Dynamic load identification method based on sensor layout

Abstract

The application discloses a dynamic load identification method based on a structural sensor layout strategy. First, the Green kernel function method is used to obtain the transfer function under different sensor positions of the structure; second, the sensor position corresponding to the transfer function curve of the maximum response amplitude at each frequency is judged, and the envelope line of the transfer function curve is obtained; third, a prediction point is selected for dynamic load identification, and the load information is preliminarily determined, and then the corresponding sensor position is selected according to the load information, and multi-scale regularization is used for dynamic load identification; finally, the dynamic load identification results under different sensor positions are extracted in the frequency domain according to the optimal frequency range corresponding to the sensor position, and the final dynamic load identification result is obtained by accumulating each component. The application can solve the problem of poor dynamic load identification precision caused by sensor errors, and can improve the dynamic load identification precision to the greatest extent by changing the sensor layout.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of load identification, and particularly relates to a dynamic load identification method based on sensor layout. BACKGROUND

[0002] In practical engineering vibration problems such as vibration isolation technology, vibration reduction technology, reliability optimization design, health monitoring and fault analysis, the determination of dynamic load information is always the premise and condition of these problems. Improving the accuracy of dynamic load identification is the key to the problem of dynamic load identification. Generally speaking, the accuracy of dynamic load identification can be improved from the following three aspects: ① dynamic model, establishing the relationship between load and response is the positive problem of dynamic load identification and the basis of dynamic load identification ② dynamic load identification method, at present, various time-domain and frequency-domain dynamic load identification methods have been developed, and accurate load information can be obtained to a certain extent by combining the regularization method ③ structure dynamic response test, including test and signal processing, which is also an important problem of dynamic load identification. Among them, the sensor layout is an important part of the structure dynamic response test, and how to improve the accuracy of dynamic load identification through reasonable sensor layout has always been the research direction of many scholars and has important practical significance. SUMMARY

[0003] In view of the problem that sensor precision error is difficult to avoid, the application provides a dynamic load identification method based on sensor layout, so as to provide accurate and effective external load information for structure vibration control, dynamic modification and dynamic optimization design.

[0004] The technical scheme of the application provides a dynamic load identification method based on sensor layout, characterized by comprising the following steps:

[0005] Step 1: obtaining the Green kernel function from the structure load point position to all other sensor positions, and converting it into a transfer function spectrum diagram;

[0006] Step 2: obtaining the envelope line of the transfer function spectrum diagram and determining the sensor positions corresponding to the transfer function curves constituting the envelope line and the corresponding frequency range;

[0007] Step 3: selecting the measuring point corresponding to the curve with the widest frequency band as the prediction point to inversely solve the load information, verifying the signal-to-noise ratio, if the signal-to-noise ratio meets the condition, the load frequency can be determined by the inversely solved load, if not, the next measuring point is selected until the signal-to-noise ratio meets the condition, and then the final sensor position is reselected according to the frequency of the inversely solved load;

[0008] Step 4: For each selected sensor position, the main frequency components of the response signal are extracted and the noise interference is reduced to some extent using signal decomposition techniques. The signal is decomposed into several components according to the optimal frequency range corresponding to the sensor position;

[0009] Step 5: For each selected sensor position, the load identification is performed using a multi-scale regularization method, and the Fourier transform is used to convert the identified load in the time domain to the load in the frequency domain;

[0010] Step 6: The components corresponding to the optimal frequency range are extracted from the load spectrum identified from each selected sensor position and superimposed, and the final dynamic load identification result is obtained through inverse Fourier transform.

[0011] Preferably, in the step 1, the transfer function can be represented by obtaining the response of the structure to a unit impulse load. Since the integral of the product of an arbitrary function and an impulse function is equal to the function value at the impulse time, any dynamic load can be represented in the time domain as an integral of a series of impulse loads. According to the superposition principle of linear time-invariant systems, the response of the system to any dynamic load can be represented as the superposition of the responses of a series of unit impulse loads,

[0012]

[0013] where g(t) is the unit impulse response, F(τ) is the external load of the structure, and μ(t) is the response of the structure. The transfer function H(ω) can be obtained by Fourier transform.

