Time domain transmissibility function solving method, analysis method and computer program product

Abstract

The invention discloses a time domain transmissibility function solving method, an analysis method and a computer program product, and the method comprises the steps: firstly, carrying out the conversion of a constructed time domain working condition transmission path analysis equation, and representing the relation between a target point and an indication point on a time domain working condition transmission path in a matrix equation mode, and a corresponding quadratic function is obtained. And then, a conjugate gradient algorithm can be adopted to solve the quadratic form function, so that a transmissibility function suitable for time-domain working condition transmission path analysis is quickly obtained, and the time-domain working condition transmission path analysis speed is increased.

Description

Technical Field

[0001] The present invention relates to the technical field of function calculation related to a data processing method suitable for a specific function, and in particular to a time domain transfer rate function solution method, analysis method and computer program product. Background Art

[0002] As a highly efficient test method for NVH problems, operating condition transfer path analysis is widely used in various engineering problems. However, the frequency domain operating condition transfer path analysis method requires the test data to be converted from the time domain to the frequency domain, which will average the operating condition response data, limiting the application of frequency domain operating condition transfer path analysis and only applicable to steady-state conditions or quasi-steady-state conditions. At the same time, the time domain classical transfer path analysis applicable to transient conditions is similar to the frequency domain classical transfer path in principle. It requires the unit pulse response function of the test system and the operating condition load force to calculate the path contribution. Although it has high accuracy, it has low efficiency and long processing time.

[0003] In order to ensure the high efficiency of the test, the time domain working condition transfer path analysis method is introduced. However, unlike the frequency domain working condition transfer path analysis method, the dimension of the indicator point response data matrix in the time domain is often much larger than the frequency domain matrix, and the efficiency of the matrix inversion operation is too low, which makes the commonly used Tikhonov regularization-based transfer function solution method in the frequency domain not applicable in the time domain. Therefore, there is an urgent need for a transfer function solution method that can be applied to the time domain working condition transfer path analysis to improve the solution speed of the time domain transfer function. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a time domain transfer rate function solution method, analysis method and computer program product, which can improve the speed of solving the time domain transfer rate function. The specific technical solution is as follows:

[0005] In a first aspect, a method for solving a time domain transfer rate function is provided. In a first implementable manner of the first aspect, the method includes:

[0006] Convert the constructed time domain working condition transfer path analysis equation into a quadratic function;

[0007] The conjugate gradient algorithm is used to solve the quadratic function and obtain the corresponding time-domain transmissibility function.

[0008] In combination with the first implementable manner of the first aspect, in a second implementable manner of the first aspect, the constructed time domain operating condition transfer path analysis equation is converted into a quadratic function, including:

[0009] Discretizing the time domain operating condition transfer path analysis equation to obtain a corresponding matrix equation;

[0010] Determine a conjugate transposed matrix corresponding to the indicator point response matrix in the matrix equation, and convert the indicator point response matrix in the matrix equation into a positive definite matrix by using the conjugate transposed matrix;

[0011] The quadratic function is constructed based on the transformed matrix equation.

[0012] In combination with the first implementable manner of the first aspect, in a third implementable manner of the first aspect, constructing a time domain operating condition transfer path analysis equation includes:

[0013] According to the response signals of the indicating point and the target point on the transmission path under different working conditions, the time domain response function corresponding to the indicating point and the target point, as well as the working condition load force function are determined respectively;

[0014] Based on the time domain response function corresponding to the indication point and the target point, and the working condition load force function, the time domain working condition transfer path analysis equation is constructed.

[0015] In combination with the first implementable manner of the first aspect, in a fourth implementable manner of the first aspect, a conjugate gradient algorithm is used to solve the quadratic function, including:

[0016] Setting an initial time domain transfer rate value, and determining an initial search direction by the time domain transfer rate value;

[0017] Calculate the iteration step size according to the current search direction;

[0018] Based on the current search direction, the time domain transfer rate value and the iteration step size, the current time domain transfer rate value of the quadratic function is updated;

[0019] Calculating the gradient value of the quadratic function with respect to the updated time-domain transfer rate value, and determining the search direction of the next iteration according to the gradient value and the current search direction;

[0020] The iteration is repeated until the convergence condition is met, and the time domain transfer rate function is obtained.

