JP2011238031A - Automatic generation program of tree structure which classifies situations and automatic generation device of tree structure which classifies situations - Google Patents

Abstract

PROBLEM TO BE SOLVED: To automatically generate a tree structure which classifies situations efficiently based on an objective standard by evaluating a generation situation and providing feedback to reduce many decisions and much labor/time by an analysts, reduce calculation amount needed to generate the tree structure which classifies the situations considering occurrence probability, and achieve improvement of objectivity/accuracy and man-hour reduction/calculation time reduction, etc.SOLUTION: An automatic generation program of a tree structure comprises: a retrieval step of retrieving an initial condition of an event input from input means; a branch creation step of creating an initial branch based on the initial condition; an evaluation value calculation step of calculating an evaluation value of the branch; an evaluation value difference calculation step of calculating the difference of the evaluation values of the adjacent branch; a branch addition step of adding a new branch between the branch with the biggest evaluation value difference acquired in the evaluation value difference calculation step; and an output step of outputting information acquired from a tree structure comprising the new branch added in the branch addition step.

Description

  The present invention relates to a tree structure automatic generation program that classifies situations that are preferably used when a company or the like makes an important decision, and a tree structure automatic generation apparatus that classifies situations.

When companies make important decisions, decisions are often made based on the evaluation of only a few combinations that are likely to have a high possibility, such as market and social conditions. However, the future seen from the present is a set of possibilities that can change into various situations, and it is desirable to make a judgment after considering them comprehensively and probabilistically. The main area of application of such a probabilistic approach is probabilistic safety assessment.
This probabilistic safety evaluation method has been developed mainly for large systems such as nuclear power plants that require high reliability and safety despite being large and complex. By assuming a large number of major events to be considered as scenarios, and evaluating the frequency of occurrence and the effects quantitatively, comprehensive safety is examined. In recent years, it has come to play an important role in plant design / improvement and safety review of nuclear power plants (Hirano et al., Series Lecture Introduction to Probabilistic Safety Assessment (PSA) of Light Water Reactors 1-7, Japan Atomic Energy) Academic Journal, vol.48, No.3-10).
A typical procedure for the probabilistic safety assessment method is as follows. First, starting from an event that triggers an accident, the subsequent progress and the combination of success or failure in dealing with it are expressed in an accident scenario (or accident sequence). The skeleton of the scenario is usually represented by an event tree (Event Tree, ET), and the probability of branching to each branch constituting the scenario is a fault tree (FT) analysis / GO-FLOW method (Takeshi Matsuoka, stochastic) System reliability analysis method for safety evaluation GO-FLOW-from basic concept to actual use-, CRC solutions) and other system reliability analysis. Then, the probability of occurrence of each scenario and the degree of damage in that scenario are calculated and aggregated, and the aspect of damage occurrence is clarified quantitatively. As a result, it becomes possible to extract the problem points for the system before the accident occurs and take countermeasures (T. Bedford, Fundamental and Method for Probabilistic Risk Analysis, Springer (2006)).
On the other hand, safety assessment using a deterministic approach takes only a small number of events that should be considered for safety from the frequency and severity expected in advance, and evaluates whether safety is ensured when they occur. To determine if the system is safe.
This deterministic approach has the advantage of lower evaluation costs compared to the probabilistic approach. However, the number of events to be taken up is limited, so there is a risk of failure to consider scenarios that have serious consequences. Also, since the likelihood of each scenario is not directly evaluated, a comprehensive impact assessment cannot be performed. There is.

Since the probabilistic approach enables comprehensive evaluation that takes into account the frequency and impact, safety is mainly applied in other areas of nuclear power plant design and improvement as described above and in safety reviews. Introductory research is being conducted as a basic technology to evaluate.
For example, a report by Tsu-Mu Kao et al. (Tsu-Mu Kao, Chun-Sheng Weng, Applications of Quantitative Risk Assessment Technique on Liquefied Natural Gas Tanks System, 2008, PSAM9) describes a study on safety assessment of liquefied natural gas plants. . In Tanabe et al.'S research (Yasuo Tanabe, Masahiro Yamashita, PSA in nuclear power plants and its application to general industries, REAJ, Vol. 22, No. 7, 2000, pp. 607-615), ITS (Intelligent An example of application to a future transportation system such as Transport Systems) is shown. In the maritime field, the UK proposed the introduction of a comprehensive safety assessment method (FSA) based on probabilistic safety assessment to the International Maritime Organization (IMO) in 1993. It has been adopted (Kenkichi Tamura, Risk Assessment Technology Strategy of the Marine Technology Research Institute, http://www.nmri.go.jp/main/research/happyoukai/H19/SS/SS15.pdf). As an application example from a viewpoint other than safety, Claudia et al. (Claudia Vivalda) has incorporated evaluation indicators for performance and efficiency in addition to safety in the evaluation of carbon capture technology (CCS). Laurent Jammes, Probabilistic Performance Assessment Methodology for long term subsurface CO2storage, 2008, International Probabilistic Safety Assessment and Management Conference (PSAM) 9).
In this way, probabilistic safety assessment methods that consider uncertainties as various scenarios and perform comprehensive assessments are promising not only for the nuclear field but also for other fields, and are expected to play an important role. is there.

For the probabilistic safety assessment method, for the purpose of efficiently generating fault trees and event trees, events that occur in the plant It has been proposed to generate a fault tree indicated by a relationship (Patent Document 1). However, this document does not describe any method for efficiently generating an event tree based on objective criteria.
In addition, with the objective of accurately and quantitatively assessing the fire risk of road tunnels, considering the conditions of road tunnel structure, fire prevention measures, design traffic volume, etc., the frequency of fire accidents, fire properties or damage There has been proposed a method of generating an event tree based on each event that can affect the size of the document (Patent Document 2). However, the method described in this document prepares a standard event tree in advance, and when setting a scenario, prompts the user for correction input or additional input of each event on the display device, The setting input regarding the event is performed, and the event tree is not generated from the beginning based on the objective criteria.
In addition, the scenario formed by the event tree is developed for the purpose of providing a training system and a training system scenario construction method capable of training in unexpected situations that are not in the past experience and knowledge. A training system provided with a simulation means has been proposed (Patent Document 3). In the training system described in this document, an event tree pre-configured by arranging an initial event and a plurality of progress keys in chronological order is used, but a method for generating an event tree based on objective criteria Is not described.
In addition, with the aim of improving the estimation accuracy while reducing the number of disaster progression scenarios, it is an element that directly influences the outcome in the event recalled by the disaster being evaluated, and affects the success and failure of each other. Proposes a method to generate an event tree for only given elements, generate a probability density function of success time for disaster prevention measures, and to bring out case-separated elements that bring similar branches to all sequences outside the event tree (Patent Document 4). The method proposed in this document is to generate an event tree excluding the case element that causes the same branch to all sequences, and the event tree including these events is based on objective criteria. It is not a method to generate.

