Time-domain transfer function solving method, analysis method, and computer program product

Abstract

The application discloses a time-domain transfer rate function solving method, an analysis method and a computer program product, and comprises the following steps: firstly, a time-domain working condition transfer path analysis equation is converted, so that the relationship between a target point and an indicator point on a time-domain working condition transfer path is expressed in the form of a matrix equation, and a corresponding quadratic function is obtained. Then, a conjugate gradient algorithm is used to solve the quadratic function, so that a transfer rate function suitable for time-domain working condition transfer path analysis is quickly obtained, and the time-domain working condition transfer path analysis speed is improved.

Description

Technical Field

[0001] This invention relates to the technical field of calculating relevant functions in data processing methods applicable to specific functions, specifically to a method for solving the time-domain transfer rate function, an analysis method, and a computer program product. Background Technology

[0002] Transfer path analysis, as a highly efficient testing method for NVH (Noise, Vibration, and Harshness) issues, is widely used in various engineering problems. However, frequency-domain transfer path analysis requires converting the test data from the time domain to the frequency domain, which averages the test response data, limiting its application to steady-state or quasi-steady-state conditions. Meanwhile, classical time-domain transfer path analysis, applicable to transient conditions, is similar in principle to classical frequency-domain transfer path analysis, requiring the test system's unit impulse response function and load force to calculate the path contribution. While offering high accuracy, it is less efficient and time-consuming.

[0003] To ensure high testing efficiency, a time-domain transfer path analysis method is introduced. However, unlike the frequency-domain transfer path analysis method, the dimension of the indicator point response data matrix in the time domain is often much larger than that in the frequency domain, resulting in low efficiency during matrix inversion. This renders the commonly used Tikhonov regularization-based transfer rate function solution method in the frequency domain unsuitable for the time domain. Therefore, there is an urgent need for a transfer rate function solution method applicable to time-domain transfer path analysis, which can improve the solution speed of the time-domain transfer rate function. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method, analysis method, and computer program product for solving the time-domain transfer function, which can improve the solution speed of the time-domain transfer function. The specific technical solution is as follows:

[0005] Firstly, a method for solving the time-domain transfer rate function is provided. In a first possible implementation of this method, the method includes:

[0006] The constructed time-domain load condition transfer path analysis equations are transformed into quadratic functions;

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

[0008] In conjunction with the first feasible approach of the first aspect, the second feasible approach of the first aspect transforms the constructed time-domain load condition transfer path analysis equation into a quadratic function, including:

[0009] Discretize the time-domain load condition transmission path analysis equations to obtain the corresponding matrix equations;

[0010] Determine the conjugate transpose 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 using the conjugate transpose matrix;

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

[0012] Combining the first feasible approach of the first aspect, in the third feasible approach of the first aspect, the time-domain load condition transfer path analysis equations are constructed, including:

[0013] Based on the response signals of the indicator point and the target point on the transmission path under different working conditions, the time domain response function and the working condition load force function corresponding to the indicator point and the target point are determined respectively.

[0014] Based on the time-domain response functions corresponding to the indicated point and the target point, as well as the load force function under the working condition, the time-domain working condition transmission path analysis equation is constructed.

[0015] In conjunction with the first feasible method of the first aspect, the fourth feasible method of the first aspect employs the conjugate gradient algorithm to solve the quadratic function, including:

[0016] Set an initial time-domain transfer rate value, and determine the initial search direction using this time-domain transfer rate value;

[0017] Calculate the iteration step size based on the current search direction;

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

[0019] Calculate the gradient of the quadratic function with respect to the updated time-domain transfer rate, and determine the search direction for the next iteration based on the gradient and the current search direction;

[0020] This process is repeated until the convergence condition is met, yielding the time-domain transfer rate function.

[0021] In conjunction with the fourth possible implementation of the first aspect, the fifth possible implementation of the first aspect involves determining the search direction for the next iteration based on the gradient value and the current search direction, including:

[0022] Calculate the iteration coefficients for the next iteration based on the current gradient value and the updated gradient value;

[0023] Based on the iteration coefficients, the search direction for the next iteration is calculated by combining the current search direction and the updated gradient value.

[0024] Secondly, a method for analyzing time-domain operating conditions and transmission paths is provided, including:

[0025] The time-domain transfer rate function is constructed by employing any of the first to fifth implementable methods described in the first aspect;

[0026] The response of the transmission path under different operating conditions is calculated by constructing a time-domain transfer rate function.

