阅读说明：本技术 一种基于正则化总体最小二乘法的工况传递路径分析方法 (Working condition transmission path analysis method based on regularization total least square method ) 是由 张志飞 唐中华 昝鸣 徐中明 贺岩松 于 2021-07-26 设计创作，主要内容包括：本发明公开一种基于正则化总体最小二乘法的工况传递路径分析方法,步骤为：1)确定若干指示点和若干目标点；2)在指示点和目标点布置响应信号监测装置,以监测该装置所在位置的响应信号；3)设置若干运行工况,并令机械设备在每一种工况下运行；响应信号监测装置监测指示点和目标点的响应信号,并发送至上位机；5)建立工况传递路径分析方程；6)求解得到传递率函数矩阵；7)根据传递率函数矩阵计算不同工况下各传递路径贡献量,并确定到各个传递路径的贡献量占比,完成工况传递路径分析。本发明方法克服了传统工况传递路径分析中忽略指示点数据误差的问题,提高了工况传递路径贡献量计算精度。(The invention discloses a working condition transmission path analysis method based on a regularization total least square method, which comprises the following steps: 1) determining a plurality of indication points and a plurality of target points; 2) arranging response signal monitoring devices at the indication points and the target points to monitor response signals of the positions of the devices; 3) setting a plurality of operating conditions, and enabling mechanical equipment to operate under each operating condition; the response signal monitoring device monitors response signals of the indication point and the target point and sends the response signals to the upper computer; 5) establishing a working condition transmission path analysis equation; 6) solving to obtain a transfer rate function matrix; 7) and calculating the contribution amount of each transfer path under different working conditions according to the transfer rate function matrix, determining the contribution amount ratio of each transfer path, and completing the analysis of the working condition transfer paths. The method provided by the invention overcomes the problem of neglecting the data error of the indication point in the traditional working condition transmission path analysis, and improves the calculation accuracy of the contribution of the working condition transmission path.)

1. A working condition transmission path analysis method based on a regularization total least square method is characterized by comprising the following steps:

1) determining a plurality of indication points and a plurality of target points; wherein the indication point is positioned in the area where the excitation source of the mechanical equipment is positioned; the distance between the indicating point and the excitation source in one area is less than h; the target point is the position to be observed of the mechanical equipment.

2) Arranging response signal monitoring devices at the indication points and the target points to monitor response signals of the positions of the devices;

3) setting a plurality of operating conditions, and enabling mechanical equipment to operate under each operating condition;

in the operation process of the mechanical equipment, the response signal monitoring device monitors response signals of the indication point and the target point and sends the response signals to the upper computer;

4) establishing a working condition transmission path analysis equation according to response signals of the indication point and the target point under different working conditions;

5) solving a working condition transfer path analysis equation by utilizing a Tikhonov regularization total least square method to obtain a transfer rate function matrix;

6) and calculating the contribution of each transfer path under different working conditions according to the transfer rate function matrix, obtaining the contribution ratio of each transfer path, and completing the analysis of the working condition transfer paths.

2. The working condition transmission path analysis method based on the Tikhonov regularization total least square method according to claim 1, characterized in that one indication point is arranged in the region where each excitation source is located.

3. The working condition transmission path analysis method based on the Tikhonov regularization total least square method according to claim 1, wherein the response signal monitoring device comprises an acceleration sensor, a microphone and/or a strain gauge; the acceleration sensor is used for monitoring an acceleration response signal; the microphone is used for monitoring the audio vibration response signal; the strain gauge is used to monitor the stress response signal.

4. The working condition transmission path analysis method based on the Tikhonov regularization total least square method according to claim 1, characterized in that the number of the set operating working conditions is greater than or equal to the number of the indicating points.

5. The working condition transmission path analysis method based on the Tikhonov regularization total least square method according to claim 1, characterized in that the working condition transmission path analysis equation is as follows:

Y＝XT (1)

in the formula, Y is a target point response matrix under different working conditions; x is an indication point response matrix under different working conditions; t is a transfer rate function matrix to be solved;

the working condition transmission path analysis equation expansion is as follows:

in the formula, r is the number of target points; n is the number of the indicating points; m is the number of working conditions;responding to the elements of the matrix Y for the target points under different working conditions;responding to the elements of the matrix X for the indication points under different working conditions; t is_nrIs the element of the transfer rate function matrix T to be solved.

