DE3705964A1 - Method of determining hypotheses or faults - Google Patents

Abstract

The invention concerns a method of determining the probability of the existence of hypotheses, or a method of determining a fault in a technical device or industrial plant using an established combination of incidents. The object of the invention is to give a method of this kind, by which it is simple to make a list of possible hypotheses or incidents, in descending order of probability, based on a given set of features (measured values, observations). Achieving this task requires the use of a computer with two files, one of which contains information about the possible hypotheses or incidents, and the other contains a collection of cases which have actually occurred. <IMAGE>

Description

The present invention relates to a method to determine the probabilities of hypotheses or errors caused by characteristic sets of Features (e.g. meter displays for technical Devices or the like.) Are determined.

The problem arises in many areas of knowledge that one from a number of characteristics to those "knowledge area specific Conditions ", to which these characteristics are most likely to belong. Such "knowledge-specific circumstances", about their application decided based on the characteristics identified are, for example, device errors in of the technique. They are briefly referred to as "hypotheses" called. Features are simply measurements, observations or other data that lead to such hypotheses belong.

More generally, there are a lot of hypotheses each clearly by a lot of Characteristics is characterized. Those are wanted Hypotheses of an arbitrarily given set of features can be assigned, taking the probability the affiliation must be stated.

The specified characteristics for the associated hypotheses are to be found in general  

• * Not stochastically independent of each other,
• * Not complete in the sense that the pattern of features of the hypotheses that actually apply available.

For those belonging to the specified set of characteristics Hypothesis holds that

• * They are not mutually exclusive.

Areas of knowledge in which the problems occur including technology, medicine, biology and sports science. The following tasks are to be done in these areas deal with:

• - Identification of errors in electrical and electronic Equipment, motors, engines, industrial Investments,
• - determination of pathophysiological conditions in humans, Animals and plants,
• - Suitability and performance forecast for professional and sporting activities,

etc.  

Many of the previous systems rely largely on stochastic Independence of the features and the feature products ahead. Such requirements are general not fulfilled and lead to high monitoring effort and / or wrong results.

If one avoids such prerequisites, the result is Difficulty that the number of feature probabilities on the condition of the appearance of others Characteristics become so large that the system is no longer used can be.

Some other systems try using empirical Assignment functions an assignment of the for evaluation to achieve the existing set of features for the hypotheses. Relationships are used that are related to the knowledge of classical probability theory cannot be reconciled. In the particularly important borderline cases of the pending Such systems fail.  

The problem can be formulated mathematically as follows:

• 1. { E _i | i = 1,. . ., l }, l ∈ IN , is the set of permitted characteristics (English: Evidence).
• 2. { H _j | j = 1 ,. . ., m }, m ∈ IN , is the set of allowed hypotheses. Because of the widespread formation of terms, the hypotheses H _j will therefore always be discussed below, the probability of which should be determined on the basis of features that have occurred.
• 3. Each hypothesis H _j , 1 j m has a set of features T _j for which the following applies:
• 5. The elements of the set { H _j | j = 1 ,. . ., m } are not mutually exclusive. In particular, does not apply
• 6. The elements of the set { E _i | i = 1,. . ., l } are generally not Stoachically independent. The following generally does not apply to any E _r , E _s with 1 r, s l : p (E _r | E _s ) = p (E _r ).
• Likewise, feature products are generally not stochastically independent.  
• 7. The set of features to be processed S ⊂ { E _i | i = 1,. . ., l }, which is used for determining the probabilities of the hypotheses, generally does not contain a complete set of features assigned to a H _a , 1 a m .

With the definitions 1. to 7. the problem can be formulated as follows:
Given an arbitrary set S ⊂ { E _i | i = 1,. . ., l }, wherein elements of S which are different from one another can appear negated or non-negated.

We are looking for falling probabilities ordered list ofH _j ,j= 1,. . .,m under the condition ((P ∩T _j ) ∪(P ∩ _j )), so the ordered list of p (H _j |(P ∩T _j ) ∪(P ∩ _j )),j= 1,. . .,m, in which _j  outTj  by negating all inT _j  features included.  

The present invention is based on the object Procedure for determining the probability of existence of hypotheses, errors or the like, with those in a simple way based on a given amount of features, d. H. Measured values, observations or the like, a List of sorted by falling probabilities possible hypotheses can be made.

According to the invention, this object is achieved in that, with the aid of a computer and a first file, which contains information about the possible hypotheses and the associated characteristic sets of characteristics, first of all for each possible hypothesis from the characteristic set of characteristics and the set of characteristics specified for evaluation by averaging permissible set of features is formed so that for each possible hypothesis with the help of the computer and a second file, which contains a collection of actually occurring cases with details of the respective hypothesis and the set of features determined, the probability p 1 of the event product from the individual hypothesis is first and all of their currently permissible features is determined that the probability p 2 of the event product of the currently currently permissible features is ascertained secondly, and that as a result the probability of the individual hypothesis under the condition g of the product of the characteristics specified for evaluation is calculated as the ratio of p 1 to p 2.