  Further, as existing research on a method for automatically generating an event tree, there are studies by Acosta et al. (Non-patent Document 1) and Chang et al. (Non-patent Document 2). However, these are sequential ones in which branch conditions are determined by state variables in advance, and branching is generated when the state variables calculated by the evaluation simulator that reads the scenario match those conditions. Since the generation status is not evaluated and fed back, the approach for generating the tree structure is different from the method of the present invention and the method of evaluating and feeding back the generation status of the tree structure.

Japanese Patent Laid-Open No. 2002-24337 JP 2006-318290 A JP 2004-279945 A JP 2002-288386 A

C. Acosta and N. Siu, Dynamic Event trees in Accident Secuence analysis Application to Steam Genertor Tube Rupture, Reliability Engineering and Safety, Vol.41, pp135-154, 1993. Chang YH, Mosleh A, Dynamic PRA using ADS with RELAP5 code as itsthermal hydraulic module, Probabilistic safety assessment and management (PSAM) 4, September 13-18. New York: Springer, 1998.

The probabilistic approach described above can be an effective evaluation method for supporting decision making in a company or the like, but the analysis procedure centering on the event tree requires a lot of judgment, labor and time by the analyst. There is much room for improvement in terms of objectivity / accuracy, man-hours, calculation time, and the like. If a tree structure such as an event tree can be automatically generated, these problems can be improved.
However, none of Patent Documents 1 to 4 described above proposes an objective method capable of automatically generating an event tree. In addition, the non-patent documents 1 and 2 described above generate a branch when the state variable matches the condition, and do not evaluate and feed back the generation state of the event tree.
Therefore, the present invention reduces the amount of calculation and time and effort required by the analyst, reduces the amount of calculation required to generate a tree structure that classifies the situation in consideration of the probability of occurrence, improves objectivity and accuracy, An automatic tree structure generation program that classifies the situation efficiently based on objective criteria by evaluating and feeding back the generation structure of the event tree and other tree structures in order to reduce man-hours and calculation time. An object of the present invention is to provide an automatic generation device for a tree structure for classifying situations.

An automatic generation program for a tree structure for classifying the situation of the present invention according to claim 1 reads a reading step of an initial condition of an event input from an input means into a computer, and generates an initial branch based on the initial condition Branch generation step, evaluation value calculation step for calculating the evaluation value of the branch, evaluation value difference calculation step for calculating a difference between evaluation values of the adjacent branches, and evaluation obtained in the evaluation value difference calculation step A branch addition step of adding a new branch between the branches having the largest value difference; and an output step of outputting information obtained from the tree structure including the new branch added in the branch addition step. It is characterized by that.
Here, the “initial condition” refers to a condition relating to an existing tree structure, and does not have to be a minimum structure tree structure. A “branch” is an event represented by a real number or an event that can be quantified, such as good or bad, is divided into certain intervals, and is specified by the representative value representing the interval and its occurrence probability. Is.
Further, the “evaluation value” refers to a value used for evaluating the branch, for example, an expected value. An “adjacent” branch is a branch that is adjacent when a branch related to a certain event is arranged in descending or ascending order with respect to the representative value.
In addition, the “branch addition step” compares all evaluation value differences regarding all the events calculated in the evaluation value difference calculation step, and a new branch is added between the branches having the largest evaluation value difference. However, the evaluation value difference is compared for each event, and a new branch is not added between the branches having the largest evaluation value difference in the event.
In addition, “information obtained from a tree structure with a new branch” refers to information obtained based on the tree structure, for example, the number of scenarios that combine the branches of each event constituting the tree structure, The scenario evaluation value calculated based on the scenario, the occurrence probability of the scenario, the average value of the scenario evaluation values indicated by the entire tree structure, and the like.

  According to a second aspect of the present invention, in the tree structure automatic generation program for classifying the situation according to the first aspect, the branch addition step uses the second probability distribution area of the section surrounded by the adjacent branches as the second A new branch is added to the point to be divided, the area of the probability distribution of the section surrounded by the new branch and the adjacent branch is divided into two equal parts, and each area of the probability distribution of the divided section is divided into the two equal parts. Assigned to the branch adjacent to the selected section, and the area assigned to the branch is divided by the area surrounded by the initial branch generated in the branch generation step for the same event as the event to which the branch is added. The normalized value is used as the occurrence probability of the branch.

  According to a third aspect of the present invention, there is provided the tree structure automatic generation program for classifying a situation according to the first or second aspect, wherein the termination condition input from the input unit and the information output in the output step are The evaluation value calculating step, the evaluation value difference calculating step, until the output matches the end condition if the output of the output step does not match the end condition, The branch addition step and the output step are repeated.

According to a fourth aspect of the present invention, in the tree structure automatic generation program for classifying the situation according to the third aspect, the termination condition is determined based on a transition of output in the output step. It is characterized by.
Here, the “transition of output” means that each time the evaluation value calculation step, the evaluation value difference calculation step, and the branch addition step are repeated, the tree structure includes a new branch added in the branch addition step. This is the change in output obtained based on this. For example, the end condition may be that the change in the output value is equal to or less than a certain value, the direction in which the output value changes, or the number of scenarios reaches a predetermined value.

According to a fifth aspect of the present invention, in the tree structure automatic generation program for classifying the situation according to one of the first to fourth aspects, the initial condition read in the reading step is the occurrence of each branch event. Probability data, information for generating the initial branch in the branch generation step, and an evaluation formula for calculating the evaluation value in the evaluation value calculation step are included.
Here, “branch event occurrence probability data” refers to data relating to the occurrence probability of an event in a certain section in which the event is represented by a representative value based on some basis, for example, past data related to the event. Such as statistical data on the facts and probability distribution functions. “Information for generating an initial branch” refers to information used for initial branch generation, such as the number of initial branches, a representative value of each initial branch, and the probability of occurrence of each initial branch. In addition, the “evaluation formula for calculating the evaluation value” means an expression used for calculating the evaluation value of each branch. For example, when an expected value is used as the evaluation value, a scenario for a certain branch is set. An equation for dividing the sum of values obtained by multiplying the originally calculated scenario evaluation value by the occurrence probability of the scenario by the occurrence probability of the branch can be used.

