Rod system structure internal force and boundary parameter identification method

Abstract

The invention discloses a bar system structure internal force and boundary parameter identification method, and belongs to the field of structure health monitoring, and the method comprises the steps: S1, building a finite element model; s2, arranging an acceleration sensor; s3, deriving a vibration partial differential equation; s4, constructing a feature matrix; s5, axial pressure identification; and S6, identifying boundary parameters. According to the internal force and boundary parameter identification method for the rod system structure, the problems of internal force measurement and uncertain boundary conditions after the structure is constructed are effectively solved, the health monitoring capability of the in-service rod system structure is enhanced, reliable support is provided for safety assessment of civil engineering structures, and good application prospects are shown.

Description

Technical Field

[0001] The invention belongs to the field of structural health monitoring, and in particular relates to a method for identifying internal forces and boundary parameters of a bar structure. Background Art

[0002] Bar structures are common in civil engineering, including bridge cables, roof trusses, communication towers, transmission towers, wind turbine towers, and conductor pipes. Due to factors such as the mass of the superstructure, its own gravity, and construction and installation errors, significant internal forces, especially axial pressure, exist when the structure is built. However, most current monitoring systems are installed after the structure is built, so the recorded data often ignores the impact of these pre-existing forces.

[0003] For civil engineering structures, the interaction between structures is uncertain and the boundary conditions are unknown, which makes identifying the boundary parameters of the structure a key factor in building a reliable model. Using the data obtained by the monitoring system to identify the axial pressure and boundary parameters of the structure is crucial to understanding the structural operation status and evaluating its safety.

[0004] The modal method derives the vibration equation of the beam with axial pressure, obtains the relationship between the structural modal parameters and the axial pressure, and establishes the theoretical basis for axial pressure identification. This method is based on the measured structural modal parameters and uses numerical approximation technology to determine the axial pressure. Although there are technologies for identifying structural axial pressure and boundary parameters, they usually ignore the effect of damping on vibration and are mostly applicable to structures with low stiffness. In addition, the existing technology lacks an effective means for the joint identification of axial pressure and boundary parameters. Summary of the invention

[0005] The purpose of the present invention is to provide a method for identifying the internal forces and boundary parameters of a bar structure. This method effectively overcomes the difficulties of measuring the internal forces and uncertain boundary conditions after the structure is built, enhances the ability of health monitoring of in-service bar structures, provides reliable support for the safety assessment of civil engineering structures, and shows good application prospects.

[0006] To achieve the above object, the present invention provides a method for identifying internal forces and boundary parameters of a bar structure, comprising the following steps:

[0007] S1. Establish finite element model;

[0008] Establish a finite element model based on the material and structural parameter information of the structure to be tested;

[0009] S2, laying out acceleration sensors;

[0010] Finite element software is used to dynamically load the structure model to be tested, 5 acceleration sensor measuring points are arranged on the structure to be tested, the response time history data of the structure to be tested is obtained, and the axial pressure value of the structure to be tested is recorded;

[0011] S3. Derive the vibration partial differential equation;

[0012] According to Timoshenko beam theory, the vibration partial differential equation of the beam including axial force and damping is derived;

[0013] S4, construct feature matrix;

[0014] The separation of variables method is used to solve the vibration partial differential equation in S3. The modal frequency and displacement value of the structure to be measured are obtained through modal analysis. According to the modal displacement value, combined with the displacement amplitude function, the modal displacement value ratio is obtained. The modal displacement value ratio and the modal information of the measuring point position are used to solve the simultaneous equation group to obtain the characteristic matrix equation T·B=0, where:

[0015]

[0016] B=[B1 B2 B3 B4] T ;

[0017] Among them, x i (i=1,2,3,4,5) is the coordinate of measurement point i, λ k (k=1,2,3,4) is the characteristic root, B is the boundary parameter vector, B k (k=1,2,3,4) is the boundary parameter;

[0018] S5, axial pressure identification;

[0019] The modal identification method is used to process the response time history data obtained in S2 to obtain the frequency, damping and modal displacement of the five measuring points; the relationship curve between the determinant value of the characteristic matrix T and the axial pressure, the intersection of the relationship curve and |T|=0 is the identified axial pressure value;

[0020] S6, boundary parameter identification;

[0021] Substitute the axial pressure value in S5 into the characteristic matrix T to obtain the updated characteristic matrix T i ; For the updated feature matrix T i Perform singular value decomposition; solve for boundary parameters.

[0022] Preferably, in S3, a micro-beam segment in the beam subjected to axial pressure is taken for force analysis, and a partial differential vibration equation is derived based on the force system equilibrium condition, and the calculation method is as follows:

[0023]

[0024] Where EI is the bending stiffness of the rod, P is the axial pressure on the structure, ρ is the density of the material, A is the cross-sectional area, G is the shear modulus, c is the damping coefficient, k′ is the correction factor, I is the polar moment of inertia of the section, and v(x,t) is the displacement at position x at time t.

