CN112214844B - Method and system for calculating transmission path parameters of equipment operation conditions - Google Patents
Method and system for calculating transmission path parameters of equipment operation conditions Download PDFInfo
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Abstract
The invention discloses a method and a system for calculating parameters of a transmission path of equipment operating conditions, wherein the method comprises the steps of determining the position of an excitation source and the transmission path according to the mechanical structure characteristics of an object to be tested, then determining the number of reference points and the optimal installation position by using a reference point optimization method, acquiring vibration response signals of the final reference point installation position and the target point installation position under the stable excitation of the test condition parameters under the condition of ensuring that the test condition parameters are linearly uncorrelated with different working conditions, carrying out crosstalk elimination on the acquired vibration response signals, and carrying out least square support vector regression training on an analysis model of the transmission path of the operating conditions by using the vibration response signals subjected to the crosstalk elimination to obtain a transmission function matrix.
Description
Technical Field
The invention belongs to the field of vibration and noise reduction of mechanical equipment, and particularly relates to a method and a system for calculating parameters of a transmission path of operating conditions of equipment.
Background
The high-end equipment such as the gas turbine has the characteristics of numerous internal parts and complex coupling connection, and the vibration generated by the active part in the operation process is transmitted to the whole equipment through the connecting part, so that the problems of mechanical structure deformation, aggravation of abrasion of main parts and the like are caused, the performance and the service life of the equipment are further influenced, and therefore, a vibration active control measure is carried out on the high-end equipment such as the gas turbine. The vibration active control strategy can be divided into vibration source control and transmission path control, wherein the vibration source control requires design optimization of a high-end equipment active component and is difficult to realize on the premise of not influencing the performance; and the transmission path control focuses on the connecting piece, and the vibration control is realized by the vibration damping device under the condition of not changing the structure of the vibration damping device, so that the operability is higher. The precondition for controlling the vibration transmission Path is to acquire the transmission Path characteristics, and the current main technical approaches include Transmission Path Analysis (TPA) and Operational Transmission Path Analysis (OTPA).
The basis of transmission path analysis is frequency response function test, and a mechanical structure needs to be disassembled, so that time and labor are wasted; the operating condition transmission path analysis adopts the operating condition data to replace a frequency response function, so that the integrity of a mechanical system can be ensured in the test, and the time and the efficiency are saved. When high-end equipment such as a gas turbine and the like is used for analyzing the transmission path of the operation working condition, the number of required reference points is large due to large overall dimension and complex mechanical structure, and the serious ill-condition problem of the input matrix is easily caused. According to the traditional method, the matrix ill-condition degree is reduced through a regularization means, so that part of working condition information is omitted in the solving process, and the real contribution of each transmission path cannot be completely reflected in the result, so that the control precision of the transmission path is influenced, and the vibration active control precision of high-end equipment such as a gas turbine cannot be effectively improved.
Disclosure of Invention
The invention aims to provide a method and a system for calculating parameters of a transmission path of equipment operating conditions, so as to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating parameters of a transmission path of equipment operation conditions comprises the following steps:
step 1), determining an excitation source position and a transmission path according to the mechanical structure characteristics of an object to be tested, determining a final reference point installation position and a final reference point installation number around the excitation source position and the transmission path by a reference point optimization method, then determining a target point installation position, and establishing an operation condition transmission path analysis model according to the reference point installation position, the reference point installation number and the target point installation position;
step 2), acquiring a vibration response signal of a final reference point installation position and a target point installation position under stable excitation of the test working condition parameters under the condition of ensuring the test working condition parameters with different working condition linearity irrelevant;
step 3), carrying out crosstalk elimination treatment on the obtained vibration response signals, and carrying out least square support vector regression training on the operation condition transmission path analysis model by using the vibration response signals subjected to crosstalk elimination treatment to obtain a transmission function matrix;
and 4) taking the vibration response signals of the final reference point mounting positions on different transmission paths under the actual working condition as test data, and multiplying the test data by the transfer function matrix obtained in the step 3) to obtain vibration energy occupation ratios of the different transmission paths, wherein the transmission path corresponding to the maximum value of the vibration energy occupation ratio is the vibration interference path.
