Dynamic load identification method based on sensor layout

Abstract

The invention discloses a dynamic load identification method based on a structure sensor layout strategy. The method comprises the following steps: firstly, acquiring transfer functions of a structure at different sensor positions by using a Green kernel function method; secondly, judging a sensor position corresponding to the transfer function curve of the maximum response amplitude under each frequency, and obtaining an envelope line of the transfer function curve; thirdly, selecting a prediction point to perform dynamic load identification, preliminarily determining load information, selecting a corresponding sensor position according to the load information, and performing dynamic load identification by adopting multi-scale regularization; and finally, extracting components of the dynamic load identification results under different sensor positions in the frequency domain according to the optimal frequency range corresponding to the sensor positions, and accumulating the components to obtain a final dynamic load identification result. In order to solve the problem of poor dynamic load identification precision caused by sensor errors, the dynamic load identification precision is improved to the greatest extent by changing the layout of the sensors.

Description

Technical Field

[0001] The present invention belongs to the technical field of load identification, and in particular relates to a dynamic load identification method based on sensor layout. Background Art

[0002] In practical engineering vibration problems such as structural 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, a variety of dynamic load identification methods in time domain and frequency domain have been developed, and combined with regularization methods, accurate load information can be obtained to a certain extent. ③ Structural dynamic response test, including experimental test and signal processing, is also an important issue in dynamic load identification. Among them, sensor layout is an important part of structural dynamic response test. How to improve the accuracy of dynamic load identification through reasonable sensor layout has always been a research direction of interest to many scholars and has important practical significance. Summary of the invention

[0003] In view of the problem that sensor accuracy errors are difficult to avoid, the present invention proposes a dynamic load identification method based on sensor layout, thereby providing accurate and effective external load information for structural vibration control, dynamic modification and dynamic optimization design.

[0004] The technical solution of the present invention is to provide a dynamic load identification method based on sensor layout, which is characterized by comprising the following steps:

[0005] Step 1: Obtain the Green kernel function from the structural load point position to all other sensor positions and convert it into a transfer function spectrum diagram;

[0006] Step 2: Obtain the envelope of the transfer function spectrum and determine the sensor position and the corresponding frequency range corresponding to the transfer function curve constituting the envelope;

[0007] Step 3: Select the measuring point corresponding to the curve with the widest frequency band as the prediction point to inversely obtain the load information and verify its signal-to-noise ratio. If the signal-to-noise ratio is met, the load frequency can be determined by inversely obtaining the load. If it is not met, select the next measuring point until the signal-to-noise ratio condition is met, and then reselect the final sensor position according to the inverse load frequency.

[0008] Step 4: For the response signal at each selected sensor position, 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 position;

[0009] Step 5: Use a multi-scale regularization method to identify the loads of each selected sensor location, and use Fourier transform to transform the loads identified in the time domain into loads in the frequency domain;

[0010] Step 6: Extract the components of the corresponding optimal frequency range from the load spectrum obtained by identifying each selected sensor position and superimpose them, and obtain the final dynamic load identification result through inverse Fourier transform.

[0011] Preferably, in step 1, the transfer function can be expressed by obtaining the response of the structure to a 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 in the time domain 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 response of the system to any dynamic load can be expressed as a superposition form of the response 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 structural response. The transfer function H(ω) can be obtained by performing Fourier transform on it.

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

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

[0016] For an external dynamic load with a single frequency ω0, the frequency response function from the loading point to the measuring point X is G X (ω), the problem of selecting the optimal measuring point can be described by the following optimization problem:

[0017]

[0018] Obtain the frequency response function G of all feasible measurement points by testing or numerical simulation X (ω), X = X1, X2, ..., define the frequency range ω = {ω1, ω2, ..., ω j ,…,ωN}, where N is the total number of frequency points; at different frequencies ω j Select the frequency response function with the largest amplitude and establish the envelope B(ω j ),Right now,

[0019]

[0020] In the formula, G i (ω j ) represents the frequency response function of the i-th measuring point at frequency ω j The lower value.

[0021] Preferably, in step 3, the frequency response function with the widest frequency band in the envelope 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 as the boundary, and the frequencies ω corresponding to the two intersection points of the horizontal line and the frequency response function are X,1 With ω X,2 The distance between them is taken as the bandwidth, and the frequency response function with the widest bandwidth is found based on this.

