CN106777918A - The inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach - Google Patents

Abstract

Function gradient structure material property inversion method based on guided wave and fuzzy algorithmic approach, guided wave group velocity is obtained using Legendre polynomial method forward calculations, and the volume distributed median function of FGM structural material parameters is recognized using fuzzy algorithmic approach inverting；Comprise the following steps that：1）, the given FGM structural volume distribution functions of selection, the guided wave group velocity in FGM structures is obtained using Legendre polynomial methods；2）, using genetic Algorithm Design fuzzy controller；3）, write based on genetic algorithm Fuzzy Controller Parameters optimization program；4）, write fuzzy controller program；5）The good fuzzy controller of several guided wave group velocity In-put designs at FGM structure lower mode low frequencies, inverting are exported into the material property of FGM.Parameter value and setting value error very little in the volume distributed median function of the FGM structures that inverting of the present invention is obtained, for the detection of FGM material properties provides a kind of effective method.

Description

Inversion method for material properties of functionally graded structures based on guided waves and fuzzy algorithms

technical field

The invention belongs to the technical field of inversion of material properties, in particular to an inversion method for material properties of functional gradient structures based on guided waves and fuzzy algorithms.

Background technique

Functionally Gradient Materials (FGM for short) is a new type of heterogeneous composite whose components or structures change in space regularly, making the internal interface decrease or even disappear, so that the properties of the material also change in space. Material. The volume content of FGM components changes smoothly, which brings various advantages such as reducing residual stress, alleviating stress concentration and enhancing bond strength, and the diversity of FGM internal gradient distribution makes it adaptable to different working environments. Therefore, FGM It has broad application prospects, and mastering the material properties of FGM is the prerequisite for its effective use.

Ultrasonic guided waves have dispersion and multi-mode characteristics, that is, at different frequencies, multiple modes of guided waves have different wave velocities and different wave structures, and this characteristic of guided waves is determined by the material itself, so Inversion can be considered to determine the properties of materials based on the properties of guided waves. This allows us to extract various information that characterizes the dynamic characteristics of structures from multiple modal guided wave signals at multiple frequencies, and also makes the application range of ultrasonic guided wave technology more and more extensive.

Advanced testing methods for the mechanical properties of composite structures usually use the complex relationship between the dynamic response of the structure (such as wave velocity, displacement response and vibration frequency, etc.) forward problem. This forward problem can be solved analytically or numerically. Then, if there is a series of accurate theoretical calculation data or experimentally measured structural response data, combined with a large number of forward calculations, the material properties of composite materials can be identified through correctly constructed inversion models.

The existing inversion technology has great defects and certain limitations in terms of stability, error control of data and data processing after adding noise. For example, existing literature (Jiangong Yu, Bin Wu. The inverse of material properties of functionally graded pipes using the dispersion of guided waves and an artificial neural network [J]. NDT&E International, 2009, 42:452-458) utilizes the frequency of guided waves Dispersion characteristics and artificial neural network are used to detect the material characteristics of the FGM board. The inversion network trained by the neural network system has low precision and unstable error control. The BP neural network used in the existing literature (Li Shenlei, inversion determination of material properties of functionally graded structures based on ultrasonic guided waves [D]. Jiaozuo: Henan University of Technology, 2015) also has the above problems. In addition, in order to simulate the actual situation, the BP neural network tends to fall into the local maximum value when inverting the noise-added signal, resulting in a large error. At the same time, when the adaptive neuro-fuzzy inference system used in the above literature inverts material properties, there is a Takagi-Sugeno type fuzzy system that the adaptive neuro-fuzzy inference system only supports a single output, and the number of control inputs cannot be greater than 6 and so on.

In view of the shortcomings of known methods in the art, a fast and stable inversion method for inversion of FGM material properties is highly desired.

Contents of the invention

In order to solve the deficiencies in the prior art, the present invention provides an inversion method of functional gradient structural material properties based on guided wave and fuzzy algorithm with convenient operation and stable and reliable data.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical scheme: the inversion method of the material properties of functionally graded structures based on guided waves and fuzzy algorithms, comprising the following steps:

1) Select the volume distribution function of a given FGM structure, and use the Legendre polynomial method to calculate the group velocity of guided waves in the FGM structure;

2) Design the fuzzy controller by using the genetic algorithm; establish a new hierarchical multivariable fuzzy controller according to the requirements of the multi-input multi-output fuzzy controller; write a multi-input single-output multi-layer Structure; according to the obtained multi-input single-output multi-layer structure, write the multi-layer structure of the multi-input multi-output system;

3) Write the optimization program for the parameters of the hierarchical multivariable fuzzy controller based on genetic algorithm and the optimization program for the parameters of the multi-input single-output fuzzy controller;

4) Write a program to use the fuzzy controller to invert the material properties of the FGM structure;

5) Use the well-written fuzzy controller program to invert the material properties of the FGM structure. The inversion strategy is: select the guided wave group velocity values of the low-order modes of the FGM structure at several low frequencies as the fuzzy controller The input and output are the volume distribution function of the FGM structure; choose a given volume distribution function, and use the Legendre polynomial method to obtain the corresponding group velocity of the guided wave.