[0021] In combination with the fourth implementable manner of the first aspect, in a fifth implementable manner of the first aspect, determining the search direction of the next iteration according to the gradient value and the current search direction includes:

[0022] Calculate the iteration coefficient corresponding to the next iteration according to the current gradient value and the updated gradient value;

[0023] Based on the iteration coefficient, the search direction for the next iteration is calculated in combination with the current search direction and the updated gradient value.

[0024] In a second aspect, a time domain operating condition transfer path analysis method is provided, comprising:

[0025] Using the time domain transferability function solving method as described in any one of the first to fifth possible implementations of the first aspect to construct a time domain transferability function;

[0026] The response of the transfer path under different working conditions is calculated by constructing the time domain transmissibility function.

[0027] In a third aspect, a computer program product is provided, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the method for solving the time domain transfer rate function as described in any one of the first to fifth possible implementations of the first aspect.

[0028] In a fourth aspect, a computer program product is provided, comprising a computer program / instruction, wherein when the computer program / instruction is executed by a processor, the steps of the time domain operating condition transfer path analysis method as described in the second aspect are implemented.

[0029] Beneficial effect: The time-domain transfer rate function solution method, analysis method and computer program product of the present invention can provide a basis for the subsequent use of the conjugate gradient algorithm to solve the time-domain transfer rate function by converting the time-domain operating condition transfer path analysis equation into a quadratic function. By using the conjugate gradient algorithm to solve the converted quadratic function, a transfer rate function suitable for time-domain operating condition transfer path analysis can be quickly obtained, thereby improving the speed of time-domain operating condition transfer path analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the specific implementation of the present invention, the following will briefly introduce the drawings required for use in the specific implementation. In all the drawings, each element or part is not necessarily drawn according to the actual scale.

[0031] Figure 1 A flow chart of a method for solving a time domain transfer rate function provided by an embodiment of the present invention;

[0032] Figure 2 A flow chart of a time domain operating condition transfer path analysis method provided by an embodiment of the present invention;

[0033] Figure 3 The figure is a comparison chart of the results of the analysis method of the present invention and the analysis method using Tikhonov regularization solution. DETAILED DESCRIPTION

[0034] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0035] like Figure 1The flowchart of the method for solving the time domain transmissibility function is shown in FIG. 1 , and the method for solving the time domain transmissibility function includes:

[0036] Step 1: Convert the constructed time domain working condition transfer path analysis equation into a quadratic function;

[0037] Step 2: Use the conjugate gradient algorithm to solve the quadratic function and obtain the corresponding time domain transfer rate function.

[0038] Specifically, first, the constructed time-domain working condition transfer path analysis equation can be transformed to express the relationship between the target point and the indicator point on the time-domain working condition transfer path in the form of a matrix equation, and the corresponding quadratic function can be obtained. Then, the conjugate gradient algorithm can be used to solve the quadratic function to quickly obtain the transfer rate function suitable for the time-domain working condition transfer path analysis, so as to improve the speed of the time-domain working condition transfer path analysis.

[0039] In order to verify the technical effect of the solution method disclosed in this embodiment, a time domain working condition transfer path analysis experiment was carried out on a steel simulated frame.

[0040] In the test scenario, the whole steel simulated vehicle frame is supported by three vibration isolation air cushions, and the active end is connected to the passive end through two vibration isolation blocks. Indicator point 1 and indicator point 2 are set on the passive end steel frame close to the vibration isolation block, and the target point is set on the passive end steel frame. Three B&K 4524B accelerometers are placed at indicator point 1, indicator point 2, and target point.

[0041] The vertical acceleration of the target point obtained by the acceleration sensor is the acceleration of interest in the test, so there are 6 paths from the indication point to the target point, recorded as path 1 to path 6, path 1 corresponds to indication point 1x to target point z, path 2 corresponds to indication point 1y to target point z, path 3 corresponds to indication point 1z to target point z, path 4 corresponds to indication point 2x to target point z, path 5 corresponds to indication point 2y to target point z, and path 6 corresponds to indication point 2z to target point z. The specific implementation steps of the test are:

[0042] (1) The tapping method is used to obtain the time domain response signals of the target point and the indicator point to ensure that the responses of each group of working conditions have little influence on each other;

[0043] (2) The test uses 6 sets of operating data to solve the time domain transfer rate function and then conducts time domain transfer path analysis.