Furthermore, a plurality of reference point candidate positions are preset for a single transmission path, the reference point signal matrix condition number is used as a judgment standard, after all reference point candidate position combinations are traversed, the reference point candidate position combination with the most complete retained information is selected as the final reference point installation position and the reference point installation number on the transmission path.
Further, the number of the test working condition parameters in the step 2) is larger than the installation number of the reference points.
Further, in step 3), the vibration response signal of the final reference point installation position after the crosstalk elimination processing is used as input data, the vibration response signal of the target point installation position after the crosstalk elimination processing is used as output data, and least square support vector regression training is performed on the operation condition transfer path analysis model to obtain an optimal linear regression function, wherein the regression function is the solved transfer function matrix.
t is a transfer function matrix, r is the number of parameters of the test working condition, alpha i Is LagrangeDay multiplier, x i Input data, b is an offset.
Further, specifically, the relationship between the operating condition transmission path analysis model and the reference point signal, the target point signal and the transmission function matrix may be expressed as: y = XT (1),
namely, it is
In the formula, X is a reference point signal matrix, Y is a target point signal matrix, T is a transfer function matrix, r is the number of test working condition parameters, and n is the number of reference points; the r groups of working condition data can form a training setIn which input data x i ∈R n Output data y i e.R, the linear regression function is:
calculating by adopting a secondary penalty function:
the constraint conditions are as follows:
where γ is a normalization parameter, e i Is a relaxation variable;
using lagrange multiplier alpha i To proceed withAnd (3) dual solution:
under the KKT condition, each variable respectively calculates partial derivatives of Lagrangian functions, and the optimal solution can be obtained as follows:
for ease of solution, the above equation is expressed in the form of a linear system of equations:
wherein the content of the first and second substances,e=[e 1 ,e 2 ,…,e r ] T ,y=[y 1 ,y 2 ,…,y r ] T i is an identity matrix, α = [ α ] 1 ,α 2 ,…,α r ] T ,Using Mercer conditions one can obtain:
substituting equation (9) into equation (8) while eliminating w and e, equation (8) can be converted to:
solving the system of linear equations yields:
the transfer rate function matrix can be obtained by substituting equations (7) and (9) for equation (3):
further, under the vibration response signals obtained by r groups of test working condition parameters, r-1 groups are selected as a training set to carry out r times of parameter training, and then the average value of the r times of training results is taken as a training result.
A system for calculating parameters of a transmission path of equipment operation conditions comprises a data acquisition module, a data preprocessing module and a data processing module;
the data acquisition module is used for acquiring a vibration response signal of a final reference point installation position, a vibration response signal of a target point installation position under stable excitation of test working condition parameters and a vibration response signal of a final reference point installation position on different transmission paths under actual working conditions; the data acquisition module transmits vibration response signals of the final reference point mounting positions on different transmission paths under actual working conditions to the data processing module;
the data acquisition module transmits the acquired vibration response signal under the stable excitation of the test working condition parameters to the data preprocessing module for data preprocessing, and the preprocessed vibration response signal is transmitted to the data processing module;
the data processing module is used for storing an operation condition transmission path analysis model established according to the reference point installation positions, the reference point installation number and the target point installation positions, optimizing and training the operation condition transmission path analysis model according to the preprocessed vibration response signals to obtain a transmission function matrix, and multiplying the vibration response signals of the final reference point installation positions on different transmission paths under actual conditions by the transmission function matrix to obtain vibration energy proportion results of different transmission paths and output the results.