The present invention described in claim 6 is a tree-structured automatic generation program for classifying situations according to any one of claims 1 to 5, wherein each scenario in which an output of the output step is a combination of the branches. And a scenario evaluation value of the scenario, and a scenario probability value of the scenario.
Here, “a set of representative values of branch events” refers to a combination of representative values of the branches of each event constituting the scenario. The “scenario occurrence probability” refers to a value obtained by multiplying the branch probability of each event constituting the scenario. Further, the “scenario evaluation value” refers to a value obtained by combining each event constituting the scenario.

  The present invention described in claim 7 is a tree structure automatic generation program for classifying the situation described in one of claims 1 to 6, wherein the output of the output step is a reference plan for decision making. It is characterized by being.

  An automatic generation apparatus for a tree structure for classifying a situation of the present invention according to claim 8 comprises a computer, an input means, and an output means. The situation according to one of claims 1 to 7 is provided. A program for automatically generating a tree structure to be classified is applied to the computer, a tree structure for classifying a situation is automatically generated according to an input of the input means, and a result is output to the output means.

  A tree structure automatic generation apparatus for classifying a situation of the present invention according to claim 9 includes an input means for inputting an initial condition, and an event in a certain interval based on the initial condition input by the input means. A branch generation unit that divides and generates a branch specified by the representative value representing the section and the occurrence probability, an evaluation value calculation unit that calculates an evaluation value for each of the branches, and a calculation by the evaluation value calculation unit Evaluation value storage means for storing the evaluated value, evaluation value difference calculation means for calculating a difference between evaluation values of adjacent branches among the evaluation values, and evaluation value difference calculated by the evaluation value difference calculation means A branch adding means for inserting a new branch between the largest branches, and an output means for outputting information obtained from the tree structure including the new branch added by the branch adding means. And wherein the are.

The automatic generation program of the tree structure for classifying the situation of the present invention and the automatic generation device of the tree structure for classifying the situation generate a simple initial branch by the branch generation step based on the initial condition read in the reading step. Thereafter, based on the evaluation value difference calculated in the evaluation value difference calculation step, a new branch is automatically added between the branches having the largest evaluation value difference. Therefore, it is possible to automatically generate a tree structure efficiently and accurately by reducing calculation time and man-hours based on objective criteria. Further, based on the information obtained from the tree structure with the new branch output in the output step, the accuracy of the tree structure can be evaluated.
In addition, when the tree structure automatic generation program for classifying the situation of the present invention further includes an end condition determination step, an evaluation value calculation step and an evaluation value difference calculation step until the output of the output step matches the end condition. By repeating the branch addition step, a tree structure that satisfies the condition defined as the end condition can be automatically generated.
Further, by determining the end condition based on the output transition in the output step, the execution of the program can be appropriately terminated according to the output transition.
Further, by making the output of the output step a set of representative values of branch events constituting each scenario, the occurrence probability of the scenario, and the evaluation value of the scenario, it becomes easy to make a decision with reference to these.
Further, if a reference plan for decision making is output as an output of the output step, for example, reference information useful for decision making by a company can be provided.

The flowchart explaining the event tree automatic generation method which is an embodiment of the present invention (A) Explanatory diagram of the outline structure of the event tree showing the outline of the analysis by the event tree, (B) Graph showing the relationship between the lowest evaluation value of the scenario evaluation value and the occurrence probability as the basic analysis result by the event tree Explanatory diagram of how to generate a branch by dividing events that take continuous real values into sections (A) Schematic diagram of initial event tree, (B) Schematic diagram of event tree with new branch inserted (A) Explanatory diagram showing a state before a new branch is added in the branch addition step, (B) Explanatory diagram showing a method of giving an occurrence probability to the new branch added in the branch addition step FIG. 3 is a block diagram showing a schematic configuration of an automatic event tree generation device according to Embodiment 2 of the present invention; The block diagram which shows the principal part structure of the automatic generation apparatus of the event tree of Embodiment 2 of this invention The block diagram which shows another principal part structure of the automatic generation apparatus of the event tree of Embodiment 2 of this invention The graph which shows transition of the average of the expected value of the evaluation value of the Example of this invention and Comparative Examples 1 and 2 The graph which shows transition of the minimum expected value of the scenario evaluation of the Example of this invention and the comparative example 1

(Embodiment 1)
As a tree structure for classifying the situation of the present invention, there are an event tree, a decision tree, and the like. As an embodiment of an automatic generation program for a tree structure, a method for automatically generating an event tree will be described below. In the following, before explaining the automatic event tree generation method, first, an overview of probabilistic evaluation using the event tree and generation of an event tree focusing on state quantities will be described.

[Outline of Probabilistic Evaluation Using Event Tree]
The outline of the probabilistic evaluation by the event tree is shown in FIGS.
FIG. 2A shows an event tree. For each branch event (event X _i ), a branch is generated according to success / failure or the value of the state variable, and divided into cases. At each branch, the representative value indicated by the branch and the branch probability are calculated. A set of representative values of each branch is scenario s _j .
Next, calculate the evaluation value g _j and the probability p _j of each scenario s _j. Probability p _j for each scenario s _j is the product of the probability of occurrence of each branch constituting the scenario s _j, The evaluation value g _j, the function or evaluation simulator for evaluating the set of representative values To give the result of calculation.
The most basic information obtained from the event tree is (1) an average value of evaluation values and (2) an occurrence probability graph of the lowest evaluation value, as shown in FIG. The former gives the most likely evaluation value, and the latter makes it possible to know what characteristics the evaluation value distribution has. In addition, sensitivity analysis, uncertainty analysis, importance analysis, etc. as needed (Hirano et al., Series Lecture Introduction to Probabilistic Safety Evaluation (PSA) for Light Water Reactors (PSA) 1-7, Journal of the Atomic Energy Society of Japan, vol.48, No 3-10, 2006).
In the event tree of probabilistic safety evaluation, the first event is an initiating event, but the initiating event is not necessarily required in corporate decision making. Also, in the event tree, a branch is generated by both success / failure of the event and the state quantity. In this embodiment, the event tree is generated by paying particular attention to the state quantity.