[0027] Thirdly, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the steps of the time-domain transfer rate function solution method as described in any of the first to fifth implementable embodiments of the first aspect.

[0028] Fourthly, a computer program product is provided, including a computer program / instruction, characterized in that, when the computer program / instruction is executed by a processor, it implements the steps of the time-domain operating condition transmission path analysis method as described in the second aspect.

[0029] Beneficial effects: By using the time-domain transferability function solution method, analysis method and computer program product of the present invention, the time-domain operating condition transfer path analysis equation is transformed into a quadratic function, which can provide a basis for subsequent solution of the time-domain transferability function using the conjugate gradient algorithm. The conjugate gradient algorithm can be used to solve the transformed quadratic function, which can quickly obtain the transferability function suitable for time-domain operating condition transfer path analysis, thereby improving the speed of time-domain operating condition transfer path analysis. Attached Figure Description

[0030] To more clearly illustrate the specific embodiments of the present invention, the accompanying drawings used in the specific embodiments will be briefly described below. In all the drawings, the elements or parts are not necessarily drawn to scale.

[0031] Figure 1 This is a flowchart of a method for solving the time-domain transfer rate function according to an embodiment of the present invention;

[0032] Figure 2 A flowchart of a time-domain load condition transmission path analysis method provided in an embodiment of the present invention;

[0033] Figure 3 This is a comparison chart of the results of the analysis method of the present invention and the analysis method using Tikhonov regularization. Detailed Implementation

[0034] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0035] like Figure 1The flowchart shown illustrates the method for solving the time-domain transferability function. This method includes:

[0036] Step 1: Transform the constructed time-domain load condition transfer path analysis equations into quadratic functions;

[0037] Step 2: Solve the quadratic function using the conjugate gradient algorithm to obtain the corresponding time-domain transfer rate function.

[0038] Specifically, firstly, the constructed time-domain load transfer path analysis equations can be transformed to represent the relationship between target points and indicator points on the time-domain load transfer path as matrix equations, yielding the corresponding quadratic form function. Then, the conjugate gradient algorithm can be used to solve the quadratic form function, thereby quickly obtaining the transfer rate function suitable for time-domain load transfer path analysis, thus improving the speed of time-domain load transfer path analysis.

[0039] To verify the technical effectiveness of the solution method disclosed in this embodiment, a time-domain operating condition transfer path analysis experiment was conducted on a steel simulated vehicle frame.

[0040] In the test scenario, the overall steel simulated vehicle frame was supported by three vibration-damping air cushions, with the active end connected to the passive end via two vibration-damping blocks. Indicator points 1 and 2 were set on the passive end steel frame near the vibration-damping blocks, and a target point was set on the passive end steel frame. Three B&K 4524B accelerometers were placed at indicator points 1, 2, and the target point.

[0041] The vertical acceleration of the target point acquired by the accelerometer is the acceleration of interest in the experiment. Therefore, there are 6 paths from the indicator point to the target point, denoted as paths 1 to 6. Path 1 corresponds to the path from indicator point 1x to target point z, path 2 corresponds to the path from indicator point 1y to target point z, path 3 corresponds to the path from indicator point 1z to target point z, path 4 corresponds to the path from indicator point 2x to target point z, path 5 corresponds to the path from indicator point 2y to target point z, and path 6 corresponds to the path from indicator point 2z to target point z. The specific implementation steps of the experiment are as follows:

[0042] (1) The time-domain response signals of the target point and the indicator point are obtained by tapping method to ensure that the acquired response signals of each working condition have little mutual influence.

[0043] (2) The experiment used 6 sets of operating condition data to solve the time-domain transfer rate function and then performed time-domain transfer path analysis.

[0044] (3) Set the discrete length of the time-domain transfer rate function to 1024, extract the data from the first 5 seconds for calculation, and establish an optimization model of the time-domain transfer rate function based on the conjugate gradient method.

[0045] (4) While keeping the test scenario and test conditions unchanged, use a hammer to strike a different location than when the data was obtained in the first 6 test conditions, so that the test condition data remain independent, and record them as test conditions 7 to 8. Then perform convolution calculation with the time domain transfer rate function calculated from test conditions 1 to 6 to obtain the predicted target point time domain response of test conditions 7 to 8, and compare it with the measured target point time domain response data.