Further, the position of an excitation source and the transmission path are determined according to the mechanical structure characteristics of the object to be tested, the final installation position of reference points and the installation number of the reference points are determined around the position of the excitation source and the transmission path by a reference point optimization method, and then the installation position of the target points is determined, and an operation condition transmission path analysis model is established in the data processing module.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a method for calculating parameters of a transmission path of equipment operating conditions, which determines the position of an excitation source and the transmission path according to the mechanical structure characteristics of an object to be tested, then determines the number of reference points and the optimal installation position by using a reference point optimization method, acquires vibration response signals of the final reference point installation position and the target point installation position under the stable excitation of the parameters of the test conditions under the condition of ensuring the test conditions which are linearly uncorrelated with different conditions, performs crosstalk elimination processing on the acquired vibration response signals, performs least square support vector regression training on an analysis model of the transmission path of the operating conditions by using the vibration response signals after the crosstalk elimination processing to obtain a transmission function matrix, avoids the matrix ill-condition problem of the traditional analysis method of the transmission path of the operating conditions, can completely reserve the data of the operating conditions, uses the reference point response signals under the actual conditions as model input to obtain the contribution of each path and sequence, and uses the path contribution analysis result to guide high-end equipment to take vibration reduction measures, and can still maintain good generalization performance under the test environment which is complex.
Furthermore, when a transfer function matrix is obtained, least square support vector regression is directly utilized for fitting, the matrix ill-condition problem caused by excessive reference points is avoided, working condition information is completely reserved, random interference brought by the external environment is eliminated to the maximum extent through multi-working condition training, efficient and accurate identification of vibration transfer paths of high-end equipment such as gas turbines is achieved, and vibration reduction measures are guided to be carried out.
Furthermore, under the vibration response signals obtained by r groups of test working condition parameters, r-1 groups are selected as a training set to carry out r times of parameter training, and then the average value of the r times of training results is taken as a training result, so that the working condition information is fully utilized, and random interference becomes the only factor influencing the model parameters.
Drawings
Fig. 1 is a schematic diagram of simulation setup in an embodiment of the present invention.
Fig. 2 (a) is a result diagram of a reference point a response signal after crosstalk is removed in the embodiment of the present invention, fig. 2 (B) is a result diagram of a reference point B response signal after crosstalk is removed in the embodiment of the present invention, and fig. 2 (C) is a result diagram of a target point C response signal in the embodiment of the present invention.
Fig. 3 is a comparison diagram of results of the OTPA method based on least squares support vector regression, the OTPA method based on TSVD, and theoretical values in the embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
a method for calculating parameters of a transmission path of equipment operation conditions comprises the following steps:
step 1), determining an excitation source position and a transmission path according to mechanical structure characteristics of an object to be tested, determining final reference point installation positions and reference point installation numbers around the excitation source position and the transmission path by a reference point optimization method, then determining target point installation positions, and establishing an operation condition transmission path analysis model according to the reference point installation positions, the reference point installation numbers and the target point installation positions;
specifically, mechanical structure characteristics of a test object are analyzed, the position of an excitation source is determined according to the mechanical structure characteristics of the test object, a transmission path is divided, and a reference point mounting position suitable for mounting a sensor is selected around the excitation source and the transmission path; and selecting the position of a target point suitable for additionally mounting the sensor at a position to be analyzed far away from the excitation source, and according to a reference point optimization method, namely traversing all the reference point mounting position combinations by using a reference point signal matrix condition number as a judgment standard, and then taking the reference point mounting position combination with the most retained information as the selected final reference point mounting position and the reference point mounting number.
Specifically, a plurality of reference point candidate positions are preset for a single transmission path, a reference point signal matrix condition number is used as a judgment standard, after all reference point candidate position combinations are traversed, a reference point candidate position combination with the most complete retained information is selected as a final reference point installation position and a reference point installation number on the transmission path.
Step 2), acquiring a vibration response signal of a final reference point installation position and a target point installation position under stable excitation of the test working condition parameters under the condition of ensuring the test working condition parameters with different working condition linearity irrelevant;
specifically, the number of the test working condition parameters is greater than the installation number of the reference points; the vibration response signal comprises a reference point signal and a target point signal;
step 3), carrying out crosstalk elimination processing on the obtained vibration response signal, and carrying out least square support vector regression training on an operation condition transmission path analysis model by using the vibration response signal subjected to crosstalk elimination processing to obtain a transmission function matrix;
when the operation condition transmission path analysis model is trained, under the vibration response signals obtained by r groups of test condition parameters, r-1 groups are selected as a training set to carry out r times of parameter training, and then the average value of the r times of training results is taken as a training result, so that the condition information is fully utilized, and random interference becomes the only factor influencing the model parameters.
