CN101776674A - Fuzzy dynamic mode identification-based method for testing high-temperature mechanical property of composite material - Google Patents

Abstract

The invention relates to a fuzzy dynamic mode identification-based method for testing high-temperature mechanical property of a composite material. The method comprises the following steps: forming a material into a sample set, establishing a sample property index matrix by adopting standardization and normalization of initial data, then establishing a fuzzy similar matrix and calculating a fuzzy equivalent matrix, determining lambda-cut matrix and t inspection critical parameters by continually debugging a program through a t inspection method to acquire a unique optimal classification, inputting characteristic parameters of materials to be identified, calculating the similarity of the materials to be identified, and calculating an approach degree between the materials X to be identified and each group of samples. Compared with the prior art, the method has the advantages of improving the work efficiency, reducing the workload of high-temperature heat treatment test, meeting the requirements of economy and accuracy, having practical application value, and effectively testing the properties of different composite materials at the high temperature or under other special environments and condition requirements.

Description

Method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification

Technical field

The present invention relates to a kind of method for testing high-temperature mechanical property of composite material, especially relate to a kind of method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification.

Background technology

Mechanical property is the most important performance of material.Advantages such as compound substance has that specific strength height, specific modulus are big, anti-fatigue performance and damping performance are good, the physical quantity of weighing the mechanical performance of compound substance mainly contains the rigidity and the intensity of compound substance.The stiffness characteristics of compound substance is by the character of component material, the orientation of reinforcing material and shared volume fraction decision, and, in actual compound substance, exist various unevenness and uncontinuity all can have influence on the performance of material inevitably owing to manufacturing process, stochastic factor.Compound substance except that mechanical property, often needs to have good physical property such as heat resistance simultaneously in the use of some occasion, and metal-base composites is typical representative.Metal-base composites also has high tenacity and high thermal conductivity except that having high-modulus, high-intensity characteristics, the very fast diffusion of local high temperature heat source is disappeared, and helps solving problems such as thermal current impact.

Along with science and technology development, new compound substance emerges in an endless stream, and the user is when selecting these materials for use, and Chang Yin has little understanding to their performance, causes to feel very big difficulty when selecting the compound substance type.The high-temperature mechanical property of composite material data are successfully to prepare and select data indispensable in the high-performance composite materials.And the selection of material is as one of key factor of material design, and its result is directly connected to a lot of aspects of material design, and the quality of composite products and cost etc. are had very big influence.At present, determine that the mechanical method of material at high temperature is to carry out the high-temperature heat treatment test, this is one and takes a lot of work, takes and expect extremely hard work.The present invention provides a kind of new mode identification method for quick, the intelligent selection of high-temperature mechanical property of composite material.

Certain mathematical method is promptly used in pattern-recognition, and multifactor information is handled, and with the thing heap sort, understands relation and the influence of each factor to classifying between each factor, and sums up rule and determine the affiliated classification of something.

In view of compound substance high-temperature machinery poor information integrality and determinacy, but a fuzzy notion, the method and the theory that make certainty information handle are suitable no longer fully.Therefore, attempt to utilize certain simple physical amount to come accurately to determine and measure the high-temperature machinery of material, must be difficult to obtain optimum.

It is starting point that the present invention mainly is subjected to the influence of its physics, mechanical property with the high-temperature machinery of compound substance, according to theory of fuzzy mathematics, carry out the fuzzy cluster analysis by area of computer aided, the high-temperature machinery of new material is discerned and predicted in conjunction with Fuzzy Pattern Recognition.Solved the mechanical property of material under hot environment and estimated the problem of difficulty, the advantage of comprehensive utilization fuzzy cluster and pattern-recognition reduces or has avoided carrying out follow-up simulation test or destructive test again, has saved a large amount of labor capacity and test funds.This method can be increased work efficiency, and has important significance for theories and practical value.

Summary of the invention

Purpose of the present invention is exactly to provide a kind of optimal classification, recognition efficiency height, convenient simple and direct method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification of calculating process of obtaining for the defective that overcomes above-mentioned prior art existence.

