JPH0784792A - Fuzzy inference device - Google Patents

Abstract

PURPOSE:To output desired final output to input indicating a sensual degree by adopting a Bezier function for the nonlinear mapping function of a fuzzy inference engine and adjusting a weight coefficient on a Bernstein base function value further. CONSTITUTION:The fuzzy inference engine 1 is provided with a first nonlinear mapping function 2 composed of a membership function and a second nonlinear mapping function 3 composed of the Bezier function and the functions 2 and 3 are serially connected. The function 2 respectively expresses the plural pieces of input by the sensual degrees such as small, a little small, precise and a little large and outputs them to the function 3 as intermediate output. The function 3 outputs the desired final output from the plural pieces of the input by adjusting the coefficient. Thus, the mapping function 2 of the engine 1 plays a role as a sensation filter in a sense and human and indistinct sensual judgement can be performed to an observation value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the construction of a fuzzy inference engine of a fuzzy inference device, and particularly adopts a Bezier function, an orthogonal function, a spline function, etc. as a non-linear mapping function of the fuzzy inference engine, and adjusts the coefficient by a The present invention relates to a fuzzy inference device adapted to obtain an output that approximates a signal.

[0002]

2. Description of the Related Art Generally, a fuzzy inference engine uses a membership function that outputs an intermediate output indicating a degree to an input and a group of rules that outputs a desired final output for an intermediate output of a predetermined membership function. It is configured.

When the number of observations to be input is one, the fuzzy inference engine inputs one of the observations and uses the membership function to detect this as a sensory degree, for example, large, slightly large, just good, slightly. small,
The five kinds of classifications such as small are output, the intermediate output is judged by five rules corresponding to each intermediate output, and the final output is output. By adjusting these five rules, a desired final output can be obtained from a given input.

As described above, the fuzzy reasoning apparatus can perform control in accordance with a human sense, and is therefore used as a control apparatus (called a fuzzy controller) for simultaneously controlling control parameters of various devices and a plurality of processes. It is often done.

[0005]

However, in the conventional fuzzy inference apparatus that determines the intermediate output by the rule group and obtains the final output, a combination of all inputs is used to obtain a predetermined output from a plurality of inputs. I had to combine the rules.

For example, if the fuzzy inference engine having five rules for one input has two inputs, 5 × 5 rules are required. Generally, n
For 5 inputs, 5 ⁿ rules are required, and for 5 inputs that are normally used, 5 ⁵ = 31
It was necessary to prepare 25 rules.

In order to obtain an output that approximates the teacher signal from a predetermined input, it is necessary to adjust the above-mentioned many rules and membership functions. Until now, it took a great deal of effort and time to obtain a satisfactory input / output relationship that matches experience and know-how. Therefore, it is extremely difficult to adjust the fuzzy controller, and it is difficult to make sufficient adjustment because the basis of the rule itself is unclear.

Therefore, an object of the present invention is to provide a fuzzy inference apparatus which can easily obtain an output that approximates a teacher signal without adjusting many membership functions and rules.

[0009]

In order to achieve the above object, a first fuzzy reasoning apparatus according to the present invention uses a Bezier as a non-linear mapping function of a fuzzy reasoning engine.
r) The function is adopted, the sensory degree of the observed value is expressed by the function values of the multiple Bernstein basis functions of this Bezier function, and the final output is approximated to the teacher signal by multiplying it by an adjustable weight coefficient. It is characterized in that it is configured to obtain.

A second fuzzy reasoning device according to the present invention is
A fuzzy inference engine is composed of two non-linear mapping functions connected in series. The first non-linear mapping function adopts a non-adjustable non-linear mapping function that outputs an intermediate output indicating the sensory degree, and the second non-linear mapping function. The mapping function is characterized by adopting one of a Bezier function, an orthogonal function, a spline function, and a neural network that outputs a final output that approximates the teacher signal from a predetermined intermediate output by adjusting the coefficient. is there.