[0014] H(ω) = ∫g(t)·e -iω dt (2) where e and i represent the constant e and the imaginary unit i, respectively, and ω represents the frequency.

[0015] Preferably, in the step 2, for each transfer function curve, the curve with the maximum amplitude at each frequency is determined as the envelope line part at that frequency.

[0016] For a single frequency ω0external dynamic load, let the frequency response function from the loading point to the measuring point X be G X (ω), and the optimal measuring point selection problem can be described as the following optimization problem,

[0017]

[0018] The frequency response functions G X (ω) of all feasible measuring points are obtained by testing or numerical simulation, X = X1, X2, …, and the frequency range ω = {ω1, ω2, …, ω j ,…,ω Nwhere N is the total number of frequency points; in different frequencies ω j The envelope line B(ω) is established by the selected frequency response functions. j That is,

[0019]

[0020] where G i (ω j ) represents the amplitude of the frequency response function of the i-th measuring point at the frequency ω j .

[0021] Preferably, in the step 3, the frequency response function with the widest frequency band in the envelope line is selected. Considering that too small amplitude will affect the accuracy of load identification, a horizontal line is drawn with 10% of the maximum value of the envelope line as the limit, and the distance between the frequencies ω X,1 and ω X,2 corresponding to the two intersection points of the horizontal line and the frequency response function is taken as the frequency band width, so as to find the frequency response function with the widest frequency band.

[0022]

[0023] where represents the amplitude of the envelope line at the frequency , and G (ω ) represents the amplitude of the frequency response function of the i-th measuring point at the frequency ω .

[0024] Based on the response of the measuring point corresponding to the frequency response function with the widest frequency band, the load is predicted, and the corresponding frequency response function and measuring point are reselected according to the main frequency of the predicted load.

[0025] For the composite frequency load, the selection of the optimal measuring point is described by the following optimization problem,

[0026]

[0027] where ω i is all possible load frequencies, represents the amplitude of the frequency response function of the measuring point X i at the frequency ω i ; according to the single frequency load identification strategy, the response of the measuring point corresponding to the frequency response function with the widest frequency band is predicted, and the main frequency components of the load to be solved are analyzed and determined based on the predicted load; assuming that the load contains s significant frequencies, the corresponding frequencies are ω1, ω2,…, ω s ; according to the positions of ω1, ω2,…, ω s in the envelope line, s corresponding frequency response functions are selected from the envelope line.

[0028] Preferably, in step 4, for ease of description, the measurement point positions corresponding to the selected s frequency response functions are denoted as X1, X2, ..., X... s The load is calculated inversely based on the response at the selected measurement points, denoted as... Right now,

[0029]

[0030] In the formula, Indicates measuring point X i The response at the location, Indicates load To response The Green kernel matrix is ​​then used to decompose the measured response into multiple components by frequency.

[0031]

[0032] In the formula, s represents the number of significant frequencies contained in the load.

[0033] Preferably, in step 5, the corresponding load components are solved based on these components and the Green kernel function. Since the response components are different, different regularization operators (α1, α2, ..., α...) are used in the inverse calculation of the load components. s The ill-posedness problem is corrected to improve the accuracy and stability of load component identification. Finally, the inversely calculated load components are superimposed to obtain the final result.

[0034]

[0035] In the formula, σ, u, and v represent matrices respectively. Singular values ​​and singular vectors after singular value decomposition, σ 2 ≥α i This indicates that regularization is used to correct singular values.

[0036] Preferably, in step 6, according to the principle of linear superposition, the composite frequency load can also be expressed as a superposition of sub-loads of individual frequencies. Therefore, through Fourier transform and inverse transform, respectively from... Separate ω1, ω2, ..., ω from s The corresponding load components; the separated high-precision load components are superimposed again as follows to assemble a new load with even higher precision;

[0037]

[0038] In the formula, F δ This indicates the final load identification result. Indicates based on X iThe load corresponding to the frequency ω of the response identification of the measuring point i The component at the position.

