CN101118419A - Layered fuzzy system based on unified model - Google Patents
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Abstract
The present invention discloses a hierarchy fuzzy system based on a unified model. First, a hierarchy fuzzy system with an increasing shape structure is established, namely, each basic hierarchy unit only has two physical input quantities collected from an industry production field. Through defining a uniform universe of discourse interval, the variation range of the actual physical input quantity is analyzed, the input quality is mapped uniformly on the defined interval, namely, the interval is used as the basic universe of discourse of the fuzzy system; each basic fuzzy unit adopts the same fuzzy reasoning way, namely, the same universe of discourse, the same fuzzy way and the uniform fuzzy reasoning rule, the fuzzy reasoning adopts the Mamdani composition arithmetic which is simple and convenient to calculate, based on which, a vacancy replacement processing mode is adopted for the unsure physical input quantity, the output weight sum of each layer of fuzzy basic unit is adopted for system output, and the feedback and adjusting for the system result is realized through an interval mapping adjusting way. The present invention solves the actual problems of the complexity of design and the real-time property of operation, thereby guaranteeing the practicability of the hierarchy fuzzy system.
Description
Technical Field
The invention relates to a fuzzy inference model for multiple input variables required by industrial real-time, in particular to a hierarchical fuzzy system based on a unified model.
Background
In actual industrial production, due to the complexity and uncertainty of industrial production processes, intelligent theory has been largely utilized to solve problems in production. The fuzzy theory is an effective method for solving the problems of randomness and uncertainty, the conventional fuzzy model is a plane type, namely, a system usually has two or three input quantities which enter the model at the same time for fuzzy reasoning, and theoretically, the conventional fuzzy model can also have more than three input quantities, but as the fuzzy rule number and the fuzzy subset quantization number form an exponential relationship, the more the input quantity is, the more the rule number is. Assuming that each fuzzy subset of input variables is N, and the input variables are M in total, the total number of rules is S = N M If the fuzzy subset takes the usual 5, if there are 4 input variables, there are 625 fuzzy rules, if there are 5 input variables, the fuzzy rule number will reach 3125. Therefore, the number of rules is limited, and the industrial production is generally limited to two to three input quantities, and the application of three or more multidimensional inputs is difficult.
The hierarchical fuzzy system converts the high-dimensional fuzzy system into a hierarchical system formed by hierarchically connecting low-dimensional fuzzy units, so that the rule number of the fuzzy system only linearly increases along with the input variable number, and the hierarchical fuzzy system is an effective way for effectively solving the dimension disaster problem of 'explosion' of the rule number of the multi-dimensional input fuzzy system. The hierarchical fuzzy system can be used for effectively applying the fuzzy theory in the practical occasions of multiple input variables. However, the current research on the hierarchical fuzzy system still stays in a theoretical level, such as the general equivalence and the approximation performance of the hierarchical fuzzy system. However, no reports on how to apply the hierarchical fuzzy system to practical applications on the premise of meeting the requirement of industrial practicability, especially to industrial production occasions with more physical input variables exist at present.
Disclosure of Invention
The invention aims to provide a hierarchical fuzzy system based on a unified model, which is suitable for multi-input physical variables and has industrial practicability.
In order to achieve the purpose, the invention can adopt the following technical scheme:
the layering fuzzy system based on the unified model mainly comprises a layering fuzzy system and the unified model, the layering fuzzy system aims at solving the problem of dimension disaster, the number of inference rules is greatly reduced, and an effective method is provided for the application of a fuzzy theory in a super-large dimension input system; the unified model provides a technical method for effectively applying the hierarchical fuzzy system to actual industrial production, and the characteristics of physical variables in the actual industrial production are different, so that the position and the reasoning process in the hierarchical fuzzy system have uncertainty, and the problems of design complexity and operation instantaneity brought by applying the hierarchical fuzzy system to the actual industrial production need to be solved, so that the technical method of the unified model is provided.