[0022]

[0023] in Indicates the envelope at frequency The amplitude below, Indicates the frequency response function of the i-th measurement point at the frequency The amplitude of the frequency response function under .

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

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

[0026]

[0027] Among them, ω i For all possible loading frequencies, Indicates measuring point X i The frequency response function is at a frequency of ω i The amplitude at the time of load prediction is calculated; 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 selected for load prediction, and the main frequency components of the load to be inversely determined are analyzed and determined based on the predicted load; assuming that the load contains s significant frequencies, the corresponding frequencies are recorded as ω1, ω2, …, ω s ; According to ω1,ω2,…,ω s At the corresponding position in the envelope, select s corresponding frequency response functions from the envelope.

[0028] Preferably, in step 4, for the convenience of description, the measurement point positions corresponding to the selected s frequency response functions are X1, X2, ..., X s Based on the selected measurement point responses, the loads are inversely calculated and recorded as Right now,

[0029]

[0030] In the formula, Indicates measuring point X i The response of Indicates load To the response The Green kernel matrix then decomposes the measured response into multiple components by frequency.

[0031]

[0032] Where s represents the number of significant frequencies contained in the loading.

[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 s ) to correct the ill-posed problem, thereby improving the accuracy and stability of load component identification. Finally, the inverse load components are superimposed to obtain the final result:

[0034]

[0035] Where σ, u and v represent matrices Singular values ​​and singular vectors after singular value decomposition, σ 2 ≥α i Indicates that the regularization method is used to correct the singular values.

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

[0037]

[0038] In the formula, F δ represents the final load identification result, Indicates based on Xi The load corresponding frequency ω of the measurement point response identification i The weight of the place.

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

[0040] (1) The present invention innovatively proposes a method for improving the accuracy of dynamic load identification by using a reasonable sensor layout. This method is based on the premise that the measurement error is constant. Under the condition that the load information is completely unknown, the method can determine the initial sensor position by globally comparing the structural transfer function, and perform load identification based on its measurement response. The sensor position is then adjusted based on the initially determined load information. It can be compatible with both single-frequency loads and random loads of composite frequencies. Finally, the response decomposition and multi-scale regularization methods are combined to further improve the accuracy of dynamic load identification.

[0041] (2) Due to the limitations of test equipment and economic and technical conditions, the influence of the sensor's own accuracy error on dynamic load identification is difficult to ignore. The present invention will adopt a suitable sensor layout to maximize the accuracy of dynamic load identification without changing the sensor's accuracy, which is of great significance for structural 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 positions for different frequency components for dynamic load identification, which further improves the identification accuracy of dynamic loads.

[0043] (4) When identifying dynamic loads, the present invention uses a multi-scale regularization method to adopt different regularization parameters for the responses of different components to identify the dynamic loads, thereby further improving the recognition accuracy of the dynamic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0045] Figure 1 is a flow chart of the steps of the dynamic load identification method of the present invention;

[0046] Figure 2 This is the structural diagram of the 25-bar truss in the example;

[0047] Figure 3 is the spectrum of the transfer function at each sensor position;

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

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

[0050] Figure 6 It is the preliminary determined dynamic load spectrum diagram;

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

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

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

[0054] The following is combined with Figure 1-9 Specific embodiments of the present invention are described in detail.

[0055] In this embodiment, the dynamic load on a 25-bar truss structure is taken as an example for explanation. The dynamic load on the structure cannot usually be obtained by direct measurement, but the response of the structure due to the dynamic load is relatively easy to measure. Therefore, firstly, the Green kernel function method is used to obtain the Green kernel function at different sensor positions of the structure, and convert it into a transfer function in the frequency domain; secondly, the sensor position corresponding to the transfer function curve of the maximum response amplitude at each frequency is determined, and the envelope of the transfer function curve is obtained; thirdly, 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 multi-scale regularization is used for dynamic load identification; finally, the dynamic load identification results at different sensor positions are extracted in the frequency domain according to the optimal frequency range corresponding to the sensor position, and the accumulation of each component is the final dynamic load identification result.

[0056] Figure 1 The steps of the dynamic load method based on sensor layout in a specific implementation of the present invention are shown, and the specific implementation steps are as follows:

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

[0058] The transfer function can be expressed by obtaining the response of the structure to a unit impulse load. Since the integral of the product of the impulse function and any function is equal to the function value at the time of the impulse, any dynamic load can be expressed in the time domain 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 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 of the structure, and μ(t) is the structural response. The transfer function H(ω) can be obtained by performing Fourier transform on it.

