A method and system for identifying dynamic loads in time domain of continuous system

Abstract

The present invention discloses a method and system for identifying dynamic loads in the time domain of a continuous system, including: establishing a cantilever beam vibration differential equation in a modal space; based on the cantilever beam vibration differential equation, using the Newmark‑β method in the modal space, obtaining a continuous system time domain dynamic load identification model; regularizing the dynamic load identification model; performing modal analysis on the cantilever beam finite element model to obtain a modal damping matrix and a stiffness matrix; and applying a load on the cantilever beam to obtain the acceleration response of the cantilever beam under different loads; based on the modal damping matrix, stiffness matrix and acceleration response data, and the regularized dynamic load identification model, a load identification result is obtained. The present invention utilizes a regularization method, combined with an L-curve method to determine regularization parameters, to identify different loads on the cantilever beam, and is suitable for load identification inverse problem analysis of large and complex structures.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic load identification, and in particular to a method and system for identifying dynamic loads in a continuous system in the time domain. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Accurately and effectively identifying dynamic loads is very important in ensuring the safety and reliability of engineering structures. However, with the development of science and technology, the complexity of engineering structures and the harshness of the working environment. In many cases, it is very difficult or even impossible to directly measure the dynamic loads on the structure. Accurately and efficiently obtaining these loads that are difficult to measure directly is of great significance to improving the safety and durability of the structure.

[0004] Existing dynamic force identification methods can be divided into two categories: frequency domain method and time domain method. The frequency domain method relies on Fourier transform to convert the output response between time domain and frequency domain, which requires a large amount of data to be collected, making it unsuitable for transient impact loads. Currently, the more commonly used frequency domain methods include methods based on direct inversion of frequency response functions and methods based on modal coordinate transformation. The research on time domain method started late, mainly expressing the system characteristics in the form of Duhamel integral, inverting the load through the measured response, and expressing the result in the form of time history, which can intuitively reflect the process of external load changing over time, and has certain advantages in identifying dynamic loads with a shorter time length.

[0005] The main time domain methods are state space method, Newmark-β method, orthogonal polynomial method and neural network algorithm. Among them, the state space method directly relates the response, system parameters and input force. However, this method is explicit and conditionally stable. Its performance is limited by the sampling rate and the length of the sampling duration. The time interval between consecutive steps will greatly affect the accuracy of the state space method. The solution is close to accurate only when the time step is very small. The Newmark-β method is an implicit time step integration method that has been widely used in forward dynamic analysis because it is known to be unconditionally stable when the parameters are correctly selected. In theory, the structure has an infinite number of degrees of freedom. When the structure is discretized into more degrees of freedom, the time domain dynamic load identification method in the physical space is very computationally intensive and time-consuming. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a method and system for identifying dynamic loads in the time domain of a continuous system, which transforms the multi-degree-of-freedom vibration differential equation in the physical space into the continuous system vibration differential equation in the modal space, and combines the state space method with the Newmark-β method to avoid the step size problem of the state space method and the problem of solution time of discrete multi-degree-of-freedom systems.

[0007] In some embodiments, the following technical solutions are adopted:

[0008] A method for identifying dynamic loads in a continuous system in time domain, comprising:

[0009] Establish the cantilever beam vibration differential equation in modal space;

[0010] Based on the cantilever beam vibration differential equation, the time-domain dynamic load identification model of the continuous system is obtained by using the Newmark-β method in the modal space;

[0011] performing regularization processing on the dynamic load identification model;

[0012] By performing modal analysis on the cantilever beam finite element model, the modal damping matrix and stiffness matrix are obtained; and by applying loads on the cantilever beam, the acceleration response of the cantilever beam under different loads is obtained;

[0013] Based on the modal damping matrix, stiffness matrix and acceleration response data, and the regularized dynamic load identification model, a load identification result is obtained.