Purpose of the present invention can be achieved through the following technical solutions:

A kind of method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification is characterized in that this method may further comprise the steps:

(1) material is constituted sample set, the sample properties index matrix that adopts raw data standardization and normalized to form by the various factors that influences the material at high temperature mechanical property;

(2) set up fuzzy similarity matrix, calculate fuzzy equivalent matrix R ' then, determine that by program is constantly debugged λ cuts matrix t check critical parameters T with the t method of inspection again _mObtain unique optimal classification, and set up colony's pattern waiting that evaluating material sorts out;

(3) input material characteristics parameter to be identified is calculated the similarity of material to be identified, obtain the approach degree between material X to be identified and each population sample after, as maximum similarity N (X, Y _j) during greater than defined threshold, think this unknown material and Y _jThe high-temperature machinery unanimity of family, otherwise carry out the high-temperature mechanical property classification of dynamic clustering Fuzzy Pattern Recognition material again.

Original data normalization and normalized are to be transformed to all characteristic indexs than big-difference and all to become characteristic what the unit of sample characteristics index and the order of magnitude occurred in the described step (1);

Standardized value: $y_{\mathrm{ik}}^{\′}=\frac{y_{\mathrm{ik}}-y_k}{\sqrt{s_k}},$ i＝1，2，…，n；k＝1，2，…，m， ${\stackrel{\‾}{y}}_k=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{y}_{\mathrm{ik}},$

Normalized value: $x_{\mathrm{ik}}=\frac{{y^{\′}}_{\mathrm{ik}}-{y^{\′}}_{i\max }}{{y^{\′}}_{i\max }-{y^{\′}}_{i\min }},$

Wherein n is the data number, and m is the feature number, y ' _ImaxExpression y _IkMaximal value; Y ' _IminExpression y _IkMinimum value.

Set up fuzzy similarity matrix in the described step (2) and select for use the high absolute value derivative method of resolution to determine degree of correlation, its mathematical model is:

Wherein, c is a selectable constant value, makes to satisfy 0≤r _Ij≤ 1.Can get fuzzy similarity matrix thus.

The t method of inspection adopts following steps in the described step (2):

One group observations λ of known sample ₁, λ ₂..., λ _n, λ wherein _mBe dubious value, do not comprise that the sample average of dubious value and sample standard deviation are respectively:

$\stackrel{\‾}{{\mathrm{\λ}}^{\′}}=\frac{1}{n-1}\underset{i\≠m}{\overset{n}{\underset{i=1}{\mathrm{\Σ}}}}{\mathrm{\λ}}_i$

Work as critical parameters

The time, wherein: t _p(n-2) be that degree of freedom is the P fractile of the t distribution of (n-2), p=1-α/2, α gets 0.01, at this moment λ _mBe the acceptance value, determine that by program is constantly debugged λ cuts matrix t check critical parameters T _m, to obtain unique optimal classification.

Setting up colony's pattern in the described step (2) is that set sample set is divided into M class sample material family according to getting fixed λ, and every class comprises some samples, and its set is X _M, on behalf of the comprehensive characteristics of this family, each population sample constitute colony's pattern.

The similarity of calculating material to be identified in the described step (3) adopts following method: material to be identified is regarded by the fuzzy set of p character representation, represented with M as the population sample that is formed by known materials also is the fuzzy set by p character representation, with N _jExpression, degree approaching between two fuzzy sets can be weighed with approach degree, obtains maximum similarity N (M, N _j); Enough similar between the high-temperature mechanical property for the high-temperature machinery that guarantees new material and population material family, stipulate a threshold value v, as maximum similarity N (M, N _jDuring) 〉=v, think this unknown material and N _jThe high-temperature machinery unanimity of family is as N (M, N _jDuring)＜v, think that the high-temperature mechanical property of this kind material and any gang is all inconsistent, the material that need sort is set up new colony's pattern, discerns again.

