JP2550173B2 - Fuzzy inference method, device and control device - Google Patents

Description

The present invention relates to a fuzzy inference method and a control method, and more particularly to a backward fuzzy inference method.

[Conventional technology]

An expert system (also called an AI system or a knowledge processing system) based on the production rule is, for example, as described in JP-A-62-256128, a rule that "if x is a, y is b". A forward inference method that infers the conclusion that "y is b" based on the fact that "x is a", while unknown "y"
Is a b hypothesis to be proved, and it is examined whether or not “x is a” is established from the rule that “x is a, y is b”, and the success or failure of the above hypothesis is inferred. There is a reasoning method. By combining the backward inference and the forward inference, the cause of the phenomenon can be diagnosed, and the diagnosis result can be used as a precondition for the next inference rule to draw the intended conclusion.

In the above AI inference (which will be called in order to distinguish it from fuzzy inference), it can be clearly stated by YES or NO whether or not the proposition in the premise or conclusion of each rule is satisfied (a crisp world). It is a premise.

Fuzzy reasoning, on the other hand, is a vague proposition such as "If x is a little closer to a, y is a little closer to b", and it can be described closer to human recognition, and it can be used for diagnosis or prediction or Attention is being paid to its use in a wide range of fields such as control.

[Problems to be Solved by the Invention]

However, fuzzy inference cannot easily perform backward inference like AI inference. Fuzzy backward inference has problems such as the fact that the inference result does not exist and is not uniquely determined (the 666th seminar of the Japan Society of Mechanical Engineers, artificial intelligence and fuzzy theory, pages 44-46).

In addition, regarding the backward inference of fuzzy, "Solution of inverse problem of fuzzy set (Proceedings of the Society of Instrument and Control Engineers, Vol.15, No.
1, p21-25, 1979) ”, but the theoretical calculation amount becomes m ^{m + 1} * n when the number of causes (m) and the number of symptoms (results) (n) increase. , Difficult to apply to real-time expert system.

An object of the present invention is to provide an advanced expert system that combines backward fuzzy inference and forward fuzzy inference in order to solve the above problems.

Another object of the present invention is to provide an inference apparatus that can infer information that is unknown or unobservable and is a cause or condition, and can diagnose the cause.

Another object of the present invention is to provide a highly accurate and robust predictive control method by predicting a control amount including the result of backward fuzzy inference.

[Means for solving the problem]

The above-mentioned purpose is a fuzzy production rule consisting of a predicate part that contains multiple information and is expressed by an ambiguous one proposition, and a conclusion part that is expressed by an ambiguous one proposition that contains one information, and each information as a goodness of fit. A backward fuzzy inference method comprising a backward fuzzy inference for obtaining only one unknown information included in a premise and a forward fuzzy inference for obtaining prediction information of a conclusion based on a membership function to be evaluated. Is set in advance the maximum value of the goodness of fit to the unknown information, input known information of the premise part and known information of the conclusion part, calculate the goodness of fit for each of these pieces of information from the membership function, Of the unknown information by replacing the goodness of fit of the unknown part with the goodness of fit of the conclusion part by comparing the goodness of fit of the predicate part with the goodness of fit of the predicate part. In the forward fuzzy inference, the goodness of fit of each information of the premise part and the conclusion part including the goodness of fit of the unknown information obtained by the backward inference is used as a new premise part, and the conformity of the premise part is obtained. The minimum value of the degree can be achieved by obtaining the prediction information as the goodness of fit of the prediction information of the new conclusion part.

In addition, the above-mentioned purpose conforms to each fuzzy production rule with fuzzy production rules consisting of a predicate part that contains multiple pieces of information and is expressed as an ambiguous proposition, and a conclusion part that contains one piece of information and is expressed as an ambiguous proposition. In the fuzzy inference method, the backward fuzzy inference that finds only one unknown information included in the premise part and the forward fuzzy inference that finds prediction information in the conclusion part are combined based on the membership function that is evaluated once Is a plurality of first fuzzy production rules according to the number of the propositions common to each of the information and the number of information of the premise part, the maximum value of the goodness of fit to the unknown information is set in advance,
By inputting the known information of the premise part and the known information of the conclusion part, the goodness of fit of each of these pieces of information is calculated from the membership function, and the goodness of fit of the conclusion part and the goodness of fit of the premise part are compared to calculate the goodness of fit of the conclusion part. When the goodness of fit is minimum, the goodness of fit of the unknown information is replaced with the goodness of fit of the conclusion part to obtain the goodness of fit of the unknown information, and the unknownness for each of the obtained first fuzzy production rules is calculated. The maximum value is calculated for each of the propositions from the goodness of fit of the information, and the maximum value of each of the propositions is determined as the goodness of fit of the unknown information for each of the propositions, and the forward fuzzy inference is performed by the backward inference. The relevance of each information of the premise part and the conclusion part including the relevance of the unknown information for each proposition is a new premise part, and the goodness of fit of the prediction information of the conclusion part is a new conclusion part, and each of the information The life common to Each fuzzy production rule number and the number information of the preamble and a plurality of second in response to the,
The minimum value of the goodness of fit of the premise part is obtained, the maximum value of each of the propositions is calculated from the minimum value of each of the plurality of second fuzzy production rules, and the maximum value of each of the propositions is calculated from the prediction information of each of the propositions. This can be achieved by obtaining the prediction information as the goodness of fit.