[0014] As an optional solution, the cantilever beam vibration differential equation in the modal space is established, including:

[0015] Construct the vibration differential equation of cantilever beam discrete multi-degree-of-freedom system;

[0016] The output response is converted into modal coordinates and modal superposition is performed to obtain the modal displacement response, modal velocity response and modal acceleration response;

[0017] The modal mass is normalized and the vibration differential equation of the discrete multi-degree-of-freedom system is rewritten as the vibration differential equation of the continuous system in the modal space.

[0018] As an optional solution, based on the cantilever beam vibration differential equation, the Newmark-β method in the modal space is used to obtain a continuous system time domain dynamic load identification model; specifically, it includes:

[0019] Assume that the time step and acceleration are in the time interval [t i ,t i+1 ] changes linearly, and according to the Newmark-β method, t i+1Modal displacement, modal velocity and modal acceleration at time;

[0020] Combining the Newmark-β integral equation and the cantilever beam vibration differential equation, the state space equation of the continuous system in the modal space is obtained;

[0021] Based on the continuous system state space equation, construct an output equation that represents the relationship between the state variable and the output vector;

[0022] Using the mapping matrix, the modes in the modal space are established to obtain the dynamic load identification model of the continuous system in the time domain.

[0023] As an optional solution, regularization processing is performed on the dynamic load identification model, specifically including:

[0024] Taking the output response error of the dynamic load identification model as the minimum as the goal, the regularized optimization objective function of dynamic load identification is constructed;

[0025] The optimal regularization parameter value is solved based on the L-curve method, and the regularized dynamic load identification model is obtained.

[0026] As an optional solution, the optimal regularization parameter value is solved based on the L-curve method, specifically:

[0027] With the regularization parameter λ as the independent variable, ||Y-HF|| and ||F|| are both functions of the regularization parameter λ; where H is the transfer matrix, Y is the output response of the dynamic load identification model; and F is the input load;

[0028] Choose a value of λ and calculate the values ​​of ||Y-HF|| and ||F||, corresponding to a point on the L curve;

[0029] By continuously changing the value of λ, a curve is drawn from the coordinate points (lg||Y-HF||, lg||F||), namely the "L" curve; the λ value corresponding to the inflection point in the curve is the optimal regularization parameter value.

[0030] As an optional solution, the modal damping matrix and stiffness matrix are obtained by performing modal analysis on the cantilever beam finite element model, which are as follows:

[0031] A cantilever beam finite element model is established, and modal analysis is performed to obtain the r-order circular frequency and r-order modal vibration shape of the cantilever beam. The modal damping ratio is a constant. Combined with the cantilever beam vibration differential equation in the modal space, the modal damping matrix and stiffness matrix are solved.

[0032] As an optional solution, the acceleration response of the cantilever beam under different loads is obtained, including:

[0033] Sinusoidal load, impact load and random load were applied to the cantilever beam respectively, and the acceleration responses under the three loads were obtained.

[0034] In other embodiments, the following technical solutions are adopted:

[0035] A continuous system time domain dynamic load identification system, comprising:

[0036] Cantilever beam motion differential modeling module, used to establish the cantilever beam vibration differential equation in modal space;

[0037] A continuous system time-domain dynamic load identification model modeling module is used to obtain a continuous system time-domain dynamic load identification model based on the cantilever beam vibration differential equation and using the Newmark-β method in the modal space;

[0038] A model regularization module, used for performing regularization processing on the dynamic load identification model;

[0039] The cantilever beam modal analysis module is used to obtain the modal damping matrix and stiffness matrix by performing modal analysis on the cantilever beam finite element model; and obtain the acceleration response of the cantilever beam under different loads by applying loads on the cantilever beam;

[0040] The load identification module is used to obtain a load identification result based on the modal damping matrix, the stiffness matrix and the acceleration response data, and the regularized dynamic load identification model.

[0041] In other embodiments, the following technical solutions are adopted:

[0042] A terminal device comprises a processor and a memory, wherein the processor is used to implement various instructions; the memory is used to store a plurality of instructions, wherein the instructions are suitable for being loaded by the processor and executing the above-mentioned continuous system time-domain dynamic load identification method.