Firstly, establishing a hierarchical fuzzy system with an incremental structure based on a hierarchical fuzzy system of a unified model, namely, each basic fuzzy unit only has two physical input quantities acquired from an industrial production field; the unified model is a foundation for effectively applying the hierarchical fuzzy system to practice, and mainly comprises a unified universe of discourse interval, a unified fuzzy rule, a vacancy substitution, mapping adjustment and the like; the method comprises the steps of analyzing the variation range of actual physical input quantity by defining a uniform mapping interval, and uniformly mapping the input quantity to the defined interval, wherein the interval is used as a basic discourse domain of a fuzzy system; each basic fuzzy unit adopts the same fuzzy reasoning mode, namely the same domain, fuzzification method and fuzzy reasoning rule, fuzzy reasoning adopts a simple and convenient-to-calculate Mamdani synthesis algorithm, on the basis, a processing mode of replacing missing bits for uncertain physical input quantity is adopted, namely if a certain layer lacks the input quantity, the subsequent physical input quantity can be sequentially moved forward to replace the missing physical input quantity, the output of the system adopts the output weighted sum of fuzzy basic units of each layer, and the feedback adjustment of the system result is realized through a mode of interval mapping adjustment.
The hierarchical fuzzy system with the incremental structure is formed by connecting a plurality of layers of basic fuzzy units in series, the basic fuzzy units of each layer have two input variables, except that the two inputs of the basic fuzzy unit of the first layer are actual physical input quantities, the other layers take the output of the basic fuzzy unit of the previous layer as one input variable of the unit, and the other input quantity is the actual physical variable.
The unified discourse domain refers to: the method comprises the steps of carrying out field sampling test and statistical analysis on actual physical variables to obtain the actual change range of the actual physical variables, determining a proper mapping interval by combining actual engineering application, mapping the actual physical variables to the interval through mapping relations, determining different mapping relations to be mapped to the interval according to the value change of each physical input variable, and carrying out fuzzification and fuzzy reasoning on the basis, wherein the interval is the same as the uniform mapping interval and the fuzzy domain for the whole fuzzy system.
The unified fuzzy rule is as follows: the fuzzy linguistic variables are determined according to actual production requirements, the same fuzzy linguistic variables are defined for input variables of all basic fuzzy units, the same membership functions are defined on a unified domain interval, on the basis, the same fuzzy rule is adopted for reasoning of all the basic fuzzy units, and different characteristics of the input variables such as size, polarity and the like are reflected through mapping relations mapped on domains.
The deficiency substitution means: in the industrial production process, fuzzy reasoning is not needed for some physical variables under certain conditions according to actual conditions, so that when a certain layer lacks the input quantity, the subsequent physical input quantity can be sequentially moved forward to replace the lacking physical input quantity, and the unified discourse domain interval and the unified fuzzy rule are the basis and the premise for realizing the lacking replacement.
The mapping adjustment is as follows: when the reasoning result is adjusted on line according to the system requirements and the feedback requirements of actual production, the mapping relation from the physical input variable to the unified discourse domain interval is reversely adjusted, and the adjustment process can be performed on line until the system requirements are met.
The invention has the advantages that the invention adopts the layered fuzzy system with an additional structure, uses the technical method of a unified model, carries out fuzzy reasoning by applying a unified theory domain, a unified fuzzy rule, interval mapping and a vacancy substitution mode, converts the high-dimensional fuzzy system into the layered system formed by hierarchically connecting low-dimensional fuzzy units, ensures that the rule number of the fuzzy system only linearly increases along with the input physical variable number, effectively solves the dimension disaster problem of 'explosion' of the rule number of the multidimensional input fuzzy system and the application problem of the layered fuzzy system in practice, thereby being effectively applied to industrial production control and having strong practicability.
Drawings
FIG. 1 is a diagram of a hierarchical fuzzy system of the incremental structure of the present invention.
FIG. 2 is a diagram of a fuzzy inference process of a unified model-based hierarchical fuzzy system.
Detailed Description
The hierarchical fuzzy system based on the unified model is carried out according to the following steps:
first, building a structural model of a hierarchical fuzzy system
If the system has n physical input variables of x 1 、x 2 、……x n Using a layered fuzzy system as shown in FIG. 1, layers ofThe basic fuzzy units each have two input variables, where x 1 、x 2 As input to the first layer of elementary fuzzy units, the output y thereof 1 And a third physical input variable x 3 As the input of the basic fuzzy unit of the second layer, the rest layers are analogized, so the system of the n-dimensional physical input variables can form n-1 layers in such a structure, and each layer has only two input variables.
In this configuration, the number of rules is the minimum, and assuming that each fuzzy subset of input variables is N, and the total number of input variables is M, the total number of rules is S = N 2 * (M-1). If a conventional planar type is adoptedThe total number of rules will be S = N M . Therefore, by adopting the layered fuzzy model shown in the figure, the exponential increase of the rule number along with the variable number can be changed into the linear increase along with the variable number, and the rule number is greatly reduced.