In addition, the above-mentioned purpose is a process control method that determines the manipulated variable from the difference between the target value and predicted value of the controlled variable, and describes a plurality of process variables including only one unknown information with an ambiguous one proposition and the controlled variable. A fuzzy production rule consisting of a conclusion part describing
Based on the membership function that evaluates each process amount to the goodness of fit, a predetermined maximum value is set in advance to the goodness of fit of the unknown information, and the known information and the conclusion part of the premise part at the control time acquired from the process are controlled. The suitability of each of the unknown information is calculated from the quantities, and the suitability of the conclusion part and the suitability of the premise part are compared. To determine the goodness of fit of the unknown information by substituting the known degree of the unknown information and the goodness of fit of the determined unknown information and the known information of the premise part and the known information of the conclusion part. It can be achieved by obtaining the predicted value as the goodness of fit of the predicted value of.

In addition, the above-mentioned object is ambiguous in the process control method in which the manipulated variable is determined from the difference between the target value and the predicted value of the controlled variable, and the ambiguous predicate and the controlled variable that describe a plurality of process variables including only one unknown information with an ambiguous proposition. Based on a fuzzy production rule consisting of a conclusion part described by various propositions, and a membership function that evaluates each process quantity to suitability for each ambiguous proposition, the number of the propositions common to the above information and the precondition part For each of the plurality of first production rules corresponding to the number of pieces of information, a predetermined maximum value is set in advance for the suitability of the unknown information, and the known information and the conclusion portion of the premise part at the control point acquired from the process are set. Each fitness is calculated from the control amount, the fitness of the conclusion part and the fitness of the premise part are compared, and when the fitness of the conclusion part is the minimum, the fitness of the unknown information is determined as the conclusion part. The degree of conformity of the unknown information is determined by substituting the degree of conformity, and a maximum value is calculated for each of the propositions from the determined degree of conformity of the unknown information for each of the plurality of first fuzzy production rules, and these propositions are calculated. The maximum value for each of the propositions is determined as the goodness of fit of the unknown information, and the goodness of fit of each of the premise part and the conclusion part including the goodness of fit of the determined unknown information for each of the determined propositions is newly updated. As the new predicate part, and a plurality of second predicates corresponding to the number of the propositions common to the respective information and the number of information items of the predicate part. For each fuzzy production rule, the minimum value of the goodness of fit of the premise part is obtained, and the maximum value for each proposition is calculated from the minimum value for each of the plurality of second fuzzy production rules, and the maximum value for each proposition is calculated as described above. The fit of the predicted value for each subject can be accomplished by determining the predicted value of the controlled variable from the fit of the predicted value for each 該命 problem.

In addition, the above-mentioned object is a fuzzy inference apparatus in which backward fuzzy inference of unknown information and forward fuzzy inference of prediction information are combined, and a predicate expressed by an ambiguous proposition containing a plurality of information and an ambiguous one including one information A fuzzy production rule consisting of a conclusion part expressed by the proposition 1, a storage device that stores a membership function that evaluates the ambiguous proposition of each information by the goodness of fit, and an input that inputs each information of the premise part and the conclusion part A device, a maximum value setting means for setting a predetermined maximum value in advance to the matching degree of only one unknown information included in the premise section, the matching degree of each information from the input device according to the membership function and the rule. And the fitness degree of the conclusion part by the fitness degree calculating means and the fitness degree of the premise part are compared to minimize the fitness degree of the conclusion part. Backward fuzzy inference apparatus having an inference means for replacing the degree of conformity of the unknown information with the degree of conformity of the conclusion section, and the premise section and the conclusion section including the degree of conformity of the unknown information obtained by the backward inference. Of the information is used as a new premise part, the minimum value of the goodness of fit of the premise part is taken as the goodness of fit of the prediction information of the new conclusion part, and the predictive information is obtained from the goodness of fit of the prediction information. This can be achieved by including an inference device.

In addition, the above-mentioned purpose is a fuzzy inference device that includes backward fuzzy inference of unknown information and forward fuzzy inference of prediction information. A fuzzy production rule consisting of a conclusion part that is expressed, a storage device that stores a membership function that evaluates each information by a goodness of fit for each ambiguous proposition, an input device that inputs each information of the premise part and the conclusion part, For each of the plurality of first production rules according to the number of propositions and the number of pieces of information of the premise common to each of the information, only one unknown included in the premise of the plurality of first fuzzy production rules Maximum value setting means for setting a predetermined maximum value in advance to the conformity of information, the input device according to the membership function and the rule In the case where the goodness of fit of each of the information is calculated for each of the propositions and the goodness of fit of the conclusion part by the goodness of fit calculation means and the goodness of the premise part are compared, and the goodness of fit of the conclusion part is minimum By replacing the goodness of fit of the unknown information with the goodness of fit of the conclusion part to determine the goodness of fit of the unknown information for each of the plurality of first fuzzy production rules. A backward fuzzy inference apparatus having an inference means for calculating the maximum value for each of the propositions from the suitability of the unknown information for each production rule, and the suitability of the unknown information having the maximum value for each proposition, and the backward inference. Relevance of each information of the presupposition part and the conclusion part including the relevance of the obtained unknown information as a new premise part, and the relevance of the prediction information of the conclusion part as a new conclusion part, each of which For each of a plurality of second fuzzy production rules corresponding to the number of propositions common to the information and the number of information of the premise part, the minimum value of the goodness of fit of the premise part is obtained, and from the minimum value of each rule, This can be achieved by including the forward fuzzy inference apparatus that calculates the maximum value for each proposition and obtains the prediction information by using the maximum value for each proposition as the suitability of the prediction value information for each proposition.