[0044] (3) The discrete length of the time domain transfer rate function is set to 1024, the first 5 seconds of data are intercepted for calculation, and the time domain transfer rate function optimization model based on the conjugate gradient method is established.

[0045] (4) Under the premise of keeping the test scene and test conditions unchanged, use a hammer to hit the position different from that obtained in the first 6 groups of working conditions, so that the working condition data remain independent, recorded as working conditions 7 to 8. Then perform convolution calculation with the time domain transfer rate function calculated from working conditions 1 to 6 to obtain the predicted target point time domain response of working conditions 7 to 8, and compare it with the time domain response data of the measured target point.

[0046] To illustrate the accuracy of the method of the present invention, Tikhonov regularization was used to solve the time domain transmissibility function as a comparison group, and the relative error was used to quantify the error between the method of the present invention and the comparison group method, and the calculation speed between the method of the present invention and the control group was compared. The comparison results are shown in Figure 2. Figure 3 As shown, Figure 3 The following is a comparison chart of the synthetic and actual measured responses of the target point responses for conditions 1 to 6 under the two methods. The errors of the two methods are shown in the following table:

[0047] Working condition number 1 2 3 4 5 6 Time consumed / s Error of the method of the present invention (%) 3.34 3.24 3.99 3.19 3.67 4.20 68 Control group error (%) 3.64 3.75 4.35 3.38 3.89 4.62 134

[0048] The frequency domain transfer rate function obtained in this embodiment and the acceleration response signal of the obtained indication point are used to establish the working condition transfer path analysis relationship, obtain the predicted target point response, and compare it with the actual measured target point response. The relative error is used to quantify the error between the method of the present invention and the comparison group method, and the calculation speed between the method of the present invention and the control group is compared. The results are shown in the following table:

[0049] Working condition number 7 8 Time consumed / s Error of the method of the present invention (%) 3.55 3.67 6.87 Control group error (%) 3.86 3.92 14.21

[0050] Comparison of the two shows that the calculation error of the method of the present invention is smaller, the prediction effect is better, the relative error is smaller, and the calculation speed is faster. This proves that the solution method provided by this embodiment can effectively improve the speed of time domain working condition transfer path analysis and has certain engineering application value.

[0051] In this embodiment, optionally, constructing a time domain operating condition transfer path analysis equation includes:

[0052] According to the response signals of the indicating point and the target point on the transmission path under different working conditions, the time domain response function corresponding to the indicating point and the target point, as well as the working condition load force function are determined respectively;

[0053] Based on the time domain response function corresponding to the indication point and the target point, and the working condition load force function, the time domain working condition transfer path analysis equation is constructed.

[0054] Specifically, when constructing the time domain working condition transfer path analysis equation, we can first construct the frequency domain response function of the target point and the indicator point, and simplify the constructed frequency domain response function, specifically:

[0055]

[0056] Among them, y(t) represents the time domain response of the target point; x(t) represents the time domain response of the indicator point; t and σ both represent time variables, and h x (t) represents the unit impulse response function from the excitation point to the indication point, h y (t) represents the unit impulse response function from the excitation point to the target point, f(t) represents the working load force, and * represents the convolution operator.

[0057] At the same time, the deconvolution function can be used to calculate the working load, specifically:

[0058]

[0059] Among them, s ψ is a deconvolution filtering system, τ' represents the time variable, and x(t-τ') represents the time domain response of the indicated point.

[0060] Then, based on the time domain response function corresponding to the indicated point and the target point, and the working condition load function, the time domain working condition transfer path analysis equation is constructed, which is specifically:

[0061] y(t)=h y (t)*s ψ (txt);

[0062] Then we can get:

[0063] y(t)=h t (txt);

[0064] Among them, h t (t) = h y (t)*s ψ (t);h t (t) is called the time domain transfer rate function.

[0065] When the number of indicating points is limited, the time domain operating condition transfer path analysis equation can be expressed as:

[0066]

[0067] The contribution of each path between the target point and the indicated point can be calculated through the time domain transfer rate function.