Compared with prior art, the present invention has the following advantages:

(1) adopts t value check Fuzzy Cluster Analysis method, realized the adaptivity of fuzzy clustering, obtained the optimal classification in the cluster analysis;

(2) in conjunction with maximum approach value Fuzzy Pattern Recognition technology, can be according to the approach degree threshold value of setting, the high-temperature mechanical property of unknown metal-base composites is effectively classified and discerned;

(3) analysis of the high-temperature mechanical property of metal-base composites is based upon on the foundation of numerical analysis, can carry out dynamic clustering by different similarity requirements;

(4) finish algorithm with computer programming, have higher accuracy, and calculating process is convenient, simple and direct.

Description of drawings

Fig. 1 is a process flow diagram of the present invention.

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Embodiment

A kind of method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification, process chart as shown in Figure 1.Recognition methods basic process is as follows: at first material is constituted sample set, then set up the sample properties index matrix of forming by the various factors that influences the material at high temperature mechanical property, then select for use suitable method to obtain fuzzy similarity matrix, calculate fuzzy equivalent matrix then, determine that by program is constantly debugged λ cuts matrix t check critical parameters T with the t method of inspection again _mObtain unique optimal classification, and set up colony's pattern to waiting that evaluating material sorts out, import material characteristics parameter to be identified at last, calculate the similarity of material to be identified, after obtaining the approach degree between material X to be identified and each population sample, according to the maximum approach value principle, as maximum similarity N (X, Y _j) during greater than defined threshold, think this unknown material and Y _jThe high-temperature machinery unanimity of family, otherwise carry out the high-temperature mechanical property classification of dynamic clustering Fuzzy Pattern Recognition material again.

In implementation process, scale for the accuracy, typicalness and the data set that guarantee data, select for use the data of measuring in the table 1 as sample set Y, with the conventional mechanical behavior under high temperature of material as characteristic index, set up sample properties normalization index matrix X, use the absolute value counting backward technique and calculate degree of correlation, obtain fuzzy similarity matrix R, adopt Transitive Closure Method to obtain fuzzy equivalent matrix R ', will wait to evaluate the sample set dynamic clustering of material by the t method of inspection of λ intercept.Discern the classification of the high-temperature mechanical property data of a certain material with the maximum approach value principle.Key step is as follows:

1, sets up sample index

The height of material at high temperature mechanical property waits with heat treatment temperature, elastic modulus, pulling strengrth, elongation at break usually and weighs.8 kinds of metal-base composites commonly used of getting known high-temperature mechanical property are sample, and their physics, mechanical performance index are listed in table 1.

Table 1 metal-base composites physics, mechanical performance index

With eight kinds of materials is sample, and each sample has four features, and then sample set can be represented with following matrix form:

2, raw data standardization and normalized

Be transformed to all characteristic indexs than big-difference and all become characteristic what the unit of sample characteristics index and the order of magnitude occurred;

Standardized value: $y_{\mathrm{ik}}^{\′}=\frac{y_{\mathrm{ik}}-{\stackrel{\‾}{y}}_k}{\sqrt{s_k}},$ i＝1，2，…，n；k＝1，2，…，m，

Normalized value: $x_{\mathrm{ik}}=\frac{{y^{\′}}_{\mathrm{ik}}-{y^{\′}}_{i\max }}{{y^{\′}}_{i\max }-{y^{\′}}_{i\min }}$

Wherein n is the data number, and m is the feature number, y ' _ImaxExpression y _IkMaximal value; Y ' _IminExpression y _IkMinimum value.The matrix X after standardization and normalized is as follows for raw data:

3, set up the fuzzy resembling relation matrix

Select for use the high absolute value derivative method of resolution to determine degree of correlation, its mathematical model is:

Wherein, c is a selectable constant value, makes to satisfy 0≤r _Ij≤ 1.Can get fuzzy similarity matrix thus, c gets 0.09,0≤r in following formula _Ij, can get following fuzzy similarity matrix at≤1 o'clock:

4, set up the fuzzy equivalence relation matrix

Utilization asks the quadratic method of transitive closure to obtain fuzzy equivalent matrix R ':

5, fuzzy cluster

The sample average and the sample standard deviation that do not comprise dubious value are respectively:

$\stackrel{\‾}{{\mathrm{\λ}}^{\′}}=\frac{1}{n-1}\underset{i\≠m}{\overset{n}{\underset{i=1}{\mathrm{\Σ}}}}{\mathrm{\λ}}_i$

Work as critical parameters

The time, wherein: t _p(n-2) be that degree of freedom is the P fractile of the t distribution of (n-2), p=1-α/2, α gets 0.01, at this moment λ _mBe the acceptance value, determine that by program is constantly debugged λ cuts matrix t check critical parameters T _m, to obtain unique optimal classification.