[0011]

The first fuzzy reasoning apparatus of the present invention employs the Bezier function as the non-linear mapping function of the fuzzy reasoning engine. This Bezier function has a plurality of functions called Bernstein bases. The function value of the Bezier function is expressed as the sum of the product values of a plurality of Bernstein basis functions multiplied by weighting factors. By appropriately setting this weighting coefficient, it is possible to obtain an output that highly accurately approximates the target output with respect to a predetermined input.

The adjustment of the weighting factor is performed by obtaining the optimum weighting factor for the teacher data by the usual least squares method. The optimization by the least square method can be easily obtained by a computer by a general algorithm of the least square method. Therefore, according to this fuzzy inference apparatus, the input / output relation can be adjusted by mechanical processing, and the complicated adjustment of the membership function and the rule, which is performed by the conventional fuzzy inference apparatus, can be omitted.

A second fuzzy inference device of the present invention constitutes a fuzzy inference engine by connecting two non-linear mapping functions in series, and the first non-linear mapping function outputs an intermediate output indicating a degree and does not require adjustment. A non-linear mapping function is adopted, and the second non-linear mapping function employs a Bezier function, an orthogonal function, etc. that obtains an output that approximates the teacher signal by adjusting the coefficient.

With this configuration, the first non-linear mapping function, as a so-called sensory filter, converts the observed input into a degree that matches the human sense, and outputs it as an intermediate output to the second non-linear mapping function.

Next, the second non-linear mapping function converts the intermediate output into a predetermined final output and outputs it. The second non-linear mapping function employs a Bezier function, an orthogonal function, or a neural network, which is a non-linear mapping function in a broad sense, by which a desired input / output relationship can be obtained by adjusting weighting factors and the like.

The adjustment of the coefficient such as Bezier function is performed by a generally known least square method algorithm, the nonlinear mapping function such as the orthogonal function is performed by a generally known mathematical solution method, and
The adjustment of the weight of the neural network can be mechanically adjusted by the back propagation learning method or the like. Therefore, the input / output can be easily adjusted to obtain the desired final output from the predetermined intermediate output.

As a result, according to the second fuzzy reasoning apparatus, a human sense filter is applied to a predetermined observation value without adjusting complicated membership functions and rules, and the sense filter is applied. It is possible to output a judgment (final output) based on experience for the value multiplied by.

[0018]

Embodiments of the present invention will be described below with reference to the drawings. A first fuzzy reasoning device according to the present invention is
Bezier for nonlinear mapping functions of fuzzy inference engine
er) function is adopted. Here, the non-linear mapping function is a function whose input and output do not have a linear relationship (f (x + y) = f (x) + f (y)). The fuzzy inference device has no linear relationship between the input and the output, and can be called a kind of non-linear mapping function in a broad sense. In this sense, the membership function of the conventional fuzzy reasoning device is also a non-linear mapping function.

Therefore, the Bezier function of the first fuzzy reasoning apparatus of the present invention is shown in FIG. 1 in comparison with the membership function, and will be described below in comparison.

As shown in FIG. 1A, the Bezier function is the entire function represented by the sum of the functions called the Beinstein basis. The Bezier function of FIG. 1A is one-dimensional x
Is a function consisting of the sum of four-dimensional Bernstein basis functions of.

Let B (x) be the Bezier function of FIG.
If this is expressed by a mathematical expression, the following expression (1) is obtained. Here, Base _i (x) represents the i-th base of the Berstein base, and can be expressed as the following expression (2). On the other hand, the membership function of the conventional fuzzy inference engine of FIG. 1 (b) outputs the function value as follows.
This membership function u is N for the input of the state quantity x.
B: Small, NS: Small, ZO: Just right,
The degree (mj) belonging to each set of PS: slightly large and PB: large is calculated, and the output value (wj) corresponding to each is calculated.
Multiply by and output the sum. That is, the membership function u can be expressed by the following equation (3). Here, when the Bezier function B (x) and the membership function u are compared, the Bezier function B is obtained from the equations (1) and (3).
The Bernstein basis Base _i (x) of (x) is similar to NB, NS, ZO, PS, PB of the membership function u, and the weighting coefficient b _i of the Bezier function B (x) is the output value of the membership function u. It can be seen that it is similar to w _j .

