CN107085633B - Device and method for multi-point vibration response frequency domain prediction based on support vector machine - Google Patents
Device and method for multi-point vibration response frequency domain prediction based on support vector machine Download PDFInfo
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Abstract
The invention relates to an experimental device for multipoint vibration response frequency domain prediction under the condition of unknown load; an experimental data generation method for multipoint vibration response frequency domain prediction under the condition of unknown load; a method for predicting vibration response of unknown measuring points by using the experimental device and experimental data according to the vibration response of the known measuring points of the system under uncorrelated multi-source unknown load combined excitation. The vibration response prediction method directly utilizes a support vector machine to train the relationship between response data according to historical experimental data without knowing or identifying the transfer function, the load size or even the load position of a system. The method is mainly used for predicting the vibration response of the unknown node by using the vibration response of the known measuring point under the condition of irrelevant multi-source unknown load combined excitation working condition. The invention can solve the response prediction of a linear system and a nonlinear system; the invention can solve the problem of vibration response prediction of one unknown node and a plurality of unknown nodes.
Description
Technical Field
The invention relates to an experimental device for multi-point vibration response frequency domain prediction under an unknown load condition, an experimental data generation method for multi-point vibration response frequency domain prediction under an unknown load condition, and a method for predicting vibration response of an unknown measuring point according to vibration response of a known measuring point of a system based on a support vector machine under uncorrelated multi-source unknown load combined excitation by using the experimental device and the experimental data.
Background
With the development and progress of the industry and control technology, the engineering structure development in the fields of aerospace, ships, large-scale machinery, bridges and the like is more and more complicated, large-scale and intelligent. Vibration is a design factor which has to be considered in mechanical design and aerospace engineering, and particularly mechanical damage, bridge collapse and aerospace accidents caused by overlarge vibration response are frequently caused in design and use. However, under some working conditions, the vibration response of some nodes of the structure cannot be directly measured, which makes the control and vibration damping design of the node vibration difficult to be mechanically designed. If the dynamic model of the system and the load are used to solve the vibration response of the node which cannot be directly measured, the following difficulties are encountered: firstly, establishing a model of large equipment is very difficult, and a transfer function of the large equipment is difficult to obtain; secondly, under many conditions, the load working condition of the structure cannot be directly measured, for example, under the conditions that the missile flies in the air, large buildings such as an ocean platform and the like are subjected to stormy waves and traffic excitation, the external load acting on the structure is difficult to be directly measured or calculated, and even sometimes, the dynamic load cannot be measured because the load acting point cannot be reached; the method directly adopts the vibration response data measured by the sensor to predict the vibration response data of the nodes which cannot be measured.
At present, in the traditional method for predicting the vibration response of the nodes, an experimental method or a finite element simulation method is firstly adopted to establish a structural dynamic equation, a structural transfer function is solved, and then the vibration response of the structure is calculated or predicted by utilizing the load working condition of the structure. Firstly, for a complex engineering structure, the modeling of a system and the solving of a transfer function are not easy; secondly, load condition measurement of the load is very difficult or even impossible. Different from the traditional method, the method of the invention predicts the vibration response of the unknown node according to the vibration response of the known node based on the load and the response and the internal relation between the response and the response, can avoid the complex work of measurement of load working conditions, modeling of a system, solving and identifying of a transfer function and the like, and can be well applied to the response prediction of a nonlinear structure based on the response prediction of a support vector machine.