JPH07191959A - Dynamic simulation system - Google Patents

Abstract

PURPOSE: To provide a dynamic simulation system capable of processing a non-linear system such as a chaostic system. CONSTITUTION: This dynamic simulation system is provided with a molding means equipped with functions for the input and edition of model information for constructing a dynamic simulation model, the preparation of a mutual action diaphragm, and the file management of a user, simulation executing means including at least standard execution, step execution, animation execution, and sensitivity analysis execution, graph displaying means equipped with functions for a dynamic curve graph, 2D factor correlation scattered point graph, 3D factor correlation scattered point graph, and the previous term/this term curve graph or the like, auxiliary analyzing means including data analysis, error analysis, and correlation analysis or the like, and result printing means such as the printing of the outputted and inputted information of the graph, the printing of simulation results, and the printing of simulation intermediate results or the like.

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention relates to a simulation system. Simulations are used in a wide variety of formats in a wide range of fields, from scientific research to industrial management, regardless of whether they are natural sciences or social sciences. Production system,
We have various systems such as management system, economic system, military system, communication system, social system, biological and ecological system, global environment system, and traffic problems, environmental pollution problems, population problems, global resource problems, energy problems, etc. Simulation is used as the main method in the field of studying various complex problems related to our present life and future survival.

[0002]

BACKGROUND OF THE INVENTION Social systems, which are closely related to our lives, are much more complex than engineering systems.
It has a dual character of "quantitative" and "qualitative (or heuristic)". And many scholars argue "we
ll structured problem "and" ill structured problem "
m ”.

Regarding the origin of the complexity of the social system,
In addition to having the property of “quantitative” and “qualitative” duality, it has the following properties.

A dynamic system; a non-linear system; there are many factors (or subsystems); there is an interaction feedback loop between factors, and there are negative and positive feedbacks ( Not in automatic control systems).・ Causal relationships between factors are complicated, there are functional relationships, probability relationships, and influence relationships (causal relationships that cannot be formulated in the form of explicit functions at the time of modeling).・ The behavior of factors can be deterministic, stochastic, or chaotic, which seems to remove the barrier between determinism and probability.・ Including humans

Most practical systems such as a production system, a distribution system, and an economic system share a quantitative and qualitative duality. Dynamic simulation (DS Dynamic simulation) is recognized as an effective simulation for clarifying the dynamics of a complex system such as a social system.

The most well-known dynamic simulation is called industrial dynamics. This DS was invented in 1958 by JW Forrester of America. This is defined as "a methodology for handling dynamic behavior of a system including feedback".

Therefore, research in the field of system dynamics (SD) including industrial dynamics, Urban Dynamics, and World Dynamics has become popular. In particular, the world model constructed by the commission of the Roman Club and the report "Limits of Growth" that was the result of its simulation had a revolutionary impact on the whole world. FIG. 1 shows the concept of the applicable range of each DS method.

The SD method describes a target system by using five kinds of mathematical equations centering on the following level equations. (1) Level equation: (2) Late equation (3) Auxiliary variable equation (4) Supplement equation (5) Initial value equation

Industrial dynamics is a DS method applicable only to "quantitative" systems, that is, systems consisting only of "functional relations". However, it is not suitable for systems that do not have the structure represented by the level equation.

The KSIM method was used in 1972 by J.C. of Canada. Ka
It was developed by Professor ne. The KSIM method does not use mathematical formulas when modeling,
A causal relationship between system factors is described using a matrix called "impact matrix".

The KSIM method has a fatal drawback in that it cannot process functional relationships and cannot process even the simplest linear relationships that exist in real systems (eg income = profit-cost). On the other hand, there are advantages that "soft" variables that cannot be handled as conventional mathematical models can be easily processed, they are flexible, easy to use, and suitable for non-specialists.

That is, the KSIM method is considered to be a DS method applicable only to a "qualitative" system, that is, a system consisting only of "influence relations".

[0013]

As the conventional DS, the industrial dynamics method and KSIM have the following major problems. Unless these problems can be solved, the nature of the social system cannot be clarified as a whole. , It is impossible to understand the dynamics of more complex systems because it cannot meet the demands of modern system engineering.

Since the conventional method cannot simultaneously handle the quantitative and qualitative duality, it cannot be applied to a real system. In most practical systems, "functional relations" and "influence relations" are mixed. Therefore, neither the industrial dynamics method that can handle a system that has only functional relationships or the KSIM method that can handle a system that has only influence relationships cannot be applied and is limited.

Further, the knowledge assets of the conventional mathematical model cannot be inherited. Regarding mathematical models in each research field, most of dynamic models such as the Lanchester battle model and the Volterra ecosystem model are defined by minute (difference) equations. The conventional DS method cannot handle such a model.

Furthermore, it is not possible to deal with the latest research on system engineering. For example, Complex Ad
In addition to the ability to handle interactions that form positive and negative feedback loops between system factors, cutting edge research such as aptive systems) is also capable of processing chaos, which is the cause of the irregular wave behavior of the system. Is being requested. However, since the conventional DS method cannot deal with higher-order difference equations, chaotic behavior of the system cannot be easily processed.

The present invention aims at a new dynamic simulation capable of solving the above-mentioned problems. In other words, this is based on the theory of systems science and has an influence relation corresponding to an ill structure problem,
A new continuous dynamic system that can handle systems with mixed or singular influence relations and functional relations by integrating functional relations corresponding to well structure problems
Simulation (hereinafter GSIM (General SIMulati
on) called the law).