In the conventional fuzzy inference engine, a rule is applied to the output u of the membership function and the final output corresponding to this output u (intermediate output) is output.

However, with the Bezier function, an output that approximates the final output of the teacher signal can be obtained directly by adjusting the weighting factors b _i .

The weight coefficient b _i can be adjusted by a method called the least square method. That is, a point sequence (y ₁ , x ₁ ), (y ₂ , x ₂ ), which is a teacher signal, ...
…, (Y _p , x _p ), It suffices to find bi that minimizes the sum of squares of.

[0025]

[Equation 1] Then, the minimization problem can be expressed as y−A · b For the solution of this equation, the following equation may be calculated by an ordinary algorithm of least squares method. b = [A ^T A] ^-1 A ^T y As is clear from the above description, according to the fuzzy inference engine of the present invention using the Bezier function, the observed value can be expressed by the Bernstein basis function in a sensory degree. The desired output can be obtained by further adjusting the weighting coefficient.

Since the adjustment of the coefficient can be mechanically obtained by the usual least squares algorithm, the adjustment of the fuzzy controller is extremely easy. Moreover, since the optimum weighting factor can be obtained numerically, uncertain work such as the conventional fuzzy controller adjustment that considers the meaning of a rule with a weak basis is not used.

However, the Bernstein basis function of the Bezier function is fixed, the membership function (NB, N
S, ZO, PS, PB) cannot be defined by any shape and place. For this reason, in some cases, it is not possible to obtain an output that is sufficient for the operator.

Therefore, in the second fuzzy reasoning apparatus of the present invention, two nonlinear mapping functions are connected in series, and the first nonlinear mapping function simply represents the input with a sensory degree. The non-linear mapping function outputs a desired final output from a predetermined input by adjusting a coefficient such as a Bezier function.

FIG. 2 shows an example of the configuration of the second fuzzy reasoning apparatus according to the present invention, in which the membership function is the first non-linear mapping function and the Bezier function is the second non-linear mapping function.

In FIG. 2, the fuzzy inference engine 1 has a first non-linear mapping function 2 which is a membership function and a second non-linear mapping function 3 which is a Bechet function. The first non-linear mapping function 2 and the second non-linear mapping function 3
Are connected in series as shown in the figure.

The first non-linear mapping function 2 expresses these with respect to a plurality of inputs in a sensory degree such as small, slightly small, just right or slightly large, and the second nonlinear mapping function as an intermediate output. Output to.

The second non-linear mapping function 3 adjusts the coefficients to output a desired final output from a plurality of inputs.

With this configuration, the first nonlinear mapping function 2 of the fuzzy inference engine 1 of this embodiment is used.
Acts like a so-called sensory filter, and can make ambiguous human-like sensory judgments on observed values. Since the first non-linear mapping function 2 merely indicates the sensory degree of the input, it is possible to eliminate the need to adjust the coefficient and the like.

The second non-linear mapping function 3 outputs an appropriate empirical final decision (final output) for a plurality of intermediate decisions (intermediate outputs). This second non-linear mapping function 3 employs a function whose input / output can be easily adjusted.

Next, the input, intermediate output, and final output will be specifically described with reference to FIG. In FIG. 3, there are n membership functions (2 (1), 2 (2), ...) Depending on the type of input.
…, 2 (n)) are prepared.

Membership functions 2 (1), 2 (2), ...
, 2 (n) inputs inputs X ₁ , X ₂ , ..., X _n , respectively, and intermediate outputs u1, u2 ,.
Output to. The kth intermediate output uk is expressed by the following equation.