[0039] According to the above technical solution, the beneficial effects of the present application include:

[0040] (1) The present application innovatively proposes a method for improving the dynamic load identification accuracy by using a reasonable sensor layout. The method takes the constant measurement error as the premise, and can determine the initial sensor position through global comparison of the structure transfer function under the condition that the load information is completely unknown, and perform load identification according to the measurement response, and adjust the sensor position according to the preliminary determined load information, which can simultaneously compatible with single frequency load and composite frequency random load, and finally combine response decomposition and multi-scale regularization method to further improve the accuracy of dynamic load identification.

[0041] (2) Due to the limitation of the tested equipment and economic and technical conditions, the influence of the accuracy error of the sensor itself on the dynamic load identification cannot be ignored. The present application uses a suitable sensor layout to maximize the accuracy of dynamic load identification without changing the accuracy of the sensor, which is of great significance for the structure design, optimization and evaluation in actual engineering.

[0042] (3) In view of the complex frequency components that may appear in the response information, the response decomposition technology is fully utilized to select the corresponding sensor position for dynamic load identification of different frequency components, which further improves the identification accuracy of dynamic load.

[0043] (4) In the present application, different regularization parameters are used for dynamic load identification of different components of the response by using multi-scale regularization method when identifying the dynamic load, which further improves the identification accuracy of the dynamic load. BRIEF DESCRIPTION OF DRAWINGS

[0044] The accompanying drawings are included to provide a further understanding of the present application and are incorporated in and constitute a part of this specification, illustrate embodiments of the present application and together with the description serve to explain the principles of the present application, and, together with the description, to specify the characteristics of the working procedures and structures of the embodiments of the present application. In the drawings:

[0045] Figure 1 is a step flow chart of the dynamic load identification method in the present application;

[0046] Figure 2 is a 25-bar truss structure diagram in the example;

[0047] Figure 3 is a transfer function spectrum diagram under each sensor position;

[0048] Figure 4 is an envelope line of the transfer function spectrum under each sensor position;

[0049] Figure 5is the preliminary identified dynamic load time history;

[0050] Figure 6 is the preliminary identified dynamic load frequency spectrum;

[0051] Figure 7 is the response signal of the longitudinal position measurement of node 7;

[0052] Figure 8 is the response signal decomposition result of the longitudinal position measurement of node 7;

[0053] Figure 9 is the final identified dynamic load time history. DETAILED DESCRIPTION

[0054] The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. Figures 1-9 The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0055] In this embodiment, the dynamic load received by a 25-bar truss structure is taken as an example for description. The dynamic load received by the structure is generally not obtained by direct measurement, while the response of the structure due to the dynamic load is relatively easy to measure. Therefore, first, the Green kernel function method is used to obtain the Green kernel function at different sensor positions of the structure, which is converted into a transfer function in the frequency domain; second, the sensor position corresponding to the transfer function curve of the maximum response amplitude at each frequency is determined, and the envelope line of the transfer function curve is obtained; third, the prediction point is selected for dynamic load identification, the load information is preliminarily determined, and then the corresponding sensor position is selected according to the load information, and the multi-scale regularization is used for dynamic load identification; finally, the dynamic load identification results at different sensor positions are extracted according to the optimal frequency range corresponding to the sensor position in the frequency domain, and the components are accumulated to obtain the final dynamic load identification result.