Further, the above object is determined by inputting the process information including the control amount in the process control device that determines the manipulated variable from the difference between the target value of the control amount and the predicted control amount calculated including the unknown information of the process. An input / output device that outputs the manipulated variable to the process control device, and a manipulated variable determination device that calculates the manipulated variable at the present time based on the difference between the target value of the preset controlled variable and the predicted controlled variable after a predetermined time, A fuzzy production rule consisting of an antecedent part that is described by an ambiguous proposition that includes multiple process information and a conclusion part that is described by an ambiguous control quantity is a fuzzy production rule, and the ambiguous proposition of each information is quantified in goodness of fit. Storing means for storing a membership function to be stored, maximum value setting means for setting a predetermined maximum value in advance to the suitability of only one unknown information included in the fuzzy production rule A goodness-of-fit calculating means for calculating a goodness-of-fit by a membership function corresponding to each information from the input device according to the fuzzy production rule, and comparing the goodness-of-fit of the conclusion part and the goodness-of-fit of the premise part by the goodness-of-fit calculating means. Then, the backward inference means for replacing the goodness of fit of the unknown information with the goodness of fit of the conclusion part when the goodness of fit of the conclusion part is the minimum, and the defuzzying means for calculating the unknown information at the present time from the goodness of fit of the unknown information. With the backward fuzzy inference device having, and inputting the current process information including the unknown information obtained by the backward fuzzy inference device, the minimum fitness of the fitness of the process information is the predicted control amount after a predetermined time. This can be achieved by providing a predicting device that determines the predictive control amount based on the adaptability.

Further, the above object is determined by inputting the process information including the control amount in the process control device that determines the manipulated variable from the difference between the target value of the control amount and the predicted control amount calculated including the unknown information of the process. An input / output device that outputs the manipulated variable to the process control device, and a manipulated variable determination device that calculates the manipulated variable at the present time based on the difference between the target value of the preset controlled variable and the predicted controlled variable after a predetermined time, A fuzzy production rule consisting of an antecedent part that contains multiple process information and is described by an ambiguous proposition, and a conclusion part that is described by an ambiguous control quantity, and a membership that quantifies each piece of information to a goodness of fit for each ambiguous proposition. Storage means for storing a function, the plurality of first production rules for each of the plurality of first production rules according to the number of the propositions common to the respective information and the number of information of the premise part Maximum value setting means for setting a predetermined maximum value in advance to the suitability of only one unknown information included in the production rule, and a member corresponding to each information from the input device according to the plurality of first fuzzy production rules Goodness-of-fit calculation means for calculating the goodness-of-fit for each proposition by the ship function, comparing the goodness-of-fit of the conclusion part by the goodness-of-fit calculation means with the goodness of the premise part, and the unknown information when the goodness-of-fit of the conclusion part is minimum The unknown information is determined by substituting the goodness of fit of the conclusion part with the goodness of fit of the concluding part, and the maximum value is calculated for each proposition from the goodness of fit of the unknown information for each of the determined rules. A backward fuzzy inference apparatus having a value as the fitness of the unknown information, a fitness of the unknown information obtained by the backward fuzzy inference, and the current process information A plurality of second fuzzy productions according to the number of the propositions common to each piece of information and the number of pieces of information of the presupposition part, where the goodness of fit is a new premise part, and the goodness of fit of the predictive control amount is a new conclusion part. For each rule, the minimum value of the degree of conformity of the premise is found, the maximum value for each of the propositions is calculated from the minimum value for each of the rules, and the maximum value for each of these propositions is adapted to the prediction control amount for each of the propositions. And the forward fuzzy inference apparatus having an inverse fuzzification calculation means for calculating the predicted control amount from the goodness of fit of the predicted control amount for each proposition.

[Action]

The backward fuzzy reasoning of the present invention can be performed as follows.

In the fuzzy relation inference rule if A, B then C (Rule 1), where A and B are the conditions and C is the conclusion, the observation data for A, B, and C are A ′, B ′, and
If C ', of which A'and C'are known and B'is unknown, B'is inferred by the following procedure.

(Rule 1) is expressed as C = (A × B) · R (Equation 1) from the fuzzy relationship R. From (Equation 1), C ′ = (A′∧B ′) · R (A, B: C) (2) can be derived (where A′∧B ′ is the smallest of A ′ and B ′). Is shown).

This relationship becomes expressed using fitness function _{μ μc = (μ A ∧μ RA} ) ∧ (μ B ∧μ RB) = μ A ∧μ B ... ( Formula 3) for each item. Therefore, when μ _A and μ _B are known, the symbol α is defined as (aαb {1; a ≦ b, b; a> b}) is 1 when a ≦ b, and is otherwise defined as b. μ _B = μ _RB α (μ _A αμ _C ) = 1α (μ _A αμ _C ) = μ _A αμ _C (Equation 4) Replacing (Equation 4) with the inference rule format, μ _B = maximum value (= 1.0) {if μ _C <μ _A , μ _C <μ _B then μ _B = μ _C (Equation 5) This means that if the goodness of fit μ _C of the conclusion part information is smaller than the goodness of fit μ _A of the antecedent information that is observed and smaller than the maximum value of μ _B , the goodness of fit of the information B to be obtained μ _B is It is shown to be replaced by μ _C. Otherwise μ _B is the maximum.

