A method and system for identifying distributed dynamic load considering unknown initial conditions

Abstract

This invention discloses a method and system for identifying distributed dynamic loads considering unknown initial conditions. The method introduces a set of virtual responses under unknown initial conditions, combined with virtual forced vibration responses, to fit the free decay components caused by the unknown initial conditions and the forced vibration components caused by the distributed dynamic load to be identified in the actual measured response, respectively. Then, the fitting coefficients are determined by calculating the least squares inverse, thereby identifying the distributed dynamic load. This invention, by constructing novel basis functions, separates the contributions of the load to be identified and the unknown initial conditions to the structural measured response, avoiding the influence of non-zero initial conditions on the identification results, improving the accuracy of distributed dynamic load identification, expanding the application scope of the distributed dynamic load identification method, and ensuring that the identification results meet theoretical expectations and engineering requirements.

Description

Technical Field

[0001] This invention belongs to the field of dynamic load identification, and specifically relates to a method and system for identifying distributed dynamic loads that takes into account unknown initial conditions. Background Technology

[0002] In practical engineering applications, understanding the dynamic loads borne by a structure plays a crucial role in structural design optimization, structural life assessment, and structural health monitoring. However, due to constraints such as the structural working environment and measurement conditions, determining the loads acting on a structure through direct measurement using force sensors is extremely difficult. Therefore, dynamic load identification technology has emerged. Dynamic load identification, based on easily measurable structural dynamic responses and known structural dynamic characteristics, reconstructs the dynamic loads acting on the structure through inversion operations. After decades of development, dynamic load identification technology has formed a series of mature methods. Among these methods, frequency domain methods, represented by the direct inversion of the frequency response function, and time domain methods based on the temporal convolution relationship between structural loads and structural responses are the most widely used. In recent years, dynamic load identification methods based on wavelet transform, Kalman filtering, and deep learning have been applied. Distributed dynamic loads are a common form of load in engineering, containing both a time dimension variable exhibiting dynamic characteristics and a spatial dimension variable with a certain continuous distribution. Therefore, the identification of distributed dynamic loads requires the simultaneous reconstruction of the load's time history and spatial distribution. Distributed dynamic load identification methods originated in the 1980s for solving the inverse dynamic problem of thick plate structures subjected to distributed dynamic loads. Current methods primarily rely on function fitting, selecting a set of linearly independent orthogonal basis functions as virtual excitations, and using the linear superposition principle to identify distributed dynamic loads.

[0003] Current methods identify distributed dynamic loads on structures under the assumption that the initial vibration state is zero. However, in engineering environments, structures are usually in a state of vibration before the dynamic load identification task begins, making such an ideal situation rare. Furthermore, dynamic load identification, especially distributed dynamic load identification, is highly sensitive to the initial conditions of the structure, meaning that even small disturbances in the initial conditions can lead to significant identification errors. Therefore, to further broaden the engineering application scope of distributed dynamic load identification methods, researching methods for identifying distributed dynamic loads under unknown initial conditions is of great significance. Summary of the Invention

[0004] Purpose of the invention: To address the shortcomings of existing technologies, this invention proposes a distributed dynamic load reconstruction method considering unknown initial conditions. By constructing novel basis functions, the contribution of the load to be identified and the unknown initial conditions to the structural measurement response is separated, avoiding the influence of non-zero initial conditions on the identification results, improving the accuracy of distributed dynamic load identification, expanding the application scope of the distributed dynamic load identification method, and ensuring that the identification results meet theoretical expectations and engineering requirements.

[0005] Another object of the present invention is to provide a distributed dynamic load reconfiguration system, electronic device, and computer storage medium that take into account unknown initial conditions.

[0006] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] Firstly, a method for identifying distributed dynamic loads considering unknown initial conditions includes the following steps:

[0008] Obtain the true structural response under the distributed load to be identified x is the location where the load is applied, and t is the time. Based on the measured actual structural response, the start time of the distributed dynamic load and the identification duration T are determined.

