A dynamic load position recognition method and system based on mode comparison

Abstract

The application discloses a dynamic load position recognition method and system based on mode shape comparison. The method comprises the following steps: constructing a modal load identification equation according to the parameters of the Newmark explicit method and the modal shape information of a response measuring point; solving the obtained equation to obtain the modal load by combining the truncated singular value regularization method according to the measured response information; selecting any order modal load and calculating the least square inverse thereof, and determining the proportional relationship between the modes at the load excitation position; calculating the mode shape deviation function for quantitative comparison to determine the load excitation position; and solving the inverse problem of the modal force vector and the true load conversion relationship formula according to the load excitation position to determine the size of the load. The application does not need to identify the load at each possible loading point, only needs to identify the modal load once, greatly improves the speed of dynamic load position recognition, and has good accuracy and excellent noise resistance in various load recognitions.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of dynamic load identification, and particularly relates to a dynamic load position identification method and system based on mode shape comparison. BACKGROUND

[0002] In actual engineering application, the dynamic load borne by a structure is crucial in the design, optimization and health monitoring of the structure. However, it is very difficult to determine the position and size of the load acting on the structure through direct measurement, and therefore, the dynamic load identification technology emerges as the times require. The dynamic load identification, that is, inversely reconstructing the dynamic load acting on the structure through easily measured structural dynamic response and known structural dynamic characteristics, belongs to the second inverse problem of structural dynamics and is a typical source identification inverse problem in mathematics. The dynamic load identification method originated in the 1970s and was first applied in the military aviation field. In the following decades, a large number of dynamic load identification methods were proposed and widely applied in various fields. Traditional dynamic load identification methods are mostly used to identify the size of the load under the condition that the position of the load is known. These methods can be divided into three categories, namely, the frequency domain method, the time domain method and the intelligent method. The frequency domain method is a method of identifying in the frequency domain, which is started early, mature and suitable for identifying long-time or stationary load. The time domain method establishes a mapping relationship between the response and the load in the time domain to identify the time domain history of the load, which is obviously advantageous in the case of short-time impact load. However, due to the influence of cumulative error and ill-posed problem, there is still a large research space. The intelligent method is a series of new methods represented by machine learning proposed in recent years, which is still in the initial stage of research.

[0003] At present, the research on dynamic load position identification is relatively less, and mainly focuses on impact load positioning. It is difficult to achieve rapid and accurate positioning of other types of loads. The method of parameter optimization for dynamic load position identification needs to solve a large number of inverse problems, which has high calculation cost, long calculation time and poor economy. The existing rapid positioning methods mostly need to know the type of dynamic load borne by the structure in advance, and are mainly used for rapid positioning of impact load. There are limited means for rapid positioning of other types of loads. Therefore, it is the research focus of dynamic load position identification to propose a rapid, accurate and applicable dynamic load position identification method for various types of loads. SUMMARY

[0004] The application aims at the deficiencies of the prior art, and provides a dynamic load position identification method and system based on mode shape comparison, which can obtain high-precision identification results only by identifying modal load once, improves the speed of dynamic load position identification, and has high precision and stability on various types of loads, meeting the theoretical expectation and engineering requirement.

[0005] Technical scheme: To achieve the above object, the application adopts the following technical scheme:

[0006] A dynamic load position recognition method based on mode shape comparison, comprising the following steps:

[0007] Step 1: According to the parameters alpha and beta of Newmark explicit method and the modal shape information of response measurement point, a modal load identification equation Y = Hf is constructed, Y represents the system modal response, H represents the mapping matrix of time domain response and excitation, and f represents the system modal load;

[0008] Step 2: According to 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 the system modal load f is obtained;

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

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

[0011] Step 5: According to the load excitation position x f determined in step 4, the inverse problem of the modal force vector and the true load conversion relationship formula is solved to determine the size of the load.

[0012] Wherein, when constructing the modal load identification equation, the vector y(t) ∈ R 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 truncation order, is the system modal response.

