is , , The corresponding covariance matrix is:

[0092]

[0093] In most practical problems, the unknown disturbance inputs are bounded, meaning the inputs contain inequality constraints. To address this situation, the present invention applies a projection method to estimate the unconstrained input values. Projecting onto a constrained polyhedron, this invention now solves the following problem.

[0094]

[0095] This is a quadratic programming problem. This invention solves quadratic programming problems using the effective set method. In the effective set method, only those constraints that are effective in solving the problem are beneficial to the optimization conditions. Through the effective set method, this invention finds the constraints corresponding to the effective constraints. of OK and of element That is, converting inequality constraints into valid equality constraints. .

[0096] Introduce virtual noise into the input of the valid equality constraints. ,Right now

[0097]

[0098] in It is a zero-mean random noise with a covariance of , and measurement noise Unrelated. By combining the effective constraint information of the equation with the linear measurement model, a new measurement model is obtained.

[0099]

[0100] in , , , Applying the MLS algorithm to this measurement model yields random parameters. and input The optimal unbiased estimate is as follows:

[0101]

[0102]

[0103] The expression for the gain matrix is:

[0104]

[0105]

[0106] in .

[0107] The corresponding covariance matrix is

[0108]

[0109] Step 3) Solve the system model;

[0110] The ICMLS algorithm proposed in step 2 is applied to the linear discrete stochastic model established in step 1 to solve the simultaneous state and input estimation problem of a linear stochastic system with input inequality constraints, including the following:

[0111] Step 3.1) State Propagation: Definition and They are respectively in Always and The optimal unbiased estimate, and the corresponding covariance matrices are respectively , , According to the state equation, the prior representation of the state is as follows:

[0112]

[0113] Therefore, its covariance matrix can be expressed as

[0114]

[0115] in .

[0116] Step 3.2) Measurement Update: Based on the measurement equation, use the ICMLS algorithm, noting the corresponding initialization conditions. , Then, the state and unknown input estimate at time t can be easily obtained in the following form:

[0117]

[0118]

[0119] Gain matrix and It is given by the following formula:

[0120]

[0121]

[0122] in .

[0123] The corresponding covariance matrix is:

[0124] ;

[0125] in .

[0126] In this way, the present invention can obtain the structural vibration state response and excitation input information, and use the obtained structural vibration state estimate and excitation input estimate as structural vibration detection feature parameters for the detection of abnormal vibration states.

[0127] Step 4) Perform comparative simulation.

[0128] by Figure 2 The proposed structural vibration detection method based on the hybrid least squares algorithm with inequality constraints is verified using the two-layer shear structure shown as an example, i.e., degrees of freedom. The mass and stiffness values ​​of the structure are as follows: Figure 2 As shown, the resonant frequencies of the structure are 1.67 Hz and 4.5 Hz. Assume the modal damping ratio for both modes is 2%. Excitation... Acting on the first degree of freedom, i.e., the mass is The position. Therefore, the mass, stiffness, damping, input position matrix, and output position matrix in this example are:

[0129] ;

[0130] ;

[0131] ;

[0132] , ;

[0133] After discretization using a zero-order hold, the system matrix is ​​as follows:

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] For both unconstrained and inequality-constrained input scenarios, a square wave signal with an amplitude of 10N and a frequency of 1Hz was used as the excitation input. Each run lasted 10 seconds, and the obtained structural vibration response was compared with the excitation input estimate. The simulation results are as follows: Figures 3 to 5 As shown.

[0139] according to Figure 3 It can be seen that when the input has inequality constraints, the estimated curve can track the real curve very well. While the estimated curve without constraints can also track the real curve, its tracking accuracy is significantly lower than that of the constrained curve, and it exhibits large fluctuations at the initial tracking moment. This demonstrates that by utilizing existing physical constraint information, the excitation input can be estimated more accurately, leading to a more precise estimation of the structural vibration state response. This verifies the effectiveness of the method proposed in this invention.

[0140] The displacement and velocity responses of the structure in the two degrees of freedom after being subjected to an excitation input are as follows: Figure 4 and Figure 5 As shown in the figure, when the excitation input has inequality constraints, the vibration state response of the building structure, namely the displacement and velocity estimation curves, can track the actual values ​​well, thus establishing more effective structural vibration detection characteristic parameters and more accurately detecting abnormal vibration states. However, when the input is unconstrained, the displacement and velocity tracking effect is poor, the curves have large fluctuations, and the detection effect of abnormal vibration states is poor.

[0141] Figure 6 and Figure 7 These are comparison charts showing the estimation errors of vibration state response and input excitation for two different scenarios: one with no input constraints and the other with inequality constraints. From... Figure 6 As can be seen, after fully utilizing the input inequality constraint information, the estimation error of the system's vibration state response decreases significantly, while the estimation error of the system's vibration response is larger without constraints. According to... Figure 7 It can be seen that the estimation error is smaller when there is an inequality constraint on the input. Although the estimation error decreases later when there is no constraint, there is a large error fluctuation at the beginning of the estimation.

[0142] This invention also calculates the mean squared error (MSE) of the system's dynamic response estimate and input estimate under two conditions. MSE is a statistic used to measure the difference between the estimate and the true value, and the calculation formula is as follows:

[0143] ,

[0144] A smaller MSE value indicates higher estimation accuracy. The calculation results are shown in the table below:

[0145]

[0146] As can be seen from the table, the MSE of the vibration state response estimate and the excitation input estimate are smaller when the input has inequality constraints than when the input has no constraints. This indicates that by utilizing the constraint boundary information of the input, the estimation accuracy is higher and a better estimation effect can be obtained. This allows for the establishment of more effective structural vibration detection characteristic parameters and more sensitive detection of abnormal vibrations.