The specific process of step 2) is: the first layer of the hierarchical multivariable fuzzy controller takes three fuzzy subsets for each variable: {N, Z, P}; the second layer takes two fuzzy subsets: { N, P}, the total number of fuzzy rules is 3 ² +3 ² +2 ² = 22, and with formula (1) as the membership function, there are 24 parameters to be determined in the first layer, and 8 in the second layer The parameters need to be determined; in the multi-input and single-output multi-layer structure, the parameters of the first layer and the second layer are the same as the hierarchical multivariable fuzzy controller, and each variable of the third layer takes 2 fuzzy subsets: {N,P}, Then the number of fuzzy rules is 4, and formula (1) is also used as the membership function, and there are 8 parameters to be determined in the third layer; there are 40 parameters to be determined in the membership function, and 22 control rules need to be determined;

(1)

In formula (1), x _i is the input variable, a _i is the width of the membership function _, and ci is the center position of the membership function.

In the step 3), the population of the genetic algorithm is 100, the maximum number of iterations is 500, the variable dimension is 66, the crossover probability is 0.85, and the mutation uses adaptive mutation , G is the algebra of evolution.

In the step 3), using the formula (2) as the evaluation function, the genetic algorithm is used to find the parameter that minimizes the F value, and the parameter is the parameter to be optimized and the control rule;

(2)

In formula (2), m is a constant of 0.01, T is the sampling time, N is the number of samples selected, e is the error between different sampling points, and de is the rate of change of error between different sampling points.

In the step 4), the universe of the input variable is selected as [0,20], and the universe of the output variable is selected as [0,12] and [0,20].

In the above step 5), in the high frequency band, the guided wave attenuation is very serious, and it is difficult to excite each mode; therefore, in actual selection, first, the frequency point should be selected in the lower frequency range; secondly , since different distribution functions will cause different modal numbers of the guided wave at the same frequency, the selected frequency point should try to make the modal numbers of the dispersion curves of various distribution functions at this frequency The difference is not large; finally, the distance between the measured frequency points should not be too small, otherwise the guided wave velocity between the two points will not change much; the two materials selected to form the FGM are stainless steel and silicon nitride, respectively. , , as well as is the volume distribution function of the FGM structure.

In the step 2), the parameters used in the hierarchical multivariable fuzzy controller structure and the parameters in the multi-input single-output multi-layer structure and the multi-input multi-output system in step 2) are used Genetic algorithm is used to optimize, and the various parameters include fuzzy set distribution of input variables, control rules and proportional factors.

Adopt above-mentioned technical scheme, compared with prior art, the beneficial effect of the present invention is:

The inversion method of functionally graded structural material properties based on guided wave and fuzzy algorithm of the present invention combines genetic algorithm and fuzzy algorithm, uses their respective advantages to improve the stability of the inversion process, and solves the problem of traditional calculation inversion to a certain extent. Due to the problems of ill-posed solution and low solution efficiency in the inversion method, the error between the n value obtained by the inversion method and the corresponding set value is very small. The invention provides a fast and simple method for the detection and evaluation of the characteristics of FGM materials.

Description of drawings

Fig. 1 is the flowchart of solving the guided wave group velocity in the FGM plate by the Legendre polynomial method;

Fig. 2 is the group velocity dispersion curve of a 10mm thick silicon nitride plate;

Fig. 3 is the group velocity dispersion curve of a 10mm thick stainless steel plate;

Fig. 4 is the group velocity dispersion curve of the silicon nitride-stainless steel FGM plate whose gradient function is 10mm thick;

Fig. 5 is the structural diagram of hierarchical multivariable fuzzy controller;

Figure 6 is a multi-layer structure diagram of multiple input and single output;

Figure 7 is a multi-layer structure diagram of the MIMO system;

Fig. 8 is the membership function of the input variable x ₁ in the first layer variable in the hierarchical multivariable fuzzy controller structure;