[0061] H(ω)=∫g(t)·e -iωt dt (2) Wherein, 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 is subjected to dynamic load at the transverse position of node 1. The length of the transverse and longitudinal bars in the truss is 15.24m, and the density of all bars is ρ = 2800kg / m 3 , the elastic modulus is E = 2.1 × 10 11 Pa, Poisson's ratio is μ=0.3, the cross-sectional area of ​​rods (1)~(4) is 400mm2, the cross-sectional area of ​​rods (16)~(25) is 500mm2, the cross-sectional area of ​​rods (11)~(15) is 600mm2, and the cross-sectional area of ​​rods (5)~(10) is 800mm2. Assume that the damping of the truss is Rayleigh damping, that is, the damping is a linear superposition of stiffness and mass, and the weight coefficients of the mass matrix and the stiffness matrix are 0 and 0.003 respectively. Connection points 6 and 12 are subject to fixed constraints, and connection points 8 and 10 are subject to rolling constraints. The transfer function from the load point position to other positions is obtained by the Green kernel function method. In this embodiment, the transfer function spectrum diagram obtained at each sensor position is as shown in Figure 3 shown.

[0063] Step 2: Obtain the envelope of the transfer function spectrum and determine the sensor position and the corresponding frequency range corresponding to the transfer function curve constituting the envelope;

[0064] The frequency response function G of all feasible measurement points can be obtained by numerical simulation. X (ω), X = X1, X2, ..., define the frequency range f = {ω1, ω2, ..., ω j ,…,ω N}, where N is the total number of frequency points, in this example N is 19; at different frequencies ω j Select the frequency response function with the largest amplitude and establish the envelope B(ω j ),Right now,

[0065]

[0066] In the formula, G i (ω j ) represents the frequency response function of the ith measurement point at frequency ωj The lower value.

[0067] For each transfer function curve, determine the curve with the largest amplitude at each frequency as the envelope part at that frequency. The envelope is as follows: Figure 4 shown.

[0068] Step 3: Select the measuring point corresponding to the curve with the widest frequency band as the prediction point to inversely obtain the load information and verify its signal-to-noise ratio. If the signal-to-noise ratio is met, the load frequency can be determined by inversely obtaining the load. If it is not met, select the next measuring point until the signal-to-noise ratio condition is met, and then reselect the final sensor position according to the inverse load frequency.

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

[0070]

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

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

[0073] Step 4: For the response signal at each selected sensor position, 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 position;

[0074] The measurement points corresponding to the s selected frequency response functions are X1, X2, ..., X s Based on the selected measurement point responses, the loads are inversely calculated and recorded as Right now,

[0075]

[0076] In the formula, Indicates measuring point X i The response of Indicates load To the response The Green kernel matrix then decomposes the measured response into multiple components by frequency.

[0077]

[0078] Where s represents the number of significant frequencies contained in the loading.

[0079] In this example, the sensor positions are determined to be the lateral position of node 2, the lateral position of node 5, and the longitudinal position of node 7 according to the dynamic load spectrum diagram. Figure 7 As shown, taking the response signal of the longitudinal position measurement of node 7 as an example, the response decomposition is performed, and the decomposition result is as follows Figure 8 shown.

[0080] Step 5: Use the multi-scale regularization method to identify the load for each selected sensor location’s response, and superimpose the inverse load components;

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

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

[0083]

[0084] Where σ, u and v represent matrices Singular values ​​and singular vectors after singular value decomposition, σ 2 ≥α i Indicates that the regularization method is used to correct the singular values.

[0085] Step 6: Extract the components of the corresponding optimal frequency range from the load spectrum obtained by each selected sensor position identification and superimpose them, and obtain the final dynamic load identification result through inverse Fourier transform;

[0086] According to the linear superposition principle, the load of the composite frequency can also be expressed as the superposition of the sub-loads of each single frequency. Therefore, through Fourier transform and inverse transform, we can get Separate ω1, ω2, …, ω s The separated high-precision load components are superimposed as follows to assemble a new load with higher precision.

[0087]

[0088] In the formula, F δ represents the final load identification result, Indicates based on Xi The load corresponding frequency ω of the measurement point response identification i The inverse result is Fig. 9 As shown in the figure, the fitting effect is better with the original dynamic load.

