JPH04213752A - Method for modeling and inverse modeling object system - Google Patents

Abstract

PURPOSE:To offer the method for facilitating the modeling and inverse modeling of an object system containing a non-linear element with regard to the method for modeling and remodeling a control object, etc. CONSTITUTION:In the case of modeling a system which becomes an object, the model concerned is constituted of approximate expression models 1a, 1b, and an auxiliary model using neural networks 2a, 2b for making good the expression models concerned 1a, 1b, and in the case of inverse modeling the system which becomes the object, the inverse model concerned is constituted of the expression models 1a, 1b by an approximate inverse function, and an auxiliary model using the neural networks 2a, 2b for making good the expression models concerned 1a, 1b.

Description

[Detailed description of the invention]

0001

[Industrial Application Field] The present invention relates to a target system (
For example, regarding modeling and inverse modeling methods for "controlled objects", etc., models of target systems that can relatively easily achieve modeling and inverse modeling of systems that include nonlinear elements, which have been difficult to obtain in the past. and inverse modeling methods.

0002

2. Description of the Related Art Conventionally, modeling of controlled objects, mathematical analysis of experimental results, modeling of simulations, etc. have been widely considered to be important elemental technologies of control technology or analysis technology.

However, when attempting to model or analyze an actual object, the object often includes nonlinear elements, and it is generally difficult to model or analyze a nonlinear object. This problem is dealt with by approximation using a linear function, or by mathematical methods such as the method of least squares and multiple regression analysis. Further, the above situation is the same when obtaining an inverse model of the target system.

That is, FIG. 8 is a diagram for explaining the inverse model, and as shown in FIG. 8(a), input signal x is input to the target system 51, output y is obtained, and
If we know the functional relationship f(x) between input x and output y,
The mathematical model of the target system 51 is represented by a function f, and y
= f(x).

On the other hand, when an inverse function of the above function f(x), that is, a function g (an inverse function of the function f) that satisfies the relationship x=g(y), the element represented by the function g is It is called an inverse model 52 of the target system 51. Also in this case, if the target system 51 includes nonlinear elements, its inverse model 52
is extremely difficult to obtain.

[0006]

[Problems to be Solved by the Invention] As mentioned above, it is often difficult to model or inversely model objects that include nonlinear elements, and there has been a need for some kind of solution.

The present invention has been made in view of the above-mentioned problems, and provides a method for modeling and inverse modeling of a target system that can relatively easily realize modeling and inverse modeling of a target system including nonlinear elements. The purpose is to provide

[0008]

According to the invention, the above objects are achieved by the means set out in the claims.

[0009] In other words, the present invention provides that when a target system is modeled, the model is an approximate mathematical model and a neural network that supplements the mathematical model. This is a method for modeling the target system, which consists of the auxiliary model used.

[0010] Furthermore, in the invention as claimed in claim 2, when inverse modeling of a target system is performed, the inverse model is replaced by a mathematical model based on an approximate inverse function and a neural network supplementing the mathematical model. This is a method for inverse modeling of the target system, which consists of an auxiliary model using .

[0011]

[Operation] The present invention overcomes the above-mentioned problems by combining conventional modeling or analysis methods such as linear function approximation, least squares method, multiple regression analysis, etc. with a neural network. Although it is easy to express target linear elements using conventional methods, neural networks can approximate any nonlinear function with any precision, making it possible to express nonlinear elements that could not be expressed using conventional methods.

Although it is possible to model objects using neural networks, there are problems with accuracy and learning. Neural networks self-organize through learning, but when precision is required, a significant amount of learning time is required.

[0013] Furthermore, when a neural network is trained a large number of times (when trained with high accuracy), the problem of overfitting occurs. In general, the teaching data collected through actual measurements contains noise, and if you perform highly accurate learning on that data, you will be learning data that contains noise, and the interpolation function that is a feature of neural networks will not work. Distorted.

[0014] The present invention attempts to roughly describe a target model using conventional methods, and then express characteristic portions that could not be described by learning a neural network. Furthermore, the above situation is the same when performing inverse modeling of the target system, and as in the case of the above modeling, the inverse model of the target is roughly described, and the characteristic parts that could not be described are applied to the neural network. This is what we try to express through learning.

A more specific example will be explained below. That is, FIG. 1 is a diagram showing an example of the basic configuration of a model according to the present invention, and FIG. b) is an example in which the output of the mathematical approximation model 1b is input to the neural network 2b, and a model is constructed by adding the outputs of the neural network 2b and the mathematical approximation model 1b.