[0025] Preferably, in S4, it is assumed that the lateral vibration equation is in, is the displacement amplitude function, ω is the angular frequency, and the lateral vibration equation is substituted into the partial differential vibration equation to obtain the ordinary differential equation. The calculation method is as follows:

[0026]

[0027] Among them, the coefficients α, β, and γ are defined as:

[0028]

[0029] Preferably, the displacement amplitude function is Among them, B k As the boundary parameter, substitute it into the ordinary differential equation to obtain the characteristic root λ k ,λ k Related to the α, β, and γ coefficients, the expression is:

[0030]

[0031] Preferably, the modal displacement value is β ij The calculation method is as follows:

[0032]

[0033] After simplification, we get:

[0034]

[0035] Among them, x i is the coordinate of the measuring point i on the beam, x j is the coordinate of the measuring point j on the beam, λ k is the characteristic root.

[0036] Preferably, in S6, the updated feature matrix T i Perform singular value decomposition, the process is expressed as:

[0037] T i =USV T ;

[0038] Among them, U and V are orthogonal matrices composed of left and right singular vectors respectively, and S is a diagonal matrix.

[0039] Preferably, in order to make T i The determinant of S is zero, and the singular values ​​S in the S matrix 44 Set to 0 to construct a new diagonal matrix S r , expressed as:

[0040]

[0041] The modified feature matrix T r The calculation formula is:

[0042] T r =US r V T .

[0043] Preferably, in S6, the boundary parameter B is solved k (k=1,2,3,4) includes the following steps:

[0044] S601, using the modified feature matrix T r Substitute T in T·B=0 to obtain the new equation system T r B = 0;

[0045] S602, solve the equation group T r B = 0, where B = [B1 B2 B3 B4] T , let B1=1;

[0046] S603, starting from B2, solve the remaining B one by one k (k=2,3,4) values ​​until all B k The values ​​are determined.

[0047] Preferably, the above computer program implements the steps of any one of the above methods when executed by a processor.

[0048] Preferably, the processor implements the steps of any one of the methods when executing the computer program.

[0049] Therefore, the present invention adopts the above-mentioned method for identifying internal forces and boundary parameters of a bar structure. Compared with the prior art, the present invention has the following significant beneficial effects:

[0050] (1) The present invention not only considers the influence of axial pressure on structural vibration, but also introduces the damping coefficient. Because damping is an important factor that cannot be ignored in actual engineering structures, the accuracy of identifying internal forces is improved;

[0051] (2) The present invention uses a vibration differential equation including axial pressure and damping and utilizes the measured modal parameters to more accurately identify the axial pressure and boundary parameters of the bar structure. Compared with the previous methods that ignore damping or are only applicable to structures with low stiffness, this method has higher applicability and accuracy.

[0052] (3) The sensors of the present invention only need to be arranged along the same axis, and their spacing will not affect the accuracy of the recognition results. This provides greater flexibility for on-site installation and reduces dependence on specific measurement conditions;

[0053] (4) The present invention adopts a method of singular value decomposition and assigning a zero value to the minimum singular value, thereby effectively solving the problem of non-unique solutions and enabling boundary parameters to be reasonably determined;

[0054] (5) The present invention can solve the problem that the internal forces in the structure are difficult to measure after the structure is built, and the problem that the boundary conditions are difficult to obtain. Therefore, it has certain engineering application prospects and helps to better evaluate the safety status of the structure.

[0055] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 The present invention is a flow chart of a method for identifying internal forces and boundary parameters of a bar structure. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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 part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used in the present invention should be the common meaning understood by people with general skills in the field to which the present invention belongs.

[0058] Embodiment 1

[0059] like Figure 1 As shown, a method for identifying internal forces and boundary parameters of a bar structure of the present invention comprises the following steps:

[0060] S1. Establish finite element model;

[0061] A finite element model is established based on the material and structural parameter information of the structure to be tested, a load is applied to the structure to be tested according to its operating conditions, and the data of the structure to be tested is extracted from the finite element software as a reference value for subsequent identification results.

[0062] S2, laying out acceleration sensors;

[0063] Finite element software is used to dynamically load the structure model to be tested. Five acceleration sensor measuring points are arranged on the structure along the axial position to obtain the vibration response time history of the structure to be tested. The modal parameters of the structure to be tested are obtained using the random subspace method, and the axial pressure value P in the structure to be tested is recorded. i .