[0046] To illustrate the accuracy of the method of this invention, a Tikhonov regularization solution for the time-domain transfer rate function was used as a control group. Relative error quantification was employed to compare the error between the method of this invention and the control group, and the computational speed of the method of this invention was compared with that of the control group. The comparison results are as follows: Figure 3 As shown, Figure 3 The graph shows a comparison between the synthesized target point responses and the actual measured responses under the two methods for conditions 1 to 6. The errors of the two methods are shown in the table below:

[0047] Error (%) of the method of this invention 3.34 3.24 3.99 3.19 3.67 4.20 68 Error (%) in the control group 3.64 3.75 4.35 3.38 3.89 4.62 134

[0048] The frequency domain transfer rate function obtained in this embodiment is used to establish a working condition transfer path analysis formula with the acceleration response signal of the obtained indicator point. The predicted target point response is then obtained and compared with the actual measured target point response. Relative error quantification is used to differentiate the error between the method of this invention and the control group method, and the calculation speed of the method of this invention is compared with that of the control group. The results are shown in the table below:

[0049] Error (%) of the method of this invention 3.55 3.67 6.87 Error (%) in the control group 3.86 3.92 14.21

[0050] A comparison of the two methods shows that the method of this invention has smaller calculation errors, better prediction results, smaller relative errors, and faster calculation speed. This demonstrates that the solution method provided in this embodiment can effectively improve the speed of time-domain load condition transfer path analysis and has certain engineering application value.

[0051] In this embodiment, optionally, the time-domain load condition transfer path analysis equations are constructed, including:

[0052] Based on the response signals of the indicator point and the target point on the transmission path under different working conditions, the time domain response function and the working condition load force function corresponding to the indicator point and the target point are determined respectively.

[0053] Based on the time-domain response functions corresponding to the indicated point and the target point, as well as the load force function under the working condition, the time-domain working condition transmission path analysis equation is constructed.

[0054] Specifically, when constructing the time-domain load transfer path analysis equations, the frequency domain response functions of the target point and the indicator point can be constructed first, and then simplified as follows:

[0055]

[0056] Where 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 load force under the working condition, and * represents the convolution operator.

[0057] Simultaneously, the deconvolution function can be used to calculate the load under the working condition, specifically:

[0058]

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

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

[0061] y(t)=h y (t)*s ψ (txt);

[0062] Therefore, we can obtain:

[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 indicator points is finite, the time-domain load condition transmission path analysis equation can be expressed as:

[0066]

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

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

[0069] Discretize the time-domain load condition transmission path analysis equations to obtain the corresponding matrix equations;

[0070] Determine the conjugate transpose 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 using the conjugate transpose matrix;

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

[0072] Specifically, when transforming the time-domain load condition transfer path analysis equations, the equations can first be discretized and expressed as matrix equations, as follows:

[0073]

[0074] Where i represents the number of operating conditions and N represents the number of indicator points.

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

[0076]

[0077] Where Δt represents the sampling time interval, n is the length of the discretized time-domain response sequence, G is the length of the time-domain transfer rate function, and X... ij The filter matrix represents the response of the j-th indicator point under the i-th operating condition. This represents the j-th time-domain transfer rate function.

[0078] When there are M sets of working conditions, the discretized time-domain working condition propagation path analysis equation can be expressed as:

[0079]

[0080] Since the indicator response matrix X is asymmetric and non-positive definite, both sides of the above expression can be multiplied by the conjugate transpose of the indicator response matrix X. H This transforms 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, where A is a symmetric matrix, from which we can obtain:

[0083] B-AH t=0;

[0084] This allows us to construct a quadratic form function, specifically:

[0085]

[0086] Where p and q represent the dimensions of the matrix, a qp This represents the element in the q-th row and p-th column of matrix A. Similarly, b p h represents the element in the p-th row of matrix B. p Represents the elements of the p-th row of the H matrix

[0087] Since matrix A has become a positive definite matrix, the time-domain transfer rate function H will then be solved. t The problem of finding the inverse of the form becomes a problem of finding the minimum value of a quadratic function. The solution when its partial derivative is equal to 0 is the time-domain transfer rate function we are looking for.

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

[0089] Set an initial time-domain transfer rate value, and determine the initial search direction using this time-domain transfer rate value;

[0090] Calculate the iteration step size based on the current search direction;

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

[0092] Calculate the gradient of the quadratic function with respect to the updated time-domain transfer rate, and determine the search direction for the next iteration based on the gradient and the current search direction;

[0093] This process is repeated until the convergence condition is met, yielding the time-domain transfer rate function.