The proposed method initially has the advantage that there are no requirements about the stochastic Independence of characteristics required. Furthermore has it has the advantage of using large quantities avoids conditional feature probabilities.

For the determination of the ratio p 1 to p 2, only the definition of the conditional probability is used

p (H | E _k .. E ₁) = p (HE _k ... E ₁) / p (E _k ... E ₁)

based on. The product probabilities then required are made from a case collection won simple counting. Here are the cases counted that contain at least the characteristics that indicated by the product under discussion are. For the determination of a product probability then it is assumed that a sufficiently large number of cases can be found that match the characteristics of the Have event product; a sufficiently large collection real cases is therefore essential.

The procedure according to the invention results additional advantages:

• - Basically all (known) hypotheses are for used an evaluation so that no hypothesis, the probability of which exceeds a threshold, can be forgotten.  
• - Every probability value used is a calculated one Value; it is based on statistical material, that is kept available in the computer and can be expanded continuously.
• - Additional features that may be required requested only for the most probable hypotheses, so that directionless reporting "on good Happiness "is avoided.

Using an example, namely the error detection on radar devices, the method according to the invention is intended are explained in more detail. However, it is explicitly pointed out noted that it is the representation of the procedure acts. For reasons of clarity specified small number of cases allowed no statement about the probability of events or event products.

The following situation is assumed:
A larger number of radars of the same type are used under comparable conditions.
Any accidents that occur are documented centrally.

Designations:

H _j       Error (hypothesis)       E        _i       Characteristic (Evidence)               _i       searched for but not confirmed characteristic     

Code description

H1 condensate in waveguide HL 102 H2 resistance R 65 above tolerance limit H3 voltage drop due to leakage currents above C 14
·
·
E1Display of radar echo washed out E2Screen display stretched in x direction E3Screen display oscillates E4 Antenna rotation unevenly E5 Warning lamp L 208 flickers E6 Smoke from power supply E7 Friction noise from antenna transmission ·
·
·

Tools 1 Card file of possible errors with associated characteristic Feature patterns Principles for the structure of the file

• 1. All features are the result of malfunctions, i. H. Normal values are not characteristics.
• 2. For each error there is an initially unordered collection of features, such as those from construction documents and based on theoretical considerations can be won. Every feature is in a causal relationship to the related Error.  
• 3. For each characteristic E _j , i ∈ {1,. . ., 7} are used for all hypotheses H _j , j = 1 ,. . ., 3, which determines the probabilities p (E _j | H _j ).
  Tool 2 (see below) is used for this.
• 4. Every error H _j , i ∈ {1,. . ., 3} becomes its after decreasing p (E _i | H _j ), i = 1 _,. . ., 7 sorted feature set assigned.
• 5. Negated characteristics are not included; for any i, j is _i  Withp ( _i |H _j ) synonymous toE _j   with 1-p ( _i |H _j ).

Tools 2 Card index of the documented incidents Principles for the structure of the file

• 1. The documented incidents are classified according to errors H _j , j = 1 ,. . ., 3 sorted.
• 2. The set of characteristics determined in the event of a malfunction must contain information about the presence or absence of all those characteristics which, according to Tools 1 belong to the respective error.
  (Characteristic set of features.)
• 3. In addition, any Features listed. Features not listed, that do not belong to the respective error are marked as scored indefinitely.

method

The feature product (E7 E3 E1) is given. From (E7 E3 E1) the p (H _j | E7 E3 E1), j = 1 ,. . ., 3 can be determined.

• Principles for the procedure:
  1. For every p (H _j | E7 E3 E1), j = 1 ,. . ., 3, those characteristics are deleted in the condition that acc. Aid 1 does not belong to H _j .
• 2. The required product probabilities are determined by counting in tools 2.
  Here, all cases are counted that contain at least the features specified by the event product, regardless of any non-affiliation of the features to the characteristic feature set.
• 3. If the p (H _j | E7 E3 E1), j = 1 ,. . ., 3, then further, as yet unexamined features can be queried for the hypothesis with the highest probability (priority according to tool 1, the feature that is as high as possible in tool 1 is selected).

It results in
3 characteristics:

p (H1 | E7 E3 E1) ⇒ p (H1 | E3 E1) = p (H1 E3 E1) / p (E3 E1) = 5/7
p (H2 | E7 E3 E1) ⇒ p (H2 | E3) = p (H2 E3) / p (E3) = 3/9
p (H3 | E7 E3 E1) ⇒ p (H3 | E7 E1) = p (H3 E7 E1) / p (E7 E1) = 1/3

4 characteristics:
For the most probable hypothesis H1, the next feature that has not yet been examined is E2. E2 is found to be non-existent, ie 2 applies.