6. The working condition transfer path analysis method based on the Tikhonov regularization total least square method according to claim 1, wherein the step of solving a working condition transfer path analysis equation to obtain a transfer rate function matrix comprises:

1) adding an error interference term into the operating condition transmission path analysis equation, thereby updating the operating condition transmission path analysis equation to obtain:

Y+ΔY＝(X+ΔX)T (3)

in the formula, Δ Y and Δ X are errors of the target point response matrix Y under different working conditions and the indication point response matrix X under different working conditions respectively;

2) establishing a Tikhonov regularization target function and a constraint condition of a total least square method, namely:

in the formula, L represents a regularization matrix; rho is a regularization parameter;

3) construction of Lagrange polynomialsNamely:

where μ is a Lagrange multiplier;

where Lagrange multiplier μ satisfies the following condition, (Δ X, Δ Y) is an optimal solution, that is:

in the formula (I), the compound is shown in the specification,represents a gradient;refers toLagrange polynomials;

4) combining the formula (4) and the formula (6), solving to obtain an error delta Y of the target point response matrix Y under different working conditions and an error delta X of the indication point response matrix X under different working conditions, namely:

5) substituting the formula (7) into the formula (4), updating the objective function to obtain:

6) and solving by using an iterative method to obtain a regularized total least square solution T of the transmissibility matrix.

7. The working condition transmission path analysis method based on the Tikhonov regularization total least square method according to claim 6, wherein the step of solving the regularization total least square solution T of the obtained transmissibility matrix comprises:

1) given a calculation parameter lambda_LAn initial value;

2) setting the iteration initial value of the regularized total least square solution as T ═ X^HX)^TX^HY；

3) Updating the parameter lambda_INamely:

4) calculating an updated regularized overall least squares solution T, i.e.:

T＝(X^HX+λ_II+λ_LL^HL)^-1X^HY (10)

in the formula, λ_IAnd λ_LTo calculate the parameters;

5) returning to the step 3) until the | | | T is met^k-T^k-1||₂＜ε＝10^-3；

6) Let lambda_L＝λ_L+Δλ_LAnd returning to step 2) until lambda_L≥λ_Lmax；Δλ_LFor calculating a parameter lambda_LThe iteration step size of (2); lambda [ alpha ]_LmaxFor calculating a parameter lambda_LThe iteration threshold of (2);

7) at each lambda_LCalculated parametersAnd parametersDrawing an L curve for the coordinate; regularization parameter lambda corresponding to the maximum point of curvature of the L-curve_LThe optimal regularization parameter value; and substituting (10) the optimal regularization parameter value to calculate a regularization total least square solution T.

8. The working condition transfer path analysis method based on the Tikhonov regularization total least square method according to claim 1, characterized in that the contribution of each transfer path under different working conditions is the product of the response signal of the indication point under different working conditions and the transfer rate function matrix.

Technical Field

The invention relates to the field of vibration and noise reduction of mechanical equipment, in particular to a working condition transmission path analysis method based on a regularization total least square method.

Background

Vibration noise of automobiles, high-speed trains, and the like is an important index for evaluating the riding comfort of vehicles. The good vibration noise performance brings good driving experience to users, is more favored by the users, and effectively improves the product competitiveness; poor vibration noise performance can not only cause discomfort of drivers and passengers, but also easily bring fatigue to the drivers and the passengers, and potential safety hazards exist. Therefore, the control and improvement of the vibration noise have important engineering significance. How to identify the transmission path of vibration or noise is a prerequisite and key to control and improve the performance of vibration noise. At present, common methods for identifying the vibration noise transmission path include a traditional transmission path analysis method and a working condition transmission path analysis method. Because the traditional transmission path analysis method needs to split the mechanical equipment into an active part containing the excitation source and a passive part containing the target point, the frequency response function is tested, and the identification of the working condition load is complex, the traditional transmission path analysis method has low efficiency and is difficult in engineering application. The recently proposed working condition transmission path analysis method only needs response data under different operating conditions to identify the transmission path of the vibration noise, so that equipment is prevented from being disassembled, and complicated frequency response function testing and load identification are avoided, the efficiency is greatly improved, and the method is widely applied to engineering practice.

