REASONING IN INTELLIGENT DIAGNOSIS SYSTEMS

Vadim Vagin and Alexandr Eremeev

Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya str.14, Moscow, Russia

Keywords: Artificial Intelligence, Assumption-based Truth Maintenance System, Reasoning by Analogy, Intelligent

Diagnosis System, Knowledge Base.

Abstract: The paper is devoted to research and modeling reasoning based on Assumption-based Truth Maintenance

Systems (ATMS) and reasoning by analogy in intelligent diagnosis systems. The new heuristic approaches

of current measurement point choosing on the basis of supporting and inconsistent environments are

presented. Reasoning by analogy method is viewed. This work was supported by the Russian Fund for Basic

Research.

1 INTRODUCTION

The diagnostic systems are one of the most actively

used systems in technical areas: electronics

engineering, motor industry, robotics, space

vehicles, thermal and atomic power stations and

many others. Many diagnostics problems require

building the behaviour prognoses, the work with

contradictions and defaults, effective treatment of

new facts and assumptions. The typical problem of

diagnostics is to find a fault (faults) of a diagnosed

device on the basis of some set of observations.

At first model-based diagnostics on the basis of

Assumption-based Truth Maintenance Systems

(ATMS) and heuristic methods of choosing a

measurement point in a diagnosed device are

viewed. Modeling results of the best measurement

point choosing for the 9-bit parity checker are given.

Then we consider case-based reasoning by analogy

method for diagnostics of complex object states.

2 MODEL-BASED DIAGNOSIS

The generalized problem of diagnostics can be

formulated as follows. There is a device exhibiting

an incorrect behaviour. The device consists of

components, one or several of which are not

working properly what is the reason of incorrect

behaviour. There is a structure of connections

between components and a possibility to get

measurements on their inputs and outputs. It is

necessary to determine what of components are

faulty with minimal resource expenses.

There are several approaches to a solution of the

given problem one of which is model-based

diagnosis (Clansey, 1985; de Kleer et al., 1987;

Forbus et al., 1993). This approach is based on the

knowledge of device component functionality. The

model of a device is a description of its physical

structure, plus the models for each of its

components. A compound component is a

generalized notion including simple components,

processes and even logical inference stages.

Model-based diagnosis process is the comparison

of predicted device behavior with its observed

behaviour. It is supposed, that the model is correct,

and all differences between device behaviour and a

device model indicate availability of broken

components.

Main advantages of the model-based approach:

 Diagnosing the multiple faults;

 Unexpected fault recognition;

 A precision of a component model

description does not depend on the

expert experience;

 A possibility of new device diagnosing;

 Multiple using the models;

 Detailed explanations.

3 ASSUMPTION-BASED TRUTH

MAINTENANCE SYSTEMS

For building a prognosis network, a component

Vagin V. and Eremeev A..

REASONING IN INTELLIGENT DIAGNOSIS SYSTEMS.

DOI: 10.5220/0003427400180025

In Proceedings of the 13th International Conference on Enterprise Information Systems (ICEIS-2011), pages 18-25

ISBN: 978-989-8425-54-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

behaviour model, finding minimal conflicts

characterizing uncorrespondence of observations

with prognoses and minimal candidates for a faulty,

it is profitable to use possibilities given by ATMS

(de Kleer et al., 1987; Forbus,1993).

The truth maintenance systems (TMS) are the

systems dealing with the support of a coherence in

databases. They save the assertions transmitted to

them by a problem solver and are responsible for

maintaining their consistency. Each assertion has the

justification describing what kind of premises and

assumptions this justification was obtained. The

environment is a set of assumption.

The inference of an inconsistency characterizes

assumption incompatibility within the

presuppositions of which this conclusion was made.

Also there is introduced the environment set which

contains some inconsistency (de Kleer et al., 1986).

The sets of inconsistency environments E1, E2 ,…,

Em are Nogood={E1, E2 , … Em}. A consistent

ATMS environment is not Nogood.

There are the following correspondences

between ATMS and the model-based diagnosis

approach:

· ATMS premises – an observed device

behaviour;

· ATMS assumptions – components of a device;

· inferred ATMS nodes – predictions of an

diagnostic system;

· Nogood - the difference between predicted and

observed device behaviour.