p (H1 | E7 E3 E1 2) ⇒ p (H1 | E3 E1 2) = p (H1 E3 E1 2) / p (E3 E1 2) = 1/2
p (H2 | E7 E3 E1 2) ⇒ p (H2 | E3) = 3/9
p (H3 | E7 E3 E1 2) ⇒ p (H3 | E7 E1 2) = p (H3 E7 E1 2) / p (E7 E1 2) = 1/2
5 characteristics:
For the probable hypothesis H1, the next feature that has not yet been examined, namely E6, is examined. The presence of E6 is determined.

p (H1 | E7 E3 E1 2 E6) ⇒ p (H1 | E3 E1 2 E6) = 0
p (H2 | E7 E3 E1 2 E6) ⇒ p (H2 | E3 E6) = p (H2 E3 E6) / p (E3 E6) = 2/3
p (H3 | E7 E3 E1 2 E6) ⇒ p (H3 | E7 E1 2 E6) = 0

The method can be used for any number of features be canceled. Relate the probabilities then on the level of knowledge achieved with this number.

The procedure must be terminated if the number of the features available for selection becomes so large that for the determination of the required product probabilities only a "too small" number of cases remain. A statistical statement is then no longer possible. The limit for "too small" is set by the Depend on the nature of the task and under Under certain circumstances, this can only be determined by trial runs.  

The invention is further to be explained on the basis of the figures will. It shows

Fig. 1 shows a device for performing the method according to the invention and

Fig. 2 is a flow chart.

The device 1 shown in Fig. 1 includes the computer 2 for the controlled process sequence according to the example shown in Fig. 2 flowchart. With input 3 , the set of features to be processed is entered once. With 4 the tax input is designated, which takes place after a request. Communication means 5 known per se are provided between the input 4 and the computer 2 . During the course of the method, the computer 2 accesses the information stored in the files 6 and 7 . The file I (reference number 6 ) contains information about the possible hypotheses or errors and the associated characteristic feature sets. File II (reference number 7 ) stores a collection of actually occurring accidents with details of the respective hypothesis and the set of characteristics determined in each case. The output of the computer 2 is designated 8 . Via communication means 9 known per se, it supplies a list of hypotheses or errors sorted according to decreasing probability.

The course of the method can be seen from the flow chart shown in FIG. 2. Mean

n (A · B): Number of accidents with the properties A and B H _i : i th hypothesis G : Total number of hypotheses VerMerk: feature product to be processed AktMerk: currently considered feature product

From the flowchart, the last part, is next to those already Advantages mentioned another advantage of the invention evident. The result is said to be improved then the error determination (or hypothesis determination) continue with the error, most likely to exist.

At this point, the user decides on the basis of the hypothesis list that has been reached about the possibly meaningfulness of the feature set evaluated up to that point. Based on the number of cases counted so far, he decides whether the scope of the available statistical material allows an improvement in the result, and he uses tool 1 to decide which characteristic, in the sense of a confirmation strategy, will contribute most to further increasing the probability of the best hypothesis increase.

This type of error detection is quick and easy simple means of doing so, the errors in question narrow down decisively.

Claims (4)

1. A method for determining the probability of the existence of hypotheses which are determined by characteristic sets of characteristics, characterized in that, with the aid of a computer and a first file, which contains information about the possible hypotheses and the associated characteristic sets of characteristics, initially for each possible hypothesis From the characteristic set of features and the set of features specified for evaluation, the currently admissible set of features is formed by averaging, that for each possible hypothesis with the help of the computer and a second file, a collection of actually occurring cases with details of the respective hypothesis and the thereby determined The set of features contains, first the probability p 1 of the event product is determined from the individual hypothesis and all of its currently permissible features, and secondly the probability p 2 of the event product is the currently permissible one n characteristics are determined, and that as a result the probability of the individual hypothesis is calculated under the condition of the product of the characteristics specified for evaluation as the ratio of p 1 to p 2. 2. Method for determining an error in a technical device, in an industrial system or the like on the basis of a determined set of features now available for evaluation, characterized in that with the aid of a computer and a first file, the information about the possible errors and the associated ones contains characteristic sets of features, first for each possible error from the characteristic set of features and the set of features specified for evaluation by averaging the currently permissible set of features, and then for each possible error with the help of the computer and a second file that contains a collection of actually occurring faults with specification of the respective error and the quantity of features determined, contains first the probability p 1 of the event product from the individual error and all of its currently permissible features, and secondly the probability p 2 of the event product of the currently permissible characteristics is determined, and that as a result the probability of the individual error under the condition of the product of the characteristics available for evaluation is calculated as the ratio of p 1 to p 2. 3. The method according to claim 1 or 2, characterized in that - in the event that the conditional probabilities of the hypotheses or errors do not differ significantly - is searched for additional features, starting with the hypothesis H or the error F with the highest conditional probability, and since again starting with the not yet examined feature with the highest probability of occurrence under the condition H or F. 4. The method according to claim 3, characterized in that - in the event that for the additionally examined Characteristic non-existence is determined - which for Evaluation of the set of features by the negated one Feature is expanded.