[Generate an event tree focusing on state quantities]
The branching in the event tree automatically generated in the present embodiment means that an event having a continuous real value is handled discretely. FIG. 3 shows an example in which events having continuous real values are divided into sections and branches are generated. As shown in the figure, it is assumed that v is a representative value of a divided section among events having continuous real values. Further, the probability of occurrence of the representative value v is p, and this is called the branching probability. That is, each branch is constituted by a set ω = (v, p) of the representative value v and its branch probability p, and the branch is to treat a continuous event discretely using the representative value v and the branch probability p. .
Therefore, the event tree in the proposed method of the present embodiment can be expressed as follows. Assuming that the events to be handled are A and B independent of each other, the branch of each event is a set of ω. Therefore, if the events A and B are respectively branched by l (el), the sets A and B are

It can be expressed as. Here, the sum of branch probabilities in the respective A and B events is 1.
The event tree can be expressed as a Cartesian product set A × B of events A and B.
A × B = {(ωa, ωb) | ωa∈A, ωb∈B} (3)
The element s of this set is called a scenario,
s = {(ωsa, ωsb) | s∈A × B} (4)
It can be expressed as. Furthermore, the total number of scenarios obtained from the event tree is the size L of the set A × B. And the probability ps that these scenarios occur is

And the sum is 1. Further, the probability ps that this scenario occurs is called the scenario occurrence probability. Various environments are expressed by these scenarios.
In the present embodiment, an event tree is generated in this way, and future changes of each element are expressed using representative values and branch probabilities. By using the scenario obtained from the event tree, it is possible to comprehensively express future environmental changes.

[Event tree automatic generation method]
The outline of the event tree automatic generation method (method) according to the embodiment of the present invention will be described below with reference to FIGS.
FIG. 4 shows the basic idea of the event tree generation method. First, as shown in FIG. 4A, an initial event tree with a small number of branches is prepared. Next, the expected value of the evaluation value in all scenarios including each branch is calculated, and then the difference (expectation sensitivity between branches) d of the evaluation value between the adjacent branches is calculated. Finally, as shown in FIG. 4B, a new branch (branch) is inserted in a section having the largest difference, that is, the highest sensitivity (between adjacent branches). Repeat the above until an event tree with sufficient detail is created.
In this way, starting from a simple event tree consisting of a small number of branches, the evaluation status of the scenario generated by the event tree is fed back, and new branches are dynamically generated in the interval that can be expected to be most effective. This is a feature of the method of the present invention.
In the following, an event tree consisting of n events will be taken and a procedure for embodying the above will be described. The distribution function F _i and the probability density function f _{i of} the event Xi (i = 1, 2,..., N) are assumed.

  FIG. 1 is a flowchart illustrating an event tree automatic generation method according to the present embodiment. As shown in the figure, the event tree automatic generation method of the present embodiment includes a reading step (S10) for reading an initial condition of an event input from an input means, and a branch generation for generating an initial branch based on the initial condition. Step (S20), an evaluation value calculation step (S30) for calculating the evaluation value of the branch, an evaluation value difference calculation step (S40) for calculating a difference between evaluation values of the adjacent branches, and the evaluation value difference calculation A branch addition step (S50) for adding a new branch between the branches having the largest evaluation value difference obtained in the step, and information obtained from the event tree including the new branch added in the branch addition step. Whether the output step (S60) to output and the information output in the output step and the end condition are compared to satisfy the end condition A termination condition determination step (S70) for deciding, and if the output of information obtained from the event tree does not match the termination condition, the output of information obtained from the event tree matches the termination condition Until the evaluation value calculation step (S30), the evaluation value difference calculation step (S40), the branch addition step (S50), and the event tree including the new branch added in the branch addition step (S50). The output step (S60) is repeated. Below, each said step is demonstrated.

[(1) Generation of initial event tree]
The initial event tree is generated by a reading step (S10) for reading an initial condition of an event input from the input means and a branch generation step (S20) for generating an initial branch based on the initial condition.
In order to start with as small a tree as possible, the initial event tree has only two branches for each event. However, as will be described later, since a new branch is inserted inside an existing branch, the outside of both branches (initial tree) of the initial branch is not considered. Therefore, it is desirable that the width of both branches be as large as possible. Therefore, in the initial event tree, a value corresponding to upper and lower a% (a is a small value) of the probability distribution of each event is set to branch as a representative value. In the present embodiment, the branching probability p to the two branches is both set to 0.5.
That is, the representative values of the two initial branches (represented by the subscripts 1 and 2) of the event X _i are v _i1 = F ⁻¹ (X _i = a) and v _i2 = F ⁻¹ (X _i = 1−a). The branch probability is p _i1 = p _i2 = 0.5. A branch is represented by ω, and a set of a representative value of an event X _i representing a branch and its branch probability is ω _i = {v _i , p _i }, and an initial branch set x _i of the event Xi is x _i = {ω _i1 , ω _i2 }. The initial event tree made of n events are represented as Cartesian product of _{x 1, x 2, ... x} n by the following equation.
x ₁ × x ₂ × ... × x _n
= {(Ω ₁ , ω ₂ ,..., Ω _n ) | ω ₁ ∈x ₁ , ω ₂ ∈x ₂ ,..., Ω _n ∈x _n }
The event tree is also a set S of scenarios s.
S = {s = (ω ₁ , ω ₂ ,..., Ω _n ) | ω ₁ ∈x ₁ , ω ₂ ∈x ₂ ,..., Ω _n ∈x _n }
Assume that the evaluation value is obtained by the evaluation function g (s) for the scenario s (sεS). The above is also a common expression for the event trees after the initial stage.

In this embodiment, the occurrence probability data of the branch event and the information for generating the initial branch are read as the initial condition of the event input from the input means read in the reading step. Thereby, a desired initial branch can be generated in the branch generation step.
In this embodiment, as an initial condition for generating an initial branch, the number of branches of each event is 2 branches, and the branch probability of each branch is 0.5. However, the initial branch is not limited to this, and the number of branches of each event may be three or more, and the number of branches of each event may be different. A branch having a different branch probability may be used as the initial branch.
In the reading step, an evaluation formula for calculating an evaluation value is also read as an initial condition, which will be described later.