Specifically, crosstalk elimination processing is carried out on a final reference point installation position obtained under the condition that test working condition parameters which are linearly uncorrelated under different working conditions are ensured and a vibration response signal obtained at a target point installation position, then the vibration response signal of the final reference point installation position after the crosstalk elimination processing is used as input data, the vibration response signal of the target point installation position after the crosstalk elimination processing is used as output data, least square support vector regression training is carried out on an operation working condition transmission path analysis model, and an optimal linear regression function is obtained and is a solved transmission function matrix; the specific process is as follows:
the OTPA model (operation condition transfer path analysis model) can be expressed as follows according to the relationship between the reference point signal, the target point signal and the transfer function matrix:
Y=XT (1)
in the formula, X is a reference point signal matrix, Y is a target point signal matrix, T is a transfer function matrix, r is the number of test working condition parameters, and n is the number of reference points; the r groups of working condition data can form a training setWherein the input data x i ∈R n Output data y i e.R, the linear regression function is:
and (3) calculating a regression problem by adopting a secondary penalty function, and converting the regression problem into a quadratic programming problem:
the constraint conditions are as follows:
where γ is the normalization parameter, e i Is a relaxation variable, J is a penalty function, and the optimization goal is to minimize the penalty function;
the direct solution of the quadratic programming problem is difficult, and a Lagrange multiplier alpha is introduced i To inquire about the quadratic planThe title is converted into dual form:
under the KKT condition, each variable respectively calculates partial derivatives of Lagrangian functions, and the optimal solution can be obtained as follows:
for ease of solution, the above equation is expressed in the form of a linear system of equations:
wherein the content of the first and second substances,e=[e 1 ,e 2 ,…,e r ] T ,y=[y 1 ,y 2 ,…,y r ] T i is an identity matrix, α = [ α ] 1 ,α 2 ,…,α r ] T ,Using Mercer conditions one can obtain:
wherein Ω is a kernel function satisfying the Mercer condition;
substituting equation (9) into equation (8) while eliminating w and e, equation (8) may be converted to:
solving the system of linear equations yields:
the transfer rate function matrix can be obtained by substituting equations (7) and (9) into equation (3):
wherein r is the number of test working condition parameters, alpha i Is Lagrange multiplier, x i For the i-th input data, b is the offset, ψ is the kernel function, and a gaussian kernel is generally taken.
Step 4), specifically, selecting a working condition with serious abnormal vibration as an actual working condition, and collecting a vibration response signal of the installation position of the reference point under the actual working condition after starting up; taking vibration response signals of final reference point installation positions on different transmission paths under actual working conditions as test data, multiplying the test data by the transfer function matrix obtained in the step 3) to obtain vibration energy occupation ratios of the different transmission paths, namely contribution amounts, sequencing all the transmission paths according to the contribution amounts, wherein the transmission paths with high contribution amounts are vibration interference paths with obvious vibration, vibration reduction measures need to be taken, the vibration reduction measures can be taken from high to low according to actual conditions, in the process of the vibration reduction measures, the vibration reduction measures can be taken to influence the contribution amounts of other transmission paths after the vibration reduction measures with high contribution amounts, and the steps are repeated until the transmission path with the highest contribution amount does not need to be subjected to vibration reduction, and the vibration reduction is within a meeting requirement range.
According to the method, when the reference point is selected, an empirical method is not simply relied on, but a condition number is utilized to screen out a reference point position combination which retains most transmission path information; on the other hand, the regularization method is not adopted when the transfer function matrix is solved, so that the ill-conditioned problem involved in inverse problem solving is avoided, the working condition information is completely reserved, and the accuracy and the reliability of transfer path analysis are effectively improved.