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

[0014] When determining the proportional relationship between the modes at the load excitation position, for a continuous system, t i The modal force vector at time t and the real load conversion relationship is: Where k is the number of concentrated loads on the system, F k (t i ) represents the value of the k-th load at time t i , represents the position of the k-th load.

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

[0016]

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

[0018] Where, when quantitatively compared by the mode deviation function, the x value corresponding to the minimum g(x) is taken as the load excitation position x f .

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

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

[0021] A modal load solving module is used to solve the modal load according to the response information measured, and the equation obtained by the modal load identification equation construction module is combined with the truncated singular value decomposition regularization method to obtain the system modal load f.

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

[0023] A load position determination module is configured to calculate a mode shape deviation function For quantitative comparison, determine the load excitation position x f ;

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

[0025] The application further provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs are executed by the processor to implement the steps of the mode shape comparison-based dynamic load position identification method as described above.

[0026] The application further provides a computer storage medium having a computer program stored thereon, and the computer program is executed by the processor to implement the steps of the mode shape comparison-based dynamic load position identification method as described above.

[0027] Beneficial effects: The mode shape comparison-based dynamic load position identification method provided by the application 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 mode shape of the load action position by calculating the least square inverse to further determine the position of the load action. This method does not need to identify the load for each possible loading point, only needs to identify the modal load once, greatly improves the speed of dynamic load position identification, and has good accuracy in sine, random and impact load identification, and has excellent anti-noise ability. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 is a method flowchart for determining the position and size of the dynamic load on the structure based on the mode shape comparison of the application;

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

[0030] Figure 3 is the modal load of each order of the system under the condition of the sine load in an embodiment of the application;

[0031] Figure 4 is the modal load of each order of the system under the condition of the impact load in an embodiment of the application;

[0032] Figure 5is the modal load of each order of the system in the random load working condition in the embodiment of the application;

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

[0034] Figure 7 is the deviation function of the vibration mode at each position on the beam in the impact load working condition in the embodiment of the application;

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

[0036] Figure 9 is the identification result of the sinusoidal load in the embodiment of the application;

[0037] Figure 10 is the identification result of the impact load in the embodiment of the application;

[0038] Figure 11 is the identification result of the random load in the embodiment of the application. DETAILED DESCRIPTION

[0039] The technical solutions of the application are further described below with reference to the drawings.

[0040] The application proposes a continuous system concentrated dynamic load rapid positioning method based on the Newmark explicit method and vibration mode comparison, that is, the modal load of each order of the vibration system is determined based on the Newmark explicit method, 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 through the calculation of the least square inverse to further determine the position of the load action.

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

[0042] Step 1: constructing a modal load identification equation Y=Hf according to the parameters α and β of the Newmark explicit method and the modal vibration mode information of the response measurement point.

[0043] The mapping relationship between the modal load and the modal response under the modal coordinates is constructed:

[0044]

[0045] In formula (1) is the modal response of each order of the system, is the modal load of each order of the system, and The mapping relationship between the modal response and the modal load of the system can be obtained from equation (1) by the Newmark method, which is a classical algorithm and will not be described here.

[0046] In practical engineering, although the load acting on the system is difficult to be directly measured, the response of the system can be easily measured by sensors and other measuring devices. Therefore, the vector y(t) e R m×1 represents the output of the system.

[0047]

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

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

[0050]

[0051] By selecting the acceleration in the physical coordinate system as the measured response and combining equations (2) and (3), R d , R v and R a are obtained as follows:

[0052]

[0053] Substituting equation (4) into equation (1) and rearranging it gives equation (5):

[0054] Y=Hf (5)

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

[0056] Step 2: According to the measured response information, the modal load is solved by combining the equation obtained in step 1 with the truncated singular value regularization method.

[0057] Solving equation (5) can get a series of values of each order modal load f. In the solving 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 order modal load and calculate its least square inverse and determine the proportional relationship between each order mode shape at the load excitation position

[0059] For continuous systems, t i The modal force vector at time t and the true load conversion relationship are:

[0060]

[0061] In equation (6), k is the number of concentrated loads on the system, F k (t i ) represents the value of the kth load at time t i x fk represents the position of the kth load.