[0009] Assuming the load only acts within a time period And time period The internal load value is 0, and the construction is as follows: Legendre polynomials within a time period and their union The basis functions are obtained by combining all zero values ​​over a time period. These basis functions are then applied as virtual excitations to the structural finite element model, and calculations are performed. The structural dynamic response over a given time period is used as a virtual response, which is divided into... The virtual forced response generated by the basis function excitation within the time period and During the time period by Virtual free decay response caused by initial conditions at time;

[0010] The forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response are respectively fitted using virtual forced vibration response and virtual free decay response. The real structural response is then constructed as a combination of the virtual forced vibration response, the virtual free decay response, and the fitting coefficients. A system of equations involving multiplication;

[0011] The fitted coefficients are obtained by solving the constructed system of equations using least squares. ;

[0012] The fitting coefficients are linearly superimposed with the corresponding virtual excitations to obtain the distributed dynamic load identification results considering the initial conditions.

[0013] Secondly, a distributed dynamic load identification system considering unknown initial conditions includes:

[0014] The measurement data acquisition module is used to acquire the actual response of the structure under the distributed load to be identified. x is the location where the load is applied, and t is the time. Based on the measured actual structural response, the start time of the distributed dynamic load and the identification duration T are determined.

[0015] The virtual response calculation module is used to assume that the load only acts within a time period. And time period The internal load value is 0, and the construction is as follows: Legendre polynomials within a time period and their union The basis functions are obtained by combining all zero values ​​over a time period. These basis functions are then applied as virtual excitations to the structural finite element model, and calculations are performed. The structural dynamic response over a given time period is used as a virtual response, which is divided into... The virtual forced response generated by the basis function excitation within the time period and During the time period by Virtual free decay response caused by initial conditions at time;

[0016] The real response fitting module is used to fit the forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response using virtual forced vibration response and virtual free decay response, respectively. The real structural response is constructed as a combination of the virtual forced vibration response, the virtual free decay response, and fitting coefficients. A system of equations involving multiplication;

[0017] The coefficient solving module is used to solve the constructed system of equations using least squares to obtain the fitting coefficients. ;

[0018] The distributed dynamic load reconstruction module is used to linearly superimpose the fitting coefficients with the corresponding virtual excitations to obtain the distributed dynamic load identification results considering the initial conditions.

[0019] Thirdly, an electronic device includes: 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 distributed dynamic load identification method considering unknown initial conditions as described in the first aspect of the invention.

[0020] Fourthly, a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the distributed dynamic load identification method considering unknown initial conditions as described above.

[0021] Fifthly, a computer program product includes a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the distributed dynamic load identification method considering unknown initial conditions as described above.

[0022] Beneficial Effects: The distributed dynamic load identification method considering unknown initial conditions proposed in this invention is based on the basis function fitting idea. It treats the actual measured response of the structure as a combination of the contribution of the load to be identified and the contribution of unknown initial conditions. A novel basis function is constructed based on the traditional generalized orthogonal polynomial. A set of free decay responses under virtual initial conditions is added to fit the decayed part of the actual response, and the forced response under the action of the virtual basis functions is used to fit the forced part of the actual response. The fitting coefficients are solved by calculating the least squares inverse. The linear superposition of the fitting coefficients corresponding to the forced part under the action of the virtual basis functions and the basis functions yields the distributed dynamic load identification result considering unknown initial conditions. This method avoids the influence of non-zero initial conditions on the identification results, improves the accuracy of distributed dynamic load identification, expands the application scope of distributed dynamic load identification methods, and the identification results meet theoretical expectations and engineering requirements. Attached Figure Description

[0023] Figure 1 The flowchart of the distributed dynamic load identification method under unknown initial conditions in this invention is shown below;

[0024] Figure 2 This is a schematic diagram of a cantilever beam model under distributed dynamic load in an embodiment of the present invention;

[0025] Figure 3 The values ​​represent the actual values ​​of randomly distributed dynamic loads in the embodiments of this invention.

