Dynamic load position identification method and system based on vibration mode comparison

Abstract

The invention discloses a dynamic load position identification method and system based on vibration mode comparison. The method comprises the following steps: constructing a modal load identification equation according to parameters of a Newmark explicit method and modal shape information of a response measurement point; according to response information obtained through measurement, the modal load is solved through the obtained equation in combination with a truncated singular value regularization method; selecting a modal load of any order, calculating the least square inverse of the modal load, and determining a proportional relation among all orders of vibration modes at a load excitation position; calculating a vibration mode deviation function for quantitative comparison, and determining a load excitation position; and according to the load excitation position, carrying out inverse problem solving on the modal force vector and real load conversion relation formula, and determining the size of the load. According to the method, load identification does not need to be carried out on each possible loading point, only one-time identification needs to be carried out on the modal load, the dynamic load position identification speed is greatly improved, and the method has good precision and excellent anti-noise capability in various load identification.

Description

Technical Field

[0001] The present invention belongs to the field of dynamic load identification, and in particular relates to a method and system for dynamic load position identification based on vibration mode comparison. Background Art

[0002] In practical engineering applications, the dynamic loads on structures are crucial in the design, optimization, and health monitoring of structures. However, it is very difficult to determine the position and size of the loads acting on the structure by direct measurement. Therefore, dynamic load identification technology has emerged. Dynamic load identification, that is, reconstructing the dynamic loads acting on the structure by inversely reconstructing the dynamic loads acting on the structure through the easily measured structural dynamic response and the known structural dynamic characteristics, belongs to the second type of inverse problem in structural dynamics and is a typical source identification inverse problem in mathematics. The dynamic load identification method originated in the 1970s and was first used in the field of military aviation. In the following decades, a large number of dynamic load identification methods have been proposed and widely used in various fields. Traditional dynamic load identification methods mostly identify the size of the load when the load position is known. These methods can be divided into three categories, namely frequency domain method, time domain method, and intelligent method. The frequency domain method is a method for identification in the frequency domain. This method started early and has matured. It is suitable for the identification of long-term or stable loads. The time domain method establishes a mapping relationship between response and load in the time domain, identifies the time domain history of the load, and has obvious advantages in short-term situations such as impact loads. However, due to the influence of cumulative errors and ill-posed problems, there is still a lot of room for research. Intelligent methods are a series of new methods represented by machine learning that have been proposed recently and are still in the early stages of research.

[0003] At present, there are relatively few studies on dynamic load position identification, and they are mainly focused on impact load positioning. It is difficult to achieve fast and accurate positioning of other types of loads at the same time. Dynamic load position identification through parameter optimization methods requires a large number of inverse problem solutions, which has high computational costs, long calculation times, and poor economic efficiency. Most of the existing rapid positioning methods require prior knowledge of the type of dynamic loads that the structure will bear, and are mainly aimed at the rapid positioning of impact loads. There are limited means for rapid positioning of other types of loads. Therefore, proposing a dynamic load position identification method that is fast, accurate, and applicable to various load types is the focus of research on dynamic load position identification. Summary of the invention

[0004] Purpose of the invention: In view of the shortcomings of the prior art, the present invention proposes a method and system for dynamic load position identification based on vibration mode comparison, which can achieve high-precision identification results by only identifying the modal load once, thereby improving the speed of dynamic load position identification, and having a very high accuracy and stability on various types of loads, which meets theoretical expectations and engineering requirements.

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

[0006] A method for dynamic load position identification based on vibration mode comparison comprises the following steps:

[0007] Step 1: Construct the modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point, where Y represents the system modal response, H represents the mapping matrix between the time domain response and the excitation, and f represents the system modal load;

[0008] Step 2: Based on the measured response information, the equation obtained in step 1 is combined with the truncated singular value decomposition regularization method to solve the modal load and obtain the system modal load f;

[0009] Step 3: Select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position Where W i (x f ) is the load excitation position x f The influence weight of the i-th modal acceleration at , r is the modal cutoff order;

[0010] Step 4: Calculate the mode deviation function For quantitative comparison, determine the load excitation position x f ;

[0011] Step 5: Based on the load excitation position x determined in step 4 f The inverse problem of the conversion formula between the modal force vector and the real load is solved to determine the magnitude of the load.