[0094] Specifically, when solving for a quadratic function, one can first set an initial time-domain transfer rate value. The initial search direction is determined using this time-domain transfer rate value. The specific formula for calculating the search direction is as follows:

[0095]

[0096] After obtaining the initial search direction, the iteration step size can be calculated based on the current search direction. The specific calculation formula is as follows:

[0097]

[0098] Where k is the number of iterations.

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

[0100]

[0101] Then, the gradient value of the updated time-domain transferability is calculated based on the calculated time-domain transferability value, and the search direction for the next iteration is determined based on 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] Where, β k+1 These are the iteration coefficients.

[0105] After calculating the search direction for the next iteration, the iteration step size for the next iteration can be calculated using the formula described above. Combining the next search direction, the updated time-domain transferability value, and the next iteration step size, the time-domain transferability value of the quadratic function is updated. This process is repeated until the convergence condition is met, completing the iteration and obtaining the time-domain transferability function. In this embodiment, the convergence condition can be set as |r... k |<ξ, where ζ is a pre-set convergence threshold.

[0106] In this embodiment, optionally, determining the search direction for the next iteration based on the gradient value and the current search direction includes:

[0107] Calculate the iteration coefficients for the next iteration based on the current gradient value and the updated gradient value;

[0108] Based on the iteration coefficients, the search direction for the next iteration is calculated by combining the current search direction and the updated gradient value.

[0109] Specifically, when calculating the search direction for the next iteration, the iteration coefficients for 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, based on the iteration coefficients, combined with the current search direction and the updated gradient value, the search direction for the next iteration is calculated. The specific calculation formula is as follows:

[0112] d k+1=-r k+1 +β k+1 d k .

[0113] like Figure 2 The flowchart shown illustrates the time-domain load condition transfer path analysis method, which includes:

[0114] Step S1: Using the above-described method for solving the time-domain transfer rate function, construct the time-domain transfer rate function;

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

[0116] Specifically, firstly, the time-domain transferability function can be quickly constructed using the aforementioned method. Then, the contribution of each path between the target point and the indicator point can be calculated using the time-domain transferability function, thus achieving the purpose of time-domain load condition transfer path analysis.

[0117] A computer program product includes a computer program / instructions, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of the above-described time-domain transfer rate function solution method.

[0118] A computer program product includes a computer program / instructions, characterized in that, when the computer program / instructions are executed by a processor, they implement the steps of the above-described time-domain operating condition transmission path analysis method.

[0119] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A time-domain operating condition transmission path analysis method, targeting NVH problems, characterized in that, include: Based on the response signals of the indicator point and the target point on the transmission path under different working conditions, the time domain response function and the working condition load force function corresponding to the indicator point and the target point are determined respectively. Based on the time-domain response functions corresponding to the indicated point and the target point, as well as the load force function under the working condition, the time-domain working condition transmission path analysis equation is constructed. The constructed time-domain load condition transfer path analysis equations are transformed into quadratic functions; The conjugate gradient algorithm is used to solve the quadratic function to obtain the corresponding time-domain transferability function; By establishing the working condition transfer path analysis formula with the time-domain transfer rate function and the time-domain acceleration response signal of the indicator point, the predicted target point response can be obtained.

2. The time-domain operating condition transmission path analysis method according to claim 1, characterized in that, The constructed time-domain load condition transfer path analysis equations are transformed into quadratic functions, including: Discretize the time-domain load condition transmission path analysis equations to obtain the corresponding matrix equations; Determine the conjugate transpose 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 using the conjugate transpose matrix; The quadratic function is constructed based on the transformed matrix equation.

3. The time-domain operating condition transmission path analysis method according to claim 1, characterized in that, The conjugate gradient algorithm is used to solve quadratic functions, including: Set an initial time-domain transfer rate value, and determine the initial search direction using this time-domain transfer rate value; Calculate the iteration step size based on the current search direction; Based on the current search direction, time-domain transfer rate value, and iteration step size, update the current time-domain transfer rate value of the quadratic function; Calculate the gradient of the quadratic function with respect to the updated time-domain transfer rate, and determine the search direction for the next iteration based on the gradient and the current search direction; This process is repeated until the convergence condition is met, yielding the time-domain transfer rate function.

4. The time-domain operating condition transmission path analysis method according to claim 3, characterized in that, Determining the search direction for the next iteration based on the gradient value and the current search direction includes: Calculate the iteration coefficients for the next iteration based on the current gradient value and the updated gradient value; Based on the iteration coefficients, the search direction for the next iteration is calculated by combining the current search direction and the updated gradient value.

5. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the time-domain operating condition transmission path analysis method as described in claim 1.

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