From the above, the goodness of fit μ _B of the unknown information B is determined, and accordingly B ′ can be determined. The same applies when the number of conditions of the inference rule reaches n. That is, if B ′ is unknown by the inference rule if A ₁ , A ₂ ... A _n , B then C (rule 2) μ _B = 1.0 {if μ _C <μ _A1 , μ _C <μ _A2 , :: μ _C <μ _An , μ _C <μ _B then μ _B = μ _C } (Equation 6). This (formula 6) is an extension of (formula 5), and the goodness of fit μ _C of the conclusion part information is smaller than the goodness of fit μ _Ai (i = 1, 2, ... If it is smaller than the maximum value of μ _B (= 1.0), the goodness of fit μ _B of the information B to be obtained is equal to μ _C. Otherwise, μ _B becomes the maximum value.

This (Equation 6) is a direct expression of the backward fuzzy reasoning of the present invention, and can be intuitively understood as follows.

That is, in forward fuzzy reasoning by MIN-MAX, the smallest value of the goodness of fit included in the preamble of each rule is taken as the minimum value for each inference rule to make it the goodness of fit of the conclusion part (when uniquely determined, Take the maximum value by proposition for the minimum value of each rule). Looking at this relationship backwards, when less than the known fitness fitness is the preamble of the conclusion section (μ _C <μ _A), unknown fit of preamble has been adopted (mu _C <mu _B ) In case.

Therefore, when the fitness of unknown information is the smallest among the fitness of the premise part, the unknown fitness can be obtained by the backward inference of the present invention. It should be noted that a predetermined maximum value (usually the maximum value of the goodness of fit = 1.0) is set in advance so that the solution does not become indefinite even when it does not become the minimum.

According to the present invention as described above, in the case where the matching degree of unknown information in the premise is the minimum (the reasoning is simplified by limiting the range), the backward fuzzy reasoning based on the simple solution algorithm is realized. Therefore, it is possible to realize highly accurate prediction and control by diagnosing the cause from the symptom and by fuzzy inference including unknown information that is difficult to measure.

According to the inference method of the present invention, if there is a relation that can be described by an inference rule between known or observable information and unknown information, if the unknown information is in the conclusion part of the inference rule, a forward fuzzy reasoning is performed. Also, if unknown information is present in the preamble, it can be determined by backward fuzzy reasoning.

According to the present invention, the inference result does not become indefinite or cannot be uniquely determined. Therefore, the present invention enables backward inference not only in a crisp region such as AI inference but also in a general natural region including ambiguity.

〔Example〕

An embodiment of the present invention will be described below with reference to FIGS. 1 to 7.

FIG. 1 is a functional block diagram of an inference device according to an embodiment of the present invention. The inference apparatus 1 receives the observed data A ′ _t , C ′ _t of the observable information A, C at time t, and inputs the value C ′ of the information C at time t + 1 (1 indicates a unit time).
_It infers _{t + 1} .

The device 1 is provided with a storage device 6 which stores a predetermined membership function for the information A and C, and a central processing unit (CPU) not shown, and inputs the input values A ′ _t and C ′ _t . set of quantified goodness of fit by each of the membership function _{mA t (= {μ Atp,} μ Atz, μ Atn} defined at) mC _t a _{(= {μ Ctp, μ Ctz} , μ Ctn} defined at) Goodness of fit calculation means 2 for calculation and mA _t , mC _t are input,
Fuzzy inference rules, such as if A (large), B (large) then C (large) or if μ _A , μ _B then μ _C , are known between information A and C, although observation is impossible Backward fuzzy inference means 3, which infers a fitness set mB _t (= {μ _Btp , μ _Btz , μ _Btn }) at time t of information B, mA _t , mB _t , mC _t
Forward fuzzy inference means which outputs the fitness set mC _t +1 of the inference information C at time t + 1 as input 4, mC _{t + 1}
Is used as an input, and it is constituted by an inverse fuzzy conversion means 5 for obtaining C't _{+ 1} by a member function stored in the storage device 6.

FIG. 2 shows the configuration and operation of the fitness calculating means 2. It is an example when the observed data A _t ′ at time t is input. For information A in advance, for example, P (if A is positive), Z (if A is zero), N (if A is negative)
For each of the three fuzzy propositions, the membership function tuned based on the actual measurement value or a priori information is stored in the storage device 6. The input data A _t ′ is the CPU
The goodness of fit is obtained for each proposition by the membership function of the information A read by, and the ambiguous description is quantified.

That is, the goodness-of-fit calculation means 2 applies A _t ′ to the membership function, and the goodness-of-fit set mA _t = {μ _Atp , μ _Atz ,
Output μ _Atn }.

FIG. 3 shows the configuration of the backward fuzzy inference means 3. The generator 7 that outputs the maximum value of the goodness of fit stored in advance, the unknown goodness of fit determining means 8 and the maximum value determining means 9 are the basic means, and the goodness of fit set mA _t from the goodness of fit calculating means 2
And mC _t as input, the inference is performed according to the inference rule shown in FIG. 4, and the set of goodness of fit of unknown information B at time t
Output mB _t .

For example, in the relation of rule 1 if At _t is P, B _t is P then C _t is P in FIG. 4, the unknown information B _t of the premise is inferred as follows.

The generator 7 outputs 1.0 as the initial value of the fitness of B _t ′.

