A dynamic load identification method and system for a multi-degree-of-freedom system

Abstract

The application discloses a dynamic load identification method and system for a multi-degree-of-freedom system. The method analyzes the dynamic characteristics of the multi-degree-of-freedom system, establishes a system dynamics model, fuses the Newmark-beta method based on system modal information and time-domain displacement responses of partial degrees of freedom, and deduces an identification equation of the load borne by the system when the number n of displacement response degrees of freedom is greater than or equal to the number n of unknown loads. u The method can identify the size of the load borne by the system and the response information on other degrees of freedom of the system by solving the equation. f The method combines the modal coordinate conversion method and the Newmark-beta method, has high identification precision for identification of a multi-degree-of-freedom system subjected to periodic excitation, impact excitation and random excitation, breaks through the limitation that dynamic load time-domain identification cannot be realized based on modal coordinate conversion when dynamic response information is incomplete at the present stage, and realizes the function of simultaneous identification of the load and the system response.

Description

Technical Field

[0001] This invention belongs to the field of dynamic load identification, specifically relating to a method and system for dynamic load identification of multi-degree-of-freedom systems. Background Technology

[0002] Accurate and effective identification of dynamic loads is crucial for ensuring the safety and reliability of engineering structures. However, in many cases, due to the high complexity of engineering structures or harsh working environments, it is impossible to directly measure the dynamic loads acting on the structure. This has spurred the development of dynamic load identification technology. Dynamic load identification can also be called dynamic load recognition. Currently, dynamic load identification technology mainly includes two types: frequency domain methods and time domain methods. Frequency domain methods rely on Fourier transform to convert the output response between the time and frequency domains, requiring a large amount of data acquisition, making them unsuitable for transient impact loads. Time domain methods, on the other hand, can directly identify loads based on the time-domain information of the structural response, facilitating engineering applications and thus possessing strong engineering application value.

[0003] For dynamic load identification of multi-degree-of-freedom systems, it is necessary to classify the load and response into various models based on their quantitative relationship, such as single-input single-output, single-input multiple-output, and multiple-input multiple-output. Then, different methods are used to solve these models in modal space, obtaining modal space solutions which are then converted into physical space solutions. This type of method is complex, computationally intensive, and the identification accuracy accumulates significantly with time. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method and system for identifying dynamic loads in multi-degree-of-freedom systems, which at least partially solves the problems of the prior art.

[0005] Technical solution: To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for dynamic load identification of multi-degree-of-freedom systems includes the following steps:

[0007] S1. Establish the system dynamic equations. Based on the known modal information and partial response information, transform the system into modal space and establish the system modal space dynamic equations.

[0008] S2. Based on modal information, the system modal spatial displacement, velocity, acceleration response and modal force are represented by the system time-domain spatial displacement, velocity, acceleration response and excitation;

[0009] S3. Substitute the modal space response into the system modal space dynamic equation, return to the time domain, discretize the displacement, velocity, and acceleration of each degree of freedom in the time domain based on the Newmark-β method, and obtain the recursive relationship of the system response of each degree of freedom at time t and time t+Δt, and at the same time obtain the load solution equation;

[0010] S4. Solve the equations to obtain the loads acting on the system and / or the system's displacement response.

[0011] Further, step S1 includes:

[0012] For a multi-degree-of-freedom system with N degrees of freedom, where any n... f Loads act on Nn degrees of freedom, with the remaining Nn f With zero load on each degree of freedom, the time-domain dynamic equations of the linear system are established as follows:

[0013]

[0014] u(t) represents the system's time-domain acceleration, velocity, and displacement response vectors, respectively; C, M, and K represent the system's damping matrix, mass matrix, and stiffness matrix, respectively; and f(t) represents the excitation force vector.

[0015] in,

[0016] [M] = diag(M1, M2, ..., M) N )

[0017]

[0018]

[0019] {f(t)}=(F1(t), F2(t),...,F N (t))

[0020] Given the system's modal shape matrix Φ, transform the system into modal space and establish a modal space dynamic model:

[0021]

[0022] M r =diag(m1, m2, ... m) N )=Φ T [M]Φ

[0023] C r =diag(c1, c2, ..., c) N )=Φ T [C]Φ

[0024] K r=diag(k1, k2, ... k) N )=Φ T [K]Φ

[0025]

[0026] Step S2 includes:

[0027] Let the modal shape matrix

[0028]

[0029]

[0030]

[0031] This multi-degree-of-freedom system is subject to a known position n. f One load transforms the time-domain spatial load into the modal space:

[0032]