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

[0063] Therefore, each order modal load 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 square inverse is selected to minimize the residual sum of squares:

[0064]

[0065] where j is any order modal. Through equation (7), the proportional relationship vector between each order mode shape at the load excitation position can be obtained:

[0066]

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

[0068] By comparing the η(x) vector at each point on the structure, the load excitation position can be determined. Introducing the mode shape deviation function for quantitative comparison, when x=x f , considering the influence of noise on the identification accuracy, g(x) cannot be strictly taken to 0, but should take a value close to 0. That is, when g(x) is the smallest, the value of x 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 shape function as in the modal load identification process mentioned above should be used for comparison.

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

[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 the 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 sets of single-point concentrated loads were applied: a sinusoidal load, an impact load, and a random load. The time-varying relationship of the sinusoidal load was F = 5 × sin[100πt]. The impact load amplitude was 10N, and the impact duration was 0.005s. The random load was generated using the random phase method with a frequency range of 100Hz to 300Hz. Nine evenly distributed points on the beam were used as response measurement points for dynamic load identification. During the identification process, the modal cutoff order r = 5 was set. To demonstrate the stability of the method, 1% white noise was 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: selecting any modal load and calculating its least square inverse and determining the proportional relationship between the modes of vibration at the load excitation position The calculation results are as follows:

[0078] Under the sine load condition, η(x f ) = [0.9441 0.5722 -0.5674 -1.1453 0.3683];

[0079] Under the impact load condition, η(x f ) = [0.9534 0.5675 -0.4478 -0.5914 -0.0809];

[0080] Under the random load condition, η(x f ) = [0.8765 0.5264 -0.5478 -0.8715 0.0184].

[0081] Step 4: calculating the mode shape deviation function For quantitative comparison, g(x) should take the minimum value when x = x f . The mode shape deviation functions of points on the beam are shown in Figure 6 , Figure 7 and Figure 8 .

[0082] As can be seen from Figure 6 , Figure 7 and Figure 8 , the present application can quickly and accurately locate the action position of the dynamic load suffered by the structure.

[0083] Step 5: according to the load position x f determined in step 4, the inverse problem of formula (6) is solved to further determine the size of the load, and the identification results are shown in Figure 9 , Figure 10 and Figure 11 . As can be seen, the load signal-to-noise ratio obtained by the sine load identification is 20.7dB, the peak relative error obtained by the impact load identification is 1.5%, and the load signal-to-noise ratio obtained by the random load identification is 18.27dB, all of which have very high precision.

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

[0085] A modal load identification equation construction module is used for constructing a modal load identification equation Y = Hf according to the parameters alpha and beta of the Newmark explicit method and the modal shape information of the response measurement point, Y represents the system modal response, H represents the mapping matrix of the time domain response and the excitation, and f represents the system modal load.

[0086] A modal load solving module is configured to solve the modal load according to the measured response information and the equation obtained by the modal load identification equation constructing module, to obtain the system modal load f by using the truncated singular value decomposition regularization method.

[0087] A mode shape comparison module is configured to select any order modal load, calculate the least square inverse thereof, and determine the proportional relationship between the mode shapes at the load excitation position Wherein W i (x f ) is the influence weight of the i-th order modal acceleration at the load excitation position x f r is the modal truncation order.

[0088] A load position determining module is configured to calculate the mode shape deviation function for quantitative comparison, to determine the load excitation position x f .

[0089] A load size determining module is configured to determine the load size by solving the inverse problem of the modal force vector and the real load conversion relationship formula according to the load excitation position x f determined by the load position determining module.

[0090] The present application also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs are executed by the processors to implement the steps of the mode shape comparison based dynamic load position identification method as described above.

[0091] The present application also provides a computer storage medium having a computer program stored thereon, and the computer program is executed by the processors to implement the steps of the mode shape comparison based dynamic load position identification method as described above.

[0092] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, device, computer device or computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in 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 code.