4 THE CURRENT

MEASUREMENT POINT

DETERMINATION

One of the key aspects of the model-based fault

search algorithm is to determine the optimal current

measurement in a diagnosed device (de Kleer,

1987). Efficiency of the current measurement

choosing allows essentially reducing a decision

search space while the inefficiency of choice will

increase an operating time, the space of a searching

algorithm, and also require additional resource

spends to implement a measurement.

The best measurement point in a diagnosed

device is a place (point) of measuring a value giving

the largest information promoting the detection of a

set of fault components at minimal resource

spending.

One of the best procedures for reducing resource

expenses is to produce the measuring giving the

maximal information concerning predictions made

on the basis of the current information on a system.

Heuristic Methods of Choosing a Measurement

Point

The purpose of the best choosing a measurement

point is to derive the maximal component state

information. After each measuring there is a

confirmation or refutation of prediction values in a

point of measurement. So, it is possible to use the

following aspects (Vagin et al., 2006 a,b,c):

 knowledge about environments that

support predicted values in the

measurement points which can be confirmed

or refuted;

 knowledge about inconsistent environments;

 knowledge about coincided assumptions of the

inconsistent environments.

Knowledge About Supporting Environments

The diagnostic procedure constructs predictions of

values for each device point with the list of

environments in which the given prediction is held.

The list of environments represents assumption sets

about correctness of corresponding device

components.

The mismatch between observations and

predictions speaks about a fault in a device. Based

on measured observations additional predictions of

values are formed. In general, it is obtained some

set of predictions with appropriate environments.

As we are interested with a measurement point

with the greatest information on failure the point is

selected from a quantity of assumptions.

Designate an environment set as Envs(x). Let’s

introduce the function Quan(x), by which we will

designate the information quantity obtained at

measuring values in the point x.

If the environment J represents a unique

assumption, then obviously the set cardinality will

be equal 1: |J| = 1. The information quantity

obtained from such environment is equal to 1. If the

environment consists more than one component the

information quantity obtained at confirming or

refuting a value is less because we have knowledge

not about a concrete valid / fault components but

about a component set among of which are faulty.

Therefore the information quantity obtained from a

environment consisting of more than one

assumption, we heuristically accept equal to half of

set cardinality. Thus the function Quan(x) is:

±±



∑∑

() ()

||1

() ||

J Envs x J Envs x

Quan x J

( 1 )

REASONING IN INTELLIGENT DIAGNOSIS SYSTEMS

Summing is produced on all possible values in

the point x.

Points with the greatest value of the function

Quan(x) have the greatest priority of a choice. We

will call the given method of choosing a

measurement point as SEH (Supporting

Environment Heuristics).

Knowledge about the Sets of Inconsistent

Environment

As a result of each measurement there is a

confirmation or refutation of some prediction. The

environments E

,...,E

of refuted prediction form

the set Nogood = {E

, E

,...,E

}. It can be used for

directional searching for more precise definition

what kind of components from Nogood is broken.

Obviously the more of the components from

Nogood are specified by measuring a value in some

device point the more the information about which

components of Nogood are broken will be obtained.

For using this possibility, it is necessary to take the

intersection of each environment from Envs(x) with

each set from Nogood:

Envs(x) ª Nogood = {A ª B : A± Envs(x), B±

Nogood}.

For this approach the equation (1) can be

changed as follows:

±ª ±ª



∑∑

() ()

||1

() ||

J Envs x Nogood J Envs x Nogood

QuanN x J

Points with the greatest value of function

QuanN(x) have the greatest priority of a choice. We

will call the given method of choosing a measuring

point as SIEH (Supporting and Inconsistent

Environment Heuristics).

Knowledge about Coincided Assumptions of the

Inconsistent Environments

During diagnostics of faulty devices as a result of

confirmations and refutations of some predictions

there is a modification of a set of inconsistent

environments Nogood.

In each component set from Nogood one or more

components are broken what was a reason of

including a supporting set into the inconsistent

environments Nogood. Taking the intersection of all

sets of the inconsistent environments, we receive a

set of components which enter into each of them, so

their fault can be a reason explaining an

inconsistence of each set holding in Nogood. Thus,

we obtain the list of components a state of which is

recommended to test first of all, i.e. the most

probable candidates on faultiness.

The set intersection of inconsistent environments

is expressed by the following equation:

∩

E Nogood

SingleNogood E

If SingleNogood = ©, it means that there are

some disconnected faults. In this case the given

approach is inapplicable and it is necessary to define

more precisely the further information by any other

methods.

