CN106991252A - Sophisticated testing Evaluation of Uncertainty method - Google Patents
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Abstract
The present invention relates to a kind of sophisticated testing Evaluation of Uncertainty method, according to the probability density distribution of influence sophisticated testing result input parameter, input data is generated with Latin Hypercube Sampling method；Using numerical experimentation or actual loading test, the output data of corresponding input data is obtained；The mathematical modeling set up by least square method SVMs by the data obtained between input and output data；According to the mathematical modeling established, the output result corresponding to input data is predicted, and verify the accuracy of mathematical modeling；Random generation input data, as the input item of mathematical modeling, so as to produce output data, Mathematical Modeling Methods is combined with monte carlo method, for evaluating sophisticated testing result uncertainty.The evaluation method is more more accurate than existing conventional GUM methods.
Description
Technical field
The present invention relates to a kind of product test technology, more particularly to a kind of sophisticated testing Evaluation of Uncertainty method.
Background technology
Uncertainty of measurement is the important indicator in measurement process, and it can be used for the attribute of analysis product, assesses product
Quality simultaneously sets up its criteria of quality evaluation.Requirement due to industrial products to tolerance is more and more tighter, and uncertainty of measurement is also therewith
It is increasingly appearing among theoretical research and engineering practice.In fact, measurement is not limited solely to industry, business, science and technology
And the field such as environmental project, also almost it is present among the mankind each activity, therefore, the evaluation of its uncertainty has to be weighed very much
The meaning wanted.
At this stage, the evaluation on uncertainty of measurement, Main Basiss test measurement uncertainty guide (GUM).If
Measurement model is linear, and output quantity probability distribution is normal distribution, then GUM methods can provide accurate result.But when survey
Measure that model is complicated, output quantity probability distribution is substantially asymmetric, or ask local derviation complicated using being run into GUM procedures and obtain
The problems such as not meeting actual comprising interval when, evaluate the obtained resultant error of uncertainty of measurement using GUM methods larger.
For sophisticated testing, the probability density function of its measurement model and input quantity is evaluated substantially in non-linear with GUM methods
The uncertainty of its measurement result is difficult to provide accurate result.However, the mathematical modeling hair for being inputted and being exported based on sophisticated testing
The Method of Stochastic that exhibition is got up, i.e., monte carlo method (MCM) is with regard to that can efficiently solve this problem.
The content of the invention
Substantially utilized the present invention be directed to measurement model and the probability density function of input quantity in nonlinear sophisticated testing
The problem of GUM method error of quality appraisement is big, it is proposed that a kind of sophisticated testing Evaluation of Uncertainty method, by by Mathematical Modeling Methods
Combine with monte carlo method, for evaluating sophisticated testing result uncertainty.Under the guide for method that the present invention is provided,
The foundation of influence sophisticated testing result input/output argument mathematical modeling is completed, and result of the test uncertainty is divided
Analysis, gives sophisticated testing result estimate, standard uncertainty and includes interval corresponding to comprising probability.
The technical scheme is that：A kind of sophisticated testing Evaluation of Uncertainty method, specifically includes following steps：
1), according to the probability density distribution of influence sophisticated testing result input parameter, given birth to Latin Hypercube Sampling method
Into input data, it is specially：
Tested by historical data statistics and Calibration Simulation, respectively obtained the main input ginseng of influence sophisticated testing result
Number and its probability density distribution, further according to the Latin Hypercube Sampling method of input probability Density Distribution, obtain some groups of inputs
Data, are divided into modeling input data and checking input data by the input data of generation；
2), using numerical experimentation or actual loading test, corresponding step 1 is obtained) the modeling output data of input data and test
Demonstrate,prove output data；
3) step 1, is passed through by least square method SVMs) and modeling data 2) set up input and output data it
Between mathematical modeling；
4), according to step 3) mathematical modeling that establishes, by step 1) checking input data is input to the mathematics established
In model, output result, output result and step 2 are obtained) verify that output data is compared, verify the accurate of mathematical modeling
Property, such as inaccurate return to step 1) readjust sample size progress modeling and the checking again for generating input data；
5) input data, is randomly generated using Monte Carlo sampling, and output number is produced according to the mathematical modeling after checking
According to the estimate of monte carlo method analysis sophisticated testing result, standard uncertainty and corresponding to most short comprising probability
Include interval.
The beneficial effects of the present invention are：Sophisticated testing Evaluation of Uncertainty method of the present invention, according to the mathematical modulo of foundation
The sophisticated testing Evaluation of Uncertainty method of type and monte carlo method is more more accurate than existing conventional GUM methods.