FIG. 2 is a diagram showing an example of the basic configuration of an inverse model according to the present invention, and FIG. 2(a) shows an inverse model constructed by connecting a mathematical approximation inverse model 3a and a neural network 4a in parallel. , input the target output y to the inverse model,
This is an example in which the output x of the inverse model is input to the target system 5. As shown in this example, by using the inverse model, when manipulating the output of the target system 5, it becomes possible to input the target output y corresponding to the final output y, and the handling of the target system 5 becomes easier. It becomes easier.

In addition, FIG. 2(b) shows a mathematical approximation inverse model 3b.
This is an example in which the output of the neural network 4b is input to the neural network 4b, and the outputs of the neural network 4b and the mathematical approximation inverse model 3b are added to form an inverse model.

FIG. 3 also shows a target system 5 according to the present invention.
FIG. 3 is a diagram showing a learning method of a neural network in the case of modeling, and shows a method of learning a neural network. Now, as shown in FIG. 3(a), the input of the target system 5 is "I" and the output is "O". Figure 3
In the example (b), the output O′ of the target mathematical approximation model 1a
The error e between the output O of the target system 5 and the output O of the target system 5 is given as teaching data to the neural network 2a. The example in FIG. 3(c) is an example in which the output of the mathematical approximation model 1b is given as the input to the neural network 2b.

Furthermore, FIG. 4 is a diagram showing a learning method of a neural network in the case of inverse modeling of a target system according to the present invention. In the example of FIG. Error e from input I to the system
is given as teaching data to the neural network 4a. The example shown in FIG. 4(b) is an example in which the output J' of the mathematical approximation inverse model 3b is given as an input to the neural network 4b.

[0020]

[Embodiment] An embodiment of the present invention will be described below. FIG. 5 is a diagram for explaining one embodiment of the present invention, and is an example of modeling a simple function. That is, as shown in FIG. 5(a), this is an example where the mathematical model of the target system 6 is given by f(x), and the relationship between input x and output y is given by y=f(x). . Normally, the function f(x) is a black box and is not known, but here it is defined as follows. y=f(x)=x+sin(x)

This function is expressed as shown in FIG. 5(b), where the mathematical approximation model 7 is g(x)=x and its output is yg
and the output of neural network 8 is ynet
Then, it can be realized as yg = g(x) = x y' = yg + ynet = x + ynet. In this example, the neural network 8 shown in FIG. 6 will learn the function sin(x). Moreover, FIG. 7 shows the simulation results in the above example, and shows the error (y') between the model output y' and the target output y.
-y) is shown to be sufficiently small. Note that, although the above embodiment takes the case of modeling the target system as an example, the same applies to the case of inverse modeling of the target system.

[0022]

[Effects of the Invention] As explained above, according to the present invention,
Modeling or inverse modeling of nonlinear objects, which has been difficult to achieve in the past, can now be done relatively easily. Furthermore, compared to modeling or inverse modeling using only a neural network, overfitting can be prevented, learning time can be shortened, and high accuracy can be achieved.

[Brief explanation of the drawing]

FIG. 1 is a diagram showing an example of the basic configuration of a model according to the present invention.

FIG. 2 is a diagram showing an example of the basic configuration of an inverse model according to the present invention.

FIG. 3 is a diagram illustrating a neural network learning method for modeling according to the present invention.

FIG. 4 is a diagram illustrating a neural network learning method for inverse modeling according to the present invention.

FIG. 5 is a diagram for explaining one embodiment of the present invention.

FIG. 6 is a diagram showing the configuration of a neural network.

FIG. 7 is a diagram showing simulation results of an example of the present invention.

FIG. 8 is a diagram for explaining an inverse model.

[Explanation of symbols]

1a, 1b Formula approximation model 2a, 2b Neural network 3a, 3b
Mathematical approximate inverse model 4a, 4b Neural network 5, 6
Target system 7 Mathematical approximation model 8 Neural network

Claims (2)

[Claims] [Claim 1] When modeling a target system, the model is composed of an approximate mathematical model and an auxiliary model using a neural network that supplements the mathematical model. A method for modeling the target system. [Claim 2] When performing inverse modeling of a target system, the inverse model is a mathematical model using an approximate inverse function and an auxiliary model using a neural network that supplements the mathematical model, A method for inverse modeling of a target system characterized by the following configuration.