Further, the present invention has the following conventional SD.
The purpose is to obtain a method for solving a problem that could not be solved as a law or was very difficult to process.

(1) Develop a new dynamic simulation method that can simultaneously handle quantitative and qualitative duality of social systems. That is, a dynamic simulation of a system in which an influence relationship and a functional relationship are mixed, hereinafter referred to as GSIM (General SIMration).

(2) Dynamic that can be adapted to the model defined by the subdivisional equation and inherits the conventional knowledge assets
simulation

Conventionally, most of the models developed for studying the dynamics of the system in each field are defined by differential equations and difference equations. Each of them reveals the nature of the social system from different angles. If it can be applied to such a model, it will be possible to inherit the conventional research results and knowledge, support the research in each field, and shorten the research period significantly.

(3) Dynamic simulation capable of processing the properties of nonlinear systems such as chaos so that it can be adapted to the requirements of modern system science.

(4) Dynamic simulation that can be applied to a system that does not have a structure represented by a level equation as industrial dynamics.

(5) Develop a simulator, which is a device on a computer, that can sufficiently bring out the capabilities of the DS method. (6) When solving problems such as social systems, only experts can solve the problems, and decision makers must participate. Therefore, a simulator having a new man-machine interface which is not available in the conventional simulator (for example, DANMON), which can be easily used by non-specialists, is obtained.

[0025]

[Means for Solving Problems] Quantitative & Social System
Until now, there is no DS that can handle qualitative duality at the same time. The present invention separately considers the causal relationship between the factors constituting the system into “functional relationship” and “influence relationship” with respect to the quantitative and qualitative dual nature of a complex system, Handle relationships simultaneously.

That is, it is a dynamic simulation of a system in which functional relationships and influence relationships are mixed. Therefore, according to the present invention, since the system can be analyzed more generally, rationalization, optimization, dynamic evaluation, future prediction, etc. of the industrial system can be performed. Therefore, the present invention can also be used in the following fields.

(1) National and regional economic business cycle model; (2) Dynamic forecasting system of stocks; (3) Market forecasting model with competitive action; (4) Complex Adaptive System; (5 ) Policy science; (6) Ecology and global environment system; (7) Business strategy simulation of enterprises; (8) Long-term investment dynamic evaluation problem; (9) Population problem; (10) Production system (11) Others

In order to solve the above-mentioned problems, inputting and editing of model information for constructing a dynamic simulation model, creation of an interaction diagram, and modeling means having a user file management function, at least standard execution, Simulation execution means including step execution, animation execution, sensitivity analysis execution, dynamic curve diagram, 2D factor correlation scatter diagram, 3D factor correlation scatter diagram, first-term curve plot function, etc., graph display means, data Auxiliary analysis means, including analysis, error analysis, correlation analysis, etc.
A dynamic simulation system having a result printing means for outputting graphs, printing input information, printing simulation results, printing intermediate simulation results, etc. is used. The principle of the present invention will be described below.

Generally, when a certain event occurs or a certain result occurs, it is considered that there is a cause. The "relationship" between the "cause" and the "effect" is "causal rel".
ationship) ". In the present invention, the causal relationship is defined as follows:

Definition 1: For system factors X and Y, if there is a phenomenon that factor X can act on factor Y, or that Y undergoes some change due to the presence of X, then The relationship that exists between them is called a causal relationship. The causal relationship is classified into the following "functional relationship", "probability relationship" and "influence relationship".

The functional relationship is a causal relationship in which the relationship between system factors is represented by a normal function formula. In the present invention,
Define the functional relationship as follows:

Definition 2: When the system factors X and Y have a causal relationship, the direction (increase / decrease) and width of the change that Y undergoes as X transitions to the next state
The case where both degrees (magnitude) can be uniquely defined is defined as a functional relationship. This functional relationship is expressed in the following form, for example: Y = f (x ₁ , x ₂ , _... T)

In the present invention, the probability relationship is defined as follows:

Definition 3: When the system factors X and Y have a causal relationship, Y is changed by the transition of X to the next state.
Change ( direction of increase / decrease) and width of change
Both degrees (magnitudes) cannot be uniquely determined, but a probability relationship is defined when a certain probabilistic discipline is followed.

This probability relationship is expressed in the following form, for example: y = P (x), y to N (f (x), σ ² ) (normal distribution)

The problem which can be drawn by the probability relation is a completely defined problem or a poorly defined problem (poor defined p).
roblem) is recognized as a problem. This probability relationship can be expressed by a probability distribution function (for example, a normal distribution function, an exponential distribution function, etc.) and can be treated in the same manner as the above-mentioned “functional relationship”. Therefore, in the present invention, it is treated as a functional relationship.

An impact relation is an ordinary explicit function because it is technical, due date, economical, etc. at the time of modeling, and the data for determining model parameters is not available. Although it cannot be formulated in the form of, it is a causal relationship that certainly exists between each system factor. In the present invention, the influence relationship is defined as follows:

Definition 4: When the system factors X and Y have a causal relationship, Y is changed by the transition of X to the next state.
The impact relationship is that only the direction (increase / decrease) of the change that is subject to change is determined. It is possible to empirically determine the existence of a causal relationship for an influence relationship.