Example 1:
1) A metal flat plate is used as a simulation object, and the material is Q235, the length is 1m, and the thickness is 5mm. Presetting 2 excitation sources A and B, selecting 4 candidate reference points around each excitation source, and presetting a target point C at a position far away from the excitation source, wherein the position is shown in figure 1. Under a given working condition, traversing all the alternative reference point combinations to obtain the reference point signal matrix condition number average value, as shown in the following table:
condition of matrix | A1 | A2 | A3 | A4 |
B1 | 128.5 | 127.2 | 127.0 | 129.1 |
B2 | 127.1 | 128.5 | 126.9 | 129.7 |
B3 | 127.2 | 126.5 | 128.7 | 129.4 |
B4 | 129.3 | 129.9 | 127.3 | 130.4 |
Obtaining the optimal reference point combination of A4 and B4;
2) Selecting 5 groups of test condition parameters to ensure linear independence among different conditions, wherein reference point response signals after crosstalk elimination are shown in figures 2 (a) and 2 (b), and target point response signals are shown in figure 2 (c) as shown in the following table:
vibration source A frequency (Hz) | Vibration source B frequency (Hz) | |
Working |
10 | 17 |
|
12 | 15 |
|
14 | 10 |
|
16 | 20 |
|
18 | 13 |
3) Performing crosstalk elimination processing on reference point and target point response signals under a test condition, respectively using the processed reference point and target point response signals as input data and output data, training a least square support vector regression model, and constructing an optimal linear regression function, wherein the regression function is a transfer function matrix;
4) Selecting an actual working condition of a vibration source A with the frequency of 20Hz and a vibration source B with the frequency of 25Hz, and collecting signals of a reference point and a target point;
5) And taking the response signals of each reference point under the actual working condition as test data, and multiplying the test data by the transfer rate function matrix obtained in the step 3) respectively to obtain the vibration energy ratio of each path and obtain the path contribution value. Comparing the contribution quantity value obtained by the invention with a theoretical value, and comparing the contribution quantity value obtained by the OTPA method based on TSVD with the theoretical value, as shown in FIG. 3, calculating the path contribution relative error, as shown in the following table:
the method can effectively reduce the error value of the path contribution amount, can completely reserve the working condition data and improve the accuracy.
Claims (9)
1. A method for calculating parameters of a transmission path of equipment operation conditions is characterized by comprising the following steps:
step 1), determining an excitation source position and a transmission path according to mechanical structure characteristics of an object to be tested, determining final reference point installation positions and reference point installation numbers around the excitation source position and the transmission path by a reference point optimization method, then determining target point installation positions, and establishing an operation condition transmission path analysis model according to the reference point installation positions, the reference point installation numbers and the target point installation positions;
step 2), acquiring a vibration response signal of a final reference point installation position and a target point installation position under stable excitation of the test working condition parameters under the condition of ensuring the test working condition parameters with different working condition linearity irrelevant;
step 3), carrying out crosstalk elimination treatment on the obtained vibration response signals, and carrying out least square support vector regression training on the operation condition transmission path analysis model by using the vibration response signals subjected to crosstalk elimination treatment to obtain a transmission function matrix;
and 4) taking the vibration response signals of the final reference point mounting positions on different transmission paths under the actual working condition as test data, and multiplying the test data by the transfer function matrix obtained in the step 3) to obtain vibration energy occupation ratios of the different transmission paths, wherein the transmission path corresponding to the maximum value of the vibration energy occupation ratio is the vibration interference path.
2. The method for calculating the parameters of the transmission path of the equipment operation condition according to claim 1, wherein a plurality of reference point candidate positions are preset for a single transmission path, a reference point signal matrix condition number is used as a judgment standard, and after traversing all the reference point candidate position combinations, a reference point candidate position combination with the most complete retained information is selected as a final reference point installation position and a reference point installation number on the transmission path.
3. The method for calculating the transmission path parameter of the operating condition of the equipment according to claim 1, wherein the number of the test operating condition parameters in the step 2) is larger than the installation number of the reference points.