[0033] Step S3 includes:

[0034] Substituting the modal response and modal load into the equation, we obtain

[0035]

[0036] According to the Newmark-β method, the acceleration response and velocity response are expressed as displacement responses as follows:

[0037]

[0038]

[0039] make

[0040]

[0041] a6=Δt(1-γ), a7=γΔt

[0042] Substituting the load solution equations, the final set of time-domain space load solution equations is as follows:

[0043]

[0044] in

[0045] Step S4 includes:

[0046] Analyze the right side of the system of equations F i(t+Δt) represents the load to be determined, and u is the value on the left side of the equation. i (t+Δt) is the displacement to be determined, and any n is known. u There are Nn displacements, therefore the left side of the equation has Nn u One unknown quantity;

[0047] When n f <n u When the number of loads to be identified is less than the number of displacement responses, the equation can be solved for F. i The least squares solution of (t) can be obtained, that is, the load can be approximated by the least squares method;

[0048] When n f =n u When the number of loads to be identified equals the number of displacement responses, the equation has only one solution, meaning there is only one type of load, and this solution is the true solution for the load.

[0049] When n f >n u When the number of loads to be identified is greater than the number of displacement responses, the equation has no solution, meaning dynamic load identification cannot be performed.

[0050] The present invention also provides a dynamic load identification system for multi-degree-of-freedom systems, comprising:

[0051] The modal space dynamics equation construction module is used to establish system dynamics equations. Based on known modal information and partial response information, the system is transformed into modal space to establish the system modal space dynamics equations.

[0052] The temporal-space dynamics representation module is used to represent the system's modal spatial displacement, velocity, acceleration response, and modal force using the system's temporal-space displacement, velocity, acceleration response, and excitation based on modal information.

[0053] The time-domain load equation recursion module is used to substitute the modal space response into the system modal space dynamic equation, return to the time domain, discretize the displacement, velocity, and acceleration of each degree of freedom in the time domain based on the Newmark-β method, obtain the recursive relationship of the system response of each degree of freedom at time t and t+Δt, and at the same time obtain the load solution equation;

[0054] The solver module is used to solve equations to obtain the loads acting on the system and / or the system's displacement response.

[0055] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the dynamic load identification method for a multi-degree-of-freedom system as described above.

[0056] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the dynamic load identification method for a multi-degree-of-freedom system as described above.

[0057] Beneficial effects: (1) The dynamic load identification method for multi-degree-of-freedom systems proposed in this invention has no requirements on the magnitude, quantity, location, or type of the load on the structure, or on the distribution of the degrees of freedom of the known response, and has strong universality; (2) The method of this invention can identify load and response simultaneously, reducing the cumbersome steps in existing dynamic load identification technologies that require load identification first and then response calculation based on the identified load, and can monitor the dynamic response on other unknown degrees of freedom in real time; (3) This invention is based on the system time domain information for identification, with high identification accuracy, low computational cost, and low implementation difficulty. It can also be applied to continuous and linear systems through the extension method, so it has a very broad application prospect in the engineering field. Attached Figure Description

[0058] Figure 1 This is a flowchart of the dynamic load identification method for multi-degree-of-freedom systems according to the present invention;

[0059] Figure 2 This is a multi-degree-of-freedom model diagram under the periodic excitation effect of an embodiment of the present invention;

[0060] Figure 3 This is a comparison of the load identification results under sinusoidal excitation in the embodiments of the present invention;

[0061] Figure 4 This is a comparison of the load identification results under impact excitation in the embodiments of the present invention;

[0062] Figure 5 This is a comparison of the load identification results under random excitation in the embodiments of the present invention;

[0063] Figure 6 It is the absolute value of the load identification error under sinusoidal excitation in the embodiment of the present invention;

[0064] Figure 7 This is a comparison chart of the response of the first degree of freedom identified when the load is subjected to sinusoidal excitation in an embodiment of the present invention, and the response of the first degree of freedom calculated theoretically. Detailed Implementation

[0065] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0066] Reference Figure 1 The dynamic load identification method for multi-degree-of-freedom systems described in this invention includes the following steps:

[0067] S1. Establish the system dynamic equations. Based on the known modal information and partial response information, transform the system into modal space and establish the system modal space dynamic equations.