μ _Btp = 1.0 Next, the means 8 conforms to the conformity μ of the conclusion part according to (Equation 5).
_Compare the conformance between _Ctp and the premise, and when μ _Ctp is minimum,
_Replace μ _Btp with μ _Ctp . That is, if μ _Ctp <μ _Atp , μ _Ctp <μ _Btp then μ _Btp = μ _Ctp are executed. Qualitatively describing this, if μ _Ctp is _less than μ _Atp and _less than μ _Btp , then μ _Btp is μ
_It is equal to _Ctp . "

After this processing is processed in parallel for all rules, the maximum value determining means 9 determines the maximum value for each proposition (P, Z, N). In this way, the value of each element of mB _t is uniquely and always determined.

FIG. 5 shows the configuration of the forward fuzzy reasoning means 4. The forward inference is constructed according to the inference rules shown in FIG. For example, with respect to rule 1 if _Att is P, B _t is P, C _t is P then C _{t + 1} is P of the inference rule, the inference is performed by the MIN-MAX method as follows.

The minimum value determining means 10 of each rule obtains the minimum value from the conformances μ _Atp , μ _Btp , and μ _Ctp of the premise. Next, the maximum value determining means 11 determines the minimum value of each rule for each proposition (P, Z,
N), the maximum value of each proposition is determined, and the fitness set mC _{t + 1 at} the time t + 1 of the target information C is inferred.

FIG. 7 shows the configuration and operation of the inverse phasing means 5. The information C read out from the storage device 6 is the fitness C _{t + 1} input from the forward fuzzy inference means 4 for each proposition (P, Z, N).
Of the member function P, Z, N of the graph and the cutting line on the y-axis, and the center of gravity (CG) is calculated from the area of the shaded area,
The value (physical quantity) of the information C on the x-axis corresponding to the center of gravity is output. This value is the predicted value C ′ of the information C at time t + 1.
_{t + 1} .

What should be noted here is that the inference apparatus of the present invention shown in FIG.
In the process of inferring mB _t , the membership function of information B is not needed. This is because even if the information B is a disturbance and it is difficult to set the membership function,
It shows that it can be effectively realized.

Next, in the pollution generation process of road tunnels,
An example in which the inference device shown in the figure is applied will be described.

Now, the observable pollution concentration in the air due to the smoke of vehicles passing through the tunnel is C (PPM), and the factor that causes it is the observable number of vehicles A (units / minute), and it is already accumulated in the tunnel. Amount of accumulated pollution as an unobservable conceptual quantity is B
If it is (PPM), it can be described as if A, B then C. This shows a set of rules such as "if the number of vehicles is large (A) and the accumulated pollution amount is large (B), the pollution amount concentration is large (C)".

First, in the inference apparatus 1, the backward fuzzy inference means 3 infers the goodness of fit of the unknown information B from the observed values of A and C. Actually, mB _t is calculated from the fitness sets mA _t and mC _t of A and C. Then, the goodness of fit of these three pieces of information is calculated as mC at time t + 1.
_The forward fuzzy inference means 4 infers _{t + 1} , and the inverse fuzzy inversion means 5 estimates the target contamination amount concentration C't _{+ 1} .

On the other hand, FIG. 8 shows a conventional inference apparatus 20. Compared with FIG. 1 of the present invention, there is no backward fuzzy inference means 3 and the information B is not considered. The reasoning rules are as shown in FIG.
"If information A _t at time t is in the (+), and if information C _t is (+), the information C _{t + 1} at time t + 1 is a is (+)" the like.

FIG. 10 shows the simulation results of the pollution generation process in the tunnel for the inference apparatus of the present invention shown in FIG. 1 and the conventional example shown in FIG. In the figure, the observed value of the number A of vehicles at time 0 is A ₀ =
50 (units), the observed value of pollution concentration C is C ₀ = 25 (PPM). The predicted value C _{1 at} t = 1 is 25 (PPM) in the conventional example (marked with Δ) as shown in FIG.
The prediction accuracy is lower than that of 5 (PPM), and the same is true for other times. .

On the other hand, in the example of the present invention, when the fitness set mB _t0 obtained from the backward fuzzy inference is used as a premise with the fitness of A ₀ and C ₀ , C ₁ at t = 1 time is inferred, C ₁ = 60 ( PPM) is obtained, and the prediction accuracy is significantly improved compared to the conventional example.
Similarly, when the process is repeated until time t = 10, C according to the present invention is obtained.
It can be seen that the predicted value (neck) of 1 closely follows the actual value (solid line). It should be noted that FIG. 10B shows an example in which the fitness set mB _t0 is inversely fuzzy and B ₀ is calculated, which can be realized by a cause diagnosis expert system described later.

Although the above example takes the process of generating the amount of pollution in the tunnel as an example, the present invention is not limited to this. For example,
It can be applied when measuring or predicting the concentration or transparency in a fluid such as air or water, and when there is an unmeasurable conceptual amount or disturbance such as an accumulated amount that affects the process.

It is clear from the above description that the present invention can also be used as a cause diagnosis expert system. First
Figure 11 shows the basic configuration. The causal diagnosis expert system 30 inputs the observation values A ', C', and calculates the fitness of each member function. The fitness calculation means 2, A ', C', the fitness set mA, mC of unknown information The backward fuzzy inference means 3 infers the degree set mB, and the inverse fuzzy inversion means 5 for obtaining the value B ′ of the unknown information B from the mB. Taking the above-mentioned tunnel as an example, the present system 30 makes it possible to estimate an unknown contamination accumulation amount B that contributes to the contamination concentration C.