[0026] Figure 4 This refers to the identification results of randomly distributed dynamic loads in this embodiment of the invention.

[0027] Figure 5 This is for identifying relative errors in embodiments of the present invention;

[0028] Figure 6 This is the load identification result at x=0.5m in an embodiment of the present invention. Detailed Implementation

[0029] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0030] In the field of distributed dynamic load identification, the orthogonal polynomial method, represented by Legendre polynomials, is one of the earliest established systematic technical approaches. Its core idea is to utilize the excellent mathematical properties of Legendre orthogonal polynomials to transform the problem of identifying infinite-dimensional, continuously distributed unknown loads into the problem of solving a finite number of "polynomial coefficients".

[0031] Assume the target structure is a structure of length... For a one-dimensional structure (such as a beam or shaft), let x represent the position of a point on the structure. Let t represent the moment when the load is applied, and the range is... That is, from time 0 to time T; the distributed dynamic load to be identified is expressed as It is a bivariate function of position x and time t, representing the magnitude of the load acting at position x at time t.

[0032] According to the Legendre orthogonal polynomial principle, the target structure in the spatial domain is expressed as follows:

[0033] (1)

[0034] The time-domain Legendre orthogonal polynomial expression is:

[0035] (2)

[0036] Where n is the order of the polynomial in the spatial domain, and m is the order of the polynomial in the time domain. and These are the nth-order Legendre polynomial in the spatial domain and the mth-order Legendre polynomial in the time domain, respectively. In this paper, the spatial domain is also referred to as the spatial field, and the time domain is also referred to as the time field.

[0037] After normalizing the two formulas above, we have:

[0038] (3)

[0039] Continuous Infinite Dimensional Distributed Dynamic Load Can be used Legendre polynomials in order space The first-order time Legendre polynomial is expressed as:

[0040] (4)

[0041] in Representing the Legendre polynomial of order space field The weighting coefficients corresponding to the Legendre polynomials of the first-order time field. and These represent the spatial basis functions and the time basis functions, respectively. It is a combined basis function obtained by multiplying the spatial basis function and the time basis function. This means that the complex dynamic load identification problem can be transformed into... The problem of identifying individual coefficients.

[0042] by Indicates the initial moment of load application, when identified When the structure is subjected to distributed dynamic loads over a time period, the structure is in Since the structure is already in a state of vibration, directly using the Legendre polynomial to identify the distributed dynamic load will result in a large identification error. The vibration state at time t is The initial conditions of the time period, and the vibration state in The response during this time period is a free decay response. Therefore, the structural response during this time period can be considered as the superposition of free decay vibration caused by the initial conditions and forced vibration caused by the distributed dynamic load during this time period. However, the initial conditions are difficult to obtain through measurement or other means, so it is very important to propose a method for identifying distributed dynamic loads under unknown initial conditions. This invention addresses the problem of identifying distributed dynamic loads under unknown initial conditions by introducing a set of fitting free decay responses caused by different initial conditions. The response caused by the initial conditions at time is used to improve the traditional Legendre polynomial distributed dynamic load identification method.

[0043] Figure 1 A flowchart of the distributed dynamic load identification method of the present invention considering unknown initial conditions is shown. (Refer to...) Figure 1 Based on the concept of function fitting, this invention constructs a new set of basis functions, namely, introducing a set of virtual unknown initial conditions for the response, combined with virtual forced vibration response, to fit the free decay component caused by unknown initial conditions and the forced vibration component caused by the distributed dynamic load to be identified in the real measured response, respectively. Then, the fitting coefficients are determined by calculating the least squares inverse, thereby determining the distributed dynamic load.

[0044] The method of the present invention specifically includes the following steps:

[0045] Step S1: Obtain the actual structural response under the distributed load to be identified. Based on the measured structural geometric parameters And determine the start time of the distributed dynamic load. and recognition time Information such as...