[0068] S2. Based on modal information, the system modal spatial displacement, velocity, acceleration response and modal force are represented by the system time-domain spatial displacement, velocity, acceleration response and excitation;

[0069] S3. Substitute the modal space response into the system modal space dynamic equation, return to the time domain, discretize the displacement, velocity, and acceleration of each degree of freedom in the time domain based on the Newmark-β method, and obtain the recursive relationship of the system response of each degree of freedom at time t and time t+Δt, and at the same time obtain the load solution equation;

[0070] S4. Solve the equations to obtain the load acting on the system at time t+Δt and / or the system's displacement response. The obtained system displacement response is used as a known condition for load identification at the next time step. Substitute it into the time-domain spatial dynamic equations in S3 to continue identifying the load and / or the system's displacement response at the next time step.

[0071] The specific implementation method is as follows: Theoretically, a multi-degree-of-freedom linear system is practically non-existent in engineering. However, based on certain methods, continuous and / or nonlinear systems in engineering can be abstracted into a multi-degree-of-freedom linear system. For example, a beam structure in engineering, within a certain error range, can be abstracted into a multi-degree-of-freedom system based on the modal truncation method. The structural damping of the system is nonlinear damping, but it can be characterized by modal damping. Thus, a continuous nonlinear system becomes a multi-degree-of-freedom linear system. Let the number of degrees of freedom of this multi-degree-of-freedom system be N, where any n f Loads act on Nn degrees of freedom, with the remaining Nn f With zero load on each degree of freedom, establish the time-domain dynamic model of this multi-degree-of-freedom system:

[0072]

[0073] In the formula u(t) represents the system's time-domain acceleration, velocity, and displacement response vectors, respectively; C, M, and K represent the system's damping matrix, mass matrix, and stiffness matrix, respectively; and f(t) represents the excitation force vector, i.e., the load vector.

[0074] in

[0075] [M] = diag(M1, M2, ..., M) N )

[0076]

[0077]

[0078] {f(t)}=(F1(t), F2(t),...,F N (t))

[0079] Since the load location is known, the load vector {f(t)} can be written as:

[0080]

[0081] System modes are parameters characterizing the inherent properties of a system, such as its natural frequencies and mode shapes. Once the structural form of a system is determined, its modes are also determined. In engineering practice, modal parameter tests can be used to obtain the modal parameters of a given structure. In this invention, it is assumed that the mass matrix, stiffness matrix, and damping matrix of the structure are known conditions; therefore, the mode shapes Φ and modal mass matrix M of the structure can be calculated. r Modal damping matrix C r Modal stiffness matrix K r Let's consider:

[0082] M r =diag(m1, m2, ... m) N )

[0083] C r =diag(c1, c2, ..., c) N )

[0084] K r =diag(k1, k2, ... k) N )

[0085] modal force F r Represented as:

[0086]

[0087] Let the modal shape matrix

[0088] This dynamic model can then be transformed into modal space to establish a modal space dynamic model:

[0089]

[0090] Let the structural displacement response vector be u(t). From the coordinate transformation, we obtain the modal displacement q(t) = Φ. -1 u(t)

[0091]

[0092] Similarly, modal acceleration Modal velocity Right now

[0093]

[0094]

[0095] Substituting equations (3), (4), and (5) into equation (2), we get:

[0096]

[0097] Discretize the displacement, velocity, acceleration, and load of each degree of freedom in the time domain. According to the Newmark-β method, the acceleration and velocity can be expressed by the displacement response as follows:

[0098]

[0099]

[0100] In the formula, β = 1 / 4 and γ = 1 / 2. This method of determining the value assumes that the acceleration over the discrete time interval Δt is the average of the accelerations at both ends of Δt, which is a constant. Therefore, this method is also called the average acceleration method.

[0101] For ease of representation, let:

[0102]

[0103] a6=Δt(1-γ), a7=γΔt

[0104] Simplify equations (7) and (8) to get:

[0105]

[0106]

[0107] Given zero initial conditions, we solve for the displacements of each degree of freedom at time t+Δt. Therefore, we can assume that the displacements, velocities, and accelerations of each degree of freedom at time t are known constants. Let... Therefore, equations (9) and (10) can be simplified as follows:

[0108]

[0109]

[0110] Substituting equations (11) and (12) into equation (6), we get:

[0111]

[0112] Given the location of the loads, let's represent the loads sequentially according to their degrees of freedom, from smallest to largest. From the modal force transformation formula

[0113]

[0114] Substituting equation (14) into equation (13), we get:

[0115]

[0116]

[0117] Analyze the system of equations (15), the right side of the system F i (t+Δt)(i=n1、n2……n f Let u be the load to be determined. As can be seen from the previous analysis, the left side of the equation is u. i (t+Δt)(i=1、2……N) is the variable to be determined, and any n in it is known. u Therefore, the left side of the equation has Nn. u An unknown quantity.