Fig. 9 is the membership function of the input variable x ₂ in the first layer variable in the hierarchical multivariable fuzzy controller structure;

Fig. 10 is the membership function of the input variable x ₃ in the first layer variable in the hierarchical multivariable fuzzy controller structure;

Fig. 11 is the membership function of the input variable x ₄ in the first layer variable in the hierarchical multivariable fuzzy controller structure;

Fig. ₁₂ is the membership function that the second layer variable is the middle layer y1 in the hierarchical multivariable fuzzy controller structure;

Fig. 13 is the membership function that the second layer variable is the middle layer y ₂ in the hierarchical multivariable fuzzy controller structure;

Fig. 14 is the multi-input single-output multi-layer structure third layer variable is the membership function _of the middle layer F1 ;

Figure 15 is the multi-input single-output multi-layer structure third layer variable is the membership function of the middle layer F2 _;

Fig. 16 is the membership function of the output U ₁ in the multi-input and single-output multi-layer structure.

detailed description

The inversion method of material properties of functionally graded structures based on guided waves and fuzzy algorithms includes the following steps:

1) Select the volume distribution function of a given FGM structure, and use the Legendre polynomial method to calculate the group velocity of guided waves in the FGM structure;

2) Design the fuzzy controller by using the genetic algorithm; establish a new hierarchical multivariable fuzzy controller according to the requirements of the multi-input multi-output fuzzy controller; write a multi-input single-output multi-layer Structure; according to the obtained multi-input single-output multi-layer structure, write the multi-layer structure of the multi-input multi-output system;

3) Write the optimization program for the parameters of the hierarchical multivariable fuzzy controller based on genetic algorithm and the optimization program for the parameters of the multi-input single-output fuzzy controller;

4) Write a program to use the fuzzy controller to invert the material properties of the FGM structure;

5) Use the well-written fuzzy controller program to invert the material properties of the FGM structure. The inversion strategy is: select the guided wave group velocity of the low-order modes of the FGM structure at several low frequencies as the input of the fuzzy controller , the output is the volume distribution function of the FGM structure; select a given volume distribution function, and use the Legendre polynomial series to obtain the corresponding guided wave group velocities.

In the step 2), the parameters required in the structure of the hierarchical multivariable fuzzy controller and the multi-layer structure of the multi-input single-output in step 2 and the fuzzy set distribution of the input variables of the multi-input multi-output system, control rules and Each parameter of the scale factor is optimized by genetic algorithm, as shown in Fig. 8-Fig. 16.

The specific process of step 2) is: the first layer of the hierarchical multivariable fuzzy controller takes three fuzzy subsets for each variable: {N, Z, P}; the second layer takes two fuzzy subsets: { N, P}, the total number of fuzzy rules is 3 ² +3 ² +2 ² = 22, and with formula (1) as the membership function, there are 24 parameters to be determined in the first layer, and 8 in the second layer The parameters need to be determined; in the multi-input and single-output multi-layer structure, the parameters of the first layer and the second layer are the same as the hierarchical multivariable fuzzy controller, and each variable of the third layer takes 2 fuzzy subsets: {N,P}, Then the number of fuzzy rules is 4, and formula (1) is also used as the membership function, and there are 8 parameters to be determined in the third layer; there are 40 parameters to be determined in the above membership function, and 22 control rules need to be determined;

(1)

In formula (1), x _i is the input variable, a _i is the width of the membership function _, and ci is the center position of the membership function.

In the step 3), the population of the genetic algorithm is 100, the maximum number of iterations is 500, the variable dimension is 66, the crossover probability is 0.85, and the mutation uses adaptive mutation ; G is the algebra of evolution.

In the step 3), using the formula (2) as the evaluation function, the genetic algorithm is used to find the parameter that minimizes the F value, and the parameter is the parameter to be optimized and the control rule;

(2)

In formula (2), m is a constant of 0.01, T is the sampling time, N is the number of samples selected, e is the error between different sampling points, and de is the rate of change of error between different sampling points.

In the step 4), the universe of the input variable is selected as [0,20], and the universe of the output variable is selected as [0,12] and [0,20].

In the above step 5), in the high frequency band, the guided wave attenuation is very serious, and it is difficult to excite each mode; therefore, in actual selection, first, the frequency point should be selected in the lower frequency range; secondly , since different distribution functions will cause different modal numbers of the guided wave at the same frequency, the selected frequency point should try to make the modal numbers of the dispersion curves of various distribution functions at this frequency The difference is not large; finally, the distance between the measured frequency points should not be too small, otherwise the guided wave velocity between the two points will not change much; the two materials selected to form the FGM are stainless steel and silicon nitride, respectively. , , as well as is the volume distribution function of the FGM structure.