[(2) Calculate the expected value of the evaluation value for each branch]
The evaluation value calculation step (S30) for calculating the evaluation value of each branch will be described below. Hereinafter, a method for calculating the expected value of the evaluation value as the evaluation value of each branch will be described.
The “evaluation value of the evaluation value” of each branch refers to the sum of values obtained by multiplying the scenario evaluation value of each scenario by the occurrence probability of that scenario for only a scenario including a representative value of a certain branch. A set S _θ of scenarios including a branch θ with respect to a branch θ (θ∈x _i , θ = {v _θ , p _θ }) having an event X _i is as follows.
S _θ = {s = (ω ₁ , ω ₂ ,..., Θ,..., Ω _n ) |
ω ₁ ∈x ₁ , ω ₂ ∈x ₂ ,..., θ∈x _i , ..., ω _n ∈x _n }
= {S _θ1 , s _θ2 ,..., S _θm }
A set P _θ of occurrence probabilities of each scenario s belonging to S _θ is expressed as follows.
P _θ = {p = f ₁ (v ₁ ) * f ₂ (v ₂ ) *... * F _θ (v _θ ) *... * F _n (v _n ) |
_{s∈S θ, v 1 ∈s, v} 2 ∈s, ..., v θ ∈s, ..., v n ∈s}
= {P _θ1 , p _θ2 ,..., P _θm }
The expected value E _theta of evaluation of the branch theta from above, is expressed as follows using the probability p _theta branch theta.

This equation is, as an evaluation formula for calculating the expected value E _theta evaluation values are read as an initial condition in reading step.

[(3) Calculate sensitivity between branches]
The evaluation value difference calculating step (S40) for calculating the difference between the evaluation values of adjacent branches will be described below.
In the evaluation value difference calculation step, the sensitivity between branches in the same event, that is, the difference between the expected values of evaluation values between adjacent branches is calculated for all events. That is, the set D _i of the sensitivity d between the branches is obtained for all the events, assuming that the event X _i branches to l _i lines.

[(4-1) Add branch to sensitive section]
The branch adding step (S50) for adding a new branch between the branches having the largest evaluation value difference obtained in the evaluation value difference calculating step will be described below.
In the branch addition step of the present embodiment, a new branch (branch) is inserted at a point that bisects the area of the probability distribution in the section of the branch section having the greatest sensitivity through all events.
Specifically, if the most sensitive section is between the branches ω _ik and ω _ik−1 of the event X _i , the area U of the probability distribution of the section surrounded by both branches is U = 2A _k = F (v _ik ) -F (v _ik-1 ), and the new branch will be inserted at the following location.
v _new = F ⁻¹ (X _i = F (v _ik−1 ) + A _k )
In this embodiment, a new branch (branch) is inserted at a point that bisects the area of the probability distribution. However, the position at which the new branch is inserted is not limited to this point. It is also possible to insert a new branch at the middle point of the high section.

[(4-2) Calculate branch branch probability]
The branch probability of the added branch and the branches on both sides thereof is calculated. At that time, the area surrounded by the branches on both sides is divided into four equal parts and assigned to adjacent branches. However, since the upper and lower a% of the probability distribution are not considered in the generation of the initial event tree of (1) above, the area U ₀ (= F (v ₂ ) A value obtained by dividing by -F (v ₁ )) is defined as the occurrence probability of the branch.
FIG. 5A shows the state before the branch is inserted, and the occurrence probabilities of v _k−1 and v _k are p _k−1 = (A _k−1 + A _k ) / U ₀ and p _k =, respectively. (A _k + A _{k + 1} ) / U ₀ . Next, in FIG. 5B, a new branch is inserted at a location v _new that equally divides the area surrounded by the branches represented by v _k and v _k−1 . At that time, the area 2A _k surrounded by the branches represented by v _k and v _k−1 is divided into four equal parts, and the new branch probability is p _k−1 = (A _k−1 + A _k / 2) / U ₀ , p _new = the _{a k / U 0, p k} = (a k / 2 + a k + 1) / U 0.
However, for the branch generated in the initial event tree, A _k−1 = A _{k + 1} = 0 because the both sides of the probability density function are not considered.

As described above, starting from (1), (2) to (4) are repeated until a sufficiently accurate event tree is generated.
More specifically, in the end condition determination step (S70), the end condition input from the input means is compared with the output in the output step (S60), and the output of information obtained from the event tree is set as the end condition. If they do not match, the evaluation value calculation step (S30) and evaluation based on the event tree with the new branch added in the branch addition step (S50) until the output of information obtained from the event tree matches the end condition The value difference calculation step (S40), the branch addition step (S50) and the output step (S60) are repeated.
As the termination condition, for example, those determined based on the transition of the output in the output step can be used. Specifically, the end condition can be that the change in the average value of the evaluation values, which is information obtained from the event tree, falls within a predetermined range. In this way, it is possible to complete the generation of the event tree after confirming that the change in the average value of the evaluation values has become small, and thus it is possible to obtain a highly reliable event tree. An example of the end condition other than the above is the number of scenarios.

[Advantages of automatic generation method]
By using the event tree automatic generation method of the present embodiment described above, the following merits (advantageous effects) with respect to the generation of the event tree as compared with the conventionally widely used methods: Is obtained.

(A) Improvement of objectivity In the conventional method, it is necessary to always pay attention so that the number of scenarios does not increase rapidly and the amount of calculation does not increase. For this reason, it is usual to minimize the number of branch events to be taken up.
However, how the branch event affects the analysis results can be understood only after the branch event is taken up and analyzed. There is a risk of excluding necessary events.
In the event tree generation method of the present embodiment described above, attention is necessary for so-called combined explosion, but even if a new event is picked up, it is not sensitive and it is not important. Therefore, it can be expected that the influence on the increase in the calculation amount is small compared to the conventional method. The objectivity can be improved in that it is relatively easy to calculate even if it cannot be judged whether it is important or not.