However, errors are inevitably introduced into the indicated point data and the target point data under different working conditions in the test process, and the equation to be solved for the analysis of the working condition transfer path is often seriously ill-conditioned, and at this time, a smaller error also causes a larger secondary fluctuation of the final solution, so that a larger error exists in the contribution of each path obtained by the analysis and calculation of the working condition transfer path. At present, a Tikhonov regularization least square method is usually adopted to reduce target point data errors and ill-conditioned influence in an inversion process, however, influence caused by an indication point data error is not considered, so that contribution of each path obtained by the method still has certain errors, and precision requirements are difficult to achieve.

Disclosure of Invention

The invention aims to provide a working condition transmission path analysis method based on a regularization total least square method, which comprises the following steps of:

1) a number of indication points and a number of target points are determined. Wherein the indication point is located in the area of the excitation source of the mechanical device. An indication point is arranged in the area of each excitation source. The distance between the pointing point and the excitation source within a region is less than h. The target point is the position to be observed of the mechanical equipment.

2) A response signal monitoring device is disposed at the indication point and the target point to monitor a response signal of a position where the device is located.

The response signal monitoring device comprises an acceleration sensor, a microphone and/or a strain gauge. The acceleration sensor is used for monitoring an acceleration response signal. The microphone is used to monitor the audio vibration response signal. The strain gauge is used to monitor the stress response signal.

3) A plurality of operating conditions are set, and the mechanical equipment is enabled to operate under each operating condition.

The number of the set operating conditions is larger than or equal to the number of the indicating points.

In the operation process of the mechanical equipment, the response signal monitoring device monitors the response signals of the indication point and the target point and sends the response signals to the upper computer.

4) And establishing a working condition transmission path analysis equation according to the response signals of the indication point and the target point under different working conditions.

The operating condition transmission path analysis equation is as follows:

Y＝XT (1)

in the formula, Y is a target point response matrix under different working conditions. And X is an indication point response matrix under different working conditions. And T is a transfer rate function matrix to be solved.

The working condition transmission path analysis equation expansion is as follows:

in the formula, r is the number of target points.n is the number of the indicating points. m is the number of working conditions.And the elements of the target point response matrix Y under different working conditions.The elements of the matrix X are responded to the indication points under different working conditions. T is_nrIs the element of the transfer rate function matrix T to be solved.

5) And solving the working condition transfer path analysis equation by using a Tikhonov regularization total least square method to obtain a transfer rate function matrix.

Solving an analysis equation of a working condition transfer path to obtain a transfer rate function matrix, wherein the step of obtaining the transfer rate function matrix comprises the following steps:

5.1) adding an error interference term into the working condition transmission path analysis equation, thereby updating the working condition transmission path analysis equation and obtaining:

Y+ΔY＝(X+ΔX)T (3)

in the formula, Δ Y and Δ X are errors of the target point response matrix Y under different working conditions and the indication point response matrix X under different working conditions, respectively.

5.2) establishing a Tikhonov regularization objective function and constraint conditions of the overall least square method, namely:

in the formula, L represents a regularization matrix.

5.3) construction of Lagrange polynomialsNamely:

μ is the Lagrange multiplier. ρ is the regularization parameter.

Where Lagrange multiplier μ satisfies the following condition, (Δ X, Δ Y) is an optimal solution, that is:

in the formula (I), the compound is shown in the specification,represents a gradient;refers to Lagrange polynomials;

5.4) combining the formula (4) and the formula (6), solving to obtain the error delta Y of the target point response matrix Y under different working conditions and the error delta X of the indication point response matrix X under different working conditions, namely:

5.5) substituting the formula (7) into the formula (4), updating the objective function to obtain:

5.6) solving by using an iterative method to obtain a regularized total least square solution T of the transmissibility matrix.