Brief description of the drawings
Fig. 1 is least square method SVMs system assumption diagram；
Fig. 2 is least square method SVMs overall flow figure；
Fig. 3 is cervical injuries of embodiment of the present invention exponential forecasting and actual measurement comparison diagram；
Fig. 4 is the prediction of neck moment of torsion and actual measurement comparison diagram in the embodiment of the present invention；
Fig. 5 is the prediction of neck shear power and actual measurement comparison diagram in the embodiment of the present invention；
Fig. 6 is the prediction of neck pulling force and actual measurement comparison diagram in the embodiment of the present invention；
Fig. 7 is that comparison diagram is predicted and surveyed to low portion of neck of embodiment of the present invention shearing force；
Fig. 8 is that comparison diagram is predicted and surveyed to low portion of neck of embodiment of the present invention pulling force；
Fig. 9 is that comparison diagram is predicted and surveyed to low portion of neck of embodiment of the present invention moment of torsion；
Figure 10 is the basic flow sheet that monte carlo method analyzes sophisticated testing uncertainty；
Figure 11 is sophisticated testing result Y of the present invention based on least square method supporting vector machine model and MCM distribution letter
Number GY(η) figure.
Embodiment
The sophisticated testing Evaluation of Uncertainty method based on sophisticated testing result and model construction of SVM of foundation, including such as
Lower step：
S1：According to the probability density distribution of influence sophisticated testing result input parameter, given birth to Latin Hypercube Sampling method
Into input data, the input data of generation is divided into modeling input data and checking input data.
S2：Using numerical experimentation or actual loading test, obtain the modeling output data of corresponding S1 input datas and verify defeated
Go out data.
S3：By least square method SVMs by step S1 and S2 modeling data set up input and output data it
Between mathematical modeling.
S4：The mathematical modeling established according to S3, verifies that input data is input to the mathematical modeling established by step S1
In, output result is obtained, output result is compared with step S2 checkings output data, verifies the accuracy of mathematical modeling, such as
The sample size that inaccurate return to step S1 readjusts generation input data model and verify again.
S5：It is combined using the mathematical modeling and monte carlo method set up based on SVMs, analyzes sophisticated testing
As a result estimate, standard uncertainty and corresponding to the shortest coverage interval comprising probability.
Result of the test uncertainty specific embodiment is whipped with the automotive seat of certain model below in conjunction with the accompanying drawings to this hair
It is bright to be described further.
The present invention sets up the mathematical method of sophisticated testing result analysis on Uncertainty so that seat whips experiment as an example, including
Following steps：
S1：According to the probability density distribution of influence sophisticated testing result input parameter, given birth to Latin Hypercube Sampling method
Into input data.
Tested by historical data statistics and Calibration Simulation, respectively obtained influence sophisticated testing result six are main defeated
Enter parameter and its probability density distribution is as shown in table 1 below：
Table 1
| Sequence number | Input parameter | Probability density distribution |
| 1 | H point X-axis coordinates | HxN(0.1498,1.23782) |
| 2 | H point Z axis coordinates | HzN(-7.4775,4.05272) |
| 3 | Head post gap | BS~N (- 0.1098,0.73772) |
| 4 | Backrest angle | BA~U (17.5,22.5) |
| 5 | Pretightning force F1 | F1~N (58.095,12.5432) |
| 6 | Pretightning force F2 | F2~N (132.76,16.982) |
Using the Latin Hypercube Sampling method according to input probability Density Distribution, some groups of input datas are obtained.
S2：Using numerical experimentation or actual loading test, corresponding output data is obtained.
The input data obtained for S1, corresponding output data is obtained by numerical experimentation or actual loading test.At this
In example, FEM Numerical Simulation is contrasted with whipping result of the test, it is found that relative error is within 10% between the two,
The complexity of experiment is whipped in view of seat, usable finite element simulation replaces actual loading test.The input ginseng obtained using sampling
Test simulation is whipped in number progress, obtains 50 groups of inputoutput datas.
S3：The mathematical modeling set up by least square method SVMs between input and output data.
SVMs is a kind of learning-oriented mechanism, and its principle is to utilize mathematical method and optimisation technique, is returned
Prediction or the process of classification.The robustness and validity of the mechanism are very good, and with spies such as applied widely, convenience of calculation
Point.This process choosing is the least square method SVMs for supporting the kernel function of multiple-input and multiple-output for RBF
(LS-SVM), shown in its architecture and overall flow below figure 1 and Fig. 2.