Secondly, determining the reasoning mode of the unified model
The hierarchical fuzzy system adopts fuzzy reasoning of a unified model, the unified model mainly comprises a unified domain interval, a unified fuzzy rule, a vacancy substitution, mapping adjustment and the like, namely, the fuzzy reasoning process of each basic fuzzy unit adopts the same mode, each input variable adopts the same fuzzification mode, fuzzification and defuzzification are carried out on the same domain interval, and the same fuzzy analysis method is adopted. Therefore, the unified model has good openness, expansibility and simplicity in operation, so that the fuzzy inference model applied in actual industrial production has good universality, physical input variables can be conveniently adjusted according to actual production needs, fuzzy rules can be conveniently adjusted according to requirements of actual production processes, the complexity of the system is reduced, real-time operation of the system is facilitated, and the hierarchical fuzzy system can be effectively applied to an actual engineering system.
Thirdly, establishing discourse domain mapping of input variable
In the unified model, for eachHow to fuzzify the input variables by adopting a proper fuzzy domain is an important problem of whether the system can be applied to actual engineering. In an actual system, the types of system input variables are different, the numerical values and the positive and negative polarities are different, engineering units are also different, and if different fuzzy reasoning modes are adopted for each input variable, the complexity of system design is greatly improved, and the system is difficult to be applied in practice. Therefore, in order to facilitate fuzzy reasoning by using a unified model of a hierarchical fuzzy system, the input variables of the system are determined by detecting and collecting the actual physical variables and then performing statistical analysis, a suitable interval is determined by combining actual engineering application, all the physical input variables are mapped onto the interval through different mapping relations, for the whole fuzzy system, the interval is the same and is used as a unified domain interval, each input variable is determined to be mapped onto the interval according to different mapping relations of the value size of the input variable, and fuzzy reasoning is performed by a fuzzy unit of the unified model after fuzzification. Let v be the variation range of a certain input variable v 1 ～v 2 The actual variation range v is mapped linearly 1 ，v 2 ]Mapping to a unified discourse domain interval [ d ] 1 ，d 2 ]Above, the mapping relation is d = k 1 v+k 2 ，k 1 、k 2 Respectively, are mapping coefficients, which can be determined as
k 2 ＝d 1 -k 1 *v 1 . Fourthly, establishing a unified fuzzy inference rule
Fuzzification of two input variables and an output variable in a basic fuzzy unit is carried out on a uniform domain interval, the input variables are mapped to the interval through different mapping relations, a uniform membership function is used for obtaining fuzzy quantities of the input variables, and the specific algorithm is as follows:
1. defining linguistic variables: fuzzy linguistic variables capable of reflecting production rules and requirement indexes are defined according to production requirements and analysis on physical input variables, generally four to seven fuzzy linguistic variables are defined, and the membership function of the fuzzy linguistic variables is a continuous or discrete membership function in a unified theory domain interval.
2. Determining a fuzzy rule:
determining fuzzy rules of the hierarchical fuzzy system according to the control requirements of industrial production and the defined linguistic variables, wherein the fuzzy rules are in the form of: ifx 1 Is A and x 2 Is B then y is C. Wherein x 1 、 x 2 Respectively representing two input quantities of the basic fuzzy unit, y representing the output quantity of the basic fuzzy unit, wherein the quantities are mapping values of actual physical quantities on a domain interval, A, B and C respectively represent language variables of the input quantities and the output quantity, the number of fuzzy rules can be determined according to the defined language variable number, and if the input variable x is subjected to fuzzy rule matching, the fuzzy rule number is determined 1 、 x 2 And the output variable y defines n linguistic variables, the fuzzy rule number of the basic unit is n 2 . The layers of the hierarchical fuzzy model are also carried out according to the rules during reasoning. And carrying out fuzzy synthesis operation on each fuzzy rule. If A and B are input fuzzy sets and C is an output fuzzy set, the ternary fuzzy relation R determined by the rule 'ifAandBthn C' is
R＝(A×B)×C
The membership degree of each discrete element in the domain corresponding to the fuzzy set A is mu A (i) Degree of membership μ corresponding to fuzzy set B B (j) Degree of membership μ corresponding to fuzzy set C C (m), the specific operation process is as follows:
A×B＝μ A (i)^μ B (j)
R k ＝μ A (i)^μ B (j)^μ C (m)
the symbol ^ represents a small operation, i.e. mu A (i)^μ B (j)＝min(μ A (i)，μ B (j) I, j, m are discrete values over the universe of discourse.