By the way, in order to measure the unknown amount B of accumulated contaminants, all the accumulated contaminants must be sampled and weighed, or the concentration must be measured by completely agitating the air, which is not possible. Is. Even if such a measurement is made, as a result, the property as an accumulated amount is lost and it does not reflect the actual process state, so this is meaningless.

As described above, the present invention is extremely effective as a means for measuring information that is substantially unmeasurable and for diagnosing the cause.

FIG. 12 is an example of a control device 100 in which fuzzy inference according to the present invention is applied to predictive control. In this example process information
A, B, C, D are observed by the sensor, and based on those values, the predicting means 101 such as fuzzy or linear model predicts the controlled variable after a predetermined time. The manipulated variable determining means 102 determines the manipulated variables of the control devices X1 and X2 based on the difference between the predicted value and the control target value.

In this control, the backward inference means 103 having the same function as that of the above-mentioned cause diagnosis system is input with the observation data A to D as the information E, F, and G that cannot be ignored due to the unobservable information. It is possible to add it like an input from a virtual sensor. Note that E to G are individually inferred.

When the predicting means 101 is composed of a fuzzy inference device as shown in FIG. 1, the information E, F, G does not have to be converted into physical quantities by the inverse fuzzy means, and only the degree of matching needs to be obtained.

According to such a control method of the present invention, even if there is unobservable information, disturbance or information of unknown cause, which has a non-negligible effect on the state of the process, such information is properly Since the behavior of the process can be predicted by inferring the above, it is possible to perform highly accurate prediction and control.

〔The invention's effect〕

According to the present invention, backward fuzzy inference can be realized with a simple configuration, and by combining backward fuzzy inference and forward fuzzy inference, the accuracy of process prediction and control can be significantly improved.

[Brief description of drawings]

FIG. 1 is a block diagram showing a functional configuration of an inference apparatus which is an embodiment of the present invention, FIG. 2 is an explanatory view explaining the function of a fitness calculation means, and FIG. 3 is a functional block diagram of a backward-looking fuzzy inference means. , FIG. 4 is a table showing the inference rules between the information A _t , B _t , and C _{t in} FIG. 3, FIG. 5 is a functional block diagram of the forward fuzzy inference means, and FIG. 6 is the information in FIG.
A table showing inference rules among A _t , B _t , C _t , and C _{t + 1} , FIG. 7 is an explanatory diagram for explaining the function of the inverse fuzzy-ized means, and FIG. 8 is a functional block diagram of a conventional inference device, FIG. 9 is a table showing inference rules between the information A _t , C _t , and C _{t + 1 in} FIG. 8, and FIG. 10 is a graph showing a comparison between the present invention and the conventional inference result in the tunnel contamination process. FIG. 11 is a functional block diagram of a cause diagnosis expert system which is another embodiment of the present invention, and FIG. 12 is a configuration diagram of a control device of the present invention. DESCRIPTION OF SYMBOLS 1 ... Inference device, 2 ... Fitness calculation means, 3 ... Backward fuzzy inference means, 4 ... Forward fuzzy inference means, 5 ... Inverse fuzzy inversion means, 6 ... Storage device, 7 ... Generator, 8 ... Unknown fitness determination means, 9 ... Maximum value determining means, 10 ... Minimum value determining means, 11 ... Maximum value determining means.

Front page continuation (72) Inventor Seiji Funabashi 1099 Ozenji, Aso-ku, Kawasaki-shi, Kanagawa Hitachi Systems Development Laboratory, Inc. (72) Inventor Yoshiyuki Sato 5-2-1 Omika-cho, Hitachi City, Ibaraki Prefecture Inside the Omika Plant of Hitachi, Ltd.

Claims (10)