After obtaining a set SingleNogood ≠ ©, on the

basis of environments of value predictions in device

points it is necessary to select those measurement

points that allow to effectively test components to be

faulted from SingleNogood.

For this purpose we will work with the sets

obtained as a result of an intersection of each

environment from Envs(x) with SingleNogood:

Envs(x) ª SingleNogood = {J ª SingleNogood :

J ± Envs{x)}

The following versions are possible:

a)  J± Envs(x): J



SingleNogood. One of

environments of the value prediction in the point x

coincides with the set SingleNogood. The given

version allows to test faulty components from the

set SingleNogood most effectively so this

measurement point x is selected with the most

priority.

b)  J± Envs(x): _J ª SingleNogood_ <

_SingleNogood_. The cardinality of SingleNogood is

more than the cardinality of a set obtaining as result

of an intersection SingleNogood with a set

from Envs(x). We evaluate this version as

()

max | |

JEnvsx

J SingleNogood

i.e. the more of

components from SingleNogood are intersected with

any environment from Envs(x), the more priority of

a choice of the given measurement point for the

observation.

c)  J± Envs(x): SingleNogood ¯ J. The

SingleNogood includes in a set from Envs(x). We

evaluate this version as



()

min (| | | |)

JEnvsx

J SingleNogood

i.e.

the less a difference between SingleNogood and

Envs(x), the more priority of a choice of the given

measurement point for the current observation.

d) J± Envs(x): J ª SingleNogood = ©, i.e. no-

one of the most probable faulty candidates includes

in environments Envs(x) supporting predictions at

the point x. We evaluate this version as the least

priority choice, i.e. 0 in the numerical equivalent.

Also to the version (d) there are referred other

methods of definition of current measurement point

priorities which happen when SingleNogood = ©.

Thus in the estimations of a choice priority a

numerical value returned as a result of call of other

method is accepted. We call it by ResultD(x).

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

Figure 1: The quantity of stages required to each method for fault localization.

At appearance of the greater priority choosing

between versions (b) and (c), heuristically we accept

the version (b) as at this choice the refinement of

faulty candidates is produced better.

Note for various supporting sets of the same

Envs(x), the availability both the version (b) and the

version (c) is also possible. In this case, as a

resulting estimation for the given Envs(x) the version

(b) is also accepted.

Let's estimate the obtained results.

Designate by maxd the maximal numerical value

among versions (d) for all assessed measurement

points, and by CompCount a quantity of device

components.

Accept in reviewing the following assessments:

()

max | |

JEnvsx

JSin

leNo

ood

< CompCount.The quantity

of components which are the intersection result is

always less than the quantity of whole device

components;



()

min ( | | | |)

JEnvsx

J SingleNogood

< CompCount. The

quantity of components in the prediction

environment is always less than the quantity of the

device components.

Taking into account these assessments, one can

introduce a numerical assessment of the obtained

results:

ResultD(x),

maxD

± ª ©



± ¯

ª



()

0, if ( ) :

min (| | | |),

()

if ( ) :

max| |,

JEnvsx

JEnvsxJSingleNogood

SingleNogood

CompCount J SingleNogood

QuanSNG x

J Envs x SingleNogood J

CompCount J SingleNogood

maxD

⎧

⎪

⎨

⎪

±ª 

⎪

±

⎪

⎩

():| || |

2* , if ( ):

J Envs x J SingleNogood SingleNogood

Com

Count J Envs x J Sin

leNo

ood

The points with the greatest value of function

QuanSNG(x) have the greatest priority of choice.

We will call the given method as SCAIEH

(Supporting and Coinciding Assumptions of

Inconsistent Environment Heuristics).

The developed methods of heuristic choice of the

best current measurement point are recommended to

use for devices with a great quantity of components

as quality of guidelines directly depends on the

quantitative difference of environments.

5 PRACTICAL RESULTS

Let's test the developed methods of the best

measurement point choosing for the 9-bit parity

checker (Frohlich, 1998).

For each experiment one of device components

is supposed working incorrectly what is exhibited in

a value on its output opposite predicted. A

consequence of the incorrect component work is

changing of outputs of those components which

produce the results depending on values on the

output of a faulty component. These changed results

of component operations are transmitted to

appropriate inquiries of a diagnostic system.

In the beginning of each experiment to inputs of

components (Invl, Inv2, Inv3, Inv7, Inv8, Inv9,

Invl3, InvI4, Invl5) in a diagnostic complex the

vector of values (1,0,1, 0,1,0, 1,0,1) enters. Then to

the diagnostic system the value 0 retrieved from the

output of the component Nor5 that depends on the

work of a broken component and differs from

predicted is transferred. It leads to the appearance of

an inconsistency in the diagnostic system and starts

the automatic process of testing.