(B) Improvement of accuracy Event tree is an approach that divides the analysis target that is originally continuous into non-continuous cases. If the number of branches increases, it can be expected that it will approach the continuous handling of the target and the accuracy will improve. However, if many branches are added, the amount of calculation increases rapidly, making it difficult to perform analysis within a practical time.
In the conventional method, an event tree is generated by determining the number of branches in each event according to the judgment of the analyst. For this reason, in many cases, branching is often added to a location that is not effective, in other words, has little contribution to accuracy, and there is a risk that computer resources are wasted and necessary accuracy cannot be ensured.
On the other hand, the event tree automatic generation method of the present embodiment described above starts with a minimum event tree and adds a branch to the most effective part. As a result, the event tree generated by the method of the present embodiment can be expected to be a more accurate event tree than the conventional one.

(C) Reduction of calculation time For the reason of (b), it can be expected that the proposed method of the present invention will be a more accurate event tree when compared with the same number of scenarios as the conventional method.
When a new branch is inserted, it is necessary to newly calculate the occurrence probability of all scenarios including the inserted branch and its evaluation value (scenario evaluation value), and the scenario including the branches before and after the inserted branch. (Since the scenario related to the front and back branches is the same as the previously calculated evaluation value, it is not necessary to recalculate the evaluation value. The event tree generation method of the present embodiment has been performed in the past. The evaluation calculation result will not be unnecessary). The calculation of evaluation values usually takes the most time, and the time required for other calculations is very small (especially when a route search is involved when dealing with the problems of maritime transportation systems, it takes time to calculate the scenario evaluation values. This trend is prominent when necessary). The increase in calculation time due to the increase in branches is minimized.
Conventionally, the results cannot be obtained unless all branches have been evaluated, whereas the proposed method can finish the calculation at any point in time if the analyst is satisfied with the quality of the analysis results.
From the above, it is also an advantage that it is difficult to be restricted by an increase in calculation amount due to a combination explosion.
In the past, it was impossible to grasp the accuracy of the value obtained as a result of the calculation, but with the proposed method, the transition of the value can be easily observed, so the target of the accuracy of the solution is expected. It is possible to attach. In the conventional method, it is not impossible to observe the transition of the average value while gradually increasing the number of scenarios in the event tree, but it is unrealistic from the viewpoint of man-hours.

(D) Reduction of man-hours Compared with the conventional method, it is necessary to prepare an automatic branch generation system and the probability occurrence data of the event in the probability density distribution format to perform the proposed method.
As for the automatic branch generation system, since there are no elements specific to the analysis target, a general-purpose analysis system can be developed. Once a general-purpose automatic branch generation system is created, it can be reused, so there is no disadvantage in man-hours compared to the conventional system.
Next, with regard to occurrence probability data in the probability density distribution format, even in the conventional approach, the analyst assumes that the branch probability is given regardless of whether it is conscious or unconscious. Moreover, even if it is a conventional method, it is necessary data when performing uncertainty analysis. For this reason, in this method, there is an effort to explicitly generate the occurrence probability data in the form of probability density distribution, but it does not increase the man-hours to the extent that becomes a problem.
From the above, if the analysis system is in place, it is possible to obtain analysis results having the characteristics (a) to (c) almost automatically thereafter. Considering the traditional cycle of generating an event tree, reviewing the results, and making the necessary corrections, the man-hours required to obtain analysis results of similar quality can be greatly reduced. It is.
Note that this method can be used not only for corporate decision making, but also for decision trees that divide cases into states in a tree structure and conventional probabilistic approaches in general, regarding the procedure for branching state quantities.

(Embodiment 2)
Implementation of the present invention as an event tree automatic generation apparatus will be described below with reference to FIGS.
FIG. 6 is a block diagram showing a schematic configuration of the automatic event tree generation apparatus of the present embodiment. As shown in the figure, the event tree automatic generation device 40 of this embodiment includes a computer 10, input means 20, and output means 30. The configuration of the event tree automatic generation device 40 will be described below.

  The computer 10 includes a CPU (central processing unit) 11, a memory (main storage unit) 12, a storage unit (auxiliary storage unit) 13, and an input / output unit 14. The CPU 11 is a device that decodes and executes a program. The memory 12 stores an intermediate result or the like generated in the process of executing the event tree automatic generation program described in the first embodiment, and is configured by a semiconductor storage device such as a DRAM. The storage means 13 stores an initial condition, an initial branch, an evaluation value, an evaluation value difference, a new branch, an event tree with a new branch, a past output, an end condition, and the like when the program is executed by the CPU 11. For example, a known storage device such as a magnetic disk device (Hard Disk), a magneto-optical disk device, a flash memory device such as a USB memory, or an optical disk device such as a DVD or CD can be used. The storage unit 13 is not necessarily provided in the computer 10 and may be configured to be connected to the computer 10 as an external device electrically or through a line. The input / output unit 14 is used to exchange information between the CPU 11 and the memory 12 and the input unit 20 and the output unit 30, and is normally controlled by the CPU 11.

  FIG. 7 is a block diagram showing a more detailed configuration of the main part of the automatic event tree generation apparatus 40 of the present embodiment. As shown in the figure, the event tree automatic generation device 40 of this embodiment includes an input unit 20, an initial branch generation unit 111, an evaluation value calculation unit 112, an evaluation value difference calculation unit 113, a branch addition unit 114, information Output means 115, output means 30, and storage means 13 are provided. Each unit constituting the automatic event tree generation apparatus 40 will be described below. In addition, the memory | storage means 13 can share a part of function with the memory 12 (refer FIG. 6).

  The input unit 20 is a unit for inputting an initial condition which is information necessary for generating an initial branch, and the initial condition is sent to the initial branch generation unit 111 and / or the storage unit 13. When the initial condition is sent to the storage unit 13, after the initial condition is stored in the storage unit 13, the initial condition is read as necessary by the initial branch generation unit 111. As described above, by storing the initial condition in the storage unit 13, when necessary later, a unit that requires the information stored as the initial condition can read and use the initial condition. . The information read and used as necessary is common to the information stored in the storage unit 13.

  The initial branch generation unit 111 generates a branch based on an initial condition. More specifically, an event that generates a branch is divided into a plurality of sections based on an initial condition, and a branch specified by a representative value that represents each section and its branch probability is generated. As a specific branch generation method, the method described in the first embodiment is used. The generated branch is sent from the initial branch generation unit 111 to the evaluation value calculation unit 112 and / or the storage unit 13.