4. The method for calculating the parameters of the transmission path of the equipment operating condition according to claim 1, wherein in the step 3), the vibration response signal of the final reference point installation position after crosstalk elimination is used as input data, the vibration response signal of the target point installation position after crosstalk elimination is used as output data, and least square support vector regression training is performed on the operating condition transmission path analysis model to obtain an optimal linear regression function, wherein the regression function is the solved transmission function matrix.
5. The method for calculating the parameters of the transmission path of the equipment operation condition according to claim 4, wherein the matrix of the transmission function is as follows:
t is a transfer function matrix, r is the number of parameters of the test working condition, alpha i Is Lagrange multiplier, x i For the i-th entry, b is the offset and ψ is the kernel function.
6. The method for calculating the parameters of the transmission path of the equipment operating conditions according to claim 5, wherein the relationship between the analysis model of the transmission path of the operating conditions according to the reference point signal, the target point signal and the transmission function matrix is expressed as follows: y = XT (1),
namely, it is
In the formula, X is a reference point signal matrix, Y is a target point signal matrix, T is a transfer function matrix, r is the number of test working condition parameters, and n is the number of reference points; the r groups of working condition data can form a training set { x } i ,y i } 1 r Wherein data x is input i ∈R n Output data y i e.R, the linear regression function is:
calculating by adopting a secondary penalty function:
the constraint conditions are as follows:
where γ is the normalization parameter, e i Is a relaxation variable, J is a penalty function, and the optimization goal is to minimize the penalty function;
using lagrange multiplier alpha i And carrying out dual solution:
under the KKT condition, each variable respectively calculates partial derivatives of Lagrangian functions, and the optimal solution can be obtained as follows:
for ease of solution, the above equation is expressed in the form of a linear system of equations:
wherein the content of the first and second substances,e=[e 1 ,e 2 ,…,e r ] T ,y=[y 1 ,y 2 ,…,y r ] T i is an identity matrix, α = [ α ] 1 ,α 2 ,…,α r ] T ,Using Mercer conditions we can obtain:
wherein Ω is a kernel function satisfying the Mercer condition;
substituting equation (9) into equation (8) while eliminating w and e, equation (8) can be converted to:
solving the system of linear equations can result in:
the transfer rate function matrix can be obtained by substituting equations (7) and (9) for equation (3):
7. the method for calculating the parameters of the transmission path of the equipment running condition according to claim 1, wherein r-1 groups are selected as training sets to perform r times of parameter training under the vibration response signals obtained by r groups of test condition parameters, and then the average value of the r times of training results is taken as the training result.
8. A system for calculating parameters of a transmission path of equipment operation conditions is characterized by comprising a data acquisition module, a data preprocessing module and a data processing module;
the data acquisition module is used for acquiring a vibration response signal of a final reference point installation position, a vibration response signal of a target point installation position under stable excitation of test working condition parameters and a vibration response signal of a final reference point installation position on different transmission paths under actual working conditions; the data acquisition module transmits vibration response signals of the final reference point mounting positions on different transmission paths under actual working conditions to the data processing module;
the data acquisition module transmits the acquired vibration response signal under the stable excitation of the test working condition parameters to the data preprocessing module for data preprocessing, and the preprocessed vibration response signal is transmitted to the data processing module;
the data processing module is used for storing an operation condition transmission path analysis model established according to the reference point installation positions, the reference point installation number and the target point installation positions, optimizing and training the operation condition transmission path analysis model according to the preprocessed vibration response signals to obtain a transmission function matrix, and multiplying the vibration response signals of the final reference point installation positions on different transmission paths under the actual condition by the transmission function matrix to obtain vibration energy ratio results of different transmission paths and outputting the vibration energy ratio results.
9. The system of claim 8, wherein the excitation source location and the transmission path are determined according to the mechanical structure characteristics of the object to be tested, the final reference point installation location and the final reference point installation number are determined around the excitation source location and the transmission path by a reference point optimization method, and then the target point installation location is determined to establish the operation condition transmission path analysis model in the data processing module.
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