[0037]

[Equation 2] Where h _i is the membership function 2 for input x
Each function value of (k), V _i (k), represents a weighting coefficient. The division by Σh _i is for scaling the intermediate output to a predetermined range.

These plural inputs u1, u2, ..., U
With respect to n, the Bezier function 3 outputs the final output y which is the determination result.

In this case, the weighting coefficient b of the Bezier function 3 is adjusted in advance so that the input / output relationship is approximated by the teacher signal. By the way, the Bezier function when the input is three-dimensional (x, y, z) has the form of the following formula.

[0040]

[Equation 3] Next, it will be shown by using a concrete function that the approximation to the teacher signal by this Bezier function is performed with high accuracy.

FIG. 4 shows the fourth order (Bernstein base is 4
Number) Bezier function

[0042]

[Equation 4] The result of approximating is shown.

Since this function is a four-dimensional hyperplane, it cannot show the whole. Therefore, using Z as a parameter, Z = 1.0 is shown in FIG. 4A, Z = 0.5 is shown in FIG.
Z = 0.0 is shown in FIG. In FIG. 4, a curved surface with contour lines shows an approximated function, and a curved surface without contour lines shows the original function. The vertical distance between both curved surfaces indicates a difference due to approximation.

As can be seen from FIG. 4, the Bezier function has the ability to approximate a teacher signal with extremely high accuracy and smoothly interpolate (insert an appropriate value at an arbitrary point between two points).

The fuzzy inference apparatus in the case of adopting the membership function for the first nonlinear mapping function and the Bezier function for the second nonlinear mapping function has been described above, but the nonlinear mapping function is not limited to the case of the above embodiment.

That is, the first non-linear mapping function is sufficient if it can output a function value indicating a sensory degree with respect to the observed value, membership function, Bezier function, orthogonal function (trigonometric function, Legendre function, Bessel function, etc.), It can be one of a spline function and, in a broad sense, a neural network included in a non-linear mapping function. The second non-linear mapping function need only be a function that can output a value that approximates the output of the teacher signal by adjusting the coefficients (the weights by which each output of the hidden layer is multiplied in the neural network) for a large number of inputs, Any of Bezier function, orthogonal function, spline function, and neutral network may be used.

A method of approximating these functions and the like can be performed by a generally known mathematical method, and a neural network can be performed by a generally known learning method, and therefore description thereof will be omitted.

By the way, in the fuzzy control by the usual fuzzy inference apparatus, the so-called linear control part (input / output by processing such as addition, integration, differentiation, and counting) is also possible due to the flexible input / output capability of the fuzzy inference apparatus. It was controlled by a fuzzy reasoning device.

However, if the input / output of such a linear relationship is also controlled by fuzzy control, the amount of processing in the fuzzy inference apparatus increases, the processing takes time, and the configuration of the fuzzy inference apparatus must be complicated. There was a problem.

Therefore, in the present invention, the fuzzy inference apparatus is constructed by arranging the linear controller in front of the fuzzy inference engine.

FIG. 5 shows a configuration for controlling a controlled object such as a robot by fuzzy inference equipped with a linear controller. In FIG. 5, a fuzzy inference device 4 has a linear control device 5 and a fuzzy inference engine 6, and performs feedback control on a controlled object 7 such as a robot.

The linear controller 5 is like an adder, an integrator, a differentiator, a counter, and an intermediate control command according to the position of the controlled object 7 such as a robot, the amount of motion, the speed of motion, etc. Is output. The fuzzy inference engine 6 is any one of the fuzzy inference engines according to the present invention, receives the output of the linear controller 5 and outputs a desired value (control command) corresponding to the input.

According to the fuzzy inference apparatus 4 having the above configuration,
Most of the calculation for control is processed by the linear controller 5, and the input / output relationship to be processed by the fuzzy inference engine 6 is simplified. As a result, the control can be performed quickly by the fuzzy inference engine having a simple structure.