[0118] When n f <n u When the number of loads to be identified is less than the number of displacement responses, the equation can be solved for F. i (t)(i=n1、n2……n f The least squares solution of the load can be obtained by using the least squares method;

[0119] When n f =n u When the number of loads to be identified equals the number of displacement responses, the equation has only one solution, meaning there is only one type of load, and this solution is the true solution for the load.

[0120] When n f >n u When the number of loads to be identified is greater than the number of displacement responses, the equation has no solution, meaning dynamic load identification cannot be performed.

[0121] In the embodiments, establish as follows Figure 2 The system shown is a multi-degree-of-freedom system. The masses of each degree of freedom are m1 = 1 kg, m2 = 2 kg, m3 = 3 kg, and m4 = 4 kg, respectively. The stiffness coefficients of the elastic elements connecting the various degrees of freedom are k1 = 800 N / m, k2 = 1600 N / m, k3 = 3200 N / m, and k4 = 6400 N / m, respectively. It is known that the system is only subjected to excitation in the first degree of freedom, and load identification is performed using only the displacement response information in the second degree of freedom.

[0122] Based on the above structural parameters, the system dynamic equations are established as follows:

[0123]

[0124] [M] = diag(1,2,3,4)

[0125]

[0126] The damping of a linear system satisfies [C] = α[M] + β[K] (α and β can be any positive numbers; in this example, we take α = 0.05 and β = 0.02).

[0127] Establish the system characteristic equation:

[0128]

[0129] Find the eigenvectors This is the r-th mode shape of the system. The system mode shape matrix can be obtained by combining the eigenvectors. And find its transpose and inverse.

[0130]

[0131]

[0132]

[0133] The displacement response vector, velocity response vector, and acceleration response vector are transformed into modal space. The system dynamic equations are then established in modal space, and by substituting time-domain information, the final solution equations are obtained.

[0134]

[0135]

[0136]

[0137]

[0138] Solving the above system of equations yields F1(t+Δt), which represents the magnitude of the load on the system at time t+Δt. Simultaneously, while identifying the load on the system, u1(t+Δt), u3(t+Δt), and u4(t+Δt) can also be calculated, thus simultaneously identifying the responses of other unknown degrees of freedom. This achieves the function of simultaneously identifying both load and response. Figure 3 The load results are identified by the displacement response in the second degree of freedom after applying a sinusoidal excitation to the first degree of freedom of the system. Figure 4 The load results are identified by the displacement response in the second degree of freedom after applying an impact excitation to the first degree of freedom of the system. Figure 5 The load results are identified by the displacement response in the second degree of freedom after applying a random excitation to the first degree of freedom of the system. Figure 6 To apply sinusoidal excitation to the first degree of freedom of the system, the absolute error value between the identified load and the original load is determined by the displacement response of the second degree of freedom. Figure 7 To apply sinusoidal excitation to the first degree of freedom of the system, a comparison diagram is generated between the identified displacement response of the first degree of freedom and its actual displacement response while identifying the load. This invention combines the modal coordinate transformation method and the Newmark-β method, achieving high identification accuracy for multi-degree-of-freedom systems subjected to periodic, impact, and random excitations. It overcomes the current limitation that modal coordinate transformation alone cannot achieve time-domain identification of dynamic loads when dynamic response information is incomplete, and realizes the function of simultaneously identifying loads and system responses.

[0139] The present invention also provides a dynamic load identification system for multi-degree-of-freedom systems, comprising:

[0140] The modal space dynamics equation construction module is used to establish system dynamics equations. Based on known modal information and partial response information, the system is transformed into modal space to establish the system modal space dynamics equations.

[0141] The temporal-space dynamics representation module is used to represent the system's modal spatial displacement, velocity, acceleration response, and modal force using the system's temporal-space displacement, velocity, acceleration response, and excitation based on modal information.

[0142] The time-domain load equation recursion module is used to substitute the modal space response into the system modal space dynamic equation, return to the time domain, discretize the displacement, velocity, and acceleration of each degree of freedom in the time domain based on the Newmark-β method, obtain the recursive relationship of the system response of each degree of freedom at time t and t+Δt, and at the same time obtain the load solution equation;

[0143] The solver module is used to solve equations to obtain the loads acting on the system and / or the system's displacement response.

[0144] It should be understood that the dynamic load identification system for multi-degree-of-freedom systems can implement all the technical solutions in the above method embodiments. The functions of each functional module can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can be referred to the relevant descriptions in the above embodiments, which will not be repeated here.

