DE3800147A1 - Fast procedure to determine the most probable hypothesis on the basis of given features - Google Patents

Abstract

The measured values and data (features) of a wrongly functioning object are evaluated using the procedure, in such a way that wrongly recorded features can be eliminated and the causes (hypotheses) can be ranked in descending order of probability. Two files are used for this purpose. File 1 contains the list of permissible hypotheses, and for each hypothesis Hj, the set of those features which are characteristic for this hypothesis (CHARMENG(Hj)). Fast access file 2 contains, for all hypotheses: - p(Hj), - p( pi (CHARMENG(Hj))/Hj), - and all probabilities which follow from p( pi (CHARMENG(Hj))/Hj) by negation of any number of features of pi (CHARMENG(Hj)). ( pi (T) here represents the event product of the event set T.) If the features of a wrongly functioning object are known, for any hypothesis Hj a selection Bj is made of them, and used in a simple formula to calculate p(Hj/ pi (Bj)). Bj must now be varied - using an accelerating heuristic - so that the feature set which is actually applicable "gives itself away".

Description

B) Usability of the invention

The invention is to be used if from a Set of hypotheses based on characteristics the most likely Hypothesis is to be determined. In particular the invention is to be used if the possible expenditure of time, computing power and Cost is very limited. There are only a few here restrictive requirements to be demanded:

• - It must be possible by using more extensive Samples are good approximations for the required probabilities to achieve.
• - If two or more hypotheses exist at the same time, so it is assumed that each caused Feature sets only a small average own whose elements for at most one of the hypotheses that exist at the same time has an enhancing effect.

Two features of the invention extend its usefulness on the other hand considerable:

• - Stochastically dependent features are permitted.
• - The system remains functional, if not all characteristics submitted for processing are valid.

Several areas of knowledge can be named in who experience such problems as medicine, Biology, engineering, geology and sports science. There are then many in these areas of knowledge of tasks to cope with, which in principle a Determination of hypothesis probabilities represent from given characteristics. Such tasks are for example:

• - Determination of pathophysiological conditions Humans, animals and plants.
• - Detection of errors in electrical and electronic Devices, motors, engines, industrial Investments. In particular, is the self-diagnosis to name technical devices, with incoming Error messages or out of tolerance lying self-check results processed in this way be that the device itself is the most likely Can name the cause.
• - Determination of geological formations based on Readings and observations.
• - Aptitude and performance prognosis for professional and sporting activities.

C) State of the art and advantages of the process

• 1. Existing concepts save the samples of subpopulations with propertyH _μ, μ= 1,. . . ,Jto get the required to determine relative frequencies. Innovation:
• For any H _j , j ε {1,. . ., J }, the approximate values of the probabilities p (H _j ) and p ( π (CHARMENG (H _j )) | H _j ) are to be stored, as well as all probabilities obtained from p ( π (CHARMENG (H _j )) | H _j ) result from negating any number of features of π (CHARMENG (H _j )). Limited to the number of elements of CHARMENG (H _j) on a depending of H _j value A (H _j), so only the number of (+1) probabilities is kept available.
• 2. Existing procedures create a potent set γ (VERMENG) in order to find that subset of VERMENG that delivers the best hypothesis according to defined decision criteria. Innovation:
• With the help of a heuristic, the number of of the subsets of VERMENG, which for a closer Choice at all come into question, greatly reduce it.

D) Presentation of the solution and examples

The invention is based on the following device scheme:

The presentation of the solution is therefore in four parts structured:

• I) Calculation of p (H _j | π (T)) .
• II) File 1.
• III) File 2.
• IV) Elimination of falsifying features and decision-making process.

I) Calculation of p (H _j | f (T))

Be itH _j any hypothesis from {H _μ|μ= 1,. . .,J}, T be a set of elements from CHARMENG(H _j , the inT negated or unnegated, and π (T) be the feature product formed from it.