[0056] Figure 1 The step flow of the dynamic load method based on the sensor layout in the specific embodiments of the present application is shown, and the specific implementation steps are as follows:

[0057] Step 1: Obtain the Green kernel function from the load point position of the structure to all other sensor positions, and convert it into a transfer function frequency spectrum;

[0058] The transfer function can be expressed by obtaining the response of the structure to the unit impulse load. Since the integral of the product of the impulse function and any function is equal to the function value at the impulse time, any dynamic load can be expressed as an integral form of the superposition of infinite impulse loads. According to the superposition principle of linear time-invariant systems, the response of the system to any dynamic load can be expressed as the superposition of the responses of a series of unit impulse loads,

[0059]

[0060] where g(t) is the unit impulse response, F(τ) is the external load on the structure, and μ(t) is the structural response. The transfer function H(ω) can be obtained by Fourier transform of g(t).

[0061] H(ω) = ∫g(t)·e -iωt dt (2) where e and i represent the constant e and the imaginary unit i, respectively, and ω represents the frequency.

[0062] Consider Figure 2 the 25-bar truss structure shown in FIG. 25, the lateral position of node 1 is subjected to a dynamic load. The length of the lateral and longitudinal bars in the truss is 15.24 m, the density of all bars is ρ = 2800 kg / m 3 , the elastic modulus is E = 2.1 x 10 11 Pa, the Poisson's ratio is μ = 0.3, the cross-sectional area of bars (1) to (4) is 400 mm2, the cross-sectional area of bars (16) to (25) is 500 mm2, the cross-sectional area of bars (11) to (15) is 600 mm2, and the cross-sectional area of bars (5) to (10) is 800 mm2. It is assumed that the damping of the truss is Rayleigh damping, i.e., the damping is a linear superposition of the stiffness and mass, and the weight coefficients of the mass matrix and the stiffness matrix are 0 and 0.003, respectively. The connecting points 6 and 12 are fixedly constrained, and the connecting points 8 and 10 are rollably constrained. The transfer functions from the load point position to other positions are obtained by the Green's kernel function method. In this embodiment, the transfer function frequency spectrum diagrams at various sensor positions are shown in FIG. 26. Figure 3

[0063] Step 2: Obtain the envelope line of the transfer function frequency spectrum diagram and determine the sensor positions corresponding to the transfer function curves constituting the envelope line and the corresponding frequency ranges;

[0064] The frequency response functions G X (ω) of all feasible measuring points are obtained by numerical simulation, X = X1, X2, …, and the frequency range f = {ω1, ω2, …, ω j , …, ω N} is defined, where N is the total number of frequency points, and in this example, N is 19; the frequency response function with the largest amplitude is selected at different frequencies ω j , and an envelope line B(ω j ) composed of the selected frequency response functions is established, i.e.,

[0065]

[0066] where G i (ω j ) represents the amplitude of the frequency response function of the i-th measuring point at the frequency ω j .​

[0067] For each transfer function curve, the curve with the largest amplitude at each frequency is determined as the envelope at that frequency, and the resulting envelope is as follows: Figure 4 As shown.

[0068] Step 3: Select the measurement point corresponding to the curve with the widest bandwidth as the prediction point to reverse the load information and verify its signal-to-noise ratio. If the signal-to-noise ratio is satisfied, the load frequency can be determined by reverse the load. If not, select the next measurement point until the signal-to-noise ratio condition is met, and then reselect the final sensor position based on the reverse load frequency.

[0069] Draw a horizontal line with 10% of the maximum value of the envelope as the boundary, and use the frequencies ω corresponding to the two intersection points of this horizontal line and the frequency response function as the dividing points. X,1 With ω X,2 The distance between them is used as the bandwidth, and this is used as a criterion to find the frequency response function with the widest bandwidth.

[0070]

[0071] in Indicates the envelope at frequency The amplitude below, This represents the frequency response function at the i-th measurement point at frequency... The amplitude of the frequency response function.

[0072] In this embodiment, the sensor location is selected at the longitudinal position of node 7, and the determined dynamic load time history and spectrum are as follows: Figure 5 and Figure 6 As shown.