[0039] For example: air pollution → human health physical environment → equipment deterioration climate → plant growth human activities → global environment. In addition, the impact relationship is "constant impact relationship".
There are two influence relations, namely, "change rate influence relation". In the present invention, a constant impact relation is defined as follows.

Definition 5: An influence relation that always influences the factor y even if the level of the factor x does not change and changes the level of y is called a "constant influence relation".

For example, the time of use of the equipment → deterioration of the equipment physical environment (temperature, humidity, etc.) → growth of metal rust.

In the present invention, the change rate influence relation (differential
impact relation) is defined as follows.

Definition 6: If the level of the factor x does not change, the influence relationship in which the level of the factor y does not change is called a "change rate influence relationship".

For example, the number of factories in the country → employment population bonus → employee morals.

The influence coefficient is a unitless numerical value indicating the strength of the relation of influence between two factors. In this paper, the factor j
_Is represented by w _ij .

For example, the numerical range of w _ij can be displayed in five steps as follows:

[Equation 1] Further, for the constant influence relation, the influence coefficient from the factor j to the factor i is the constant influence coefficient α _ij , and for the change rate influence relation, the influence coefficient from the factor j to the factor i is the change rate influence coefficient β.
_{Expressed as ij} .

In the present invention, the constant influence force Im _i (S _j ) from the factor j to the factor i corresponding to the constant influence relation is expressed by the following formula as the level S _j of the factor j and the factor j from the factor j. It is defined to be the product of the constant influence coefficient α _{i j} on. Im _i (S _j ) = α _ij · S _j ... (2.1)

Therefore, all the constant influences that factor i has

[Equation 2] It can be expressed as ... (2.2).

Further, the change rate influence force Im _i (dS _j / dt) from the factor j corresponding to the change rate influence relation to the factor i is Im _i (dS _j / dt) = β _ij · dS _j / dt .. It is defined as in. (2.3). Therefore, all the rate of change influences factor i has

[0050]

[Equation 3] It can be expressed as (2.4).

Here, the total influence is the sum of all the constant influences and the change rate influences received by the factors. Therefore, the total influence Im _i received by the factor i is expressed by the following equation. .

[0052]

[Equation 4] ... (2.5)

The positive total influence is the total influence of only the positive influence coefficients in the total influence exerted by the factors. That is, the positive total influence I ⁺ m _i received by the factor i is given by the following equation.

[Equation 5] ... (2.6)

The negative total influence I ^-- m _{i which the} factor i receives is given by the following equation.

[Equation 6] (2.7) It should be noted that this positive total influence can increase the level of the factor affected, and is also called excitatory influence, and the negative influence can decrease the level of the opponent's factor, and the inhibitory influence. Also called.

As shown in FIG. 2, an arbitrary factor i in a multi-factor system is subjected to a plurality of actions from other factors (1 ... n). The plurality of actions received by the factor include a function action corresponding to the functional relation and an influence action corresponding to the influence relation. In summary, the factor level is considered to be composed of two parts, which are generated by the functional relation and by the influence relation.

As shown in FIG. 2, the i-th system factor S
The level of _i is composed of two parts, that is, a part F _i corresponding to the functional relation and a part I _i corresponding to the influence relation, and is expressed by the following equation.

S _i = F _i + I _i (3.1) Assuming that the total period of the simulation is T and the even intervals thereof are t, the factor S _{i (t) in the} t period is in the present invention. The level before being affected is ψ _{i (t)} , the “net impact” (net impact) affected is P _{i (t),} and the net impact P _{i (t)} is a factor in the form of an exponential function. The following expression applied to
It is represented by.

[Equation 7] _{... (3.2) S i (t} ): t -life of factor S _i level P i of _(t): the net impact of the factors S _i of the period t (3.2 _reference) ψ _{i (t):} the influence of the factors S _i Level before being affected I _{i (t)} : Level corresponding to the influence relation of the factor S _i F _{i (t)} : Level corresponding to the functional relation of the factor S _i

The level ψ _{i (t)} before being affected
For, as shown in FIG. 3, because the level of before the affected action factors Si period t, impact levels I _i
The increment ΔI _i of can be expressed by the following equation (3.3): ΔI _{i (t)} = S _{i (t)} −ψ _{i (t)} ... (3.3)

Then, according to equation (3.1), this equation (3.3)
Can be converted as ΔI _{i (t)} = F _{i (t)} + I _{i (t)} −ψ _{i (t)} ... (3.4)

Further, for the time interval Δt, ΔI _{i (t)} = I _{i (t)} −I _{i (t−} Δt ₎ ... (3.5), so that the equation (3.4) is It becomes like the formula (3.6). I _{i (t)} -I _{i (t-} △ _t) = F _{i (t)} + I _{i (t)} -ψ _{i (t)} ... (3.6)

In summary, the factors S _i before being affected are
As shown in FIG. 3, the level ψ _{i (t)} of the above is composed of I _{i of} the immediately preceding period and F _{i of the} relevant period. That is,

Ψ _{i (t)} = I _{i (t-} Δt ₎ + F _{i (t)}
... (3.7) Further, according to the equation (3.1), I _{i (t-} △ _t) = S _{i (t-} △ _t) -F _{i (t-} △ _t) ... (3.8)

Since the expression of (3.) holds, this expression is changed to the expression (3.
Substituting into 7), ψ is finally expressed as in Eq. (3.9). ψ _{i (t)} = S _{i (t-} △ _t) + Fi _(t) -Fi _(t- △ _t) ... (3.9)

Therefore, the equation (3.2) becomes the equation (3.10). For convenience, the non-linear difference equation representing the level of this factor S _{i (t)} is called an “integration equation”.