(57) [Claims] 1. A fuzzy production rule consisting of a predicate part containing a plurality of pieces of information and represented by an ambiguous proposition, and a conclusion part containing one piece of information and represented by an ambiguous proposition, and each piece of information. A backward fuzzy inference method that combines a backward fuzzy inference for finding only one unknown information included in a premise part and a forward fuzzy inference for finding prediction information of a conclusion part based on a membership function evaluated in accordance with Inference, the maximum value of the goodness of fit is set in advance to the unknown information, the known information of the premise part and the known information of the conclusion part are input, and the goodness of fit of each of these pieces of information is calculated from the membership function. Of the unknown information by replacing the goodness of fit of the conclusion part with the goodness of fit of the conclusion part and comparing the goodness of fit of the predicate part with the goodness of fit of the predicate part. Obtaining the goodness of fit, the forward fuzzy inference is a new premise of the goodness of fit of each information of the premise part and the conclusion part including the goodness of fit of the unknown information obtained by the backward inference, and the premise of the premise part A fuzzy inference method, wherein the prediction information is obtained by using the minimum value of the fitness as the fitness of the prediction information of the new conclusion part. 2. A fuzzy production rule consisting of a predicate part containing a plurality of pieces of information and represented by an ambiguous proposition, and a conclusion part containing one piece of information and represented by an ambiguous proposition, and each piece of information adapted to each ambiguous proposition. In the fuzzy inference method, the backward fuzzy inference that finds only one unknown information included in the premise part and the forward fuzzy inference that finds the prediction information of the conclusion part are combined based on the membership function that is evaluated once. Is set to the unknown information in advance to the maximum value of the goodness of fit for each of the plurality of first fuzzy production rules according to the number of propositions common to the respective information and the number of information of the premise part. The known information of the part and the known information of the conclusion part are input, and the goodness of fit of each of these pieces of information is calculated from the membership function. The fitness of the unknown part is calculated by replacing the fitness of the unknown part with the fitness of the unknown part when the fitness of the premise part is compared and the fitness of the conclusion part is minimized. Calculating a maximum value for each of the propositions from the suitability of the unknown information for each of the plurality of first fuzzy production rules, and determining the maximum value for each of these propositions as the suitability of the unknown information for each of the propositions; The forward fuzzy inference uses a relevance of each information of the premise part and the conclusion part including a relevance of the unknown information for each of the propositions determined by the backward inference as a new premise part, and predictive information of the conclusion part. Is adopted as a new conclusion part, and a minimum of the goodness of fit of the premise part is set for each of a plurality of second fuzzy production rules according to the number of propositions common to the respective information and the number of information of the premise part. Find the value and Fuzzy reasoning, characterized in that the maximum value for each proposition is calculated from the minimum value for each second fuzzy production rule, and prediction information is determined as the maximum value for each proposition as the goodness of fit of the prediction information for each proposition. Method. 3. The prediction information is obtained by an inverse fuzzification operation using as input the goodness of fit of the prediction information inferred by the forward fuzzy inference. Fuzzy reasoning method. 4. A process control method for determining a manipulated variable from a difference between a target value and a predicted value of a controlled variable, and a predicate and a control for describing a plurality of process variables including only one unknown information by an ambiguous one proposition. Based on a fuzzy production rule consisting of a conclusion part that describes the quantity with an ambiguous proposition, and a membership function that evaluates each process quantity to the goodness of fit, a predetermined maximum value is set in advance to the goodness of fit of the unknown information. A goodness of fit is calculated from the known information of the premise part at the time of control acquired from the process and the control amount of the conclusion part, and the goodness of fit of the conclusion part and the goodness of fit of the premise part are compared to obtain the conclusion part. When the goodness of fit is the minimum, the goodness of fit of the unknown information is determined by replacing the goodness of fit of the unknown information with the goodness of fit of the conclusion part. Known information Process control method characterized by obtaining the predicted value of the minimum adaptability of the fit of the known information of the decision part as fit of the predicted value of the controlled variable. 5. A process control method for determining a manipulated variable from a difference between a target value and a predicted value of a controlled variable, wherein a predicate and a controlled variable describing a plurality of process variables including only one unknown information by an ambiguous proposition. Based on a fuzzy production rule consisting of a conclusion part described by an ambiguous proposition, and a membership function that evaluates each process quantity to suitability for each ambiguous proposition, the number of the propositions common to each information and the precondition part For each of the plurality of first production rules according to the number of information items, a predetermined maximum value is set in advance for the suitability of the unknown information, and the known information and the conclusion portion of the premise part at the control time acquired from the process are set. Compute the goodness of fit of each of the control quantities, and compare the goodness of fit of the conclusion part and the goodness of fit of the premise part, and if the goodness of fit of the conclusion part is the minimum, the goodness of fit of the unknown information Determine the fitness of the unknown information by replacing by the fitness, calculate the maximum value for each of the propositions from the fitness of the unknown information for each of the plurality of first fuzzy production rules determined,
The maximum value of each proposition is determined as the goodness of fit of the unknown information for each proposition, and the goodness of fit of each information of the premise part and the conclusion part including the suitability of the unknown information for the determined proposition As a new premise part, and the fitness of the predicted value of the control amount of the conclusion part as a new conclusion part and a plurality of first numbers according to the number of the propositions common to the respective information and the number of information of the premise part. For each of the two fuzzy production rules, the minimum value of the goodness of fit of the premise part is obtained, and the maximum value of each of the propositions is calculated from the minimum value of each of the plurality of second fuzzy production rules, and the maximum value of each of the propositions is calculated. Is a goodness of fit of the predicted value for each of the propositions, and a predicted value of the control amount is determined from the goodness of fit of the predicted value for each of the propositions. 