The 50 groups of inputoutput datas obtained according to Latin Hypercube Sampling and S2, training group, 10 groups of works are used as using 40 groups
For prediction group, LS-SVM founding mathematical models are utilized.
S4：According to the mathematical modeling established, the output result corresponding to input data is predicted, and verify mathematical modeling
Accuracy.
When being modeled using LS-SVM, Selection of kernel function radial direction base kernel (RBF), the six prediction output datas finally given
Contrast and its relative error, mean square error with the obtained output results of S2 is as shown in Fig. 3-Fig. 9, and Predict exports for prediction
Data, Test is that S2 obtains output result, and MRE refers to relative error, and MSE refers to mean square error.
Using the result of the LS-SVM mathematical model predictions set up, compared with S2 output result, experiment knot is whipped in influence
Two principal elements of fruit, i.e., the relative error of cervical injuries index and upper neck moment of torsion is within 3%, and mean square error
It is all smaller.Therefore, the mathematical model prediction results contrast that LS-SVM is set up is accurate, available for sophisticated testing analysis on Uncertainty
Modeling method.
S5：It is combined using the mathematical modeling and monte carlo method set up based on SVMs, analyzes sophisticated testing
As a result estimate, standard uncertainty and corresponding to the shortest coverage interval comprising probability.
M=10 is generated at random using the Monte Carlo methods of sampling6The input data of individual sample, and it is used as LS-SVM input
, so as to produce output data, the step of further according to monte carlo method and flow (such as Figure 10 monte carlo methods analysis is complicated
Test the basic flow sheet of uncertainty), calculate the estimate for whipping result of the test, standard uncertainty and corresponding to bag
Shortest coverage interval containing Probability p, the uncertainty point of the sophisticated testing result as shown in table 2 based on LS-SVM models and MCM
Analyse result.
Table 2
The sophisticated testing result of M sample is sorted according to strictly increasing, Y distribution function G is obtainedY(η) such as Figure 11 institutes
Show, then, the Evaluation of Uncertainty system set up in example preferably analyzes the uncertainty of seat DYNAMIC COMPLEX experiment, and
For other sophisticated testings, the theory and flow of this method are equally applicable.Therefore, the sophisticated testing that the present invention is set up is not known
Degree analysis Monte Carlo method has certain practice significance.
S1 and S2 correspond to 50 groups of inputs and output data respectively, with respective 40 groups of data come founding mathematical models, and in addition 10
Group input data substitutes into output result in model, and 10 groups of data comparisons corresponding with S2, according to relative error and mean square error
It is smaller and in the reasonable scope, it is believed that can be with model output result come Approximate Equivalent S2 result.Under normal circumstances, because
M=10 is at least needed with monte carlo method analysis sophisticated testing uncertainty6Individual sample, and S2 corresponds to S1 input datas
Numerical value or actual loading test result are then very limited, so the result that must export large sample with model is equivalent to complete.
If model output result and S2 Comparative result error are larger, that is, verify that data model is inaccurate, illustrates modeling
Inputoutput data sample size not enough, return to S1, generate more multisample, afterwards repeatedly S2-S4, until error it is smaller or
In zone of reasonableness, i.e., model is relatively accurate.
Claims (1)
1. a kind of sophisticated testing Evaluation of Uncertainty method, it is characterised in that specifically include following steps：
1）, according to influence sophisticated testing result input parameter probability density distribution, with Latin Hypercube Sampling method generate it is defeated
Enter data, be specially：
By historical data statistics and Calibration Simulation test, respectively obtained influence sophisticated testing result main input parameter and
Its probability density distribution, further according to the Latin Hypercube Sampling method of input probability Density Distribution, obtains some groups of input datas,
The input data of generation is divided into modeling input data and checking input data；
2）, using numerical experimentation or actual loading test, obtain corresponding step 1）The modeling output data of input data and checking are defeated
Go out data；
3）, step 1 passed through by least square method SVMs）With 2）Modeling data set up input output data between
Mathematical modeling；
4）, according to step 3）The mathematical modeling established, by step 1）Checking input data is input to the mathematical modeling established
In, obtain output result, output result and step 2）Checking output data is compared, and verifies the accuracy of mathematical modeling, such as
Inaccurate return to step 1）The sample size for readjusting generation input data model and verify again；
5）, using Monte Carlo sampling randomly generate input data, and output data is produced according to the mathematical modeling after checking, used
The monte carlo method analysis estimate of sophisticated testing result, standard uncertainty and include area corresponding to most short comprising probability
Between.
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Application publication date: 20170728 |