[Equation 8] ... (3.10)

Further, in the GSIM method, the initial conditions of the net effect P _{i (0)} at the initial value point t ₀ = 0, the factor level S _{i (-1)} and the function level F _{i (-1) at} the period of t = -1. Are set as P _{i (0)} = 1, S _{i (-1)} = 0, and F _{i (-1)} = 0.

Therefore, the dynamics of the factor S _i can be expressed as follows for the time interval Δt using the integral equation. (See Figure 2)

[Equation 9]

[0067] When the present invention defines the net effect P as in Equation _{(3.15), P i = (} 1+ inhibitory influence I ^- m _i) / (1+ excitatory influence I ⁺ m _i) .. . (3.15) The net effect P _{i (t)} of the factor s _{i (t) in} period _t is
Desired.

[Equation 10] ... (3.16)

Therefore, the defined net effect has the following properties. Inhibitory influence> excitatory influence, 1 <P <∞; Inhibitory influence = excitatory influence, P = 1; Inhibitory influence <excitatory influence, 0 <P <1; P = 1 when not affected.

With respect to the response characteristic (instantaneous change rate) of the factor level defined in the integrated equation of the equation (3.10), the increment of the functional relation is represented by the equation (3.17) and considered. △ F _(t) = F _{(t +} △ _t) -F _(t) ... (3.17)

Generally, it is difficult to calculate the instantaneous rate of change of the factor defined by the difference equation, but the Euler method shown in the equation (3.18) used when solving the ordinary differential equation by the numerical solution method is used to approximate it. It is possible to investigate its properties.

[Equation 11] ... (3.18) Therefore, equation (3.10) and equation (3.18) yield equation (3.19):

[Equation 12] ... (3.19) By rearranging this, formula (3.20) is obtained.

[0071]

[Equation 13] ... (3.20) Moreover, since the range of the factor in the normal space is 0 ≤ s ≤ 1, the response characteristic of the factor is as follows. Net effect P
For P = 1 (no effect or positive,
If the negative influences are the same), then equation (3.20) becomes equation (3.21).

DS _(t) / dt = ΔF _(t) / Δt ... ₍ 3.21) That is, the rate of change of the factor in this case is equal to the rate of change of the functional relation, and the change of the level of the factor is complete. Will be decided by the functional relation. For the function increment, Δ
If F _(t) = 0 (or no function action), then the expression
(3.20) gives the following equation (3.22).

[Equation 14] ... (3.22) And from this equation, if S _(t) → 1, then dS _(t) / dt → 0, and if S _(t) → 0, then dS _(t) / dt → 0. . That is,
It can be seen that the rate of change becomes 0 when the level of the factor in the normal space approaches the upper limit (= 1) or the lower limit (= 0).

Further, when P → 1, dS _(t) / dt → 0, when P> 1, dS _(t) / dt <0, and when P <1,
dS _(t) / dt> 0.

Generally speaking, the rate of change of the factor P <
If 1 and <F _(t) > 0, then dS _(t) / dt> 0, P = 1,
When <F _(t) = 0, dS _(t) / dt = 0, and when P> 1, and <F _(t) <0, dS _(t) / dt <0. There is a property.

A case where the functional relationship is a constant will be described in consideration of the integrated equation. If Fi _(t) = d (d = time-invariant constant, -∞ <d <+ ∞)

[Equation 15] , T = simulation period), the integration equation is
It becomes like (3.23).

[0076]

[Equation 16] ... (3.23) The factor level in this case will be determined only by the influencing effect. The integrated equation represented by the equation (3.23) at this time is similar to the equation of the KSIM method shown in the equation (3.24).

[0077]

[Equation 17] (3.24) That is, if the function part of the GSIM method is defined as a constant, GS
It can be said that the IM method is complementary to the KSIM method.

Therefore, for a system composed of only influence relations, the functional relations of all factors are set to their initial values.
If defined as S (0) (ie: Fi _(t) = Si ₍₀₎ ), GSIM
The method is a dynamic simulation method that can be applied to a system consisting of only influence relationships.

When the pure influence P = 1, the influence exerted by the factor in the normal space is the inhibitory influence = excitatory influence, or when all the influence coefficients are “0”, the formula (3.23) ), The numerical value of the net effect P becomes 1, and the integrated equation at this time becomes as shown in equation (3.25):

[Equation 18] ... (3.25)

That is, the change in the factor level in this case is determined only by the function action. Therefore, for a system composed only of functional relationships, there is neither a constant influence relationship nor a change rate influence relationship.

[Formula 19] Then, the GSIM method becomes a dynamic simulation method capable of handling a system consisting of only functional relationships.

In the present invention, the space in which the system exists is
As shown in FIG. 5, the space is divided into three spaces, that is, “real space”, “model space”, and “normal space”.

In the structural state of the “real system” in the real space, the number of factors is infinite and the range of factors is −∞.
~ + ∞. Also, in general, a factor has a unit of measure. Examples are social systems, ecological systems, and production systems.

What is created in the model space using the factors extracted from the physical space is the "model system", that is, the model. The number of factors in the structural state is finite (n), and the range is -∞ to + ∞. The unit of measurement of the factor is also associated with the factor of the real system. In addition, the causal relationship between factors is defined.