Take the FGM board as an example to elaborate on the technical solution of the present invention below:

Based on the Legendre polynomial method and Mathematica software, the calculation program for the dispersion characteristics of guided waves is written.

As shown in Figure 1, in order to use the Legendre polynomial method to solve the wave problem in the guided wave, the dispersion characteristics of the guided wave in the FGM plate are calculated. The FGM plate used in this example is composed of silicon nitride and stainless steel. The material parameters are: stainless steel: density ρ= 7932kg/m ³ , elastic constant C ₁₁ =282×10 ⁹ N/m ² , C ₁₃ =113×10 ⁹ N/m ² , C ₃₃ =282×10 ⁹ N/m ² , C ₄₄ =84×10 ⁹ N/m ² , C ₅₅ =84×10 ⁹ N/m ² , C ₆₆ = 84×10 ⁹ N/m ² ; silicon nitride: density ρ= 2370kg/m ³ , elastic constant C ₁₁ =38×10 ¹⁰ N/m ² , C ₁₃ =12×10 ¹⁰ N/m ² , C ₃₃ = 38×10 ¹⁰ N/m ² , C ₄₄ =13×10 ¹⁰ N/m ² , C ₅₅ =13×10 ¹⁰ N/m ² , C ₆₆ =13×10 ¹⁰ N/m ² . The guided wave characteristics of the gradient plate composed of two materials are between the two materials, so the uniform plate dispersion curves of the two materials can be referred to when selecting the frequency point.

Figure 2 and Figure 3 are the group velocity curves of 10mm thick silicon nitride plate and stainless steel plate respectively, and Figure 4 is the guided wave group velocity curve of silicon nitride-stainless steel FGM plate with gradient function .

As shown in Figure 5, x ₁ , x ₂ , x ₃ , and x ₄ are different group velocities of guided waves, and each variable in the first layer of the hierarchical multivariable fuzzy controller takes 3 fuzzy subsets: {N,Z ,P}; y ₁ and y ₂ are the middle layer, and each variable takes two fuzzy subsets: {N,P}, so there are 22 rules to be determined in total. Taking formula (1) as the membership function, there are 24 parameters to be determined in the first layer, and 8 parameters to be determined in the second layer.

As shown in Fig. 6, x ₁ is different guided wave group velocity, the parameters of the first layer and the second layer in the multi-input single-output multi-structure are the same as NHFLC, F ₁ and F ₂ are the input of the third layer, each Variables take two fuzzy subsets: {N, P}, then the number of fuzzy rules is 4, and formula (1) is also used as the membership function, and there are 8 parameters to be determined in the third layer. Then there are 40 parameters to be determined in the membership function to be optimized by the genetic algorithm, and 26 control rules need to be determined.

(1)

In formula (1), x _i is the input variable, a _i is the width of the membership function _, and ci is the center position of the membership function.

In order to make the iterative convergence of the genetic algorithm the fastest, the parameters of the genetic algorithm are selected as follows: the population is 100, the maximum number of iterations is 500, the number of variables is 66, the crossover probability is 0.85, and the mutation uses adaptive mutation ; G is the algebra of evolution. Other parameters can also be selected according to actual conditions.

Using formula (2) as the evaluation function, the genetic algorithm is used to find the parameter that minimizes the F value, which is the parameter to be optimized and the control rule.

(2)

In formula (2), m is a constant of 0.01, T is the sampling time, N is the number of samples selected, e is the error between different sampling points, and de is the rate of change of error between different sampling points.

As shown in Figure 7, each layer of the structure of the MIMO system is made up of a multi-layer structure of MIMO, assuming that MISO of each layer has 8 inputs and 1 output, the scheme adopted by the present invention : Each layer of 5 layers is designed with a multi-input and single-output multi-layer structure, so a total of 40 inputs and 5 outputs of the MIMO system are obtained.

The frequency points of ultrasonic guided waves are selected as 50, 100, 150 and 200KHz. At these 4 frequencies, the gradient plate has at most 3 modes and at least two modes. For the frequency points where there is no mode 3, let the wave velocity of mode 3 be 0. choose , , as well as is the volume distribution function of the FGM structure, and according to the selected given volume distribution function, the corresponding guided wave group velocities are respectively obtained by using the Legendre polynomial method. The guided wave group velocity is used as the input of the fuzzy controller, and the value of n in the volume distribution function of the FGM plate is used as the output.