[0043] In other embodiments, the following technical solutions are adopted:

[0044] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the above-mentioned continuous system time-domain dynamic load identification method.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] (1) Aiming at the problem that discrete multi-degree-of-freedom systems in physical space have a long time to solve and poor accuracy when there are many degrees of freedom, this paper proposes a dynamic load identification algorithm for continuous systems in modal space. By using the Tikhonov regularization method and combining the L-curve method to determine the regularization parameters, the cantilever beam is identified for sinusoidal loads, impact loads and random loads. The algorithm is suitable for the inverse problem analysis of load identification of large and complex structures, and provides technical support for the online load identification of complex engineering structures.

[0047] (2) The present invention combines the state-space method and the Newmark-β method, and the load identification effect for complex structures is more significant and accurate. The state-space method is explicit and does not require iteration in each time step; Newmark-β is unconditionally stable for structural load identification when the parameters are correctly selected. The load identification method constructed based on the state-space method and the Newmark-β method has a faster calculation speed and realizes the identification of complex structures subjected to different load categories. It has broad prospects and high engineering application value.

[0048] Other features and advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flow chart of a method for identifying a dynamic load in a continuous system in a time domain in an embodiment of the present invention;

[0050] Figure 2 is a schematic diagram of acceleration response under different loads in an embodiment of the present invention;

[0051] Figure 3 Schematic diagram of load identification under a continuous system in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0053] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0054] Embodiment 1

[0055] In one or more embodiments, a method for identifying dynamic loads in a continuous system in the time domain is disclosed, combining Figure 1 , specifically including the following process:

[0056] (1) Establish the cantilever beam vibration differential equation in modal space;

[0057] Specifically, the discrete multi-degree-of-freedom system vibration differential equation is established as follows:

[0058]

[0059] Where: M, C, K represent the mass, damping and stiffness matrices of the system respectively. x(t) represents the acceleration response, velocity response, and displacement response of the system respectively, and F(t) is the input load of the system.

[0060] The output response is transformed into modal coordinates and modal superposition is performed at the same time. The displacement response can be expressed as:

[0061]

[0062] Where: is the i-th order mode, q i (t) represents the i-th order modal coordinate. Similarly, the modal velocity and modal acceleration can be obtained. After the modal mass is normalized, the vibration differential equation (1) is rewritten as the vibration differential equation of the continuous system in the modal space:

[0063]

[0064] Where: n ,ω n 、f n (t) represent the n-th order modal damping ratio, circular frequency and modal force, respectively.

[0065] is the modal acceleration, is the modal velocity, q n (t) is the modal displacement and n is the degree of freedom.

[0066] A continuous system has an infinite number of degrees of freedom and an infinite number of modes. High-order modes do not contribute much to the vibration response of the system, so the modal truncation method can be used to reduce the system's degrees of freedom. Assuming the modal truncation order is r, equation (3) can be converted into a finite number of independent equations:

[0067]

[0068] Where:

[0069]

[0070] (2) Based on the cantilever beam vibration differential equation, the time domain dynamic load identification model of the continuous system is obtained by using the Newmark-β method in the modal space;

[0071] Specifically, the Newmark-β method in modal space is:

[0072] Assume that the time step is Δt and the acceleration is in the time interval [t i ,t i+1 ] changes linearly, according to the Newmark-β method,

[0073]

[0074]

[0075] Where: Δt is the time step, α and β are integration parameters, α = 0.5, β = 0.25.

[0076] Combining the Newmark-β integral equation (5)(6) and the oscillating differential equation (4), we obtain

[0077]

[0078] set up:

[0079] Equation (7) can be written as the state space equation of the continuous system in the modal space:

[0080]

[0081] set up It represents the mapping matrix between the actual load and the modal force between the physical space and the modal space, r is the modal order, and s is the number of loads (r≥s).

[0082] The relationship between the state variable and the output vector, that is, the output equation, is expressed as:

[0083]

[0084] set up: Represents the mapping matrix of the response vector between the physical space and the modal space, m represents the number of response points, and r is the modal order (r≤m).