[0012] Among them, when constructing the modal load identification equation, the vector y(t)∈R is selected m×1 represents the output of the system, Where R d , R v and R a ∈R m×r are the influence weights of modal displacement, modal velocity and modal acceleration on the system output, m is the number of known responses, r is the modal cutoff order, are the modal responses of the system.

[0013] According to the acceleration response conversion formula between physical coordinates and modal coordinates: Select the acceleration in the physical coordinate system as the measurement response and get R d , R v and R a for: Where W i (x j) represents the influence weight of the i-th modal acceleration at the position corresponding to the j-th measured response.

[0014] When determining the proportional relationship between the vibration modes at the load excitation location, for a continuous system, t i The conversion relationship between the modal force vector and the real load at the moment is: Where k is the number of concentrated loads on the system, F k (t i ) indicates the kth load at t i The value of the moment, Indicates the position where the kth load acts.

[0015] In the case of single-point excitation, t i The conversion relationship between the modal force vector and the real load at the moment is:

[0016]

[0017] Select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position, which is expressed as: Where j is any mode.

[0018] When the vibration mode deviation function is used for quantitative comparison, the x value corresponding to the minimum g(x) is taken as the load excitation position x. f .

[0019] The present invention also provides a dynamic load position identification system based on vibration mode comparison, comprising:

[0020] The modal load identification equation construction module is used to construct the modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point, where Y represents the system modal response, H represents the mapping matrix between the time domain response and the excitation, and f represents the system modal load;

[0021] The modal load solving module is used to solve the modal load by combining the equation obtained by the modal load identification equation building module with the truncated singular value decomposition regularization method according to the measured response information to obtain the system modal load f;

[0022] The vibration mode comparison module is used to select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position. Where W i (x f ) is the load excitation position x f The influence weight of the i-th modal acceleration at , r is the modal cutoff order;

[0023] Load position determination module for calculating mode shape deviation functions For quantitative comparison, determine the load excitation position x f ;

[0024] The load magnitude determination module is used to determine the load excitation position x according to the load position determination module. f The inverse problem of the conversion formula between the modal force vector and the real load is solved to determine the magnitude of the load.

[0025] 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the dynamic load position identification method based on vibration mode comparison as described above are implemented.

[0026] The present invention also provides a computer storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the dynamic load position identification method based on vibration mode comparison as described above are implemented.

[0027] Beneficial effects: The dynamic load position identification method based on vibration mode comparison proposed in the present invention determines the modal loads of each order of the vibration system based on the Newmark explicit method, rewrites the traditional "response-system-load" dynamic load identification structure into "response-modal response-system-modal load", and then determines the modal vibration mode of the load action position by calculating the least squares inverse method to determine the load action position. This method does not need to identify the load for each possible loading point, but only needs to identify the modal load once, which greatly improves the speed of dynamic load position identification. This method has good accuracy in the identification of sinusoidal, random and impact loads, and has excellent anti-noise ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of a method for determining the position and magnitude of a dynamic load on a structure based on vibration mode comparison according to the present invention;

[0029] Figure 2 is a simply supported beam model under a single point concentrated load in an embodiment of the present invention;

[0030] Figure 3 are the modal loads of each order of the system under the sinusoidal load condition in the embodiment of the present invention;

[0031] Figure 4 are the modal loads of each order of the system under the impact load condition in the embodiment of the present invention;

[0032] Figure 5are the modal loads of each order of the system under the random load condition in the embodiment of the present invention;

[0033] Figure 6 is the deviation function of the vibration mode at each position on the beam under the sinusoidal load condition in the embodiment of the present invention;

[0034] Figure 7 is a deviation function of the vibration mode at each position on the beam under the impact load condition in the embodiment of the present invention;