The linear controller 5 has a plurality of constituent devices such as an adder, an integrator, and a differentiator, each of which inputs information from the controlled object 7, performs linear control, and fuzzy results. You may make it output to the inference engine 6.

[0055]

As is apparent from the above description, in the fuzzy reasoning apparatus of the present invention in which the Bezier function is adopted as the non-linear mapping function of the fuzzy reasoning engine, the Bernie basis function of the Bezier function is used to determine the sensory degree of the observed value. It can be expressed, and further, by adjusting the weighting coefficient applied to the value of the Bernstein basis function, it is possible to output a desired final output with respect to an input indicating a sensory degree.

Since the adjustment of the weighting coefficient of the Bezier function can be mechanically processed by a predetermined algorithm, it is possible to avoid the conventionally difficult adjustment of the membership function and the rule, and to obtain a desired input / output relationship by simple adjustment. A fuzzy reasoning device can be obtained.

Further, a fixed first non-linear mapping function for converting an observed value into a sensory degree and a second non-linear mapping function for obtaining a desired input / output relationship by adjusting a simple coefficient are connected in series. According to the fuzzy inference apparatus of the present invention, the first non-linear mapping function can output an intermediate output having an appropriate sensory degree for a wide variety of observed values, and the second non-linear mapping function can be used to adjust simple coefficients and the like. It is possible to output a final output that is close to the teacher signal.

According to the fuzzy inference apparatus of the present invention in which the linear controller is used as a preprocessor for the fuzzy inference engine, most of the control calculations can be performed by the linear controller, so the input / output relations of the fuzzy inference engine. Is simplified, and a fuzzy controller that performs quick control can be obtained with a simple structure.

[Brief description of drawings]

FIG. 1 is a diagram illustrating a relationship between fuzzy control by comparing a Bezier function, which is a non-linear mapping function of a first fuzzy reasoning apparatus according to the present invention, with a conventional membership function.

FIG. 2 shows a series of a first non-linear mapping function that outputs an intermediate output indicating a degree of sensation to an observed value and a second non-linear mapping function that can obtain a desired input / output relationship by adjusting simple coefficients and the like. The figure which showed the structure of the 2nd fuzzy inference apparatus by this invention connected.

FIG. 3 is a diagram for explaining input / output of a second fuzzy reasoning device according to the present invention by mathematical expressions.

FIG. 4 is a diagram showing an approximation result of a teacher signal by the second fuzzy reasoning apparatus according to the present invention.

FIG. 5 is a diagram showing a configuration of a third fuzzy reasoning device according to the present invention in which a linear control device and a fuzzy reasoning engine according to the present invention are connected in series.

[Explanation of symbols]

 1 Fuzzy Inference Engine 2 First Nonlinear Mapping Function 3 Second Nonlinear Mapping Function 4 Fuzzy Inference Device 5 Linear Controller 6 Fuzzy Inference Engine 7 Controlled Object

Claims (3)

[Claims] 1. A Bezier function is adopted as a non-linear mapping function of a fuzzy inference engine, and the sensory degree of an observed value is expressed by the function values of a plurality of Bernstein basis functions of this Bezier function, and adjustment is made to this. A fuzzy reasoning device characterized by being configured to obtain a final output that approximates a teacher signal by multiplying by a possible weighting factor. 2. A fuzzy inference engine is constituted by two non-linear mapping functions connected in series, and the first non-linear mapping function employs a non-adjustable non-linear mapping function that outputs an intermediate output indicating a sensory degree. , The second non-linear mapping function employs any one of a Bezier function, an orthogonal function, a spline function, and a neural network that outputs a final output that approximates a teacher signal from a predetermined intermediate output by adjusting the coefficient. Features fuzzy reasoning device. 3. A linear controller is provided, which is configured to input an observed value and output a function value of a transfer function corresponding to the input to a fuzzy inference engine. The fuzzy inference apparatus according to claim 1 or 2.