[0085] Where: y(t i ) is the response vector (displacement, velocity, acceleration) in physical space, D is the output influence matrix, and the present invention selects acceleration as the response vector (not limited to acceleration response, displacement, velocity are all OK), that is, D = [0 0 I]T . So far, the state space equation of the continuous system has been established.

[0086] Assuming that the initial state q(t0) is known, substitute equation (7) into equation (9), then equation (9) can be finally expressed as:

[0087]

[0088] Use the mapping matrix to establish the modes in the modal space;

[0089] set up k represents the total time.

[0090] Formula (10) can be rewritten as the expression for load identification:

[0091] F=H -1 Y (11).

[0092] (3) performing regularization processing on the dynamic load identification model;

[0093] Specifically, the condition number of the transfer matrix H in general equation (10) is large, which makes equation (10) ill-conditioned. The error of the response Y will be amplified, and the overall accuracy of the identified load will drop sharply, requiring regularization technology to control. The Tikhonov regularization method can be regarded as an optimization problem:

[0094]

[0095] Where: represents the square of the 2-norm of the vector, and λ is the regularization parameter.

[0096] The exact form of the objective function of equation (12) can be written as:

[0097] F T (H T H+λ 2 I) F-2Y T HF+Y T Y (13)

[0098] Since the gradient of the objective function is equal to zero, the least squares solution of equation (13) is

[0099] (H T H+λ 2 I) F=H T Y (14)

[0100] The load identification regularization model is

[0101] F=(H T H+λ 2 I) -1H T Y (15)

[0102] The regularization parameter λ in this model is an unknown number. Only when λ is calculated can the load identification regularization model be solved.

[0103] The L-curve criterion selects the optimal λ as the parameter value with the maximum curvature on the curve. The curve has lg||Y-HF|| as the horizontal coordinate and lg||F|| as the vertical coordinate.

[0104] According to formula (12), the expressions of ||Y-HF|| and ||F|| can be derived:

[0105]

[0106]

[0107] With the regularization parameter λ as the independent variable, ||Y-HF|| and ||F|| are both functions of the regularization parameter λ. Select a value of λ and calculate the values ​​of the two, corresponding to a point in the L curve. Keep changing the value of λ and draw a curve from the coordinate point (lg||Y-HF||, lg||F||), namely the "L" curve. The λ value corresponding to the inflection point in the curve (i.e. the point with the largest curvature) is the optimal regularization parameter value.

[0108] The curvature of the L curve is calculated as:

[0109]

[0110] Then the optimal regularization parameter λ selected by the L-curve method is op satisfy:

[0111] L(λ op )=maxL(λ) (19).

[0112] Assume that equation (16) is ρ = lg || Y-HF ||, where only λ is an unknown; equation (17) is θ = lg || F ||, where only λ is an unknown; substitute equations (16) and (17) into equation (18), and then find the maximum curvature, which is equation (19). The maximum curvature L(λ op ) is the optimal regularization parameter λ.

[0113] (4) By performing modal analysis on the cantilever beam finite element model, the modal damping matrix and stiffness matrix are obtained; and by applying a load on the cantilever beam, the acceleration response of the cantilever beam under different loads is obtained;

[0114] In this embodiment, a finite element model of the cantilever beam is established, and modal analysis is performed to obtain the r-order circular frequency ω and r-order modal vibration shape of the cantilever beam. The modal damping ratio is a constant (in this embodiment, ξ=0.05), combined with equation (4) and The modal damping matrix and stiffness matrix are obtained.

[0115] Sinusoidal load, impact load and random load are applied to the cantilever beam respectively, and the acceleration responses under the three loads are obtained, such as Figure 2 shown.

[0116] (5) Based on the modal damping matrix, stiffness matrix and acceleration response data, as well as the regularized dynamic load identification model, a load identification result is obtained.

[0117] Combination Figure 3 , the transfer matrix of formula (10) and the obtained modal damping matrix, stiffness matrix, and acceleration response are input into the regularized dynamic load identification model, and the load identification result is output.