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an experimental device for multi-point vibration response frequency domain prediction under the condition of unknown load, an experimental data generation method for multi-point vibration response frequency domain prediction under the condition of unknown load and a method for predicting vibration response of an unknown measuring point based on vibration response of a known measuring point of a system by using the experimental device and the experimental data under uncorrelated multi-source unknown load combined excitation. The method mainly aims at predicting the vibration response of the unknown measuring points by using the vibration response of the known measuring points under the condition of irrelevant multi-source unknown load combined excitation working condition. The method can predict the vibration response condition of one unknown measuring point and can also predict the vibration response conditions of a plurality of unknown measuring points at the same time; the invention can not only solve the response prediction of a linear system, but also solve the response prediction of a nonlinear system. The method is applied to the fields of vibration measurement and vibration response prediction, and particularly can obtain a good vibration response prediction effect when the vibration response of certain measuring points cannot be directly measured (or a vibration sensor is damaged) and the load cannot be directly measured under the working condition of joint excitation of a plurality of irrelevant loads.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an experimental device for multipoint vibration response frequency domain prediction under the condition of unknown load comprises: the method comprises the following steps: the system comprises a time-invariant system, a plurality of excitation sources capable of generating uncorrelated stable random excitation and a plurality of response sensors arranged on the system and used for recording system vibration, wherein the position and the direction of each loading of the excitation are fixed and unchanged, and the plurality of response sensors are distributed in each place of the system and can reflect the main vibration of the system;
the vibration structure adopted by the experimental device is a fixed disc, and the vibration structure is used as a time-invariant system; two unrelated excitation sources are adopted, one is excited by the vibration table, the other is excited by hammering of the PCB force hammer, and the positions and the directions of an excitation point of the vibration table and an excitation point of hammering are fixed; the fixed disk is provided with a plurality of vibration sensors for measuring the vibration of the disk and reflecting the main vibration of the disk, and a plurality of the vibration sensors are used as sensors with known nodes and a plurality of sensors with unknown nodes for predicting the vibration response of a plurality of response points.
A method for generating experimental data of multipoint vibration response frequency domain prediction under the condition of unknown load comprises the following steps:
multiple groups of uncorrelated steady random excitations are generated by combining multiple excitation sources, and the magnitude is gradually increased, so that an uncorrelated multi-source load combined application experimental environment is realized, and the vibration response of the measuring points under m uncorrelated load combined excitations is measured by multiple response sensors arranged on the system
And calculates its power spectrum
Wherein j is the measuring point number, j is 1,2, n represents the number of all the responding measuring points; q represents the number of times of multiple unrelated multi-source load joint application experiments, q is 1,2, p represents the total number of times of multiple unrelated multi-source load joint application experiments; ω represents frequency;
dividing the response measuring points into known response measuring points and unknown response measuring points; grouping according to different historical working conditions under actual working conditions, wherein the total number of the working conditions is p groups; working condition environment t for vibration response by using known measuring points under uncorrelated multi-source unknown load combined excitation working condition environment
Predicting the vibration response of the unknown measuring point and predicting the result
And n2Vibration response of unknown measurement points
Comparing to evaluate the quality of the multipoint vibration response prediction method based on the support vector machine; wherein n is n1+n2Representing all responsesThe number of measuring points, j is 1,2, n1Is the number of the known measuring point, j ═ n1+1,,n1+h,n1+n2And numbering unknown measuring points.