  The evaluation value calculation means 112 calculates branch evaluation values. As a specific evaluation value calculation method, the method described in the first embodiment is used. The calculated evaluation value of the branch is sent from the evaluation value calculation means 112 to the storage means 13. At this time, the evaluation value of the branch may also be sent to the evaluation value difference calculation unit 113.

  The evaluation value difference calculating unit 113 calculates a difference between evaluation values of adjacent branches. As a specific calculation method, the method described in the first embodiment is used. The difference between the calculated evaluation values of the branches is sent from the evaluation value difference calculating unit 113 to the storage unit 13. At this time, a branch evaluation value difference may also be sent to the branch addition means 114.

  The branch addition means 114 inserts a new branch between the branches having the largest difference in the evaluation values of the branches. The position at which a new branch is inserted and the calculation method of the occurrence probability are not particularly limited, but for example, the method described in the first embodiment can be used. The branch added by the branch addition means 114 is specified by the representative value and the branch probability. The information on the added branch is sent from the branch adding means 114 to the storage means 13. At this time, the added branch information may also be sent to the evaluation value calculation unit 112 and the information output unit 115.

  The evaluation value calculation unit 112 calculates an evaluation value for the branch added by the branch addition unit 114. Based on this evaluation value, calculation of the evaluation value difference by the evaluation value difference calculation unit 113 and addition of a new branch by the branch addition unit 114 are repeated. By repeating this, an event tree is generated. At this time, the evaluation value calculation unit 112 only needs to calculate the evaluation value for only the added branch, and the evaluation value already calculated can be used as it is, so that an event tree is efficiently generated. It is possible.

  The information output unit 115 obtains information such as an average value of expected values of evaluation values, a graph of occurrence probability-minimum expected value, and the number of scenarios from the event tree having the added branch, and outputs the information to the output unit 30. Is. By outputting the information to the output means 30, the accuracy of the event tree at the stage where the information is output is known via the output means 30 based on the transition of the average value of the expected values of the evaluation values. Can do. For this reason, for example, if the output means 30 is configured with a monitor and the like and the transition of the average value of the expected value of the evaluation value is displayed, the operator can assume that the average value of the expected value of the evaluation value has not changed. If it is determined, the event tree generation can be ended by inputting an instruction to stop the calculation of the branch evaluation value by the evaluation value calculation means 112 from the input means 20.

  FIG. 8 is a block diagram showing a main configuration of an event tree automatic generation apparatus 40 provided with an end condition determination unit 116 instead of the output unit 30 of FIG. The event tree automatic generation apparatus 40 shown in the figure includes an input unit 20, an initial branch generation unit 111, an evaluation value calculation unit 112, an evaluation value difference calculation unit 113, a branch addition unit 114, an information output unit 115, and an end condition determination unit. 116, an output means 30 and a storage means 13 (12). Components having the same functions as those described with reference to FIG.

As shown in FIG. 8, the information output means 115 in FIG. 8 obtains an average value of expected values of evaluation values, an occurrence probability-minimum expected value graph, the number of scenarios, and the like from an event tree having added branches. Information is obtained and output to the end condition judging means 116. By outputting these pieces of information to the end condition determination unit 116, the end condition input in advance from the input unit 20 is compared with the above information, and the event tree generation is automatically ended based on objective criteria. be able to.
That is, the end condition determining unit 116 outputs an instruction to end the evaluation value calculation to the evaluation value calculating unit 112 only when the information output from the information output unit 115 satisfies the end condition. Thereby, the generation of the event tree ends. As the termination condition, for example, the transition of the information output from the information output unit 115, more specifically, the change of the average value of the expected value of the evaluation value is within a certain range. By using this as an end condition, it is possible to automatically generate a highly accurate event tree. The termination conditions other than the above include the number of scenarios and the change direction (up or down) of the average value.
The information output unit 115 and / or the end condition determination unit 116 can output the result to the output unit 30 for each calculation even if the end condition of the end condition determination unit 116 is not satisfied. That is, information such as an average value of expected evaluation values, a graph of occurrence probability-minimum expected value, the number of scenarios, and the like can be output every moment, and the operator can check the current situation with respect to the end condition on a monitor or the like.

In order to show that an event tree can be generated effectively by the automatic generation method of the tree structure for classifying the situation of the present invention, the following example was trial-calculated. In the following, the values corresponding to the upper and lower 2.28% of the probability distribution of each event are set to branch as representative values.
There are three types of independent events X, Y, and Z, and the probability density function f of the variables v _x , v _y , and v _z representing each follows a lognormal distribution with the following mean μ and standard deviation σ.
v _x : μ = 6.380, σ = 1.219
v _y : μ = 7.00, σ = 1.400
v _z : μ = 5.000, σ = 1.500
In contrast to the above, when the evaluation value g is defined as follows, the average value of the evaluation values is obtained by the proposed method of the present invention. At that time, a set of values (v _x , v _y , v _z ) of each branch event is a scenario s.
g (s) = v _x + v _y + v _z
Specific examples of the above include evaluation of the expected value of total reserves when oil fields are developed in three different regions (http://www.weblio.jp/content/field distribution of oil fields).

[Comparative example]
The following two types are considered as typical branch generation methods for event trees. One is to divide the change area of the random variable equally to set a branch, and the other is to equally divide the area of the probability density function. Hereinafter, the former is referred to as Comparative Example 1, and the latter is referred to as Comparative Example 2.

[Comparative Example 1 (Equal division of values)]
When the event X follows the distribution function F (x), the minimum value min and the maximum value max of the existence range of the random variable are set as follows. At this time, the area of the probability density function between the minimum value min and the maximum value max is U = 0.9554, which is regarded as the whole. The same applies to Comparative Example 2 described later.
Minimum value min = μ−2σ = F ⁻¹ (0.0228)
Maximum value max = μ + 2σ = F ⁻¹ (0.9772)
The minimum value min and the maximum value max are equally divided into n. Here, the interval δ between the representative values when equally dividing the range into n, the sets A and B of the start point a and the end point b of each branch, and the sets V and P of the respective representative values v and branch probabilities p are as follows: Become.
δ = (max−min) / 2n
A = {a _i = min + 2 (i−1) δ | a _i ∈X (i = 1, 2,..., N)}
B = {b _i = a _i + 2δ | b _i ∈ X _i , a ∈ A (i = 1, 2,..., N)}
V = {v _i = min + (2i−1) δ | v _i εX, (i = 1, 2,..., N)}
P = {p _i = (F (b _i ) − (F (a _i )) / U
| A∈A, b∈B (i = 1, 2,..., N)}