[0073] Step 4: For the response signal at each selected sensor location, use signal decomposition techniques to extract the main frequency components of the response signal and reduce noise interference to a certain extent. Decompose the signal into several components according to the optimal frequency range corresponding to the sensor location;

[0074] Let the locations of the measurement points corresponding to the selected s frequency response functions be X1, X2, ..., X... s The load is calculated inversely based on the response at the selected measurement points, denoted as... Right now,

[0075]

[0076] In the formula, Indicates measuring point X i The response at the location, Indicates load To response The Green kernel matrix is ​​then used to decompose the measured response into multiple components by frequency.

[0077]

[0078] where s represents the number of significant frequencies contained in the load.

[0079] In this example, the sensor locations determined from the dynamic load spectrum are node 2 lateral position, node 5 lateral position and node 7 longitudinal position. As shown in Fig. 2, the response signals measured at node 7 longitudinal position are taken as an example for response decomposition, and the decomposition results are shown in Fig. 3. Figure 7 Figure 8

[0080] Step 5: Load identification is performed on the response of each selected sensor location using the multi-scale regularization method, and the identified load components are superimposed;

[0081] In the identification of load components, different regularization operators (α1, α2, …, α s ) are used to correct the ill-posed problem, thereby improving the accuracy and stability of the identification of load components.

[0082] Finally, the identified load components are superimposed to obtain the final result:

[0083]

[0084] where σ, u and v represent the singular values and singular vectors after singular value decomposition of matrix , respectively, σ 2 ≥ α i represents the correction of singular values using the regularization method.

[0085] Step 6: The components corresponding to the optimal frequency range are extracted from the load spectrum identified at each selected sensor location and superimposed, and the final dynamic load identification result is obtained through inverse Fourier transform;

[0086] According to the principle of linear superposition, the load of a complex frequency can also be represented as the superposition of sub-loads of individual frequencies. Therefore, through Fourier transform and inverse transform, the load components corresponding to ω1, ω2, …, ω s can be separated from F , respectively. The separated load components with high accuracy are superimposed as follows to assemble a new load with higher accuracy,

[0087]

[0088] where F δ represents the final load identification result, represents the component at frequency ω i based on the response identification of X i measurement points. The inverse result is shown in Fig. 4.​​Figure 9 As shown, the fitting effect with the original dynamic load is good.

[0089] The above merely provides the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of the changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A dynamic load identification method based on sensor layout, characterized in that, Includes the following steps: Step 1: Obtain the Green kernel function from the structural load point location to all sensor locations, and convert it into a transfer function spectrum. Step 2: Obtain the envelope of the transfer function spectrum and determine the sensor location and corresponding frequency range corresponding to the transfer function curves that make up the envelope; Step 3: Select the measurement point corresponding to the curve with the widest bandwidth as the prediction point to reverse the load information and verify its signal-to-noise ratio. If the signal-to-noise ratio is satisfied, the load frequency can be determined by reverse the load. If not, select the next measurement point until the signal-to-noise ratio condition is met, and then reselect the final sensor position based on the reverse load frequency. Step 4: For the response signal at each selected sensor location, use signal decomposition technology to extract the main frequency components of the response signal and reduce noise interference to a certain extent; decompose the signal into several components according to the optimal frequency range corresponding to the sensor location. Step 5: For the response of each selected sensor location, a multi-scale regularization method is used to identify the load. Fourier transform is used to convert the load identified in the time domain into the load in the frequency domain. Step 6: Extract the components of the corresponding optimal frequency range from the load spectrum identified at each selected sensor location and superimpose them. Then, perform an inverse Fourier transform to obtain the final dynamic load identification result.

2. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 1, the transfer function can be represented by obtaining the structure's response to a unit impulse load; the integral of the product of the impulse function and any function is equal to the function value at the moment of impulse, and in the time domain, any dynamic load can be represented as an integral form of the superposition of an infinite number of impulse loads; according to the superposition principle of linear time-invariant systems, the system's response to any dynamic load can be represented as a superposition of the responses to a series of unit impulse loads. In the formula, g(t) is the unit impulse response, F(τ) is the external load on the structure, and μ(t) is the structural response. The transfer function H(ω) can be obtained by performing a Fourier transform on it. H(ω)=∫g(t)·e -iωt dt (2) In the formula, e and i represent the constant e and the imaginary unit i, respectively, and ω represents the frequency.

3. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 2, for each transfer function curve, the curve with the largest amplitude at each frequency is determined as the envelope portion at that frequency; For an external dynamic load with a single frequency ω0, let the frequency response function from the loading point to the measurement point X be G. X The problem of selecting the optimal measurement point (ω) can be described by the following optimization problem: The frequency response function G at all feasible measurement points is obtained through testing or numerical simulation. X (ω), X = X1, X2, ..., X n Where n is the number of feasible measurement points, and the frequency range ω is defined as {ω1, ω2, ..., ω...} j ,…,ω N }, where N is the total number of frequency points; at different frequencies ω j Next, select the frequency response function with the largest amplitude, and construct the envelope B(ω) composed of the selected frequency response function segments. j ),Right now, In the formula, This represents the frequency response function of the i-th measurement point at frequency ω. j The amplitude of the frequency response function.

4. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 3, the frequency response function with the widest bandwidth in the envelope is selected. Considering that an excessively small amplitude will affect the accuracy of load identification, a horizontal line is drawn with 10% of the maximum value of the envelope as the boundary. The frequencies ω corresponding to the two intersection points of this horizontal line and the frequency response function are used as the basis for the determination. X,1 With ω X,2 The distance between them is used as the bandwidth, and this is used as a criterion to find the frequency response function with the widest bandwidth. In the formula, Indicates the envelope at frequency The amplitude below, This represents the frequency response function at the i-th measurement point at frequency... The amplitude of the frequency response function under the given conditions; Load prediction is performed based on the measurement point response corresponding to the frequency response function with the widest bandwidth, and the corresponding frequency response function and measurement point are reselected according to the main frequency of the predicted load. For composite frequency loads, the problem of selecting the optimal measurement point is described by the following optimization problem: In the formula, ω i For all possible load frequencies, Indicates measuring point X i The lower frequency response function at frequency ω i The amplitude at time; according to the single-frequency load identification strategy, the measurement point response corresponding to the frequency response function with the widest bandwidth is selected for load prediction, and the main frequency components of the load to be inversely calculated are determined based on the predicted load analysis; assuming the load contains s significant frequencies, the corresponding frequencies are denoted as ω1, ω2, ..., ω s According to ω1, ω2, ..., ω s At the corresponding positions in the envelope, select s corresponding frequency response functions from the envelope.

5. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 4, for ease of description, the measurement point locations corresponding to the selected s frequency response functions are denoted as X1, X2, ..., X... s； The load is calculated by inversely based on the response at the selected measurement points, denoted as... Right now, In the formula, Indicates measuring point X i The response at the location, Indicates load To response The Green kernel matrix is ​​then used to decompose the measured response into multiple components by frequency. In the formula, s represents the number of significant frequencies contained in the load.

6. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 5, the corresponding load components are solved based on the response components and the Green's kernel function; The response components are all different, and different regularization operators (α1, α2, ..., α) are used in the inverse calculation of the load components. s This corrects ill-posed problems, thereby improving the accuracy and stability of load component identification; Finally, the load components obtained by inverse calculation are superimposed to obtain the final result: In the formula, σ, u, and v represent matrices respectively. Singular values ​​and singular vectors after singular value decomposition, σ 2 ≥α i This indicates that regularization is used to correct singular values.

7. The dynamic load identification method based on sensor layout according to claim 1, characterized in that, In step 6, according to the principle of linear superposition, the composite frequency load is also expressed as a superposition of sub-loads of individual frequencies; through Fourier transform and inverse transform, respectively from Separate ω1, ω2, ..., ω from s The corresponding load components; the separated high-precision load components are superimposed again as follows to assemble a new load with even higher precision; In the formula, F δ This indicates the final load identification result. Indicates based on X i The load corresponding frequency ω identified by the measurement point response i The component at that location.

Images