[0145] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the dynamic load identification method for a multi-degree-of-freedom system as described above.

[0146] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the dynamic load identification method for a multi-degree-of-freedom system as described above.

Claims

1. A method for identifying dynamic loads in a multi-degree-of-freedom system, characterized in that, Includes the following steps: S1. Establish the system dynamic equations. Based on the known modal information and partial response information, transform the system into modal space and establish the system modal space dynamic equations. S2. Based on modal information, the system's modal spatial displacement, velocity, acceleration response, and modal force are represented using the system's time-domain spatial displacement, velocity, acceleration response, and excitation, including: Let the modal shape matrix be The system has 100 degrees of freedom. , , ; ； ； ； This multi-degree-of-freedom system is subject to a known location. One load transforms the time-domain spatial load into the modal space: ； ； S3. Substitute the modal space response into the system's modal space dynamics equations, return to the time domain, and base the displacement, velocity, and acceleration of each degree of freedom on... The method is discretized in the time domain to obtain the system. time, The recursive relationship of the response of each degree of freedom at each moment is obtained, and the load solution equation is also obtained. S4. Solve the equations to obtain the loads acting on the system and / or the system's displacement response, including: Analyze the right side of the system of equations For the load to be determined, the left side of the equation Let be the displacement to be determined, and be any of them. There are displacements, therefore the left side of the equation has One unknown quantity; when When the number of loads to be identified is less than the number of displacement responses, the equation can be solved for... The least squares solution, that is, the load can be approximated by the least squares method; when When the number of loads to be identified equals the number of displacement responses, the equation has only one solution, meaning there is only one type of load, and this solution is the true solution for the load. when When the number of loads to be identified is greater than the number of displacement responses, the equation has no solution, meaning dynamic load identification cannot be performed.

2. The method according to claim 1, characterized in that, Step S1 includes: For a multi-degree-of-freedom system with N degrees of freedom, in any N... Loads act on one degree of freedom, the rest With zero load on each degree of freedom, the time-domain dynamic equations of the linear system are established as follows: ； , , These are the system's time-domain acceleration, velocity, and displacement response vectors, respectively. , , These are the system damping matrix, mass matrix, and stiffness matrix, respectively. The excitation force vector, in, ； ； ； ； Given the system's modal shape matrix The system is then transformed into modal space, and a modal space dynamics model is established: ； ； ； ； 。 3. The method according to claim 2, characterized in that, Step S3 includes: Substituting the modal response and modal load into the equation, we obtain ； according to The acceleration response and velocity response are expressed as displacement responses as follows: ； ； make ； ； Substituting the load solution equations, the final set of time-domain space load solution equations is as follows: ； in , .

4. A dynamic load identification system for multi-degree-of-freedom systems, characterized in that, include: The modal space dynamics equation construction module is used to establish system dynamics equations. Based on known modal information and partial response information, the system is transformed into modal space to establish the system modal space dynamics equations. The time-domain spatial dynamics representation module is used to represent the system's modal spatial displacement, velocity, acceleration response, and modal force using the system's time-domain spatial displacement, velocity, acceleration response, and excitation based on modal information. This includes: Let the modal shape matrix be The system has 100 degrees of freedom. , , ; ； ； ； This multi-degree-of-freedom system is subject to a known location. One load transforms the time-domain spatial load into the modal space: ； ； The time-domain load equation recursion module is used to substitute the modal space response into the system's modal space dynamics equations and return to the time domain, based on the displacement, velocity, and acceleration of each degree of freedom. The method is discretized in the time domain to obtain the system. time, The recursive relationship of the response of each degree of freedom at each moment is obtained, and the load solution equation is also obtained. The solver module is used to solve equations to obtain the loads acting on the system and / or the system's displacement response, including: Analyze the right side of the system of equations For the load to be determined, the left side of the equation Let be the displacement to be determined, and be any of them. There are displacements, therefore the left side of the equation has One unknown quantity; when When the number of loads to be identified is less than the number of displacement responses, the equation can be solved for... The least squares solution, that is, the load can be approximated by the least squares method; when When the number of loads to be identified equals the number of displacement responses, the equation has only one solution, meaning there is only one type of load, and this solution is the true solution for the load. when When the number of loads to be identified is greater than the number of displacement responses, the equation has no solution, meaning dynamic load identification cannot be performed.

5. A computer device, characterized in that, include: One or more processors; Memory; as well as One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the dynamic load identification method for a multi-degree-of-freedom system as claimed in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the dynamic load identification method for a multi-degree-of-freedom system as described in any one of claims 1-3.

Images