[0068] In this embodiment, optionally, in step 1, the constructed time domain operating condition transfer path analysis equation is converted into a quadratic function, including:

[0069] Discretizing the time domain operating condition transfer path analysis equation to obtain a corresponding matrix equation;

[0070] Determine a conjugate transposed matrix corresponding to the indicator point response matrix in the matrix equation, and convert the indicator point response matrix in the matrix equation into a positive definite matrix by using the conjugate transposed matrix;

[0071] The quadratic function is constructed based on the transformed matrix equation.

[0072] Specifically, when converting the time domain working condition transfer path analysis equation, the time domain working condition transfer path analysis equation can be discretized first and expressed in the form of a matrix equation, specifically:

[0073]

[0074] Where i represents the number of working conditions and N represents the number of indication points.

[0075] Y i (t) = [y i (0)y i (△t)…y i ((n-1)△t)] H ;

[0076]

[0077] Among them, △t represents the sampling time interval, n is the sequence length after the time domain response is discretized, G is the length of the time domain transfer rate function, X ij Represents the filter matrix of the jth indicator point response under the i-th working condition, Represents the jth time-domain transfer rate function.

[0078] When there are M groups of operating conditions, the discretized time domain operating condition transfer path analysis equation can be expressed as:

[0079]

[0080] Since the above indicator point response matrix X is asymmetric and not positive definite, the conjugate transposed matrix X of the indicator point response matrix can be multiplied on both sides of the above expression. H , thereby converting the indicator point response matrix in the matrix equation into a positive definite matrix, specifically:

[0081] X H Y=X H XH t ;

[0082] Let B = X H Y, A = X H X, in this case, A is a symmetric matrix, from which we can get:

[0083] B-AH t=0;

[0084] In this way, a quadratic function can be constructed, specifically:

[0085]

[0086] Among them, p, q represent the dimensions of the matrix, a qp represents the element in the qth row and pth column of the A matrix. Similarly, b p represents the element of the pth row of the B matrix, h p Represents the element of the pth row of the H matrix

[0087] Since the A matrix becomes a positive definite matrix, the time domain transfer function H t The inverse problem becomes a problem of minimizing a quadratic function. The solution when its partial derivative is equal to 0 is the desired time-domain transfer rate function.

[0088] In this embodiment, optionally, in step 2, a conjugate gradient algorithm is used to solve the quadratic function, including:

[0089] Setting an initial time domain transfer rate value, and determining an initial search direction by the time domain transfer rate value;

[0090] Calculate the iteration step size according to the current search direction;

[0091] Based on the current search direction, the time domain transfer rate value and the iteration step size, the current time domain transfer rate value of the quadratic function is updated;

[0092] Calculating the gradient value of the quadratic function with respect to the updated time-domain transfer rate value, and determining the search direction of the next iteration according to the gradient value and the current search direction;

[0093] The iteration is repeated until the convergence condition is met, and the time domain transfer rate function is obtained.

[0094] Specifically, when solving a quadratic function, we can first set the initial time domain transfer rate value The initial search direction is determined by the time domain transfer rate value. The specific calculation formula for the search direction is as follows:

[0095]

[0096] After calculating the initial search direction, the iteration step length can be calculated according to the current search direction. The specific calculation formula is as follows:

[0097]

[0098] Where k is the number of iterations.

[0099] Then, the time domain transfer rate value of the quadratic function is updated in combination with the current search direction, the time domain transfer rate value and the iteration step size. The specific calculation formula of the time domain transfer rate value is as follows:

[0100]

[0101] Then, the gradient value of the updated time domain transfer rate value is calculated according to the calculated time domain transfer rate value, and the search direction of the next iteration is determined according to the gradient value and the current search direction. The specific calculation formula is as follows:

[0102]

[0103] d k+1 =-r k+1 +β k+1 d k ;

[0104] Among them, β k+1 is the iteration coefficient.

[0105] After the search direction of the next iteration is calculated, the iteration step size of the next iteration can be calculated according to the above-mentioned calculation formula of the iteration step size, and the time domain transfer rate value of the quadratic function is continuously updated in combination with the next search direction, the updated time domain transfer rate value and the next iteration step size. This is repeated until the convergence condition is met to complete the iteration and obtain the time domain transfer rate function. In this embodiment, the convergence condition can be set as |r k |<ξ, where ζ is a preset convergence threshold.