A system composed of normalized factors is a "normal system", and a space in which it exists is a "normal space". The number of factors in the normal system is n, which corresponds one-to-one with the factors in the model system.
However, the range of factor level of the normal system is 0-1
However, there is no unit for measuring factors.

The process of mapping the factors from the model system X to the normal system S is called "normalization transformation", and T: X
→ Express with S. On the contrary, the process of mapping the factor from the normal system S to the model system X is called "revertive conversion" and is expressed as T ^-1 : S → X. Further, constructing the model system X from the real system is called modeling.

In the present invention, the level of the factor in the normal system S is referred to as "factor normal value" and is represented by S,
The factor level in the model system X is "actual factor value"
And is represented by X. Also, in the present invention, the normal value of the factor
We define the "revertive conversion" of Si into a factor real value Xi as in equation (4.1).

X _{i (t)} = T ⁻¹ i (S _{i (t)} ) ... (4.1) Obviously, for an n-dimensional system, n reversion functions are needed.

The function level is a level generated by the functional relationship of factors. On the other hand, in the present invention, the function level in the model system X is called a "function value", and the function level in the normal system S is called a "function normal value".

The function value is a numerical value obtained by a mathematical expression describing the functional relationship of factors in the model system X,
The range is -∞ to + ∞. The function value of the i factor is represented by FXi.

The function normal value is the normal system S
In, the function value FX of the factor is a normalized value such as 0 to 1. The function normal value of the i factor is represented by TXi. Further, in the present invention, the factor function value FX is defined as the “normal conversion” into the function normal value TX as in Expression (4.2). TX _{i (t)} = Ti (FX _{i (t)} ) ... (4.2)

Clearly, for an n-dimensional system, n
Number of normal conversion functions are required. Since the integrated equation of equation (3.10) describes the dynamic process of the normal system S, the function normal value TX must be used for the function level F in the equation. Therefore, when performing dynamic simulation, the integrated equation becomes as shown in equation (4.3).

[Equation 20]

By the definition of the equation (4.1), in the GSIM method, when the normal system factor is transformed into the model system factor, the restoration transformation is performed by the linear restoration transformation function shown in the equation (4.4):

[0093]

[Equation 21] T ^-1 i (): i factor return conversion function X _{i (t)} : t period, actual value of i factor S _{i (t)} : t period, normal value of i factor X _{i, max} : maximum of i factor Value X _{i, min} : minimum value of i factor

By the definition of the equation (4.3), in GSIM,
In order to convert the function value of the factor in the model space into the function normal value of the factor in the normal space, the normalization conversion is performed by the linear normalization conversion function shown in Equation (4.5).

[Equation 22] ... (4.5) Ti (): Normalized conversion function of i factor TX _{i (t)} : Normal value of t period, i factor FX _{i (t)} : Function value of t period, i factor

For a system having n target factors, if the proposed description system is used, the system influence relationship is described by an n * n-dimensional constant mutual influence matrix and a change rate mutual influence matrix, and The functional relation is defined by n explicit functions f1 (),
If the initial real values X1 (0), X2 (0), ... Xn (0) of the n factors are defined once f2 () ... fn () is formalized, Fig. 4 According to the proposed operation flow as shown in, it is possible to recursively find the only real value solution of each factor in each period.

GSIM proposes the following description system in order to fully fulfill the function of being able to handle both influence relations and functional relations and to handle interaction and chaos phenomena.

Regarding the influence relationship, in the GSIM method, the mutual influence existing between the factors is defined as a "cross influence matrix" (cross i).
mpact matrix).

The mutual influence matrix is an n × n-order matrix having “influence coefficient” as an element, which represents the coupling strength of the influence relation between factors for a system having n factors.
In the present invention, the conventions are as follows:

The column factor is a factor that is affected, and the row factor is a factor that exerts an effect. Furthermore, for the constant influence relation of a system having n factors, the constant influence coefficient α _ij
Is an element, and the n × n dimensional constant mutual influence matrix (constant
Cross-impact matrix) A is described.

For a change rate influence relation of a system having n factors, n × n is obtained by using the change rate influence coefficient β _ij as an element.
Dimensional change rate mutual influence matrix (differential cross-impact
matrix) B.

For functional relations, GSIM can handle various static and dynamic mathematical models.
We propose an engineering description system without using the description system centered on level equations such as MO. The GSIM method captures functional relationships as follows:

1 for each factor for an n-dimensional system
One, that is, n functional relationships are required. With respect to the factors that are not affected by the function from other factors, if the following settings are made according to the property described in 4.4.1, they will be the factors that are only affected. X _{i (k)} = f _i (X _{i (0)} ) = X _{i (0)} ... (6.3.1)

Therefore, in GSIM, a factor that receives a function action can be regarded as a dependent variable (factor variable), and a factor that produces a function action can be regarded as an independent variable (self variable), and the functional relationship between factors can be described in the form of an explicit function. Further, when a function is acted on by a plurality of factors, the function that describes the functional relationship becomes a "multivariable function". That is,

[Equation 23] ... (6.3.2)

However, in order to perform the simulation normally, the following constraint conditions must be obeyed when describing the functional relationship between the multiple factors forming the feedback loop:

[Equation 24] ... (6.3.3)