The step of solving for the regularized overall least squares solution T of the resulting transmissibility matrix includes:

5.6.1) given calculation parameter λ_LAn initial value.

5.6.2) set the iteration initial value of regularized total least square solution as T ═ X^HX)^-1X^HY。

5.6.3) update the parameter λ_INamely:

5.6.4) calculate the updated regularized overall least squares solution T, i.e.:

T＝(X^HX+λ_II+λ_LL^HL)^-1X^HY (10)

in the formula, λ_IAnd λ_LTo calculate the parameters.

5.6.5) return to step 5.6.3) until | | T is satisfied^k-T^k-1||₂<ε＝10^-3。

5.6.6) let λ_L＝λ_L+Δλ_LAnd returning to step 5.6.2) until lambda_L≥λ_Lmax。Δλ_LFor calculating a parameter lambda_LThe iteration step size of. Lambda [ alpha ]_LmaxFor calculating a parameter lambda_LThe iteration threshold of (2).

5.6.7) at each lambda_LCalculated parametersAnd parametersDrawing an L curve for the coordinate; regularization parameter lambda corresponding to the maximum point of curvature of the L-curve_LThe optimal regularization parameter value; and substituting (10) the optimal regularization parameter value to calculate a regularization total least square solution T.

6) And calculating the contribution of each transfer path under different working conditions according to the transfer rate function matrix, obtaining the contribution ratio of each transfer path, and completing the analysis of the working condition transfer paths.

The contribution quantity of each transfer path under different working conditions is the product of the response signal of the indication point under different working conditions and the transfer rate function matrix.

The invention discloses a working condition transmission path analysis method based on a Tikhonov regularization total least square method, and aims to simultaneously consider the influence caused by response data errors of an indication point and a target point in the working condition transmission path analysis and improve the working condition transmission path analysis precision. Firstly, different working condition experiments are designed for mechanical equipment, and response data of an indication point and a target point are obtained. And then establishing a total least square method working condition transmission path analysis equation, wherein the equation simultaneously considers the influence brought by the response data errors of the indication point and the target point. And finally, introducing Tikhonov regularization to improve the ill-conditioned property of the indication point response matrix in the inversion process, thereby obtaining a transfer rate function matrix. And multiplying the response matrix of the indication point under different working conditions by the transfer rate function matrix to obtain the contribution of each path under each working condition, and completing the analysis of the transmission path under each working condition.

The technical effects of the method are undoubted, the method designs test working conditions for a mechanical system to be analyzed, measures test working condition data, constructs a working condition transmission path analysis equation through the collected test working condition data, and solves a ill-conditioned equation by a regularization total least square method to obtain a transfer rate function matrix. And then multiplying the response signals of the indication points under different working conditions by the identified transfer rate function matrix to obtain a transfer path contribution quantity result, sequencing the contribution quantities of different paths to obtain the contribution quantity ratio of each transfer path, and completing the transfer path analysis under the operating conditions. The method provided by the invention overcomes the problem of neglecting the data error of the indication point in the traditional working condition transmission path analysis, and improves the calculation accuracy of the contribution of the working condition transmission path.

The regularization total least square method of the invention adopts Tikhonov regularization to overcome the ill-conditioned problem, and utilizes an L curve to select a regularization parameter lambda_LThe influence of the norm of the residual error and the norm of the solution is comprehensively considered, and the calculation accuracy of the contribution of the working condition transmission path is further improved.

Drawings

FIG. 1 is an experimental layout;

fig. 2a is a target point total response comparison graph obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 2b is a target point total response comparison graph obtained by a traditional transmission path analysis method and the method of the present invention;

fig. 3a is a comparison graph of the contribution of the path 1 obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 3b is a comparison graph of the contribution of the path 1 obtained by the traditional transmission path analysis method and the method of the present invention;

fig. 4a is a comparison graph of the contribution of the path 2 obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 4b is a comparison graph of the contribution of the path 2 obtained by the traditional transmission path analysis method and the method of the present invention;

fig. 5 is a graph of FRAC values.

Detailed Description

The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.