[0118] Embodiment 2

[0119] In one or more embodiments, a continuous system time domain dynamic load identification system is disclosed, comprising:

[0120] Cantilever beam motion differential modeling module, used to establish the cantilever beam vibration differential equation in modal space;

[0121] A continuous system time-domain dynamic load identification model modeling module is used to obtain a continuous system time-domain dynamic load identification model based on the cantilever beam vibration differential equation and using the Newmark-β method in the modal space;

[0122] A model regularization module, used for performing regularization processing on the dynamic load identification model;

[0123] The cantilever beam modal analysis module is used to obtain the modal damping matrix and stiffness matrix by performing modal analysis on the cantilever beam finite element model; and obtain the acceleration response of the cantilever beam under different loads by applying loads on the cantilever beam;

[0124] The load identification module is used to obtain a load identification result based on the modal damping matrix, the stiffness matrix and the acceleration response data, and the regularized dynamic load identification model.

[0125] The specific implementation methods of the above modules have been described in Example 1 and will not be described in detail here.

[0126] Embodiment 3

[0127] In one or more embodiments, a terminal device is disclosed, including a server, the server including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method for identifying the time domain dynamic load of a continuous system in Embodiment 1 when executing the program. For the sake of brevity, it will not be described in detail here.

[0128] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0129] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0130] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0131] Embodiment 4

[0132] In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the continuous system time-domain dynamic load identification method described in the first embodiment.

[0133] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for identifying dynamic loads in a continuous system in time domain, characterized in that: include: Establish the cantilever beam vibration differential equation in modal space; Based on the cantilever beam vibration differential equation, the time-domain dynamic load identification model of the continuous system is obtained by using the Newmark-β method in the modal space; performing regularization processing on the dynamic load identification model; By performing modal analysis on the cantilever beam finite element model, the modal damping matrix and stiffness matrix are obtained; and by applying loads on the cantilever beam, the acceleration response of the cantilever beam under different loads is obtained; Based on the modal damping matrix, stiffness matrix and acceleration response data, and the regularized dynamic load identification model, a load identification result is obtained; Among them, the cantilever beam vibration differential equation in the modal space is established, which specifically includes: Construct the vibration differential equation of the cantilever beam discrete multi-degree-of-freedom system: In the formula, M, C, and K represent the mass, damping, and stiffness matrices of the system, respectively. x(t) represents the acceleration response, velocity response, and displacement response of the system, respectively, and F(t) is the input load of the system; The output response is transformed into modal coordinates and modal superposition is performed to obtain the modal displacement response, modal velocity response and modal acceleration response; the displacement response is: In the formula, is the i-th order mode, q i (t) represents the i-th order modal coordinate; Perform modal mass normalization and rewrite the vibration differential equation of the discrete multi-degree-of-freedom system into the vibration differential equation of the continuous system in the modal space: Among them, ξ n ,ω n 、f n (t) represent the damping ratio, circular frequency and modal force of the nth order mode, respectively; is the modal acceleration, is the modal velocity, q n (t) is the modal displacement and n is the degree of freedom.

2. A method for identifying dynamic loads in a continuous system in time domain according to claim 1, characterized in that: Based on the cantilever beam vibration differential equation, the time domain dynamic load identification model of the continuous system is obtained by using the Newmark-β method in the modal space; specifically, it includes: Assume that the time step and acceleration are in the time interval [t i ,t i+1 ] changes linearly, and according to the Newmark-β method, t i+1 Modal displacement, modal velocity and modal acceleration at time; Combining the Newmark-β integral equation and the cantilever beam vibration differential equation, the state space equation of the continuous system in the modal space is obtained; Based on the continuous system state space equation, construct an output equation that represents the relationship between the state variable and the output vector; Using the mapping matrix, the modes in the modal space are established to obtain the dynamic load identification model of the continuous system in the time domain.