[Comparative Example 2 (Equal division of area)]
Divide the area of the probability density function between the minimum value min and the maximum value max into n equal parts. Here, the sets V and P of the representative value p and the branching probability p when the value range is equally divided into n are as follows.
V = {v _i = F ⁻¹ ((2i−1) U / 2n + 0.0228)
| V _i ∈X, (i = 1, 2,..., N)}
P = {p _i = 1 / n | a∈A, b∈B (i = 1, 2,..., N)}

[Evaluation results]
Observe the transition of the average value E of the expected values of the evaluation values. In this embodiment, an approximate value can be calculated, and E is about 3566.6. FIG. 9 shows a transition of an average value E of expected values of evaluation values in the event tree automatic generation method of the embodiment which is the proposed method and the comparative examples 1 and 2 which are the conventional methods.
From the transition of the average value E of the expected values of the evaluation values, the deviation from the correct value when the number of scenarios is 729 is about + 9.9% in the conventional method 1 (Comparative Example 1) and in the conventional method 2 (Comparative Example 2). Compared to -5.2%, which is still asymptotic, the proposed method (example) has a high accuracy of less than + 0.06% with 720 (the number of scenarios closest to the above). Yes. As described above, the evaluation value of the entire event tree of the event tree generated by the event tree automatic generation method of the present embodiment, which is the proposed method, is faster and more accurate.

[(2) Coverage of event tree branches]
FIG. 10 shows the transition of the probability shape of the lowest evaluation value in order to consider that the event tree branch has the necessary completeness.
In FIG. 10, P1, P2, and P3 (P: Proposed) that are the results of the example are C1, C2, and C3 (C: Conventional) that are the results of Comparative Example 1 in which the number of scenarios is approximately the same in the conventional method. Each is a corresponding comparison target.
As described above, the event tree is a technique for dividing the analysis target that is originally continuous into non-continuous cases. If the number of branches (the number of scenarios) increases, it can be expected that it will approach the continuous handling of the target and the accuracy will improve. Therefore, together with the result of (1), in the shape of FIG. 10, it can be expected that the example in the example of the comparative example 1 is closer to the more accurate shape than in the comparative example 1.
In the example, even P1 having a small number of scenarios has a shape close to P3, but in Comparative Example 1, even C3 has a shape that is considerably different from P3 at both ends of the curve. The embodiment is superior in the coverage of event tree branches.
From the examinations (1) and (2) above, it can be seen that in the embodiment, it is possible to efficiently generate an event tree superior to Comparative Examples 1 and 2 according to the conventional method.

  The present invention relates to a procedure for dividing state quantities into cases, and can be used not only for event trees for corporate decision making, but also for conventional probabilistic approaches in general and decision trees that perform state classification in a tree structure. It is.

10 Computer 11 CPU
111 Initial branch generation means 112 Evaluation value calculation means 113 Evaluation value difference calculation means 114 Branch addition means 115 Information output means 12 Memory (evaluation value storage means)
13 storage means (evaluation value storage means)
14 Input / output unit 20 Input means 30 Output means 40 Event tree automatic generation device (automatic generation device of tree structure for classifying situations)

Claims (9)

A reading step for reading an initial condition of an event input from an input means into a computer;
A branch generation step for generating an initial branch based on the initial condition;
An evaluation value calculating step for calculating an evaluation value of the branch;
An evaluation value difference calculating step for calculating a difference between evaluation values of the adjacent branches;
A branch addition step of adding a new branch between the branches having the largest evaluation value difference obtained in the evaluation value difference calculation step;
An output step of outputting information obtained from the tree structure including the new branch added in the branch addition step;   The branch addition step adds a new branch to a point that bisects the area of the probability distribution of the section surrounded by the adjacent branch, and sets the area of the probability distribution of the section surrounded by the branch adjacent to the new branch. Dividing into two equal parts, assigning each area of the probability distribution of the bisected section to the branch adjacent to the bisected section, and assigning the area allocated to the branch to the same event as the branch was added The probability of occurrence of the branch is defined as a value obtained by dividing the area divided by the area surrounded by the initial branch generated in the branch generation step. An automatic tree structure generator that classifies situations.   The method further comprises an end condition determining step of comparing the end condition input from the input means with the information output in the output step, and when the output of the output step does not match the end condition, the output is The tree structure classifying situation according to claim 1, wherein the evaluation value calculation step, the evaluation value difference calculation step, the branch addition step, and the output step are repeated until an end condition is satisfied. Automatic generation program.   4. The program for automatically generating a tree structure for classifying situations according to claim 3, wherein the termination condition is determined based on transition of output in the output step.   The initial condition read in the reading step includes occurrence probability data of each branch event, information for generating the initial branch in the branch generation step, and an evaluation formula for calculating the evaluation value in the evaluation value calculation step An automatic generation program for a tree structure for classifying a situation according to claim 1, wherein:   6. The output of the output step is a set of representative values of each branch event in each scenario that is a combination of the branches, an occurrence probability of the scenario, and a scenario evaluation value of the scenario. A tree structure automatic generation program for classifying the situation described in one of the above.   7. The program for automatically generating a tree structure for classifying situations according to claim 1, wherein the output of the output step is a reference plan for decision making.   A tree structure automatic generation program for classifying a situation according to claim 1, comprising a computer, input means, and output means, according to the input of the input means. A tree structure automatic generation apparatus for classifying a situation, characterized by automatically generating a tree structure for classifying the situation and outputting the result to the output means. Input means for entering initial conditions;
A branch generation unit that divides an event into fixed intervals based on an initial condition input by the input unit, and generates a branch specified by a representative value representing the interval and its occurrence probability;
An evaluation value calculating means for calculating an evaluation value for each of the branches;
Evaluation value storage means for storing the evaluation value calculated by the evaluation value calculation means;
Evaluation value difference calculating means for calculating a difference between evaluation values of the adjacent branches among the evaluation values;
A branch adding means for inserting a new branch between branches having the largest evaluation value difference calculated by the evaluation value difference calculating means;
An apparatus for automatically generating a tree structure for classifying a situation, comprising: output means for outputting information obtained from the tree structure having the new branch added by the branch adding means.