[0035] Figure 8 is the deviation function of the vibration mode at each position on the beam under the random load condition in the embodiment of the present invention;

[0036] Fig. 9 is the identification result of the sinusoidal load in the embodiment of the present invention;

[0037] Fig.10 is the identification result of the impact load in the embodiment of the present invention;

[0038] Fig.11 It is the identification result of the random load in the embodiment of the present invention. DETAILED DESCRIPTION

[0039] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0040] The present invention proposes a method for quickly locating concentrated dynamic loads of a continuous system based on the Newmark explicit method and vibration mode comparison, that is, the modal loads of each order of the vibration system are determined based on the Newmark explicit method, and the traditional "response-system-load" dynamic load identification architecture is rewritten into "response-modal response-system-modal load", and then the modal vibration mode of the load action position is determined by calculating the least squares inverse method to determine the position of the load action.

[0041] Reference Figure 1 , the method comprises the following steps:

[0042] Step 1: Construct the modal load identification equation Y = Hf based on the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point.

[0043] Construct the mapping relationship between modal load and modal response in modal coordinates:

[0044]

[0045] In formula (1) are the modal responses of the system, are the modal loads of the system, and It is calculated by the Newmark method. Newmark is an existing classic algorithm and will not be described here. The mapping relationship between the modal response and modal load of the system can be obtained by formula (1).

[0046] In actual engineering, although the load acting on the system is difficult to measure directly, the response of the system can be easily measured by measuring equipment such as sensors. Therefore, the vector y(t)∈R is selected. m×1 Represents the output of the system.

[0047]

[0048] In formula (2), R d , R v and R a ∈R m×r are the influence weights of modal displacement, modal velocity and modal acceleration on the system output, respectively. m is the number of known responses, and r is the modal cutoff order.

[0049] Formula (3) is the acceleration response conversion formula between physical coordinates and modal coordinates, where W i (x j ) represents the influence weight of the i-th modal acceleration at the position corresponding to the j-th measured response:

[0050]

[0051] Selecting the acceleration in the physical coordinate system as the measurement response, combined with equations (2) and (3), we can get R d , R v and R a for:

[0052]

[0053] Substituting formula (4) into formula (1) and rearranging it, we get formula (5):

[0054] Y=Hf (5)

[0055] In the formula H is the mapping matrix between response and excitation in the time domain, R = [R d R v R a ] is the influence weight of modal response on system output.

[0056] Step 2: Based on the measured response information, the equation obtained in step 1 is combined with the truncated singular value regularization method to solve the modal load.

[0057] By solving equation (5), a series of values ​​of the modal load f of each order of the system can be obtained. In the solution process, truncated singular value decomposition (TSVD) regularization is used to reduce the influence of matrix ill-conditioning and enhance the stability of the solution.

[0058] Step 3: Select any modal load and calculate its least squares inverse and determine the proportional relationship between the vibration modes at the load excitation position

[0059] For a continuous system, t i The conversion relationship between the modal force vector and the real load at the moment is:

[0060]

[0061] In formula (6), k is the number of concentrated loads on the system, F k (t i ) indicates the kth load at t i The value at the moment, x fk Indicates the position where the kth load acts.

[0062] In the case of single-point excitation, equation (6) degenerates into

[0063] Therefore, the modal loads of each order of the single-point excitation system should have the same time-varying trend and should be proportional in value. Considering the unavoidable noise, the least squares inverse method is used to minimize the residual sum of squares:

[0064]

[0065] Where j is any order mode. The proportional relationship vector between the vibration modes at the load excitation position can be obtained by formula (7):

[0066]

[0067] Step 4: Calculate the mode deviation function For quantitative comparison, when x = x f When , g(x) should take a minimum value.

[0068] By comparing the η(x) vectors at each point on the structure, the load position can be determined, and the vibration mode deviation function is introduced. For quantitative comparison, when x = x f When considering the influence of noise on recognition accuracy, g(x) cannot be strictly 0, but should be close to 0. That is, the value of x when g(x) is the smallest is the load excitation position x fIn the whole process, only one identification of the modal load and one generalized inverse operation of the first-order modal load f1 are required to complete the position identification. The computational workload is almost the same as that of the dynamic load identification problem when the load position is known. f ), the same vibration mode function as in the modal load identification process in the previous article should be used for comparison.