This constraint condition means that when the function value of a certain factor is obtained, the other factors which are the independent variables included in the function formula must be calculated after the factor. That is, for an n-factor model system X, if the i-factor FX _{i (t) in} the t period is the synchronous j-factor X _{j (t)}
If it is a function of, it means that their sequence numbers (subscripts appearing in the function expression) must be such that i> j. Furthermore, due to the nature of functional relationships, GS
The IM method classifies the functional relationships that can be handled as follows:

(1) Dynamic Relational Expression This is a relational expression defined by a difference equation that includes variables that change with the passage of time. Here, the difference equation relates the value X (t) in the t period with the value in the previous period. Ie:

[Equation 25] For example: X_{1 (t)}= a ・ X_{1 (t-1)} ... (6.3.2) X_{2 (t)}= a ・ X_{1 (t)}+ b ・ X_{2 (t-1)}+ c ・ X_{2 (t-2)} ... (6.3.3)

The maximum subscript difference appearing in the difference equation is called "order of difference equation" and is represented by "ξ". For example, the equation (6.3.2) is the first-order (ξ = 1), and the equation (6.3.3) is the second-order difference equation (ξ = 2). Furthermore, the maximum difference in subscripts that appears in all difference equations in the target system is called the "system difference rank" and is represented by "Ξ". Ie:

[0108]

[Equation 26] ... (6.3.4) where Ξ: system difference order ξ: difference equation order

Further, this system difference rank Ξ is GSI
When input as a global control variable when using the M simulator, it becomes the maximum rank of the difference equation that can be processed by the model. For differential equations, for example,
If the difference equation can be converted using Euler approximation, it can be processed by the GSIM method.
By the way, since the SD method describes the dimension of time as J (first period), K (current), and L (next period), it may not be possible to process higher-order difference equations freely.

(2) Static Relational Expression All the factors (variables) forming the relational expression are relational expressions that are synchronous. Alternatively, it is a relational expression in which both the independent variable and the dependent variable are synchronous. Ie:

[Equation 27] For example: Profit (t) = Income (t) -Cost (t)

(3) Temporal Relational Expression This is a relational expression with time t as an independent variable (factor). Ie:
X _{i (t)} = f _i (t). For example: X _{1 (t)} = X _{1 (0)}・ (1 + δ) ^t

(4) Probabilistic relational expression This is a relational expression for describing a stochastic relation. It is that feature that includes the probability function. For example: X _{i (t)} = μ + σ ・ NRAND where NRAND ~ N (0,1 ² ), N (・): standard normal distribution That is, X _{i (k)} ~ N (μ, σ ² ).

(5) Vector relational expression A relational expression describing discrete numerical values such as a time series function. For example: X _{i (t)} = v _(t) ; where v = {2,7,0,5, ...} In this case, "t" is the role that indicates the t-th number in the vector variable v. do.

(6) Logical relational expression This is a relational expression that describes a logical relation. For example, the following is performed when selecting either a large item or a small item. X _{3 (t)} = min (X _{2 (t)} , X _{1 (t)} ) X _{4 (t)} = max (0, X _{3 (t)} )

(7) Complex relational expression This is a combination of the various relational expressions described above. For example: X _{i (t)} = X _{i (t-1)} + σ · NRAND

Therefore, if the description system of the system described above is used, simulation model, econometric economy,
It will be possible to describe together the functional and impact relationships of various mathematical models such as forecasting, economic dynamics, production-inventory, etc.

In order to easily analyze the structure of a complex system, the visualization of a defined model is referred to as model visualization. In this paper, we focus on the flow of action between factors and propose a visualization method of a model called interaction tiregram that can simultaneously display influence relations and functional relations.

Interaction diagram
am) is a directed graph in which system factors are associated with nodes and various actions (function actions, constant influence actions, change rate influence actions) are associated with branches connecting the nodes. Further, if the change directions of the levels of both factors having a causal relationship are the same, "+" is shown, and if they are opposite, it is shown by "-".

The branches clearly showing the constant influence function correspond to the constant mutual influence matrix, and the branches showing the change rate influence effect correspond to the influence coefficient in the change rate mutual influence matrix. On the other hand, in the case of functional relations, the following promises are necessary. If the xi factor receives a function action from the other j factors, the function action can be formulated with multiple variables and expressed as in equation (7.1):

Xi = f (x1, x2 ... xj) (1 ≦ j ≦ n) Therefore, xi as the dependent variable and x1, x of j independent variables
The action between two lanes of 2 ... xj is represented by j arrows, and the direction of the arrows changes from the independent variable to the dependent variable.

Therefore, the interaction diagram according to the above-mentioned convention can clearly show 1) the structure of the system,
2) Various causal relationships can be expressed in a unified manner, and it becomes easy to detect an interaction or feedback loop in the system. (Fig. 6
(See)

It is practically impossible for humans to execute the simulation from the viewpoint of procedural and necessary calculation time, so that the computer must be used. Therefore, a program that is considered to be a dedicated device of a corresponding computer is required. This dedicated device is commonly called a "simulator". Also, the simulator for dynamic simulation is one type of continuous simulation.

There is only one DYNAMO (DYNAmic MOdel) for system dynamics as a commercialized simulator for conventional dynamic simulation.

As a part of the present invention, it is possible to cope with a system in which influence relations and functional relations are mixed or existent, a complicated system can be clearly described, and dynamic changes of system factors can be easily understood. He has invented a new continuous simulator (Simulater) that has a man-machine interface and can fully utilize the power of a computer. It is also called GSIM.