Example 1:

referring to fig. 1 to 5, a method for analyzing a condition transmission path based on a regularized total least square method includes the following steps:

1) a number of indication points and a number of target points are determined. Wherein the indicator point is located in the area of the excitation source of the mechanical device to be analyzed. An indication point is arranged in the area of each excitation source. The distance between the pointing point and the excitation source within a region is less than h. The target point is the position to be observed of the mechanical equipment.

2) A response signal monitoring device is disposed at the indication point and the target point to monitor a response signal of a position where the device is located.

The response signal monitoring device comprises an acceleration sensor, a microphone and/or a strain gauge. The acceleration sensor is used for monitoring an acceleration response signal. The microphone is used to monitor the audio vibration response signal. The strain gauge is used to monitor the stress response signal.

3) A plurality of operating conditions are set, and the mechanical equipment is enabled to operate under each operating condition.

The number of the set operating conditions is larger than or equal to the number of the indicating points.

In the operation process of the mechanical equipment, the response signal monitoring device monitors the response signals of the indication point and the target point and sends the response signals to the upper computer.

4) And establishing a working condition transmission path analysis equation according to the response signals of the indication point and the target point under different working conditions.

The operating condition transmission path analysis equation is as follows:

Y＝XT (1)

in the formula, Y is a target point response matrix under different working conditions. And X is an indication point response matrix under different working conditions. And T is a transfer rate function matrix to be solved.

The working condition transmission path analysis equation expansion is as follows:

in the formula, r is the number of target points. n is the number of the indicating points. m is the number of working conditions.And the elements of the target point response matrix Y under different working conditions.The elements of the matrix X are responded to the indication points under different working conditions. T is_nrIs the element of the transfer rate function matrix T to be solved.

5) And solving the working condition transfer path analysis equation by using a Tikhonov regularization total least square method to obtain a transfer rate function matrix.

Solving an analysis equation of a working condition transfer path to obtain a transfer rate function matrix, wherein the step of obtaining the transfer rate function matrix comprises the following steps:

5.1) adding an error interference term into the working condition transmission path analysis equation, thereby updating the working condition transmission path analysis equation and obtaining:

Y+ΔY＝(X+ΔX)T (3)

in the formula, Δ Y and Δ X are errors of the target point response matrix Y under different working conditions and the indication point response matrix X under different working conditions, respectively.

5.2) establishing a Tikhonov regularization objective function and constraint conditions of the overall least square method, namely:

in the formula, L represents a regularization matrix. ρ is the regularization parameter.

5.3) construction of Lagrange polynomialsNamely:

μ is the Lagrange multiplier.

Where Lagrange multiplier μ satisfies the following condition, (Δ X, Δ Y) is an optimal solution, that is:

in the formula (I), the compound is shown in the specification,represents a gradient;refers to Lagrange polynomials;

5.4) combining the formula (4) and the formula (6), solving to obtain the error delta Y of the target point response matrix Y under different working conditions and the error delta X of the indication point response matrix X under different working conditions, namely:

5.5) substituting the formula (7) into the formula (4), updating the objective function to obtain:

5.6) solving by using an iterative method to obtain a regularized total least square solution T of the transmissibility matrix.

The step of solving for the regularized overall least squares solution T of the resulting transmissibility matrix includes:

5.6.1) given calculation parameter λ_LAn initial value.

5.6.2) set the iteration initial value of regularized total least square solution as T ═ X^HX)^-1X^HY。

5.6.3) update the parameter λ_INamely:

5.6.4) calculate the updated regularized overall least squares solution T, i.e.:

T＝(X^HX+λ_II+λ_LL^HL)^-1X^HY (10)

in the formula, λ_IAnd λ_LTo calculate the parameters.

5.6.5) return to step 5.6.3) until | | T is satisfied^k-T^k-1||₂<ε＝10^-3。

5.6.6) let λ_L＝λ_L+Δλ_LAnd returning to step 5.6.2) until lambda_L≥λ_Lmax。Δλ_LFor calculating a parameter lambda_LThe iteration step size of. Lambda [ alpha ]_LmaxFor calculating a parameter lambda_LThe iteration threshold of (2).