3. A method for identifying dynamic loads in a continuous system in time domain according to claim 1, characterized in that: Regularization processing is performed on the dynamic load identification model, specifically including: Taking the output response error of the dynamic load identification model as the minimum as the goal, the regularized optimization objective function of dynamic load identification is constructed; The optimal regularization parameter value is solved based on the L-curve method, and the regularized dynamic load identification model is obtained.

4. A method for identifying dynamic loads in a continuous system in time domain according to claim 3, characterized in that: The optimal regularization parameter value is solved based on the L-curve method, specifically: With the regularization parameter λ as the independent variable, ||Y-HF|| and ||F|| are both functions of the regularization parameter λ; where H is the transfer matrix, Y is the output response of the dynamic load identification model; and F is the input load; Choose a value of λ and calculate the values ​​of ||Y-HF|| and ||F||, corresponding to a point on the L curve; By continuously changing the value of λ, a curve is drawn from the coordinate points (lg||Y-HF||, lg||F||), namely the "L" curve; the λ value corresponding to the inflection point in the curve is the optimal regularization parameter value.

5. A method for identifying dynamic loads in a continuous system in time domain according to claim 1, characterized in that: By performing modal analysis on the cantilever beam finite element model, the modal damping matrix and stiffness matrix are obtained, which are: A cantilever beam finite element model is established, and modal analysis is performed to obtain the r-order circular frequency and r-order modal vibration shape of the cantilever beam. The modal damping ratio is a constant. Combined with the cantilever beam vibration differential equation in the modal space, the modal damping matrix and stiffness matrix are solved.

6. A method for identifying dynamic loads in a continuous system in time domain according to claim 1, characterized in that: The acceleration response of the cantilever beam under different loads is obtained, including: Sinusoidal load, impact load and random load were applied to the cantilever beam respectively, and the acceleration responses under the three loads were obtained.

7. A continuous system time domain dynamic load identification system, characterized in that: include: Cantilever beam motion differential modeling module, used to establish the cantilever beam vibration differential equation in modal space; A continuous system time-domain dynamic load identification model modeling module is used to obtain a continuous system time-domain dynamic load identification model based on the cantilever beam vibration differential equation and using the Newmark-β method in the modal space; A model regularization module, used for performing regularization processing on the dynamic load identification model; The cantilever beam modal analysis module is used to obtain the modal damping matrix and stiffness matrix by performing modal analysis on the cantilever beam finite element model; and obtain the acceleration response of the cantilever beam under different loads by applying loads on the cantilever beam; A load identification module, used to obtain a load identification result based on the modal damping matrix, stiffness matrix and acceleration response data, and a regularized dynamic load identification model; Among them, the cantilever beam vibration differential equation in the modal space is established, which specifically includes: Construct the vibration differential equation of the cantilever beam discrete multi-degree-of-freedom system: In the formula, M, C, and K represent the mass, damping, and stiffness matrices of the system, respectively. x(t) represents the acceleration response, velocity response, and displacement response of the system, respectively, and F(t) is the input load of the system; The output response is transformed into modal coordinates and modal superposition is performed to obtain the modal displacement response, modal velocity response and modal acceleration response; the displacement response is: In the formula, is the i-th order mode, q i (t) represents the i-th order modal coordinate; Perform modal mass normalization and rewrite the vibration differential equation of the discrete multi-degree-of-freedom system into the vibration differential equation of the continuous system in the modal space: Among them, ξ n ,ω n 、f n (t) represent the damping ratio, circular frequency and modal force of the nth order mode, respectively; is the modal acceleration, is the modal velocity, q n (t) is the modal displacement and n is the degree of freedom.

8. A terminal device, comprising a processor and a memory, wherein the processor is used to implement each instruction; and the memory is used to store multiple instructions, characterized in that: The instructions are suitable for being loaded by a processor and executing the continuous system time-domain dynamic load identification method described in any one of claims 1-6.

9. A computer-readable storage medium storing a plurality of instructions, characterized in that: The instructions are suitable for being loaded by a processor of a terminal device and executing the continuous system time-domain dynamic load identification method described in any one of claims 1-6.

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