Since T always contains fewer elements than CHARMENG (H _j ), the approximately determined probabilities required for the calculation equation are not immediately available in file 2; however, they can be calculated from the data available there.

example

Let CHARMENG (H _j ): = { E ₇, E ₄, E ₂}. Then file 2 contains the approximations of the following probabilities:

p (E₇E.₄E.₂) |H _j ),
p (E₇E.₄ ₂) |H _j ),
p (E₇ ₄E.₂) |H _j ),
p (E₇ ₄ ₂) |H _j ),
p (₇E.₄E.₂) |H _j ),
p (₇E.₄ ₂) |H _j ),
p (₇ ₄E.₂) |H _j ),
p (₇ ₄ ₂) |H _j ).

Let T : = { E ₄}. Then for p (E ₄ | H _j ) it follows:

p (E₄ |H _j ) =p (E₇E.₄E.₂ |H _j ) +p (E₇E.₄ ₂ |H _j )
+p (₇E.₄E.₂ |H _j ) +p (₇E.₄ ₂ |H _j ).

Let T : = { E ₄, E ₃, E ₂}. . Then for p (E ₄ E ₃ E ₂ | H _j ):

p (E ₄ E ₃ E ₂ | H _j ) = 0, since E ₃ ∉ CHARMENG (H _j ).

May beT: = {E.₄, ₃,E.₂}. Then follows forp (E₄ ₃E.₂ |H _j ):

p (E₄ ₃E.₂ |H _j ) =p (E₄E.₂ |H _j )
=p (E₇E.₄E.₂ |H _j ) +p (₇E.₄E.₂ |H _j ).

II) File 1

For any H _j , j e {1,. . ., J }, it can be specified that a feature E _{i should} then belong to CHARMENG (H _j ) if

exceeds a predetermined threshold. The characteristics can be ordered within CHARMENG (H _j ), whereby the ordering criterion is the

to offer.

Example of a file 1

III) File 2

For any H _j , j ε ⟨1,. . ., J } file 2 contains the following approximate probabilities:

• - p (H _j ),
• - p ( π (CHARMENG (H _j )) | H _j ),
• - as well as all probabilities that arise from p ( π (CHARMENG (H _j )) | H _j ) by negating any number of features of π (CHARMENG (H _j )).

Example:

The CHARMENG (H μ , μ = 1,..., 3, of the example of file 1 are used as a basis. Then, as an example of file 2:

p (H ₁) = 0.300 p (E ₇ E ₄ E ₂ H ₁) = 0.450 p (E₇E.₄ ₂H₁) = 0.050 p (E₇ ₄E.₂H₁) = 0.250 p (E₇ ₄ ₂H₁) = 0.050 p ( ₇ E ₄ E ₂ H ₁) = 0.100 p (₇E.₄ ₂H₁) = 0.050 p (₇ ₄E.₂H₁) = 0.025 p (₇ ₄ ₂H₁) = 0.025

p (H ₂) = 0.300 p (E ₄ E ₅ H ₂) = 0.500 p (E₄ ₅H₂) = 0.100 p ( ₄ E ₅ H ₂) = 0.300 p (₄ ₅H₂) = 0.100

p (H ₃) = 0.400 p (E ₃ E ₆ E ₅ E ₇ H ₃) = 0.250 p (E₃E.₆E.₅ ₇H₃) = 0.050 p (E₃E.₆ ₅E.₇H₃) = 0.150 p (E₃E.₆ ₅ ₇H₃) = 0.050 p (E₃ ₆E.₅E.₇H₃) = 0.150 p (E₃ ₆E.₅ ₇H₃) = 0.050 p (E₃ ₆ ₅E.₇H₃) = 0.080 p (E₃ ₆ ₅ ₇H₃) = 0.020 p ( ₃ E ₆ E ₅ E ₇ H ₃) = 0.090 p (₃E.₆E.₅ ₇H₃) = 0.010 p (₃E.₆ ₅E.₇H₃) = 0.040 p (₃E.₆ ₅ ₇H₃) = 0.010 p (₃ ₆E.₅E.₇H₃) = 0.030 p (₃ ₆E.₅ ₇H₃) = 0.010 p (₃ ₆ ₅E.₇H₃) = 0.008 p (₃ ₆ ₅ ₇H₃) = 0.002