The method for establishing the support vector machine model comprises the following steps: for training data
Input of ith sample
Output corresponding to ith sample
If m is 1, the method corresponds to a multiple-input single-output support vector machine (MISO SVM), and if not, the method corresponds to a multiple-input multiple-output support vector machine (MIMO SVM). The goal of the support vector machine model is to construct a linear regression function, the model is as follows:
i.e. to solve for
And biSo that fi(x,w)＝yiThe regression prediction is realized, and certainly, regression prediction data cannot be truly regressed to real data, and the deviation between the prediction data and the real data is inevitable. The solution of the support vector machine model becomes an optimization problem, and the solution by the optimization method will be described later. However, in most cases, the regression effect of the data in the original space is not good, and this time, a kernel space is introduced, i.e., the data is mapped into a high-dimensional kernel space to realize better regression, and a kernel method and a kernel function are also introduced. After the introduction of the nuclear space:
non-linear mapping
The input data is mapped to a high-dimensional feature space. According to the structure risk minimization theory, a support vector machine regression model is converted into the optimization problem of solving:
where C is a regularization constant, lεAs a function of the epsilon-insensitive loss
However, under such constraints, the solution of the optimization problem can become quite difficult. Thus, introducing a relaxation variable
And
to solve the optimization problem, at this time, the optimization problem turns into the following problem:
introducing a Lagrange multiplier, and obtaining a Lagrange function of an equation (6) by a Lagrange multiplier method:
and then making the Lagrange function L to calculate partial derivatives of the Lagrange multipliers, and making the partial derivatives be 0 to obtain:
because the support vector machine model meets KKT, the formula (7) is reversely substituted to the formula (5), and the dual problem of the support vector machine regression model is obtained, wherein the dual optimization problem is as follows:
the kernel function is used to compute the inner product of the mapping space as follows:
finally, a support vector machine regression model is obtained as follows:
the introduction of the kernel function enables the function solution to bypass the feature space and be directly carried out in the input space, thereby avoiding the phenomenon that the kernel functions commonly used by the current support vector machine for calculating the nonlinear mapping mainly comprise linear kernels, polynomial kernels, Gaussian radial basis kernels, Sigmoid kernels and the like. The invention selects the Gaussian nucleus
As a kernel function, where xrIs n1Vector, x, formed from response data of known vibrationssIs n2A vector of response data for individual unknown vibrations. x is the number ofrAnd xsTogether forming an input space of the training set, which can be projected to a higher dimensional projection space by means of a gaussian kernel. Wherein sigma>0 is the bandwidth of the gaussian kernel because the gaussian kernel has higher learning efficiency and learning speed. The selection range of the penalty coefficient C is 0-1024; the parameter (width) gamma of the kernel function ranges from 0 to 1024; the range of epsilon in the epsilon-insensitive loss function is 0-1024; the searching method is the minimum Root Mean Square Error (RMSE) of the 'leave one' interactive test; "leave-one-out" cross-validation refers to screening out a group of samples of the total number of training samples from the training samples each time, modeling with the rest of samples to predict the properties of the screened samples, thus obtaining a cross-validation Root Mean Square Error (RMSE) to evaluate the model performanceThe calculation formula is as follows:
wherein, yiThe predicted value of the sample i is,
is the actual value of sample i; selecting the group of parameters corresponding to the minimum RMSE of the 'leave-one-out' interactive inspection as the optimal input parameters of the model through searching; and establishing a corresponding prediction model for regression prediction by using the searched optimal parameters as input parameters of the support vector machine.
After the support vector machine regression model is built, the built support vector machine model can be used for carrying out regression prediction. And taking vibration data in the test sample during corresponding training as input, inputting the data into the support vector machine model, and predicting the vibration output condition of other nodes through the support vector machine model. The function of the training program of the support vector machine is to form a support vector machine model similar to a regression formula through analysis, calculation and regular pattern recognition of training sample data. The support vector machine prediction program inputs corresponding parameters to the support vector machine model, such as vibration data of the known nodes, and the support vector machine model calculates the vibration condition of the unknown nodes according to the input conditions. For the selection of the kernel function and the parameters, the kernel function and the parameters thereof with smaller errors are selected based on the error between the predicted value and the experimental value.
Each sample contains vibration data for all nodes. The known node data is taken as an input layer, and the unknown node data is taken as an output layer. The number of samples is preferably at least ten times greater than the input layer. Therefore, the regression of the support vector machine can be fully trained, and the stability and the expandability of the support vector machine are improved. After the sample is selected, the sample data is divided into two parts. In order to ensure the generalizability of the support vector machine model, data left by a group of sample data is generally randomly removed to serve as training sample data and used for establishing a prediction model; and taking the sample data of the removed group as prediction sample data for evaluating and verifying the built model. And selecting a proper kernel function and parameters of the support vector machine according to the characteristics of the training sample data, so that the support vector machine can fully learn and identify the internal rules of the training sample data, and establishing a corresponding support vector machine regression model. After the kernel function and the parameters of the support vector machine are selected, the prediction sample data is substituted into the established support vector machine model for prediction, the 3dB standard used in the industry is adopted as the evaluation standard, the 3dB standard is used as an index, and the support vector machine model is qualified and can be put into application as long as the prediction data exceeding the 3dB standard is within an acceptable range. If the error is larger, the kernel function and the parameters of the support vector machine model are adjusted, and then the training and the prediction are carried out again until the standard of 3dB required by the industry can be achieved.