[0046] Step S2: Construct basis functions as virtual excitations applied to the structural finite element model, and calculate... The structural dynamic response over a given time period is used as a virtual response, which is divided into two parts: The virtual forced response generated by the basis function excitation within a time period, and During the time period by Virtual free decay response caused by initial conditions at time step.

[0047] Define a new set of virtual excitations as shown in the following equation, assuming that the load only acts on the time period. And time period The internal load value is 0:

[0048] (5)

[0049] in The time interval represents the dynamic response of the discretized structure. This represents the number of time points within the total recognition time. The basis function in the formula... The information determined in step S1 is used to calculate the result using formula (3).

[0050] In fact, due to the presence of damping, the structural vibration does not immediately stop upon the removal of the load but undergoes free decay vibration until it comes to rest. Therefore, the virtual response over the entire 2T time period can be written as:

[0051] (6)

[0052] in, represent Vibration response at all times. express Virtual forced vibration response over a time period represent Virtual free decay response over a time period.

[0053] It should be noted that calculating the virtual response within the 2T time period is not intended to identify the distributed dynamic load over the 2T time period, but rather to obtain the forced vibration response caused by the virtual excitation over the T time period in order to identify the distributed dynamic load over the time period, and the free decay response over the T time period caused by different initial conditions in order to obtain the initial conditions for fitting.

[0054] Step S3: Use the virtual forced vibration response and virtual free decay response obtained in step S2 to fit the forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by the unknown initial conditions in the real measured response, respectively, so as to separate the contributions of the two parts from the real measured response.

[0055] The actual measured vibration response of a structure over a given time period can be written as:

[0056] (7)

[0057] in Indicates by The forced vibration response caused by the distributed dynamic load to be identified within a time period. Representative by The free decay response caused by the initial conditions at time step.

[0058] Based on the fundamental principles of basis function fitting, we have:

[0059] (8)

[0060] (9)

[0061] in Indicate that each basis function is in Virtual forced vibration response over a time period Representing each basis function in Virtual free decay response over a time period;

[0062] , , Represent and Fitting coefficients of the responses of each order basis function in the middle.

[0063] Therefore, formula (7) can be written as:

[0064] (10)

[0065] The same principle applies to N sampling points. Then we have:

[0066] (11)

[0067] Step S4: Solve the system of equations shown in formula (11) using least squares to obtain the fitting coefficients. ;

[0068] (12)

[0069] Step S5: Linearly superimpose the fitting coefficients obtained in step S4 with the corresponding virtual excitations, i.e., the basis functions constructed in step S2, to obtain the structure shown in formula (13):

[0070] (13)

[0071] Due to the coefficient The initial conditions, combined with the virtual free decay response, provide the initial conditions for the identification time period, but do not involve the load to be identified; moreover, the coefficients... The corresponding basis function load is 0, so it is not reflected in Equation 13.

[0072] To verify the performance of the method of the present invention, Figure 2 The cantilever beam structure shown is subjected to a concentrated load, and the parameters of the cantilever beam are shown in Table 1:

[0073] Table 1 Geometric parameters and material properties of cantilever beams

[0074]

[0075] exist Figure 2 On the cantilever beam model shown, the application method is as follows: The randomly distributed dynamic load, the load space field is The time field was generated using the random phase method, with a frequency range of 5Hz to 55Hz. Ten points uniformly distributed on the beam were selected as response measurement points for dynamic load identification, with an identification time period of [missing information]. It is worth noting that cantilever beam structures in The system is in a state of vibration. The order of the Legendre basis functions is chosen to be 2 for the spatial field and 112 for the time field.