Please note:

• 2. The sum of all probabilities that arise from p ( π (CHARMENG (H _j )) | H _j ) by negating any number of features of π (CHARMENG (H _j )) is equal to one.
• 3. The approximate values of the conditional probabilities from file 2 are expediently from J Samples of subpopulations with trait H _μ,μ= 1,. . .,J, certainly. The approximations of the a priori probabilities p (H μ) is determined from a random sample of the total population, taking for each execution of this sample only the applicable one Hypothesis is to be established.

IV) Elimination of falsifying features and Decision-making process

It is possible that the set of features specified for processing also contains elements which do not originate from a hypothesis and which therefore falsify the result. The associated task is therefore to obtain a subset T _best ⊂ VERMENG, which only consists of valid features, from the multitude of possible subsets.

To determine this subset T _best , it is assumed that it is revealed by the following determination criteria:

• - max { p (H μ | π (T _best )) | μ = 1,. . ., J } reaches a high value compared to competing sets,
• - in { p (H μ | π (T _best )) | μ = 1,. . ., J } the difference between the best and the second best hypothesis is significantly greater than in the case of competing sets.

In principle one could now proceed in such a way that one determines the power set γ (VERMENG], for all subsets T ⊂ VERMENG obtained in this way the set { p (H μ | π (T)) | μ = 1, ..., J } is calculated and used to determine _best with the indicated decision criteria T. the number of to be tested subsets of VERMENG but can be a heuristic that is given below, reduce greatly.

It is with the arbitrarily set parameters 1.2 and 0.8:

INPUT(H _j ): = |E. _λ∈ VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j *)

where CHARMENG (H _j ) * results from CHARMENG (H _j ) by negating all characteristics,

ABOVE: = {E. _λ∈VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j ) *)

DOWN: = {E. _λ ∈VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j ) *)

IND : = index set of the most promising hypothesis,
T : = subset of VERMENG,
M : = set of subsets.

This results in the following sequence overview:

The basic idea of what is shown in the flow chart The procedure consists in that one first works for anyj ∈ {1,. . .,J}, and for a subset T⊂VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j )*), the Lot {p (H _μ|π (T))|m∈IND} forms. Then an attempt is made T to be changed in such a way that the hypothesis those in the crowd disregardingH _j has reached the highest numerical value, if possible is devalued.

This is done on the one hand by omitting elements from T that value H _j only slightly, but which under certain circumstances value the hypothesis H _{ab that is} to be devalued more.

On the other hand, it is done by adding features from the set BELOW, which devalue H _j only a little, but H _ab may under certain circumstances devalue more.

The possible subsets that can be found in this Wise carried out change ofT will result captured and as candidates for the best subsetT _best considered. One does this for everyonej= 1,. . .,J by and stores the quantities {p (H _μ|π (T))|μ∈IND} for all the subsets that occurred in the processT, then let yourself finally with the help of these stored amounts of the specified classification criteria into a sorted Bring order.