In combination with the experimental device, the generated historical experimental data and the establishment method of the support vector machine model, the multi-point vibration response prediction method based on the regression prediction of the support vector machine under the unknown load condition comprises the following steps:
a multipoint vibration response prediction method based on support vector machine regression prediction is characterized in that transfer functions of a system can be not considered, and the multipoint vibration response prediction method can be used under the condition of load input according to n1Response of a known station to System n2The vibrational response of the individual unknown nodes is predicted. The method takes the historical system vibration measured by n vibration sensors as a sample, and takes n1The response of a known measuring point is used as input, and n is used2The vibration response of the unknown nodes is output, a multiple-input multiple-output support vector machine regression model is established, and the support vector machine model is used for predicting the test group n2The vibrational response of the individual unknown nodes. The method comprises the following specific steps:
step A1, establishing sample data of a test group and a training group: according to the method, real historical vibration data is used as a sample, total p historical working conditions of experimental simulation are assumed, a support vector machine model is solved by adopting the p historical data, and then unknown node vibration response under the working condition t is predicted by the model;
step A2, solving a multi-input multi-output support vector machine model: for history sampleThis data, in n1The response of a known measuring point is used as input, and n is used2The vibration response of the unknown nodes is output, the internal relation between the unknown nodes and the internal relation between the unknown nodes is modeled by applying a multi-input multi-output support vector machine method, a quantitative functional relation between the unknown nodes and the internal relation;
the parameters for determining the performance of the support vector machine mainly comprise the selection of a kernel function, the selection of parameters of the corresponding kernel function, a penalty coefficient C and the selection of epsilon in an epsilon-insensitive loss function. The invention selects the Gaussian nucleus
As a kernel function, where σ>0 is the bandwidth of the gaussian kernel because the gaussian kernel has higher learning efficiency and learning speed. The selection range of the penalty coefficient C is 0-1024; the parameter (width) gamma of the kernel function ranges from 0 to 1024; the range of epsilon in the epsilon-insensitive loss function is 0-1024; the searching method is the minimum Root Mean Square Error (RMSE) of the 'leave one' interactive test; "leave-one-out" cross-validation means that a group of samples of the total number of training samples are screened out from the training samples each time, and the rest of samples are modeled to predict the properties of the screened-out samples, so as to obtain a cross-validation Root Mean Square Error (RMSE) to evaluate the model performance, and the calculation formula is as follows:
wherein, ykThe predicted value of the sample k is,
is the true value of sample k; selecting the group of parameters corresponding to the minimum RMSE of the 'leave-one-out' interactive inspection as the optimal input parameters of the model through searching;
applying the searched optimal parameters as input parameters of a support vector machine, and establishing a corresponding prediction model for regression prediction;
step A3, predicting the output conditions of the corresponding nodes under other working conditions: will predict n in the sample data1Support established by response data of known measuring points as input variable inputIn the vector machine model, a prediction sample n is calculated through the support vector machine model2Response data of unknown measuring points;
step a4, modifying and determining the prediction model: comparing the predicted value and the experimental value of the vibration data of the prediction sample obtained in the step (3), if the deviation of the predicted value and the experimental value exceeds an acceptable range, adjusting the relevant parameter value of the support vector machine, and then retraining and predicting until the deviation of the predicted value and the experimental value is within the acceptable range, thereby determining a support vector machine prediction model;
step a5, application of the prediction model: and predicting the node vibration which cannot be directly tested under other unknown working conditions by using the determined support vector machine prediction model.