6. A fuzzy inference apparatus in which backward fuzzy inference of unknown information and forward fuzzy inference of prediction information are combined, and a fuzzy predicate that includes a plurality of pieces of information and is ambiguous including one piece of information is ambiguous. A fuzzy production rule consisting of a conclusion part expressed by one proposition, a storage device that stores the membership function that evaluates the ambiguous proposition of each information by the goodness of fit, and each information of the premise part and the conclusion part An input device, a maximum value setting means for setting a predetermined maximum value in advance to the matching degree of only one of the unknown information included in the preconditioning part, the membership function and each information from the input device according to the rule. A goodness-of-fit calculation means for calculating goodness-of-fit and a goodness-of-fit of the conclusion part by the goodness-of-fit calculation means and a goodness of fit of the premise part are compared to determine that the goodness of fit of the conclusion part is minimum. A backward fuzzy reasoning device having inference means for replacing the degree of conformity of the unknown information with the degree of conformity of the conclusion section, the premise section and the conclusion including the degree of conformity of the unknown information obtained by the backward inference. The degree of relevance of each piece of information is a new premise section, and the minimum value of the degree of relevance of the premise section is the degree of relevance of the prediction information of the new conclusion section, and the predictive information is obtained from the relevance of the prediction information. A fuzzy inference device, comprising: a fuzzy inference device; 7. A fuzzy inference apparatus in which backward fuzzy inference of unknown information and forward fuzzy inference of prediction information are combined, and a predicate including a plurality of information and represented by an ambiguous proposition and an ambiguous proposition including 1 information A fuzzy production rule consisting of a conclusion part represented by, a storage device that stores a membership function that evaluates each information by a goodness of fit for each ambiguous proposition, and an input device that inputs each information of the premise part and the conclusion part. , For each of a plurality of first production rules according to the number of the propositions common to the information and the number of pieces of information of the premise part,
Maximum value setting means for setting a predetermined maximum value in advance to the suitability of only one unknown information included in the preamble of the plurality of first fuzzy production rules, from the input device according to the membership function and the rule. In the case where the fitness degree of the conclusion part is minimized by comparing the fitness degree of the conclusion part by the fitness degree computing means for computing the fitness degree of each information The suitability of the unknown information is replaced with the suitability of the conclusion part to determine the suitability of the unknown information for each of the plurality of first fuzzy production rules, and the plurality of determined first
A backward fuzzy inference apparatus having an inference means for calculating the maximum value for each of the propositions from the suitability of the unknown information for each fuzzy production rule, and the maximum value for each of these propositions as the suitability of the unknown information; The relevance of each information of the premise part and the conclusion part including the relevance of the unknown information obtained by inference as a new premise part, and the relevance of the prediction information of the conclusion part as a new conclusion part, For each of a plurality of second fuzzy production rules according to the number of the propositions common to each information and the number of information of the premise part, the minimum value of the goodness of fit of the premise part is obtained,
The forward fuzzy inference apparatus, which calculates the maximum value for each proposition from the minimum value for each rule, and obtains the prediction information by using the maximum value for each proposition as the goodness of fit of the prediction value information for each proposition. A fuzzy inference device characterized by: 8. An inverse fuzzification operation means for inputting a goodness of fit of the prediction information inferred by the forward fuzzy inference to obtain the prediction information by an inverse fuzzification operation. Alternatively, the fuzzy inference apparatus according to item 2. 9. A process control device for determining an operation amount from a difference between a target value of a control amount and a predicted control amount calculated including unknown information of a process, in which process information including the control amount is input and determined. An input / output device for outputting the manipulated variable to the process control device; and a manipulated variable determining device for computing the current manipulated variable based on a difference between a preset target value of the controlled variable and a predicted controlled variable after a predetermined time. , A fuzzy production rule consisting of an antecedent part that is written in an ambiguous proposition that contains multiple process information and a conclusion part that is written in an ambiguous proposition with a controlled variable, and the ambiguous proposition of each information is quantified in goodness of fit. Storage means for storing a membership function to be converted, maximum value setting means for setting a predetermined maximum value in advance to the suitability of only one unknown information included in the fuzzy production rule A goodness-of-fit calculating means for calculating a goodness-of-fit by a membership function corresponding to each information from the input device according to the fuzzy production rule, and comparing the goodness-of-fit of the conclusion part and the goodness-of-fit of the premise part by the goodness-of-fit calculating means. Then, the backward inference means for replacing the goodness of fit of the unknown information with the goodness of fit of the conclusion part when the goodness of fit of the conclusion part is the minimum, and the defuzzying means for calculating the unknown information at the present time from the goodness of fit of the unknown information. And a backward fuzzy inference device having, by inputting the current process information including unknown information obtained by the backward fuzzy inference device, the minimum fitness of the fitness of the process information as the fitness of the predictive control amount, A process control device, comprising: a prediction device that obtains a prediction control amount from the degree of conformity. 10. A process control device for determining an operation amount from a difference between a target value of a control amount and a predicted control amount calculated including unknown information of a process, in which process information including the control amount is input and determined. An input / output device for outputting the manipulated variable to the process control device; and a manipulated variable determining device for computing the current manipulated variable based on a difference between a preset target value of the controlled variable and a predicted controlled variable after a predetermined time. , A fuzzy production rule consisting of an antecedent part that is written in an ambiguous proposition that contains multiple process information and a conclusion part that is written in an ambiguous proposition with a controlled variable, and a member that quantifies each piece of information into a goodness of fit for each ambiguous proposition Storage means for storing a ship function, the plurality of first production rules for each of the plurality of first production rules corresponding to the number of the propositions common to the respective information and the number of pieces of information of the preamble. Maximum value setting means for setting a predetermined maximum value in advance to the suitability of only one unknown information included in the production rule, corresponding to each information from the input device according to the plurality of first fuzzy production rules. Goodness-of-fit calculation means for calculating a goodness-of-fit for each proposition by a membership function, and the unknownness when the goodness-of-fit of the conclusion part is minimized by comparing the goodness-of-fit of the conclusion part by the goodness-of-fit calculation part Replacing the goodness of fit of the information with the goodness of fit of the conclusion part to determine the unknown information, calculate the maximum value for each of the propositions from the goodness of fit of the unknown information for each of the determined rules, and for each of these propositions A backward fuzzy inference apparatus having a maximum value as the fitness of the unknown information, a fitness of the unknown information obtained by the backward fuzzy inference, and the current process information. As the new premise part, and the goodness of fit of the predictive control quantity as the new conclusion part, and a plurality of second fuzzy states corresponding to the number of the propositions common to the respective information and the number of information of the premise part. For each production rule, the minimum value of the goodness of fit of the premise part is obtained, the maximum value for each of the propositions is calculated from the minimum value for each of the rules, and the maximum value for each of the propositions is calculated as the predictive control amount for each of the propositions. A fuzzy inference apparatus, comprising: the forward fuzzy inference apparatus, which has a degree of goodness of fit and which calculates a predictive controlled variable from the degree of suitability of a predicted controlled quantity for each proposition.