The main functions of the simulator GSIM are divided into three main functional blocks: modeling, simulation execution result processing. These three main functional blocks are mutually supportive and interdependent. Further, various information processing functions belong to each main function block. The relationship between them is shown in FIG.

In order for the user to construct the dynamic simulation model more efficiently, the user inputs and edits the model information and the interaction diagram.
m) creation and user file management functions are provided here. It mainly includes the following functions.

-Input and edit of model information and control information-Auxiliary creation of interaction diagram-File management

As the simulation execution function, the following four execution methods are mainly provided.・ Standard execution ・ Step execution ・ Animation execution ・ Sensitivity analysis execution

Output processing: -Graph display function Dynamic curve diagram 2D factor correlation scatter diagram 3D factor correlation scatter diagram Early-term curve diagram-Auxiliary analysis Data analysis Error analysis Correlation analysis-Result print Graph output was input Print information Print simulation results Print intermediate simulation results

The input information of GSIM is divided into two types: control information for controlling the simulation process and model information for describing the structure of the target model.

The control information is information set by the user for each model in order to control the process of dynamic simulation. The control information is
It is divided into Global control information for controlling the entire system and Local information for controlling the display state of each factor.

Global control information: (1 set) Number of system factors; Maximum rank of difference equation of system;
Number of vector functions; Local control information: (N set) Number of significant digits of factor; Control flag of factor graph display:
on, off * Model information: Information on the model directly defined by the user. Simple for each factor; (N) Name for each factor; (N) Initial value for each factor; (N) Maximum value for each factor; (N) Minimum value for each factor; (N) Functional relation ; (N) constant influence matrix A; (N * N) change rate influence matrix B; (N * N) auxiliary constant;

The above information can be collected in one file and stored in the disk as information of one model of the user. In addition, during the simulation period T, which is another important Global control information, on-line is input to improve operability.

FIG. 6 shows a basic operation flow which is the core of the GSIM simulator which can handle the influence relation and the functional relation together or independently.

In the dynamic simulation simulator, the present invention first developed a unique man-machine interface capable of displaying graph information and data information, which are simulation results, by operating three-dimensional buttons on the screen on the same screen. did. This has solved the problem that the conventional DS is difficult to use.

[0136]

EXAMPLE As a typical type of example in the industrial and research fields to which the present invention can be applied, a facility management dynamic model, CIM, which is a system in which influence relationships and functional relationships are mixed, which cannot be processed by the conventional DS method. Dynamic investment evaluation model, service industry investment evaluation model and chaos, Lanchester
Examples include models and Volterra models.

Here, the CIM (Compute
An example of dynamic investment evaluation for a state-of-the-art production system called r Integrated Manufacturing) will be described.

CIM (Computer Integrated Manufactur
ing) has become widely recognized, and as the number of cases of introduction has increased, interest and demand for CIM evaluation have grown. However, in reality, the situation regarding evaluation is very unclear, from the concept of evaluation to specific evaluation methods.

Therefore, by the developed dynamic simulation (DS) method, a large number of evaluation items for CIM evaluation can be handled in an integrated manner, their temporal dynamic behaviors are clarified, and CIM is introduced. We propose an evaluation method that can predict the strategic investment effect of the production system after 5 years and 10 years. Of course, this method can also be used as a method of selecting a plurality of CIM alternatives.

The “factory investment effect simulator” developed by this method has already been exhibited at the “CIM Japan '91” exhibition.

It is desirable to carry out an appropriate evaluation at any stage of CIM concept planning, design, introduction, and update. However, it is not easy because it has the following drawbacks. -"CIM is not static but dynamic."-Not only short-term effects but also long-term and strategic effects must be taken into consideration. There are many items and many items interact with each other. -The production system that is the object of evaluation is a mixture of quantitative items and qualitative items, or functional relationships and influence relationships. -When predicting the future economic efficiency of the CIM to be introduced, it is difficult to use the ordinary prediction method because there are still few data on the introduction and use of CIM. Therefore, according to the new DS method, it is possible to solve the above problems.

CIM evaluation is performed in the following procedure. Step 1) Build a structural model (production prototype model) before introducing CIM into the production system, and perform a dynamic simulation of the future development of this production prototype model using the new DS method; Step 2) Make a production prototype model , Add CIM factor and perform simulation again; Step 3) Compare, analyze and evaluate the two results.

In this example, the target production system is set as follows (see FIG. 10 and FIG. 11): ・ Targeted production factory is targeted; ・ Market growth takes the form of a growth curve Yes ・ Order volume is affected by the market, but its value is treated as a random variable. Since this model follows a normal distribution of N (G3 ₍₀₎ , 100 ² ), it is assumed that both effects and functions are affected together; ・ When introducing CIM, the learning and maintenance process Since it is necessary, let the utilization factor be a growth curve; ・ Order quantity = order quantity, production planning quantity = sales quantity ・ CIM that is exactly the same as the final useful life of CIM
Replace with M; -See diagrams in Figures 7 and 8 for other assumptions.