In fig. 1 the quantity of the stages required to

each method for fault localization is shown. A

REASONING IN INTELLIGENT DIAGNOSIS SYSTEMS

method stage is a measurement point choosing. The

smaller the quantity of method stages, the faster a

fault is localized.

From the obtained results one can see that the

method efficiency for different fault components is

various and hardly depends on the device structure.

Let's estimate the method efficiency. The device

is consists of 46 components. The output values of

45 components are unknown (a value on the output

of Nor5 is transmitted to the diagnostic system with

input data together). So, the maximal stage quantity

necessary for a fault definition is equal 45. Let's

accept 45 stages as 100 %. For each experiment it is

computed on how many percents each of the

developed methods is more effective than exhaustive

search of all values. Then define the average value

of results. The evaluated results are represented in

table 1.

Table 1: Results of experiments.

The method SEH SIEH SCAIEH

On how many percents the

method is more effective, %

30,79 63,17 68,65

From table 1 one can see that the greatest

efficiency of current measurement point choosing

has the heuristic method based on the knowledge

about coincided assumptions of the inconsistent

environments SCAIEH.

6 REASONING BY ANALOGY

Nowdays there are a great number of various

models, schemes, and methods that describe

mechanisms of reasoning by analogy (Haraguchi et

al., 1986; Long et al., 1994; Varshavskii et al., 2005;

Eremeev et al., 2005, 2009).

In Intelligent Systems, two types of analogies -

an analogy for solving problems and an analogy for

forecasting - are usually used:

 The analogy for solving problems assumes the

application of reasoning by analogy for

increasing the efficiency of the problem

solution which, generally speaking, can be

solved without analogy as well as e.g., in

programming and proving theorems;

 The analogy for prediction (forecasting) uses

reasoning by analogy for obtaining new

facts. Due to the transformation of

knowledge based on the likeness of objects,

one can make the conclusion that new facts

probably hold.

Depending on the nature of information

transferred from an object of analogy to the other

one, the analogy of properties and the analogy of

relations can be distinguished:

 The analogy of properties considers two single

objects or a pair of sets (classes) of

homogeneous objects, and the transferred

attributes are the properties of these objects,

for example, analogy between illness

symptoms of two persons or analogy in the

structure of the surfaces of Earth and Mars,

etc.;

 The analogy of relations considers pairs of

objects where the objects can be absolutely

different and the transferred attributes are

properties of these relations. For example,

using the analogy of relations, bionics

studies processes in nature in order to use

the obtained knowledge in a modern

technology.

We consider the methods of solution search on

the basis of structural analogy which allows to take

into account a context and based on the theory of

structural mapping. We use semantic networks as a

model of knowledge representation.

Reasoning by structural analogy taking into

account the context (Varshavskii et al., 2005).

Consider an analogy as a quadruple

A = <O, C, R, p>, where O and R are the source

object and the receiver object and C is the

intersection object, i.e., the object that structurally is

intersected with the source object and receiver

object, and has a larger cardinality of the set of

properties in the comparison with these objects. In

other words, the analogy between the source object

and receiver object is considered in the context of

the intersection C, and p is a property for the

definition of an original context.

We use semantic networks (SNs) as a model of

the knowledge representation for reasoning by

analogy. The choice of an SN for the knowledge

representation possesses an important advantage,

which distinguishes it from other models, such as

natural representation of structural information and

fairly simple updating in a relatively homogenous

environment. The latter property is very important

for real-time IDSS oriented towards open and

dynamical problem domains.

A semantic network is a graph <V, E> with

labeled nodes and arcs, where V and E are sets of

nodes and arcs, respectively. The nodes can

represent objects (concepts, events, actions, etc.) of a

problem domain, and the arcs represent relations

between them.

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

By Pv , we denote the set of properties of an

object v ∈ V.

Objects v, v' ∈ V intersect each other on SN if

and only if Pvv' = Pv ∩ Pv‘ ≠ © , where Pvv' is a set

of common properties of objects v and v'.

By Vp , we denote a set of SN objects that have a

property p.

By Vv ,Vv ° V, we denote an object set of

objects that intersect v ∈ V.