The method of the invention has the following applicable conditions:
1) the system may be a linear system or a non-linear system, but must be time-invariant;
2) the positions of a plurality of load points under the working condition environment t are unchanged, and the load applied by each load point is stably, stably and randomly excited and is not related to each other;
3) the positions and the directions of the applied load points under the historical data are the same under the working condition environment t, and the loads applied by the load points are stable and are excited immediately and are not related to each other;
4) the number of the known measuring points must be more than or equal to the number of the load points, namely n1≥m；
5) The qualitative relation from the known measuring point to the unknown measuring point must be obtained by p groups of independent experiments, and p is more than or equal to the number of the known measuring points, namely p is more than or equal to n1；
6) Vibration responses of a plurality of known measuring points under irrelevant multi-source load excitation must be measured;
the evaluation indexes of the experimental results of the invention are as follows:
in order to verify the correctness and accuracy of prediction, the predicted data needs to be compared with the real data, and since the experimental data is frequency domain data, the industry generally adopts the standard of relative error 3dB to compare the predicted data with the real data to judge whether the prediction meets the standard. Assuming y is true data and y is predicted data, the 3dB criterion is as follows:
if inequality (11) holds, it indicates that the regression prediction is within 3dB of relative error, i.e., the prediction regression is correct.
If equation (11) does not hold, it indicates that the regression error exceeds 3dB, indicating that the regression is inaccurate. The prediction relative error 3dB criterion is often used in industry practice as a criterion to evaluate the accuracy of frequency domain data predictions.
In addition to the 3dB standard commonly used in the industry, there are also the error analysis evaluation indicators commonly used in MARE, SD and RMSE, which are calculated as follows:
wherein y iskThe value of the k-th component of the true value y,
is an estimate of the k-th component of the true value y. e.g. of the typekThe relative error between the true value and the predicted value of the kth component,
the relative error mean value of the real value and the estimated value. It can be shown that the above three criteria are mathematically equivalent, although they differ in their way of calculation.
The invention has the following beneficial effects:
1) the invention directly utilizes the support vector machine to train the relationship between response data without knowing or identifying the transfer function or the load size or even the load position of the system; firstly, taking the vibration response of a known measuring point as input and the vibration response of an unknown measuring point as output, and establishing a model between the two by using a support vector machine; secondly, solving the coefficient of the regression model of the support vector machine according to the historical response data; finally, the vibration response of the known measuring point under the real working condition is used as the input of a support vector machine model to predict the vibration response of the unknown measuring point;
2) the method mainly aims at carrying out frequency domain vibration response prediction on the unknown measuring points by utilizing the frequency domain vibration response of the known measuring points under the condition of irrelevant multi-source unknown load joint excitation working condition;
3) the method can predict the frequency domain vibration response condition of one unknown measuring point and can also predict the frequency domain vibration response conditions of a plurality of unknown measuring points at the same time;
4) the invention can not only solve the response prediction of a linear system, but also solve the response prediction of a nonlinear system;
5) the support vector machine model of the invention has the advantages that: the support vector machine is very suitable for classifying and regressing small samples, avoids the over-fitting problem and has strong popularization capability; the development of the kernel function enables the support vector machine to not only process the linear regression problem, but also process the nonlinear classification and regression problem, thereby greatly improving the application field of the support vector machine; the support vector machine makes full use of the optimization theory, adopts the dualization of problems, provides an SMO optimization algorithm, and improves the execution efficiency of the support vector machine; in consideration of the nonlinear characteristic among vibration response data in the problem, the support vector machine just corresponds to the nonlinear relation which can be used for searching the data; the support vector machine has higher convergence speed, more sufficient information display and higher stability and robustness;
6) the method is applied to the fields of vibration measurement and vibration response prediction, and particularly can obtain a good vibration response prediction effect when the method is used under the working conditions that the vibration response of certain measuring points cannot be directly measured (or a vibration sensor is damaged) and the load cannot be directly measured under the working conditions of joint excitation of a plurality of irrelevant loads;
7) aiming at the problems of control requirements on vibration in machinery manufacturing, bridges and ships and inconvenience of direct measurement in some areas, the method has the advantages of high prediction precision, quickness and convenience in prediction by using a support vector machine model and taking data collected by sensors which can be arranged in parts such as machinery as input variables and vibration data of corresponding interested nodes as output variables, realizes real-time calculation of vibration condition monitoring of the interested nodes according to the data measured by the sensors, achieves synchronous real-time analysis, and effectively solves the problem of solving the problem of vibration output after a transfer function is solved.