[0076] The specific process is as follows: Determine the start time of the distributed dynamic load based on the measured actual structural response. and recognition time Information such as structural parameters Construct the basis functions as shown in Equation (5); apply the basis functions as virtual excitations to the structural finite element model, and calculate... The structural dynamic response over time is used as a virtual response, which is then divided into two parts: Virtual forced response generated by basis function excitation within a time period ,as well as During the time period by Virtual free decay response caused by initial conditions at time step The forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by the unknown initial conditions in the real measured response are respectively fitted using virtual forced vibration response and virtual free decay response, thereby separating the contributions of the two parts from the real measured response; the fitting coefficients are obtained by solving the equation system shown in formula (11) using least squares. By linearly superimposing the fitting coefficients with the corresponding virtual excitations, i.e., the constructed basis functions, the structural distributed dynamic load as shown in formula (13) can be obtained. The true value of the randomly distributed dynamic load in this embodiment of the invention is as follows: Figure 3 As shown, the recognition results obtained using the above method are as follows: Figure 4 As shown, the relative error of identification is as follows Figure 5 As shown, where The load identification results at the location are as follows Figure 6 As shown in the figure, it can be seen that the relative error of the identification of randomly distributed dynamic loads under unknown initial conditions proposed in this invention is 3.37%, which has high identification accuracy, indicating that the method proposed in this invention is reliable.

[0077] According to another embodiment of the present invention, a distributed dynamic load identification system considering unknown initial conditions is provided, comprising:

[0078] The measurement data acquisition module is used to acquire the actual response of the structure under the distributed load to be identified. Based on the measured actual structural response, the start time of the distributed dynamic load and the identification duration T are determined.

[0079] The virtual response calculation module is used to assume that the load only acts within a time period. And time period The internal load value is 0, and the construction is as follows: Legendre polynomials within a time period and their union The basis functions are obtained by combining all zero values ​​over a time period. These basis functions are then applied as virtual excitations to the structural finite element model, and calculations are performed. The structural dynamic response over a given time period is used as a virtual response, which is divided into... The virtual forced response generated by the basis function excitation within the time period and During the time period by Virtual free decay response caused by initial conditions at time;

[0080] The real response fitting module is used to fit the forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response using virtual forced vibration response and virtual free decay response, respectively. The real structural response is constructed as a combination of the virtual forced vibration response, the virtual free decay response, and fitting coefficients. A system of equations involving multiplication;

[0081] The coefficient solving module is used to solve the constructed system of equations using least squares to obtain the fitting coefficients. ;

[0082] The distributed dynamic load reconstruction module is used to linearly superimpose the fitting coefficients with the corresponding virtual excitations to obtain the distributed dynamic load identification results considering the initial conditions.

[0083] It should be understood that the distributed dynamic load identification system considering unknown initial conditions provided in this embodiment can realize 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.

[0084] The present invention also provides an electronic 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 distributed dynamic load identification method considering unknown initial conditions as described above.

[0085] 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 distributed dynamic load identification method considering unknown initial conditions as described above.

[0086] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus (systems), computer devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 A device for a function specified in one or more processes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 The function specified in one or more processes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 Steps of a specified function in one or more processes.

Claims

1. A method for identifying distributed dynamic loads considering unknown initial conditions, characterized in that, Includes the following steps: Obtain the true structural response under the distributed load to be identified x is the location where the load is applied, and t is the time. Based on the measured actual structural response, the start time of the distributed dynamic load and the identification duration T are determined. Assuming the load only acts within a time period And time period The internal load value is 0, and the construction is as follows: Legendre polynomials within a time period and their union The basis functions are obtained by combining all zero values ​​over a time period. These basis functions are then applied as virtual excitations to the structural finite element model, and calculations are performed. The structural dynamic response over a given time period is used as a virtual response, which is divided into... The virtual forced response generated by the basis function excitation within the time period and During the time period by Virtual free decay response caused by initial conditions at time; The forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response are respectively fitted using virtual forced vibration response and virtual free decay response. The real structural response is then constructed as a combination of the virtual forced vibration response, the virtual free decay response, and the fitting coefficients. A system of equations involving multiplication; The fitted coefficients are obtained by solving the constructed system of equations using least squares. ; The fitting coefficients are linearly superimposed with the corresponding virtual excitations to obtain the distributed dynamic load identification results considering the initial conditions.