The effective inversion results obtained by this method have a small error with the set value and high inversion stability, which demonstrates the validity and accuracy of this method for FGM material property inversion.

It should be understood that the descriptions of the above embodiments are relatively detailed, and should not therefore be considered as limiting the scope of the patent protection of the present invention. Those of ordinary skill in the art should understand that: the present invention can still be modified or equivalently replaced without departing from In the case of the protection scope of the claims of the present invention, replacement or modification can also be made, which should fall within the protection scope of the present invention, and the protection scope of the present invention should be based on the appended claims.

Claims (7)

1. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach, it is characterised in that：Including following Step：

1）The volume distributed median function of the given FGM structures of selection, the guided wave in FGM structures is calculated using Legendre polynomial methods Group velocity；

Using genetic Algorithm Design fuzzy controller；A kind of new passing is set up in requirement according to multiple-input and multiple-output fuzzy controller Rank multi-variables Fuzzy Controller in Real；Hierarchical structure according to obtaining writes out the sandwich construction of multiple input single output；According to obtaining Multiple input single output sandwich construction, write out the sandwich construction of multi-input multi-output system；

3）The optimization program and multiple input single output of passing rank multi-variables Fuzzy Controller in Real parameter based on genetic algorithm is write to obscure The optimization program of controller parameter；

4）Write with fuzzy controller come the program of inverting FGM construction material properties；

5）The program of the fuzzy controller that will be write is used for the material property of inverting FGM structures, and refutation strategy is：Selection FGM The guided wave group velocity angle value of lower mode of the structure at several low frequencies is output as FGM structures as the input of fuzzy controller Product distribution function；The given volume distributed median function of selection, corresponding guided wave group velocity is respectively obtained using Legendre polynomial methods Degree.

2. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 2）Detailed process be：Pass the ground floor of rank multi-variables Fuzzy Controller in Real each change and measure 3 moulds Paste subset：{N,Z,P}；The second layer takes two fuzzy subsets：{ N, P }, then number of fuzzy rules has 3 altogether²+3²+2²=22, with formula （1）Be membership function, then ground floor have 24 parameters it needs to be determined that, the second layer have 8 parameters it needs to be determined that；Multi input list is defeated With passing rank multi-variables Fuzzy Controller in Real, third layer each change measures 2 moulds for ground floor in the sandwich construction for going out, the parameter of the second layer Paste subset：{ N, P }, then number of fuzzy rules is 4, equally with formula（1）Be membership function, third layer have 8 parameters it needs to be determined that； 40 parameters are then had in membership function to be determined, 22 control rule it needs to be determined that；

（1）

Formula（1）Inx _i It is input variable,a _i It is the width of membership function,c _i It is the center of membership function.

3. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 3）In, the population of genetic algorithm is 100, and greatest iteration number is 500, and dimension is 66, is intersected Probability is 0.85, and variation uses TSP question, G is the algebraically evolved.

4. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 3）In, with formula（2）It is evaluation function, the parameter for causing that F values are minimum is found using genetic algorithm, The parameter is parameter to be optimized and control rule；

（2）

Formula（2）InmIt is constant 0.01,TIt is the sampling time,NIt is the sample number of selection,eIt is the error between different sampled points,de It is the rate of change of error between different sampled points.

5. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 4）In, the domain of input variable is elected as [0,20], the domain of output variable elect as [0,12] and [0,20]。

6. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 5）In, in high band, guided wave decay is very serious, and it is also relatively more tired to motivate each mode It is difficult；Therefore during actual selection, first, Frequency point should be selected in compared with the range of low frequency；Secondly as different distribution functions can be made Mode number existing for guided wave on the same frequencies is different, and selected Frequency point should try one's best so that in this frequency, various points Mode number difference existing on the dispersion curve of cloth function is little；Finally, the interval between institute's measured frequency point can not be too small, no Then the guided wave velocity of wave change of point-to-point transmission is little；Two kinds of materials of selected composition FGM are respectively stainless steel and silicon nitride, selection、、AndIt is the volume distributed median function of FGM structures.

7. the inversion method of the function gradient structure material property based on guided wave and fuzzy algorithmic approach according to claim 1, It is characterized in that：The step 2）In, pass the parameter and step 2 used needed for rank multi-variables Fuzzy Controller in Real structure）In it is many Parameters in sandwich construction, the sandwich construction of multi-input multi-output system of the single output of input are optimized with genetic algorithm, Described parameters include the distribution of input variable fuzzy set, control rule and scale factor.