[0147] The above description of the embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A structural vibration detection method based on an inequality-constrained hybrid least squares algorithm, characterized in that, Includes the following steps: Step 1) Constructing the system model: Based on the structural kinematic equilibrium equations, establish a state-space dynamic model containing mass, damping, and stiffness parameters. Discretize the model and introduce inequality constraints from external excitation inputs to obtain a linear discrete stochastic system model with input inequality constraints. This model is used to describe the vibration response behavior of the structure under external excitation inputs. Step 2) Algorithm design: A hybrid least squares algorithm with input inequality constraints is proposed, which explicitly embeds the input constraint information into the estimation framework to achieve joint estimation of structural vibration state response and external unknown excitation input, and uses the input constraint information to improve the accuracy and stability of the estimation. Step 3) Solve the system model: Apply the algorithm proposed in Step 2) to the linear discrete stochastic model established in Step 1), so that the algorithm can simultaneously utilize the state equation, measurement equation and input constraint information to achieve the optimal estimation of the structural vibration state response and the external unknown excitation input, and obtain the structural vibration state (displacement, velocity) response information. Based on this, construct the structural vibration detection characteristic parameters. Step 4) Perform comparative simulation: Taking a two-layer shear structure as an example, perform simulation. Under the two conditions of no input constraints and inequality constraints, compare the estimation results of the structural vibration state response and the unknown external excitation input. Based on the structural vibration detection characteristic parameters, analyze and judge the structural vibration state, thereby realizing the detection of abnormal structural vibration state.

2. The structural vibration detection method based on the inequality constraint hybrid least squares algorithm according to claim 1, characterized in that, Step 1) specifically involves: based on the following... The equations of motion for the degrees of freedom establish a state-space dynamic model: ； in These are the mass, stiffness, and damping matrices, all of which are known. These are displacement, velocity, and acceleration responses, respectively. It is the input position matrix with a value of 1 at the input degrees of freedom and a value of 0 at other positions; This is the input force, which is usually bounded in practical applications. Rephrasing the above equation in state-space form, we define the state vector. The equations of motion are restated in the state space and corresponding The measurement equation for the acceleration measurement is shown below: ； ； in This indicates the measured acceleration value; It outputs the position matrix; It measures noise; and These represent the system matrix, input matrix, output matrix, and feedthrough matrix of the continuous state-space model, respectively. By using a zero-order hold to discretize the continuous-time system given by the above two equations, and considering the case where there are inequality constraints in the input, the linear discrete state-space model is obtained as follows: ； in The state space matrix is ​​the discretized state space matrix; It is process noise, and its covariance matrix is ; Measurement noise The covariance matrix is ; and It is a constraint matrix.

3. The structural vibration detection method based on the inequality constraint hybrid least squares algorithm according to claim 2, characterized in that, Step 2) specifically involves proposing a mixed least squares algorithm with input inequality constraints, the details of which are as follows: First, the specific details of the hybrid least squares algorithm are given: Consider random variables and unknown input vector A class of linear measurement models constituted: ； in, With a known mean Covariance ; Measurement value At the same time with and Related, and Given a matrix and assuming The column is full, that is ; Let be a random noise vector with zero mean, and its covariance matrix be... and with and Irrelevant; when given hour, and The linear least mean square estimator is: ； The expression for gain is , , The corresponding covariance matrix is: ； Input contains inequality constraint information The projection method is applied to estimate the unconstrained input values. Projecting onto a constrained polyhedron, solve the following problems. ； Solving quadratic programming problems using the efficient set method; finding the corresponding efficient constraints using the efficient set method. of OK and of element That is, converting inequality constraints into valid equality constraints. ; Introduce virtual noise into the input of the valid equality constraints. ,Right now ； in It is a zero-mean random noise with a covariance of , and measurement noise Unrelated; combining the effective constraint information of the equation with the linear measurement model yields a new measurement model. ； in , , , Applying the MLS algorithm to this measurement model yields random parameters. and input The optimal unbiased estimate is as follows: ； ； The expression for the gain matrix is: ； ； in ; The corresponding covariance matrix is 。 4. The structural vibration detection method based on the inequality constraint hybrid least squares algorithm according to claim 3, characterized in that, Step 3) specifically involves applying the hybrid least squares algorithm based on inequality constraints proposed in Step 2) to the linear discrete stochastic system with excitation input inequality constraints in Step 1), thereby achieving optimal estimation of the structural vibration state response and the external unknown excitation input. This includes the following: Step 3.1) State Propagation: Definition and They are respectively in Always and The optimal unbiased estimate, and the corresponding covariance matrices are respectively , , According to the state equation, the prior representation of the state is: ； Its covariance matrix is ​​expressed as ； in ; Step 3.2) Measurement Update: Based on the measurement equation, the ICMLS algorithm is used, with the corresponding initialization conditions as follows: , At any moment The state and unknown input estimation can be easily obtained in the following form: ； ； Gain matrix and It is given by the following formula: ； ； in ; The corresponding covariance matrix is: ； in .

5. The structural vibration detection method based on the inequality constraint hybrid least squares algorithm according to claim 4, characterized in that, Step 4) specifically involves: using a two-layer shear structure to verify the effectiveness of the proposed method, with the input excitation applied to the first degree of freedom; and measuring the values. The simulated acceleration response includes two degrees of freedom; considering both unconstrained input and input with inequality constraints, the obtained structural vibration state response is compared with the excitation input estimate.

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