[0069] Step 5: Based on the load position x determined in step 4 f The inverse problem of formula (6) is solved to determine the load size.

[0070] Determine the position x where the dynamic load acts f After that, it is only necessary to solve the inverse problem of formula (6) to determine the size of the dynamic load. The inverse operation of formula (6) only requires the inverse operation of a matrix of size r×1. The matrix size is small, the calculation process is simple, and no pathological problems are involved.

[0071] In order to verify the performance of the method of the present invention, Figure 2 The simply supported beam structure shown in the figure is subjected to concentrated loads for verification experiments. The parameters of the simply supported beam are shown in Table 1:

[0072] Table 1 Geometric parameters and material properties of simply supported beams

[0073]

[0074] exist Figure 2 In the simply supported beam model shown, x f = 0.4, three groups of single-point concentrated loads are applied, namely sinusoidal load, impact load and random load. The relationship between sinusoidal load and time is F = 5 × sin [100πt], the impact load amplitude is 10N, the impact duration is 0.005s, and the random load is generated using the random phase method with a frequency range of 100Hz to 300Hz. Nine points evenly distributed on the beam are taken as response measurement points for dynamic load identification. During the identification process, the modal truncation order r = 5 is taken. In order to prove the stability of the method, 1% white noise is added to the response.

[0075] Step 1: Construct the modal load identification equation Y = Hf based on the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point.

[0076] Step 2: Based on the measured response information, the equation obtained in step 1 is combined with the truncated singular value regularization method to solve the modal load. The modal loads of the system are as follows: Figure 3 , Figure 4 and Figure 5 As shown:

[0077] Step 3: Select any modal load and calculate its least squares inverse and determine the proportional relationship between the vibration modes at the load excitation position The calculation results are:

[0078] Under sinusoidal load conditions, η(x f ) = [0.94410.5722-0.5674-1.14530.3683];

[0079] Under impact load conditions, η(x f ) = [0.95340.5675-0.4478-0.5914-0.0809];

[0080] Under random load conditions, η(x f )=[0.87650.5264-0.5478-0.87150.0184].

[0081] Step 4: Calculate the mode deviation function For quantitative comparison, when x = x f When , g(x) should take the minimum value. The vibration mode deviation function of each point on the beam is as follows: Figure 6 , Figure 7 and Figure 8 As shown:

[0082] Depend on Figure 6 , Figure 7 and Figure 8 It can be seen that the present invention can quickly and accurately locate the position where the dynamic load on the structure acts.

[0083] Step 5: Based on the load position x determined in step 4 f Solve the inverse problem of formula (6) to determine the load size. The identification result is as follows: Fig. 9 , Fig.10 and Fig.11 As shown, it can be seen that the load signal-to-noise ratio obtained by sinusoidal load identification is 20.7dB, the peak relative error obtained by impact load identification is 1.5%, and the load signal-to-noise ratio obtained by random load identification is 18.27dB, all of which have high accuracy.

[0084] Based on the same technical concept as the method embodiment, the present invention also provides a dynamic load position identification system based on vibration mode comparison, comprising:

[0085] The modal load identification equation construction module is used to construct the modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point, where Y represents the system modal response, H represents the mapping matrix between the time domain response and the excitation, and f represents the system modal load;

[0086] The modal load solving module is used to solve the modal load by combining the equation obtained by the modal load identification equation building module with the truncated singular value decomposition regularization method according to the measured response information to obtain the system modal load f;

[0087] The vibration mode comparison module is used to select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position. Where W i (x f ) is the load excitation position x f The influence weight of the i-th modal acceleration at , r is the modal cutoff order;

[0088] Load position determination module for calculating mode shape deviation functions For quantitative comparison, determine the load excitation position x f ;

[0089] The load magnitude determination module is used to determine the load excitation position x according to the load position determination module. f The inverse problem of the conversion formula between the modal force vector and the real load is solved to determine the magnitude of the load.