[0093] The application is described with reference to the Figures according to which the methods of the application are illustrated. It will be understood that each flow of the flow diagram, as well as combinations of the flows of the flow diagram, 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, create means for implementing the functions specified in the flow diagram Figure 1 flow or multiple flows. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flow diagram Figure 1 flow or multiple flows. These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flow diagram Figure 1 flow or multiple flows. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flow diagram

Claims

1. A dynamic load position recognition method based on mode shape comparison, characterized by, The method comprises the following steps: Step 1: constructing a modal load identification equation Y = Hf according to parameters alpha and beta of the Newmark explicit method and modal vibration mode information of a response measurement point, Y representing system modal response, H representing a mapping matrix of time domain response and excitation, and f representing system modal load; Step 2: solving the equation obtained in step 1 in combination with a truncated singular value decomposition regularization method according to measured response information to obtain system modal load f; Step 3: Select any modal load and calculate its least square inverse, and determine the proportional relationship between each order mode shape at the load excitation position where W i (x f ) is the influence weight of the i-th order modal acceleration at the load excitation position x f , and r is the modal truncation order; Step 4: Calculate mode shape deviation function For quantitative comparison, determine the load excitation position x f ; Step 5: The load excitation position x is determined according to the load determined in step 4 f The inverse problem of the modal force vector and the real load conversion formula is solved to determine the size of the load.

2. The method of claim 1, wherein, In constructing the modal load identification equation, the vector y(t) e R m×1 represents the output of the system, where R d , R v , and R a e R m×r are the influence weights of the modal displacement, the modal velocity, and the modal acceleration on the system output, m is the number of known responses, r is the modal truncation order, is the system modal response of each order.

3. The method of claim 2, wherein, According to the acceleration response conversion formula between the physical coordinates and the modal coordinates: The acceleration in the physical coordinate system is selected as the measurement response, and R d , R v , and R a are obtained: where W i (x j ) represents the influence weight of the i-th order modal acceleration at the position corresponding to the j-th measurement response.

4. The method of claim 3, wherein, When determining the proportional relationship between the modes at the position of the load excitation, for continuous systems, t i The true load conversion relationship between the modal force vector at the moment and the real load is: where k is the number of concentrated loads on the system, F k (t i ) represents the value of the kth load at time t i represents the location of the kth load.​ 5. The method of claim 4, wherein, In the case of single-point excitation, t i The modal force vector at the time instant and the real load conversion relationship is 6. The method of claim 5, wherein, selecting any order modal load and calculating least square inverse thereof, and determining proportional relationships between vibration modes at load excitation positions, and the proportional relationships are represented as: where j is any order mode.

7. The method of claim 1, wherein, When quantitatively comparing by the 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 location identification system based on mode shape comparison, characterized by, The method comprises the following steps: a modal load identification equation construction module configured to construct a modal load identification equation Y = Hf according to parameters alpha and beta of the Newmark explicit method and modal vibration mode information of a response measurement point, Y representing system modal response, H representing a mapping matrix of time domain response and excitation, and f representing system modal load; a modal load solving module configured to solve the equation obtained by the modal load identification equation construction module in combination with a truncated singular value decomposition regularization method according to measured response information to obtain system modal load f; a mode shape comparison module for selecting any order modal load and calculating its least square inverse, and determining the proportional relationship between each order mode shape at the load excitation position where W i (x f ) is the influence weight of the i-th order modal acceleration at the load excitation position x f , and r is the modal truncation order; Load position determination module for calculating mode shape deviation function For quantitative comparison, determine load excitation position x f ; The load size determination module is configured to determine the load excitation position x according to the load position determination module f The modal force vector and the real load conversion relationship formula are solved by inverse problem to determine the size of the load.

9. A computer device, comprising: The method comprises the following steps: 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, and the programs, when executed by the processor, implement the steps of the modal shape comparison-based dynamic load position identification method as claimed in any one of claims 1-7.

10. A computer storage medium having stored thereon a computer program, characterized in that The computer program, when executed by the processor, implements the steps of the modal shape comparison-based dynamic load position identification method as claimed in any one of claims 1-7.

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