2. The method according to claim 1, characterized in that, The constructed basis functions are represented as follows: ； in Let n be the Legendre polynomial of the distributed dynamic load in the spatial domain. Let m be the Legendre polynomial of the distributed dynamic load in the time domain. The time interval represents the dynamic response of the discretized structure. This indicates the number of time points within the total recognition time.

3. The method according to claim 2, characterized in that, The Legendre polynomials of the distributed dynamic load in the spatial and time domains are obtained as follows: Let the length of the target structure be L, in The Legendre polynomial expression for the spatial field within the range is: ； exist The time-domain Legendre polynomial expression within the range is: ； Normalizing each, we get: ； 。 4. The method according to claim 3, characterized in that, The virtual response with a time length of 2T is constructed as follows: ； in, represent Constant vibration response express The virtual forced response generated by basis function excitation within a time period. represent During the time period by Virtual free decay response caused by initial conditions at time step.

5. The method according to claim 4, characterized in that, The forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response are respectively fitted using virtual forced vibration response and virtual free decay response. The real structural response is then constructed as a combination of the virtual forced vibration response, the virtual free decay response, and the fitting coefficients. A system of equations involving multiplication includes: Will The structural vibration response over a time period is expressed as follows: ,in Indicates by The forced vibration response caused by the distributed dynamic load to be identified within a time period. This represents the free decay response caused by the initial conditions at the start time; Based on the fundamental principles of basis function fitting, we have: ； ； in Indicate that each basis function is in Virtual forced vibration response over a time period Representing each basis function in Virtual free decay response over a time period; , , Represent and The fitting coefficients of the responses of each basis function in the equation; J and K are the orders of the Legendre polynomials in the spatial and time domains, respectively; The structural vibration response expression is then constructed as follows: ； Extended to N sampling points Then we have: 。 6. The method according to claim 5, characterized in that, By linearly superimposing the fitting coefficients with the corresponding virtual excitations, we obtain the distributed dynamic load identification result considering the initial conditions, which is expressed as: 。 7. A distributed dynamic load identification system considering unknown initial conditions, characterized in that, include: The measurement data acquisition module is used to acquire the actual response of the structure under the distributed load to be identified. x is the location where the load is applied, and t is the time. Based on the measured actual structural response, the start time of the distributed dynamic load and the identification duration T are determined. The virtual response calculation module is used to assume that the load only acts within a time period. And time period The internal load value is 0, and the construction is as follows: Legendre polynomials within a time period and their union The basis functions are obtained by combining all zero values ​​over a time period. These basis functions are then applied as virtual excitations to the structural finite element model, and calculations are performed. The structural dynamic response over a given time period is used as a virtual response, which is divided into... The virtual forced response generated by the basis function excitation within the time period and During the time period by Virtual free decay response caused by initial conditions at time; The real response fitting module is used to fit the forced vibration response caused by the unidentified distributed dynamic load and the free decay response caused by unknown initial conditions in the real structural response using virtual forced vibration response and virtual free decay response, respectively. The real structural response is constructed as a combination of the virtual forced vibration response, the virtual free decay response, and fitting coefficients. A system of equations involving multiplication; The coefficient solving module is used to solve the constructed system of equations using least squares to obtain the fitting coefficients. ; The distributed dynamic load reconstruction module is used to linearly superimpose the fitting coefficients with the corresponding virtual excitations to obtain the distributed dynamic load identification results considering the initial conditions.

8. An electronic device, characterized in that, include: One or more processors; 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 identifying distributed dynamic loads considering unknown initial conditions as described in any one of claims 1-6.

9. 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 distributed dynamic load identification method considering unknown initial conditions as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the distributed dynamic load identification method considering unknown initial conditions as described in any one of claims 1-6.

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