[0090] 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the dynamic load position identification method based on vibration mode comparison as described above are implemented.

[0091] The present invention also provides a computer storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the dynamic load position identification method based on vibration mode comparison as described above are implemented.

[0092] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, devices, computer equipment or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0093] The present invention is described with reference to a flowchart of a method according to an embodiment of the present invention. It should be understood that each process in the flowchart and a combination of processes in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the process in the flowchart. Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the functions specified in the process. Figure 1 The steps of a specified function in a process or multiple processes.

Claims

1. A method for identifying the position of a dynamic load based on vibration mode comparison, characterized in that: The following steps are involved: Step 1: Construct the modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point, where Y represents the system modal response, H represents the mapping matrix between the time domain response and the excitation, and f represents the system modal load; Step 2: Based on the measured response information, the equation obtained in step 1 is combined with the truncated singular value decomposition regularization method to solve the modal load and obtain the system modal load f; Step 3: Select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position Where W i (x f ) is the load excitation position x f The influence weight of the i-th modal acceleration at , r is the modal cutoff order; Step 4: Calculate the mode deviation function For quantitative comparison, determine the load excitation position x f ; Step 5: Based on the load excitation position x determined in step 4 f The inverse problem of the conversion formula between the modal force vector and the real load is solved to determine the magnitude of the load.

2. The method according to claim 1, characterized in that When constructing the modal load identification equation, the vector y(t)∈R is selected. m×1 represents the output of the system, Where R d , R v and R a ∈R m×r are the influence weights of modal displacement, modal velocity and modal acceleration on the system output, m is the number of known responses, r is the modal cutoff order, are the modal responses of the system.

3. The method according to claim 2, characterized in that According to the acceleration response conversion formula between physical coordinates and modal coordinates: Select the acceleration in the physical coordinate system as the measurement response and get R d , R v and R a for: Where W i (x j ) represents the influence weight of the i-th modal acceleration at the position corresponding to the j-th measured response.

4. The method according to claim 3, characterized in that When determining the proportional relationship between the vibration modes at the load excitation location, for a continuous system, t i The conversion relationship between the modal force vector and the real load at the moment is: Where k is the number of concentrated loads on the system, F k (t i ) indicates the kth load at t i The value of the moment, Indicates the position where the kth load acts.

5. The method according to claim 4, characterized in that In the case of single-point excitation, t i The conversion relationship between the modal force vector and the real load at the moment is:

6. The method according to claim 5, characterized in that Select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position, which is expressed as: Where j is any mode.

7. The method according to claim 1, characterized in that When making quantitative comparisons through the vibration mode deviation function, the x value corresponding to the minimum g(x) is taken as the load excitation position x f .

8. A dynamic load position identification system based on vibration mode comparison, characterized in that: include: The modal load identification equation construction module is used to construct the modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration shape information of the response measurement point, where Y represents the system modal response, H represents the mapping matrix between the time domain response and the excitation, and f represents the system modal load; The modal load solving module is used to solve the modal load by combining the equation obtained by the modal load identification equation building module with the truncated singular value decomposition regularization method according to the measured response information to obtain the system modal load f; The vibration mode comparison module is used to select any modal load and calculate its least squares inverse, and determine the proportional relationship between the vibration modes at the load excitation position. Where W i (x f ) is the load excitation position x f The influence weight of the i-th modal acceleration at , r is the modal cutoff order; Load position determination module for calculating mode shape deviation functions For quantitative comparison, determine the load excitation position x f ; The load magnitude determination module is used to determine the load excitation position x according to the load position determination module. f The inverse problem of the conversion formula between the modal force vector and the real load is solved to determine the magnitude of the load.

9. A computer 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the dynamic load position identification method based on vibration mode comparison as described in any one of claims 1 to 7 are implemented.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for dynamic load position identification based on vibration mode comparison according to any one of claims 1 to 7 are implemented.

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