[0064] S3. Derive the vibration partial differential equation;

[0065] According to Timoshenko beam theory, shear deformation and rotational inertia effects are taken into account, and the damping coefficient c is introduced to reflect the inevitable energy dissipation in actual engineering. The vibration partial differential equation of the beam including axial pressure and damping is derived. The specific process is:

[0066] Take the micro-beam section in the beam under axial pressure for force analysis. According to the force system equilibrium condition, the partial differential vibration equation of the Timoshenko beam with respect to the lateral displacement v(x, t) can be derived. The calculation method is as follows:

[0067]

[0068] Where EI is the bending stiffness of the rod, P is the axial pressure on the structure, ρ is the density of the material, A is the cross-sectional area, G is the shear modulus, c is the damping coefficient, k′ is the correction factor, I is the polar moment of inertia of the section, and v(x,t) is the displacement at position x at time t.

[0069] S4, construct feature matrix;

[0070] The vibration partial differential equation in S3 is solved by separation of variables method, assuming that the calculation method of the lateral vibration equation is as follows:

[0071]

[0072] in, is the displacement amplitude function, and ω is the angular frequency.

[0073] Substituting the above assumptions into the partial differential vibration equation, we get an ordinary differential equation about the space coordinates:

[0074]

[0075] The coefficients are defined as:

[0076]

[0077] Assume that the displacement amplitude function is Among them, Bk is the boundary parameter. Substituting the displacement amplitude function into the ordinary differential equation in S4, the characteristic root λ can be obtained k ,λ k Related to the α, β, and γ coefficients, the specific expression is:

[0078]

[0079] When the parameters of the structure to be measured are known, the displacement amplitude function The unknown quantities in the equation are the axial pressure P and the boundary parameter B. k (k=1,2,3,4). By collecting the modal information of the structure to be tested, a set of equations can be established to solve the values ​​of these five unknowns. Specifically, the frequencies of each mode of the structure to be tested and the modal displacement values ​​at different positions can be obtained through modal analysis. Based on these modal displacement values, combined with the displacement amplitude function, the modal displacement value ratio β between any two points can be obtained. ij , the expression is as follows:

[0080]

[0081] After simplification, we can get:

[0082]

[0083] Among them, x i is the coordinate of the measuring point i on the beam, x j is the coordinate of the measuring point j on the beam, λ k is the characteristic root.

[0084] Through the above modal displacement ratio, combined with the modal information of the five measuring points, the equations can be combined to finally form the characteristic matrix equation T·B=0, where:

[0085]

[0086] B=[B1 B2 B3 B4] T ;

[0087] Among them, x i (i=1,2,3,4,5) is the coordinate of measurement point i, λ k (k=1,2,3,4) is the characteristic root, B is the boundary parameter vector, B k (k=1,2,3,4) is the boundary parameter.

[0088] Under the premise that the parameters of the structure to be measured and the modal parameters are known, the characteristic matrix T only contains the axial pressure P as an unknown quantity. The above derivation is carried out under the condition of unknown boundary conditions, so it can be ensured that the boundary parameter vector B has a non-zero solution.

[0089] S5, axial pressure identification;

[0090] The modal identification method is used to process the response time history data obtained in S2 to obtain the frequency, damping and modal displacement of the five measuring points. The relevant parameters of the structure to be measured are substituted into the characteristic matrix T to obtain the relationship curve between the determinant value of the characteristic matrix T and the axial pressure P. The intersection of the relationship curve and |T|=0 is the identified axial pressure value P. i .

[0091] S6, boundary parameter identification;

[0092] Use the axial pressure value P in S5 i Substitute into the feature matrix T to obtain the updated feature matrix T i . Due to P i is obtained by numerical approximation, so T i The determinant of is extremely small but non-zero.

[0093] For the updated feature matrix T i Perform singular value decomposition to obtain its singular values ​​and corresponding singular vectors. This process can be expressed as:

[0094] T i =USV T ;

[0095] Among them, U and V are orthogonal matrices composed of left and right singular vectors respectively, and S is a diagonal matrix.

[0096] In order to make T i The determinant is zero, and the smallest singular value S in the S matrix 44 Set to 0 to construct a new diagonal matrix S r , expressed as:

[0097]

[0098] The modified feature matrix T i It can be calculated by the following formula:

[0099] T r =US r V T ;

[0100] Due to S r It is a matrix with insufficient rank, so in order to solve the boundary parameter B k (k=1,2,3,4), use the following method:

[0101] S601, using the modified feature matrix T r Substitute T in T·B=0 to obtain the new equation system T r B = 0;

[0102] S602, solve the equation group T r B = 0, where B = [B1 B2 B3 B4] T , let B1=1;

[0103] S603, starting from B2, solve the remaining B one by one k (k=2,3,4) values ​​until all B k The values ​​are determined.

[0104] This method ensures that even in the case of insufficient rank, a set of reasonable boundary parameters B can be obtained and used in subsequent analysis or structural health monitoring.