By performing such a composition operation on each rule, n can be obtained 2 Blurring of bar rulesAnd (4) relationship. Will n this 2 Fuzzy relation R of bar rule k ，k＝1，2，......，n 2 And merging to obtain a fuzzy relation matrix R corresponding to the fuzzy rule.
3. Unification of fuzzy subsets activated by fuzzy rules:
for each input variable of the basic fuzzy unit, the mapping value can activate at most two fuzzy subsets, namely linguistic variables, and for the consideration of real-time performance and simplicity of calculation, the two activated fuzzy subsets are unified into a comprehensive fuzzy subset, namely the action of the two activated fuzzy subsets is reflected in the corrected fuzzy subset. The specific method comprises the following steps:
setting the mapping value of some input variable in discrete domain interval as x, the mapping value corresponds to at most two fuzzy subsets (language variable), the two fuzzy subsets are set as A and B, and the discrete membership degree distribution in domain interval is set as [ a ] i ]And [ b) i ](i is a discrete value in the universe of discourse), and the membership degrees of the mapping value x to the two fuzzy subsets are respectively mu A (x) And mu B (x) Then, after the synthesis, C = [ C ] i ]＝a i *μ A (x)+b i *μ B (x) If [ c ] i ]In which an element greater than 1 is present, c is normalized i And converting into a numerical value between 0 and 1, and carrying out fuzzy reasoning on the fuzzification result with the C as an input variable.
4. Determining a fuzzy synthesis algorithm:
the fuzzy reasoning of each basic fuzzy unit adopts a common mamdani algorithm, and the membership degree distribution of two input variables after comprehensive fuzzification on a domain interval is set as A * And B * If the inference result is C * ＝(A * ×B * ) oR, wherein R isAnd obtaining a fuzzy relation matrix. The symbol o represents the synthesis operation.
5. And (3) a fuzzy resolving algorithm:
the inference result of the basic fuzzy unit is a membership distribution which is discretely distributed on a domain interval, namely, the distribution value of the membership degree of the result on the domain interval is obtained after fuzzy inference is carried out on two input variables, and the deblurring operation generally adopts a weighting method to deblur. The weighted method fuzzy algorithm is as follows:
i is the discourse domain interval [ n ] 1 ，n 2 ]Discrete value of (d), mu i Is the degree of membership of the corresponding discrete point.
The fifth step, the replacement of the missing bits of the input variables and the weighting processing of the outputs
In the actual process, the layering number and the variable position of the layered fuzzy model are not fixed and change along with the change of the setting of technicians and the requirement of the production process. The process mainly comprises the following steps:
(1) In an actual system, input variables needing fuzzy inference operation may vary with the change of a production process, and in some cases, individual physical variables do not need to be subjected to fuzzy inference operation, so that the problem that the number of the input variables has uncertainty must be considered in the hierarchical fuzzy system. Therefore, the method adopts a defect replacement mode to process in a layered fuzzy system. The specific treatment process comprises the following steps: it is assumed that for a certain production situation physical input variables have been defined, respectively x 1 、x 2 、x 3 、x 4 Thus, a three-layer fuzzy inference model can be formed according to the structure of the hierarchical fuzzy system, and the input variable of each layer is x 1 And x 2 、x 3 、x 4 ， But in real engineering it may happen that only the input variable x is present 1 、x 2 、x 4 Cases where fuzzy operations are required, in which caseThe method of the missing replacement replaces the variable x originally positioned at the third layer 4 Substituting to second layer original x 3 Thereby the hierarchical fuzzy system becomes a two-layer structure, each layer of input variables are x respectively 1 And x 2 、x 4 . The basis and the premise of adopting the mode are the unified universe of discourse and the unified fuzzy rule, and the problem that the input variable is uncertain in the actual engineering is flexibly solved by utilizing a unified model and the vacancy substitution.
(2) In the practical application process, the positions of the input variables in the hierarchical fuzzy model can be changed according to the difference of the input variables by adopting fuzzy membership functions and the difference of fuzzy subset definitions, so that the difference of the influence degrees of the different input variables on the fuzzy reasoning result is reflected, the structural positions of the input variables in the hierarchical fuzzy model can be determined by analyzing the influence degrees of the output variables of the basic fuzzy unit on the input variables, and the influence degrees of the different variables on the reasoning result are reflected on the positions of the hierarchical fuzzy model. Meanwhile, in order to further reflect the difference of the influence degree of different variables on the output result, the output result of each layer is weighted, and the final output of the hierarchical fuzzy system is the weighted sum of the output results of each layer, namely:
where k is the number of layers, alpha is a weighting factor,
y k and outputting the deblurred result for each layer. The determination of the weighting coefficients is obtained by a fuzzy hierarchy analysis method, so that the subjectivity and the inconsistency of the manual determination of the weighting coefficients can be avoided.