The present invention will be described in further detail with reference to the drawings and embodiments, but the method for predicting the frequency domain of the multi-point vibration response based on the support vector machine is not limited to the embodiments.
Drawings
FIG. 1 is a schematic input-output diagram of multiple-input multiple-output payload and response in the frequency domain;
FIG. 2 is an experimental setup of uncorrelated multi-source joint excitation for exciter excitation and hammer excitation;
FIG. 3 is a schematic view of the vibration measuring point inside the cylindrical shell;
FIG. 4 is a diagram of the placement of the measuring points of the external sound field;
FIG. 5 is a noise stimulus;
FIG. 6 is a vibration point inside the cylindrical shell;
FIG. 7 is a vibratory force excitation source and test site;
FIG. 8 is a comparison result of response prediction results and real results of two channels based on a multivariate multiple-input multiple-output support vector machine under a working condition environment t; wherein fig. 8(a) shows the comparison result of one channel, and fig. 8(b) shows the comparison result of another channel;
FIG. 9 is a decibel out-of-tolerance comparison of the true response results and predicted response results for the two channels of the test case of FIG. 8; in which fig. 9(a) shows the comparison result of one channel and fig. 9(b) shows the comparison result of the other channel.
Detailed Description
The invention is described in further detail below with reference to the accompanying figures 1-9 and examples.
Example 1: an experimental device for multi-source load combined application is shown in fig. 2, and a vibration structure is a fixed disc, has a large damping ratio and can be regarded as a nonlinear time-invariant structure. The experiment does not need to record vibration excitation data of an excitation table and excitation data of a force hammer, but requires that the unknown direction of an excitation point of the excitation table and the unknown direction of an excitation point of the hammering are fixed, so that the system is a time-invariant system. The vibration of the simply supported beam is measured by adopting 6 sensors, and the main vibration direction of the beam can be reflected. 2 of the 6 sensors are used as sensors of unknown nodes for vibration response prediction of a plurality of response points.
Example 2: a method for generating historical experimental data of multipoint vibration response frequency domain prediction under the condition of unknown load is disclosed, and is shown in figures 3 to 7; the independent spherical noise excitation source is used for excitation, 3-magnitude excitation is available, and the magnitude is gradually increased; the independent suspension type vibration table vibration exciter is excited in a vibration mode, 5 magnitude levels are excited, and the magnitude levels are gradually increased; when the noise excitation and the vibration excitation are loaded in a combined mode, the magnitude of the noise excitation and the magnitude of the vibration excitation are combined in pairs to form 15 different magnitudes, and therefore the simulation of a complex sound vibration environment is achieved and the simulation is used for response prediction test research. The method comprises the steps of loading 15 types of noise excitation and vibration excitation combined excitation with different magnitudes on a sound vibration experimental device, respectively measuring the excitation force of the vibration excitation, the excitation acceleration of the vibration excitation and the excitation sound pressure of the sound excitation through a sensor, measuring the response through an acceleration sensor, and recording corresponding experimental result data. In the 15 working conditions, the p-14 working conditions are selected as historical data, namely the number p of independent experiments is 14. One group is used for testing under the working condition environment t. The method comprises the steps of acquiring specific data of 15 groups of n-9 channels through experiments, firstly grouping n-9 response measuring points, and selecting n1Response number of 7 measuring pointsAccording to the response data of the known measuring points, n2Response data of 2 measuring points is used as response data of unknown measuring points. The data is frequency domain data, 1601 samples of data are taken for each channel in each group of data, and the frequency value is from low to high 0Hz to 6.4 KHz.