[0089] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A dynamic load identification method based on sensor layout, characterized in that: The steps include: Step 1: Obtain the Green kernel function from the structural load point position to all sensor positions and convert it into a transfer function spectrum diagram; Step 2, obtaining the envelope of the transfer function spectrum and determining the sensor position and the corresponding frequency range corresponding to the transfer function curve constituting the envelope; Step 3: Select the measuring point corresponding to the curve with the widest frequency band as the prediction point to inversely obtain 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 inversely obtaining the load. If it is not satisfied, select the next measuring point until the signal-to-noise ratio condition is satisfied, and then reselect the final sensor position according to the inverse load frequency. Step 4: For the response signal at each selected sensor position, 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 position; Step 5: Use a multi-scale regularization method to identify the load of each selected sensor position, and use Fourier transform 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 obtained by identifying each selected sensor position and superimpose them, and obtain the final dynamic load identification result through inverse Fourier transform.

2. The dynamic load identification method based on sensor layout according to claim 1 is characterized in that: In step 1, the transfer function can be expressed by obtaining the response of the structure 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 impulse time. In the time domain, any dynamic load can be expressed 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 response of the system to any dynamic load can be expressed as a superposition form of the response of a series of unit impulse loads. In the formula, g(t) is the unit impulse response, F(τ) is the external load of the structure, and μ(t) is the structural response. The transfer function H(ω) can be obtained by Fourier transforming it; H(ω)=∫g(t)·e -iωt dt (2) Wherein, 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 is characterized in that: In step 2, for each transfer function curve, a curve with the maximum corresponding amplitude at each frequency is determined as the envelope part at the frequency; For an external dynamic load with a single frequency ω0, the frequency response function from the loading point to the measuring point X is G X (ω), the problem of selecting the optimal measurement point can be described by the following optimization problem: Obtain the frequency response function G of all feasible measurement points by testing or numerical simulation X (ω), X=X1,X2,…,X n , where n is the number of feasible measurement points, and the frequency range is defined as ω = {ω1, ω2, …, ω j ,…,ω N }, where N is the total number of frequency points; at different frequencies ω j Select the frequency response function with the largest amplitude and establish the envelope B(ω j ),Right now, In the formula, Indicates the frequency response function of the i-th measurement point at frequency ω j The amplitude of the frequency response function under .

4. The dynamic load identification method based on sensor layout according to claim 1 is characterized in that: In step 3, the frequency response function with the widest frequency band in the envelope 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 as the boundary, and the frequency ω corresponding to the two intersection points of the horizontal line and the frequency response function is X,1 With ω X,2 The distance between them is taken as the bandwidth, and the frequency response function with the widest bandwidth is found based on this. In the formula, Indicates the envelope at frequency The amplitude below, Indicates the frequency response function of the i-th measurement point at the frequency The amplitude of the frequency response function under ; The load is predicted based on the response of the measuring point corresponding to the frequency response function with the widest frequency band, and the corresponding frequency response function and corresponding measuring point are reselected according to the main frequency of the predicted load; For composite frequency loads, the selection of the optimal measuring point is described by the following optimization problem: In the formula, ω i For all possible load frequencies, Indicates measuring point X i The frequency response function is at a frequency of ω i The amplitude at the time of load prediction is calculated; 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 selected for load prediction, and the main frequency components of the load to be inversely determined are analyzed and determined based on the predicted load; assuming that the load contains s significant frequencies, the corresponding frequencies are recorded as ω1, ω2, …, ω s ; According to ω1,ω2,…,ω s At the corresponding position 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 is characterized in that: In step 4, for the convenience of description, the measurement point positions corresponding to the selected s frequency response functions are X1, X2, ..., X s Based on the selected measurement point responses, the loads are inversely calculated and recorded as Right now, In the formula, Indicates measuring point X i The response of Indicates load To the response The Green kernel matrix is ​​then used to decompose the measured response into multiple components according to frequency; Where s represents the number of significant frequencies contained in the loading.

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

7. The dynamic load identification method based on sensor layout according to claim 1 is characterized in that: In step 6, according to the linear superposition principle, the load of the composite frequency is also expressed as the superposition of the sub-loads of each single frequency; through Fourier transform and inverse transform, Separate ω1, ω2, …, ω s Corresponding load components; the separated high-precision load components are superimposed again as follows to assemble a new load with higher precision; In the formula, F δ represents the final load identification result, Indicates based on X i The load corresponding frequency ω of the measurement point response identification i The weight of the place.

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