In R ', get λ=1,0.71,0.39,0.21 0.17 can obtain a series of λ cuts matrix, cuts the t method of inspection of matrix by λ and determines critical parameters, the classification schemes particular significant effect can be guaranteed in final definite λ=0.71 of working as, and classification results is { u1, u7}, { u2}, { u3, u5, u8}, { u4}, { u6}.

6, set up colony's pattern

Set sample set is divided into 5 class sample material families according to getting fixed λ=0.71, and every class comprises some samples, and its set is:

X ₅＝{{u1，u7}，{u2}，{u3，u5，u8}，{u4}，{u6}}

Each population sample is represented the comprehensive characteristics of this family, and these population sample promptly constitute colony's pattern, is expressed as the I of colony respectively, the II of colony, the III of colony, the IV of colony, the V of colony.

7, fuzzy diagnosis

Material to be identified is regarded by the fuzzy set of four character representations, is represented as the population sample that is formed by known materials also is the fuzzy set by four character representations, with N with M _jThe expression, obtain the approach degree between material to be identified and each population sample after, according to the maximum approach value principle, the high-temperature mechanical property of this unknown material should be close with the population material family high-temperature mechanical property with maximum approach value.For more different approach degree measures,, adopted lattice approach degrees, hamming approach degree and minimax approach degree to calculate the approach degree of sample undetermined and population model respectively to the recognition result of colony's pattern.Enough similar between the high-temperature mechanical property for the high-temperature machinery that guarantees new material and population material family, defined threshold v is 0.64.

8, emulation experiment and interpretation of result

The colony's library that forms by fuzzy clustering according to the approach degree threshold value of setting, is calculated the characteristic parameter of material to be identified and the approach degree of colony's pattern in conjunction with the approach degree method, unknown sample is carried out Model Matching, and employing table 2 data is carried out emulation experiment.

Table 2 emulation experiment test data table

The emulation recognition result of different approach degrees is as shown in table 3.According to the maximum approach value principle of selecting in the approximately principle, the consistent discrimination sample 1 of emulation is 67%, and sample 2 is 100%, and sample 3 is 100%.

Table 3 adopts the simulation result of different approach degrees to compare

This routine simulation result shows: when adopting three kinds of approach degree methods to carry out fuzzy model identification, the accuracy of identification of hamming approach degree and minimax approach degree is higher, the recognition result unanimity.

This routine calculation procedure is based on Matlab language compilation and debugging.In the above-mentioned fuzzy dynamic mode recognition methods, it is time-consuming to relate to computation process, also comparatively loaded down with trivial details.Power function that provides with Matlab fuzzy system tool box and self-editing function on this basis can realize rapidly, exactly that the high-temperature mechanics attribute of material differentiates problem, and processing procedure is succinct, reliable.

Fuzzy dynamic mode recognition methods of the present invention can alleviate the tested number that the user carries out mechanical property of materials classification greatly, for selecting alternative material, the user provides great convenience, intelligent method applying in the material design had certain practical significance, is a kind of economically viable area of computer aided material method for designing.

Technical thought of the present invention except can the mechanical property of materials of evaluating combined material under high-temperature situation, also can be applicable to the test of other environment other materials performances.