Example 3: a multipoint vibration response frequency domain prediction method based on a support vector machine is characterized in that historical data are 14 groups in total, the number of all measuring points is 9, firstly, n is 9 responding measuring points, and n is selected1Response data of 7 measuring points as response data of known measuring points, n2Response data of 2 measuring points is used as response data of unknown measuring points. The working condition environment t is used as test data, a relation between response and response is trained by using a p-14 group, namely, the response of two channels in 9 channels is predicted, a response prediction result and a real result comparison result of the two channels are shown in fig. 8, fig. 9 is a decibel super-difference graph of the prediction result and the real result, and it can be seen that the response prediction result basically meets the requirement of 3dB compared with the real result.
The invention establishes a method for predicting the vibration output data of unknown nodes by part of the vibration output data of the known nodes based on a support vector machine. Aiming at the problems of control requirements on vibration in machinery manufacturing, bridges and ships and inconvenience of direct measurement in some areas, the method has the advantages of high prediction precision, rapidness and convenience by using data collected by sensors which can be arranged in parts such as machinery as input variables and using vibration data of corresponding unknown nodes as output variables and using a support vector machine model for prediction, realizes real-time calculation of vibration condition monitoring of interested nodes according to the data measured by the sensors, achieves synchronous real-time analysis, and effectively solves the problem of vibration output after a transfer function is solved, because the machinery is used for realizing real-time prediction and analysis of vibration response.
The parts not involved in the present invention are the same as or can be implemented using the prior art. The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (4)
1. A multipoint vibration response frequency domain prediction method based on a support vector machine is characterized by comprising the following steps:
according to n without considering the transfer function and load input of the system1Response of a known station to System n2Predicting the vibration response of the unknown nodes; the method takes the historical system vibration measured by n vibration sensors as a sample, and takes n1The response of a known measuring point is used as input, and n is used2The vibration response of the unknown nodes is output, a multi-input multi-output support vector machine regression model is established, and then the support vector machine model is utilized to predict n under the real working condition2The vibrational response of the individual unknown nodes; the method comprises the following specific steps:
step A1, establishing historical experimental data and real working condition sample data: taking historical vibration data as a sample, assuming that the historical working conditions simulated by the experiment are p groups in total, and recording the prediction of the real working conditions as the vibration prediction under the working condition environment t;
step A2, solving a multi-input multi-output support vector machine model: for historical sample data, n1The response of a known measuring point is used as input, and n is used2The vibration response of the unknown nodes is output, the internal relation between the unknown nodes and the internal relation is modeled by applying a multi-input multi-output support vector machine method, a quantitative functional relation between the unknown nodes and the internal relation is sought, and a corresponding prediction model is established;
the parameters for determining the performance of the support vector machine comprise selection of a kernel function, selection of parameters of the corresponding kernel function, selection of a penalty coefficient C and selection of epsilon in an epsilon-insensitive loss function; selecting Gaussian kernels
As a kernel function, wherein
Is n1A vector of response data for known vibrations,
is n2A vector of response data for individual unknown vibrations,
and
an input space which together form a training set, which is projected by means of a Gaussian kernel to a higher-dimensional projection space, where σ>0 is the bandwidth of the gaussian kernel; selecting the range of the penalty coefficient C to be 0-1024; selecting the range of the width gamma of the kernel function to be 0-1024; selecting an epsilon range from 0 to 1024 in an epsilon-insensitive loss function; selecting a 'leave one method' search method as the minimum root mean square error of the interactive test; selecting the group of parameters corresponding to the minimum root mean square error after interactive inspection by a 'leave-one-out method' through searching as the optimal input parameters of the model; applying the searched optimal parameters as input parameters of a support vector machine, and establishing a corresponding prediction model for regression prediction;
step A3, predicting the output condition of the corresponding node under the working condition environment t: will predict n in the sample data1Response data of known measuring points are input into a support vector machine model established by the aid of the response data as input variables, and a prediction sample n is calculated through the support vector machine model2Response data of unknown measuring points;
step a4, modifying and determining the prediction model: comparing a predicted value and an experimental value of the predicted sample vibration data obtained according to the support vector machine model, if the deviation of the predicted value and the experimental value exceeds an acceptable range, adjusting the relevant parameter value of the support vector machine, then retraining and predicting until the deviation of the predicted value and the experimental value is within the acceptable range, and determining the support vector machine prediction model;
and step A5, predicting the node vibration which can not be directly tested under other unknown working conditions by using the determined support vector machine prediction model.