Sixthly, correcting the output result of the system by utilizing mapping adjustment
When the inference result is adjusted on line according to the system requirements and the feedback requirements of actual production, a new mapping coefficient meeting the requirements is reversely calculated according to the mapping value required by the production index by reversely adjusting the mapping relation from the relevant physical input variable to the unified discourse domain interval. This adjustment process can be performed on-line until system requirements are met.
Claims (6)
1. A hierarchical fuzzy system based on a unified model is characterized in that: firstly, establishing a hierarchical fuzzy system with an additional structure, namely each basic fuzzy unit only has two physical input quantities acquired from an industrial production field; by adopting a technical method of a unified model, a unified discourse domain interval is defined, the variation range of the actual physical input quantity is analyzed, and the input quantity is uniformly mapped to the defined interval, wherein the interval is used as a basic discourse domain of a fuzzy system; each basic fuzzy unit adopts the same fuzzy reasoning mode, namely the same domain, fuzzification method and unified fuzzy reasoning rule, the fuzzy reasoning adopts a Mamdani synthesis algorithm which is simple and convenient to calculate, on the basis, a processing mode of lacking bit substitution is adopted for uncertain physical input quantity, namely if a certain layer lacks the input quantity, the subsequent physical input quantity can be sequentially moved forward to substitute the lacking physical input quantity, the output of the system adopts the output weighted sum of each layer of fuzzy basic units, and the feedback adjustment of the system result is realized through a mode of interval mapping adjustment.
2. The unified model based hierarchical fuzzy system of claim 1, wherein: the hierarchical fuzzy system with the incremental structure is formed by connecting a plurality of layers of basic fuzzy units in series, the basic fuzzy units of each layer are provided with two input variables, except that the two inputs of the basic fuzzy unit of the first layer are actual physical input quantities, the output of the basic fuzzy unit of the previous layer is used as one input variable of the unit in other layers, and the other input quantity is an actual physical variable.
3. The unified model based hierarchical fuzzy system of claim 1 wherein: the unified model mainly comprises a unified discourse domain interval, a unified fuzzy rule, a vacancy substitution, mapping adjustment and the like, wherein the unified discourse domain interval is as follows: the method comprises the steps of carrying out field sampling test and statistical analysis on actual physical variables to obtain the actual change range of the actual physical variables, determining a proper discourse domain interval by combining actual engineering application, mapping the actual physical variables to the interval through a mapping relation, regarding the whole fuzzy system, determining different mapping relations to be mapped to the interval according to the value change of each physical input variable, and then carrying out fuzzification and fuzzy reasoning on the basis, wherein the interval is the same and is used as a unified mapping interval and a fuzzy discourse domain.
4. The unified model based hierarchical fuzzy system of claim 1 wherein: the unified fuzzy rule is as follows: fuzzy linguistic variables are determined according to actual production requirements, the same fuzzy linguistic variables are defined for input variables of all basic fuzzy units, the same membership functions are defined on a unified domain-of-discourse interval, the same fuzzy rules are adopted for reasoning of all the basic fuzzy units on the basis, and different characteristics of the input variables such as size and polarity are reflected through mapping relations mapped on the domain-of-discourse.
5. The unified model based hierarchical fuzzy system of claim 1 wherein: the deficiency substitution refers to: in the industrial production process, fuzzy reasoning is not needed for some physical variables under certain conditions according to the reality, so that when a certain layer lacks the input quantity, the subsequent physical input quantity can be sequentially moved forward to replace the lacking physical input quantity, and the unified domain interval and the unified fuzzy rule are the basis and the premise for realizing the lacking replacement.
6. The unified model based hierarchical fuzzy system of claim 1 wherein: the mapping adjustment is as follows: when the inference result is adjusted on line according to the system requirements and the feedback requirements of actual production, the adjustment process can be carried out on line until the system requirements are met by carrying out reverse adjustment on the mapping relation from the corresponding physical input variable to the unified discourse domain interval.
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| CN108351622A (en) * | 2015-09-10 | 2018-07-31 | 艾系统工业自动化公司 | The method for generating the fuzzy knowledge base for may be programmed fuzzy controller |
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| CN111897208A (en) * | 2020-07-16 | 2020-11-06 | 东南大学 | Multistage fuzzy controller-based cement mixing pile construction parameter determination method |
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