Claims (6)

1. method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification is characterized in that this method may further comprise the steps:

(1) material is constituted sample set, the sample properties index matrix that adopts raw data standardization and normalized to form by the various factors that influences the material at high temperature mechanical property;

(2) set up fuzzy similarity matrix, calculate fuzzy equivalent matrix R ' then, determine that by program is constantly debugged λ cuts matrix t check critical parameters T with the t method of inspection again _mObtain unique optimal classification, and set up colony's pattern waiting that evaluating material sorts out;

(3) input material characteristics parameter to be identified is calculated the similarity of material to be identified, obtain the approach degree between material X to be identified and each population sample after, as maximum similarity N (X, Y _j) during greater than defined threshold, think this unknown material and Y _jThe high-temperature machinery unanimity of family, otherwise carry out the high-temperature mechanical property classification of dynamic clustering Fuzzy Pattern Recognition material again.

2. a kind of method for testing high-temperature mechanical property of composite material according to claim 1 based on fuzzy dynamic mode identification, it is characterized in that original data normalization and normalized are to be transformed to all characteristic indexs than big-difference and all to become characteristic what the unit of sample characteristics index and the order of magnitude occurred in the described step (1);

Standardized value: $y_{\mathrm{ik}}^{\text{'}}=\frac{y_{\mathrm{ik}}-{\stackrel{\‾}{y}}_k}{\sqrt{s_k}},$ i＝1，2，…，n；k＝1，2，…，m， ${\stackrel{\‾}{y}}_k=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{y}_{\mathrm{ik}},$ $S_k=\frac{1}{m-1}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(y_{\mathrm{ik}}-{\stackrel{\‾}{y}}_k)}^2$

Normalized value: $x_{\mathrm{ik}}=\frac{{y^{\′}}_{\mathrm{ik}}-{y^{\′}}_{i\max }}{{y^{\′}}_{i\max }-{y^{\′}}_{i\min }},$

Wherein n is the data number, and m is the feature number, y ' _ImaxExpression y _IkMaximal value; Y ' _IminExpression y _IkMinimum value.

3. a kind of method for testing high-temperature mechanical property of composite material according to claim 1 based on fuzzy dynamic mode identification, it is characterized in that, set up fuzzy similarity matrix in the described step (2) and select for use the high absolute value derivative method of resolution to determine degree of correlation, its mathematical model is:

Wherein, c is a selectable constant value, makes to satisfy 0≤r _Ij≤ 1.Can get fuzzy similarity matrix thus.

4. a kind of method for testing high-temperature mechanical property of composite material based on fuzzy dynamic mode identification according to claim 1 is characterized in that the t method of inspection adopts following steps in the described step (2):

One group observations λ of known sample ₁, λ ₂..., λ _n,, λ wherein _mBe dubious value, do not comprise that the sample average of dubious value and sample standard deviation are respectively:

Work as critical parameters

The time, wherein: t _p(n-2) be that degree of freedom is the P fractile of the t distribution of (n-2), p=1-α/2, α gets 0.01, at this moment λ _mBe the acceptance value, determine that by program is constantly debugged λ cuts matrix t check critical parameters T _m, to obtain unique optimal classification.

5. a kind of method for testing high-temperature mechanical property of composite material according to claim 1 based on fuzzy dynamic mode identification, it is characterized in that, setting up colony's pattern in the described step (2) is that set sample set is divided into M class sample material family according to getting fixed λ, every class comprises some samples, and its set is X _M, on behalf of the comprehensive characteristics of this family, each population sample constitute colony's pattern.

6. a kind of method for testing high-temperature mechanical property of composite material according to claim 1 based on fuzzy dynamic mode identification, it is characterized in that, the similarity of calculating material to be identified in the described step (3) adopts following method: regard material to be identified as by p character representation fuzzy set, represent with M, the population sample that is formed by known materials also is the fuzzy set by p character representation, with N _jExpression, degree approaching between two fuzzy sets can be weighed with approach degree, obtains maximum similarity N (M, N _j); Enough similar between the high-temperature mechanical property for the high-temperature machinery that guarantees new material and population material family, stipulate a threshold value v, as maximum similarity N (M, N _jDuring) 〉=v, think this unknown material and N _jThe high-temperature machinery unanimity of family is as N (M, N _jDuring)＜v, think that the high-temperature mechanical property of this kind material and any gang is all inconsistent, the material that need sort is set up new colony's pattern, discerns again.

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