Claims (7)

1. Procedure for determining the likelihood of Presence of hypothesesH _μ,μ= 1,. . .,J, based a set of characteristics available for processing VERMENG made certain certain and in general there are stochastically dependent features, characterizedthat for any hypothesisH _j ,j∈ {1,. . .,J} and any Feature product(E. _λ . . .E.₁) to calculate the equation is used; the method is further characterized in that in the memory of the device used for the calculation or a file 1 is made available to the computer will that for everyoneH _μ,μ= 1,. . .,J the associated characteristic sets of features CHARMENG(H _μ) contains, where forj∈ {1,. . .,J} the set CHARMENG(H _j ) one generally different for each hypothesis Contains number of non-negated features whose respective in file 1 as well to be led;
there is a further identification of the procedure in that the approximate values for the calculation equation needed probabilities in one File 2 are included, for a feature set CHARMENG(H _j ),j∈ {1,. . .,J}, and what is formed from it Feature productπ(CHARMENG(H _j )) the probabilities

• - p (H _j ),
• - p ( π (CHARMENG (H _j )) | H _j ),
• - as well as all probabilities that result from p ( π (CHARMENG (H _j )) | H _j ) by negating any number of features of π (CHARMENG (H _j )),

must be in file 2, and where required Probabilities not in file 2 are available for any feature product (E. _γ . . .E.₁) the relationships

• 1.p (E _γ . . .E. _{i +1} E. _{i -1} . . .E.₁ |H _j ) =p (E _γ . . .E. _i . . .E.₁ |H _j ) +p (E _γ . . . _i . . .E.₁(H _j ) for E. _i ∈ CHARMENG(H _j ),
• 2.p (E _γ . . .E. _i . . .E.₁ |H _j ): = 0 forE. _i ∉ CHARMENG(H _j ),
• 3.p (E _γ . . . _i . . .E.₁ |H _j ): =p (E _γ . . .E. _{i +1} E. _{i -1} . . .E.₁ |H _j ) for E. _i ∉ CHARMENG(H _j ),

are to be used; the procedure is finally characterized by that the elimination erroneously merged into the set characteristics obtained and the determination of the most likely ones Hypothesis using the following actions is achieved:

• 1. compute {p (H _μ|π (QUANTITY(H _μ))) |μ= 1,. . .,J}, whereby
  INPUT(H _j ): = {E. _λ ∉VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j ) *) and where CHARMENG(H _j ) * from CHARMENG(H _j ) through the Negation of all characteristics emerges,
• 2. combine the indices of the most promising hypotheses into an index set IND ,
• 3. choose any onej∈ {1,. . .,J}, initiate the amounts
  ABOVE: = {E. _λ∈VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j ) *) DOWN: = {E. _λ∈VERMENG∩ (CHARMENG(H _j ) ∪CHARMENG(H _j ) *) T: = INPUT(H _j ),
  M.: = ⌀
  and perform:
  • a) calculate and store {p (H _μ|π (T))|μ∈IND} and determine the hypothesis to be devaluedH _away than the one Hypothesis ≠H _j for those in this crowd disregardingH _j the highest numerical value is achieved
  • b) determine the quantities and form the power set
    γ (DISPOS1∪DISPOS2) =: {A. _ϕ|d= 1,. . .,U},U∈N,
  • c) formT _ϕ: =(T DISPOS1) ∪A. _ϕ and add theT _ϕ toM. added byM.: =M.∪ {T _ϕ} for allϕ,
  • d) form M : = M { T },
  • e) if M = ⌀, continue with step 4., otherwise choose a feature set contained in M , set T : = (selected feature set) and start again with 3.a),
• 4. Perform step 3. for all j ∈ {1,. . . , J } through,
• 5. is based on the quantities calculated under 3.a) the best subsetT _best determined by the fact that
  • - Max{p (H _μ|π (T _best )) |m∈IND} compared to competing quantities reach a high value, and that
  • - in {p (H _μ|π (T _best )) |μ∈IND} the distance of the best for the second best hypothesis is significantly larger than with competing quantities.

2. Application of the method according to claim 1) for the determination pathophysiological conditions in humans, Animals and plants. 3. Application of the method according to claim 1) for the determination of errors in electrical and electronic Devices, motors, engines, industrial plants, especially when performing so-called self-checks. 4. Application of the method according to claim 1) for Determination of geological formations based on of measured values and observations. 5. Application of the method according to claim 1) for Aptitude and performance prognosis for professional and sporting activities.