2. The multi-point vibration response frequency domain prediction method based on the support vector machine according to claim 1, characterized in that the generation method of the historical experimental data and the real working condition sample data is as follows:
multiple groups of uncorrelated steady random excitations are generated by combining multiple excitation sources, and the magnitude is gradually increased, so that an uncorrelated multi-source load combined application experimental environment is realized, and the vibration response sizes of m uncorrelated load combined excitation lower measuring points are measured by multiple response sensors arranged on the outer surface and the inner surface of the system
And calculates its power spectrum
Dividing the response measuring points into known response measuring points and unknown response measuring points; grouping according to historical working conditions, wherein p groups are formed in total; working condition environment t for vibration response by using known measuring points under uncorrelated multi-source unknown load combined excitation working condition environment
Predicting the vibration response of the unknown measuring point and predicting the result
And n2Vibration response of unknown measurement points
Comparing to evaluate the quality of the multipoint vibration response prediction method based on the support vector machine; wherein q represents the number of times of multiple unrelated multi-source load joint application experiments, and q is 1,2, …, p; j is 1,2, …, n1Is the number of known measuring points, n1Response for known measuring pointNumber j ═ n1+1,…,n1+h…,n1+n2Is the number of the unknown measuring point, h is the measuring point number of the unknown measuring point, h is 1,2, …, n2，n2For the number of vibration responses of unknown nodes, n ═ n1+n2Indicating the number of all responding stations.
3. The frequency domain prediction method of multi-point vibration response based on support vector machine of claim 1, wherein the interactive verification using the "leave-one-out" search method is to screen out a group of samples of the total number of training samples from the training samples each time, and model with the rest of samples to predict the properties of the screened samples, so as to obtain the root mean square error of the interactive verification to evaluate the model performance, and the calculation formula is:
wherein, ykFor the prediction of the value of the sample k,
the true value of sample k.
4. An apparatus for implementing the support vector machine-based multi-point vibration response frequency domain prediction method according to any one of claims 1 to 3, comprising:
the system comprises a time-invariant system, a plurality of excitation sources capable of generating uncorrelated stable random excitation and a plurality of response sensors arranged on the system and used for recording system vibration, wherein the position and the direction of each loading of the excitation are fixed and unchanged, and the plurality of response sensors are distributed in each place of the system and can reflect the main vibration of the system;
the device adopts a vibration structure as a homogeneous disc fixedly supported at the center, and the vibration structure is used as a time-invariant system; two irrelevant excitation sources are adopted, one is excited by a vibration table, the other is excited by a PCB hammer, namely, the excitation of the vibration table and the excitation of the hammer are used as the excitation of the two irrelevant sources of the system, and the positions and the directions of an excitation point of the vibration table and an excitation point of the hammer are fixed; a plurality of vibration sensors are arranged on the homogenizing disc fixedly supported at the center to measure the vibration of the disc and can reflect the main vibration of the disc, a plurality of the vibration sensors are used as sensors with known measuring points, and a plurality of the vibration sensors are used as sensors with unknown nodes for predicting the vibration response of a plurality of response points.
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