[0105] Therefore, the present invention adopts the above-mentioned method for identifying the internal forces and boundary parameters of a bar system structure. This method effectively overcomes the difficulties of measuring internal forces and uncertain boundary conditions after the structure is built, enhances the ability of health monitoring of in-service bar system structures, provides reliable support for the safety assessment of civil engineering structures, and shows good application prospects.

[0106] 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 identifying internal forces and boundary parameters of a bar structure, characterized in that: The following steps are involved: S1. Establish finite element model; Establish a finite element model based on the material and structural parameter information of the structure to be tested; S2, laying out acceleration sensors; Finite element software is used to dynamically load the structure model to be tested, 5 acceleration sensor measuring points are arranged on the structure to be tested, the response time history data of the structure to be tested is obtained, and the axial pressure value of the structure to be tested is recorded; S3. Derive the vibration partial differential equation; According to Timoshenko beam theory, the vibration partial differential equation of the beam including axial force and damping is derived; S4, construct feature matrix; The separation of variables method is used to solve the vibration partial differential equation in S3. The modal frequency and displacement value of the structure to be measured are obtained through modal analysis. According to the modal displacement value, combined with the displacement amplitude function, the modal displacement value ratio is obtained. The modal displacement value ratio and the modal information of the measuring point position are used to solve the simultaneous equation group to obtain the characteristic matrix equation T·B=0, where: <h2 style=";text-align:left;direction:ltr">B=[B1 B2 B3 B4]<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> ; Among them, x i (i=1,2,3,4,5) is the coordinate of measurement point i, λ k (k=1,2,3,4) is the characteristic root, B is the boundary parameter vector, B k (k=1,2,3,4) is the boundary parameter; S5, axial pressure identification; The modal identification method is used to process the response time history data obtained in S2 to obtain the frequency, damping and modal displacement of the five measuring points; the relationship curve between the determinant value of the characteristic matrix T and the axial pressure, the intersection of the relationship curve and |T|=0 is the identified axial pressure value; S6, boundary parameter identification; Substitute the axial pressure value in S5 into the characteristic matrix T to obtain the updated characteristic matrix T i ; For the updated feature matrix T i Perform singular value decomposition; solve for boundary parameters.

2. A method for identifying internal forces and boundary parameters of a bar structure according to claim 1, characterized in that: In S3, the micro-beam segment in the beam subjected to axial pressure is taken for force analysis. According to the force system equilibrium condition, the partial differential vibration equation is derived, and the calculation method is as follows: Where EI is the bending stiffness of the rod, P is the axial pressure borne by the structure, ρ is the density of the material, A is the cross-sectional area, G is the shear modulus, c is the damping coefficient, and k is the shear modulus. ′ is the correction factor, I is the polar moment of inertia of the cross section, and v(x,t) is the displacement at position x at time t.

3. A method for identifying internal forces and boundary parameters of a bar structure according to claim 1, characterized in that: In S4, it is assumed that the lateral vibration equation is in, is the displacement amplitude function, ω is the angular frequency, and the lateral vibration equation is substituted into the partial differential vibration equation to obtain the ordinary differential equation. The calculation method is as follows: Among them, the coefficients α, β, and γ are defined as:

4. A method for identifying internal forces and boundary parameters of a bar structure according to claim 3, characterized in that: The displacement amplitude function is Among them, B k As the boundary parameter, substitute it into the ordinary differential equation to obtain the characteristic root λ k ,λ k Related to the α, β, and γ coefficients, the expression is:

5. A method for identifying internal forces and boundary parameters of a bar structure according to claim 4, characterized in that: Modal displacement ratio β ij The calculation method is as follows: After simplification, we get: Among them, x i is the coordinate of the measuring point i, x j is the coordinate of the measurement point j, λ k is the characteristic root.

6. A method for identifying internal forces and boundary parameters of a bar structure according to claim 1, characterized in that: In S6, the updated feature matrix T i Perform singular value decomposition, the process is expressed as: T i =USV T ; Among them, U and V are orthogonal matrices composed of left and right singular vectors respectively, and S is a diagonal matrix.

7. A method for identifying internal forces and boundary parameters of a bar structure according to claim 6, characterized in that: In order to make T i The determinant of S is zero, and the singular values ​​S in the S matrix 44 Set to 0 to construct a new diagonal matrix S r , expressed as: The modified feature matrix T r The calculation formula is: T r =US r V T 。 8. A method for identifying internal forces and boundary parameters of a bar structure according to claim 7, characterized in that: In S6, solve the boundary parameter B k (k=1,2,3,4) includes the following steps: S601, using the modified feature matrix T r Substitute T in T·B=0 to obtain the new equation system T r B = 0; S602, solve the equation group T r B = 0, where B = [B1 B2 B3 B4] T , let B1=1; S603, starting from B2, solve the remaining B one by one k (k=2,3,4) values ​​until all B k The values ​​are determined.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

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