The minimum, initial, maximum and auxiliary constants of the factors in the input information, the constant mutual influence matrix A, the change rate mutual influence matrix B, and the functional relationship are shown below. F3 = N (G3 ₍₀₎ , 100 ² ) F5 = A1 * G4 F7 = min (G3, G5 * G6) F8 = G7 / G6 F9 = G8 * A2 F12 = (G9 * G11 + G10 * A2 * A4) * A3 / 365 F13 = G7 * A5 F14 = G14 ₍₀₎ + A6 / A7 + G12 F15 = G13-G9-G14 F16 = max (0, (G3-G7) * A5)

As a dynamic simulation of the production prototype model, the above mutual influence matrix and functional relationship and FIG.
When the contents of FIG. 8 are input to the developed simulator GSIM, a dynamic curve diagram as shown in FIG. 11 and a real value matrix as shown in FIG. 9 are obtained.

In the present invention, CIM has a positive constant influence on the corporate image, a positive change rate influence on the factors of operating rate, production capacity, and non-defective rate, and a negative change rate influence on the factors of variable cost, work in progress, and lead time. Shall be exerted. FIG. 12 is a relationship diagram of the CIM model.

The introduction of CIM is quantified by "CIM utilization factor". Therefore, if the factor of "CIM utilization" is increased to the prototype model, a dynamic curve diagram (Fig. 13) and a new real value matrix (see Fig. 9), which means the investment effect for the next 15 years, will be obtained.

According to the analysis of the investment effect by the introduction of CIM, the “market” grows rapidly in the form of a growth curve, and
It was close to the maximum around the year. Influenced by that, "order quantity"
It can be read from FIG. 11 and FIG. 13 that there is a variation at the same time that increases in a similar manner.

For this type of "order quantity", the original production system will be full of production capacity from the 6th year and the ordering capacity will be limited, so sales can be increased to 8925 (million yen) or more. Disappear. And since then, opportunity losses have increased steadily, doubling profits in the 15th year (Figure 9).

Regarding the market share, (see Fig. 7), from the first G7 ₍₀₎ / G1 ₍₀₎ = 1000/2000 = 0.5 (50%), (see Fig. 9) the 15th year G7 ₍₁₅₎ / It decreased to G1 ₍₁₅₎ = 1785/5988 = 0.298 (29.8%). It can be considered that they lost their strategic competitiveness.

On the other hand, if CIM is introduced, "lead time" is shortened, "work in progress" is reduced, "production capacity" is improved,
Since the "good product rate" and "uptime rate" have increased, the system's order-receiving capacity has also increased, and it has been possible to adequately meet the increasing "order volume". Occupancy rate also increases from the beginning: 3094/5988 = 0.517 (51.7%)

As the “corporate image” is improved, the “order quantity” is increased. The investment of 100 million yen is necessary for the introduction of CIM, but the "profit" for 15 years has reached 85,646 million yen due to the increase of "sales" and the decrease of cost, and It is 2.08 times that of the system (production model) that is not introduced.

Although the other detailed analysis is omitted, in conclusion, it would be a good idea to introduce a CIM of this scale.

The selection problem of a plurality of CIM alternatives will be described. The selection procedure is shown below. Step 1) Build a production prototype model and perform dynamic simulation; Step 2) Increase the CIM factor of each alternative for the same production prototype model and perform dynamic simulation separately;

Procedure 3) Compare, analyze and evaluate the simulation results of each alternative.

For each alternative CI and evaluation value,
Since the function of M is different, their mutual influence matrix is also different, and the simulation result is also different. However, the G15 "profit" factor is considered to be a factor that can gather all reactions of production system factors by all the discrimination from the investment amount difference of each alternative to the function difference, so the level of this factor is With the evaluation value as, we propose the following selection formula:

[0157]

[Equation 28] Where: a ₁ , a ₂ , ... a _m : M CIM alternatives; r ₁ , r ₂ , ... r _m : corresponding evaluation values; G15 _{(t), m} : mth alternative Ordinary profit level in the t-th period of the plan; T: period of simulation.

[0158]

[Effect] If the system of the present invention is applied to a production system in which functional relationships and influence relationships are mixed, the CIM can be effectively and easily evaluated. Further, not only the evaluation but also the dynamic behavior of the production system can be grasped, which is useful for strategic planning of a company.

[Brief description of drawings]

FIG. 1 is a conceptual diagram of an applicable range of each DS method.

FIG. 2 is an explanatory diagram of a configuration of factor levels in a multi-factor system.

FIG. 3 is an explanatory diagram of a dynamics of factors that are affected by an influential action and a functional action.

FIG. 4 is a recursive operation flow of GSIM.

FIG. 5 is an explanatory diagram of three structural states of the system and their relationships.

FIG. 6 is a main functional block diagram of GSIM.

FIG. 7 is a chart showing minimum values, initial values, and maximum values of factors.

FIG. 8 is a chart showing auxiliary constants.

FIG. 9 is a chart showing results of dynamic simulation.

FIG. 10 is a relationship diagram of a production prototype model.

FIG. 11 is a dynamic curve diagram of a production prototype model.

FIG. 12 is a relationship diagram of the CIM model.

FIG. 13 is a dynamic curve diagram of the CIM model.

Claims (1)

[Claims] 1. Modeling means having input and edit of model information for constructing a dynamic simulation model, creation of interaction diagram, and user file management function, at least standard execution, step execution, animation execution, Simulation execution means including sensitivity analysis execution, dynamic curve diagram, 2D factor correlation scatter diagram,
3D factor correlation scatter diagram, graph display means having functions such as early-to-current curve chart, auxiliary analysis means including data analysis, error analysis, correlation analysis, output of graph, printing of input information, simulation A dynamic simulation system comprising result printing means for printing results, printing intermediate results of simulation, and the like.