5.6.7) at each lambda_LCalculated parametersAnd parametersDrawing an L curve for the coordinate; the L curve is in an L shape, and at the inflection point of the L curve (where the curvature of the L curve is maximum), the regularization parameter lambda is at the moment_LTo an optimum value, and thenλ_LAnd computes a regularized overall least squares solution T according to equation (10).

6) And calculating the contribution of each transfer path under different working conditions according to the transfer rate function matrix, obtaining the contribution ratio of each transfer path, and completing the analysis of the working condition transfer paths.

The contribution quantity of each transfer path under different working conditions is the product of the response signal of the indication point under different working conditions and the transfer rate function matrix.

Example 2:

an experiment of a working condition transmission path analysis method based on a regularization total least square method comprises the following processes:

fig. 1 shows an experimental layout. The experimental object is an aluminum plate, and one end of the aluminum plate is fixed on the bracket. The aluminum plate had a length, width and thickness of 800mm 400mm 5mm, a density of 2700kg/m3, a Poisson ratio of 0.31 and an elastic modulus of 71000 MPa. The excitation sources are two exciters, denoted as source a and source b. One indicator point (indicator point 1 and indicator point 2) is arranged for each excitation source, the indicator point should be as close as possible to the excitation source, and point Y is selected as the target point. The experiment comprises the following specific steps:

(1) respectively arranging an acceleration sensor at the indication point 1, the indication point 2 and the target point Y, and testing the vibration acceleration of the indication point and the target point vertical to the board surface;

(2) 4 groups of experimental working conditions are generated by changing the excitation type of the vibration exciter, and are shown in the following table;

(3) establishing a working condition transfer path analysis equation according to response signals of the indication point and the target point under different working conditions, and solving by adopting a Tikhonov regularization total least square method to obtain a transfer rate function matrix;

(4) and (4) multiplying the response signals of the indication points under different working conditions by the transfer rate function matrix in the step (3) to obtain the contribution of each transfer path under different working conditions, sequencing the contribution of each transfer path to obtain the contribution ratio of each transfer path, and completing the analysis of the working condition transfer paths. Taking the working condition 1 as an example, the contribution analysis results of fig. 2 to fig. 4 are obtained. The classic TPA represents an analysis result obtained by a conventional transmission path analysis method, and although the conventional transmission path analysis method is relatively complicated in implementation process, the accuracy is high, and thus the result obtained by the conventional transmission path analysis method is an accurate value. Results of the regularized least square method working condition transmission path analysis method (OTPA-RLSM) and the method (OTPA-RTLSM) are compared with the regularized least square method working condition transmission path analysis method (OTPA-RLSM) and the method (OTPA-RTLSM), and the accuracy of different methods is verified. Fig. 2a is a comparison graph of total responses of target points obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 2b is a comparison graph of total responses of target points obtained by the traditional transmission path analysis method and the method of the present invention. Fig. 3a is a comparison graph of the contribution of the path 1 obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 3b is a comparison graph of the contribution of the path 1 obtained by the traditional transmission path analysis method and the method of the present invention. Fig. 4a is a comparison graph of the contribution of the path 2 obtained by a traditional transmission path analysis method and a Tikhonov regularization least square method working condition transmission path analysis method, and fig. 4b is a comparison graph of the contribution of the path 2 obtained by the traditional transmission path analysis method and the method of the present invention. And finally, adopting an FRAC value quantization regularization least square method working condition transmission path analysis method and the error between the method and the traditional transmission path analysis method:

in the formula (f)₁And f₂For upper and lower limits of the frequency band analyzed, Y_OTPA(f) Representing the contribution, Y, obtained by analysis of the transmission path of the operating conditions_TPA(f) Representing the amount of contribution from classical transmission path analysis, "-" represents the complex conjugate.

FRAC values are between 0 and 1, with 1 indicating a perfect match between the two frequency domain data. FIG. 5 is FRAC values for two operating condition transmission path analysis.

Therefore, compared with the condition transmission path analysis method based on the Tikhonov regularization total least square method, the condition transmission path analysis method based on the Tikhonov regularization total least square method can weaken the influence caused by the response data error of the indication point, reduce the contribution error of the transmission path, and has better effect on improving the analysis precision of the condition transmission path.