[0106] In this embodiment, optionally, determining the search direction of the next iteration according to the gradient value and the current search direction includes:

[0107] Calculate the iteration coefficient corresponding to the next iteration according to the current gradient value and the updated gradient value;

[0108] Based on the iteration coefficient, the search direction for the next iteration is calculated in combination with the current search direction and the updated gradient value.

[0109] Specifically, when calculating the search direction of the next iteration, the iteration coefficient corresponding to the next iteration can be calculated based on the current gradient value and the updated gradient value. The specific calculation formula is as follows:

[0110]

[0111] Then, the search direction of the next iteration is calculated based on the iteration coefficient, combined with the current search direction and the updated gradient value. The specific calculation formula is as follows:

[0112] d k+1=-r k+1 +β k+1 d k .

[0113] like Figure 2 The flow chart of the time domain working condition transfer path analysis method shown in FIG. 1 includes:

[0114] Step S1, using the above-mentioned time domain transfer rate function solution method to construct a time domain transfer rate function;

[0115] Step S2: Calculate the response of the transfer path under different working conditions by using the constructed time domain transfer rate function.

[0116] Specifically, first, the above-mentioned time domain transfer rate function solution method can be used to quickly construct a time domain transfer rate function. Then, the contribution of each path between the target point and the indicated point can be calculated through the time domain transfer rate function, thereby achieving the purpose of time domain working condition transfer path analysis.

[0117] A computer program product includes a computer program / instruction, wherein when the computer program / instruction is executed by a processor, the steps of the time domain transfer rate function solution method are implemented.

[0118] A computer program product includes a computer program / instruction, wherein when the computer program / instruction is executed by a processor, the steps of the above-mentioned time domain operating condition transfer path analysis method are implemented.

[0119] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for solving a time domain transferability function, characterized in that: include: Convert the constructed time domain working condition transfer path analysis equation into a quadratic function; The conjugate gradient algorithm is used to solve the quadratic function and obtain the corresponding time-domain transmissibility function.

2. The method for solving the time domain transferability function according to claim 1, characterized in that: The constructed time domain operating condition transfer path analysis equation is converted into a quadratic function, including: Discretizing the time domain operating condition transfer path analysis equation to obtain a corresponding matrix equation; Determine a conjugate transposed matrix corresponding to the indicator point response matrix in the matrix equation, and convert the indicator point response matrix in the matrix equation into a positive definite matrix by using the conjugate transposed matrix; The quadratic function is constructed based on the transformed matrix equation.

3. The method for solving the time domain transferability function according to claim 1, characterized in that: Construct the time domain operating condition transfer path analysis equation, including: According to the response signals of the indicating point and the target point on the transmission path under different working conditions, the time domain response function corresponding to the indicating point and the target point, as well as the working condition load force function are determined respectively; Based on the time domain response function corresponding to the indication point and the target point, and the working condition load force function, the time domain working condition transfer path analysis equation is constructed.

4. The method for solving the time domain transferability function according to claim 1, characterized in that: The conjugate gradient algorithm is used to solve quadratic functions, including: Setting an initial time domain transfer rate value, and determining an initial search direction by the time domain transfer rate value; Calculate the iteration step size according to the current search direction; Based on the current search direction, the time domain transfer rate value and the iteration step size, the current time domain transfer rate value of the quadratic function is updated; Calculating the gradient value of the quadratic function with respect to the updated time-domain transfer rate value, and determining the search direction of the next iteration according to the gradient value and the current search direction; The iteration is repeated until the convergence condition is met, and the time domain transfer rate function is obtained.

5. The method for solving the time domain transferability function according to claim 4, characterized in that: Determining the search direction of the next iteration according to the gradient value and the current search direction includes: Calculate the iteration coefficient corresponding to the next iteration according to the current gradient value and the updated gradient value; Based on the iteration coefficient, the search direction for the next iteration is calculated in combination with the current search direction and the updated gradient value.

6. A time domain operating condition transfer path analysis method, characterized in that: include: Using the time domain transfer rate function solution method as described in any one of claims 1 to 5 to construct a time domain transfer rate function; The response of the transfer path under different working conditions is calculated by constructing the time domain transmissibility function.

7. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for solving the time domain transfer rate function as described in any one of claims 1-5 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the time domain operating condition transfer path analysis method as claimed in claim 6 are implemented.

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