The object C is an intersection for A if and only

if there is (C±V) & (p±PC) & (nRnC) &

»(nR<<nC) & (nRC<nR) & (

nRC >1), where nR and

nC are the numbers of properties of the receiver R

and the intersection C, respectively; nRC is the

number of their common properties, ￢(nR<<nC)

denotes that receiver R should not be much smaller

than intersection C (i.e., the possibility of absorbing

the receiver R by the intersection C, since, here, the

probability of receiving a false analogy increases).

The object O is the source for analogy A if and

only if there is (O±V) & (p±PO) & (nOnC) &

»(nO<<nC) & (nOC<nO) & (nOC >1), where nO is

the number of properties of the source O; nOC is the

number of common properties of the source O and

intersection C; and other notations are analogous to

the previous definition.

By VC, VC °Vp, we denote the set of objects

that are candidates for the role of intersection C for

analogy A.

By VO ° Vp

, we denote the set of objects that

are candidates for the role of source O for analogy A.

By VA, we denote the set of analogies A.

The set POCR = PO ª PC ª PR denotes the

context, with respect to which analogy A is

considered.

We consider the structure of the SN in detail (for

Metalevel and for Situation 1) using the example

from power engineering - operation control of the

nuclear power unit (fig. 2) (Eremeev et al., 2006a).

Let us give a semantic interpretation of the

information given in the SN for Situation 1:

 It is recommended to supply the pump

TH11D01 with boric concentrate 40g/kg

caused by switching off automatic cooling

system ACS 1 due to closing the gates

TH11S24 and TH11S25;

 ACS 2 is switched off due to the closed gates

TH12S24 and TH12S25;

 The upper setting T517B01 is equal to 63;

 The lower setting T517B01 is equal to 56;

 The upper setting TH11T500 is equal to 60;

 The lower setting TH11T500 is equal to 20.

Analogously, the SNs for Situations 2,3 which

are structurally close to Situation 1 are built.

Algorithm of reasoning by structural analogy

An SN with information about the problem

domain, a receiver R, and the property for defining

the original context p provide input data for this

algorithm.

The algorithm for the problem solution on the

basis of analogy taking into account the context

consists of the following steps:

objects of the SN, except for receiver R, that have

property p (Vp' = Vp \ {R}). If there are no objects

of this kind, then the search for a solution fails

(without finding an analogy), otherwise, go to step

Step 2. For the objects found in step 1, determine

all possible intersections of C with R taking into

account p (VC). If there are no intersections of C

otherwise, go to step 3.

Step 3. From the objects extracted in step 1,

determine all possible sources O for analogies (VO).

otherwise, the search for a solution fails.

Step 4. Construct possible analogies for R using

the sets VC and VO. Add new analogy A=〈O,C,R,p〉

to VA if and only if there exists an analogy

A'=〈O',C,R,p〉, O  O'. In the case of success (VA 

fails.

Step 5. The analogies obtained in step 4 (VA)

(which could be previously compared with each

other taking into account the context) are given to

the decision making person (DMP), which means

successful termination of the algorithm.

Having obtained analogies, the DMP may then

make the final choice of the best ones. On the basis

of these facts, the facts (properties) that hold for the

source O are transferred to the receiver R.

Let us consider the steps of the functioning of the

algorithm using the example from power

engineering - operation control of the nuclear power

unit.

As a receiver R for the analogy, we take

Situation 4 (see fig. 3) and as the property p, we take

Close TH11S24.

= {Situation 1, Situation 2, Situation 3}. Since Vp' ≠

Determine intersections of C with R taking into

account p. Add in VC only Situation 1, because the

number of common properties nRC = nR for

REASONING IN INTELLIGENT DIAGNOSIS SYSTEMS

Figure 2: A fragment of the SN that represents the Metalevel and the Situation 1 that was formed in the course of ACS

functioning.

Figure 3: A fragment of the SN that represents the Situation 4.

the step 3.

Determine all possible sources O and go to step

4. In this case VO = {Situation 2, Situation 3},

because the Situation 1 is unique intersection for

analogy.

In the fourth step, we construct only two

analogies for R - Situation 4:

A1 = <Situation 2, Situation 1, Situation 4, Close

TH11S24 >;

A2 = <Situation 3, Situation 1, Situation 4, Close

TH11S24 >.

Add new analogies to VA and go to step 5.

The analogies obtained in step 4 (A1, A2) are

given to the DMP.

As a result we obtain two analogies. Choosing

one of them, the DMP can transfer facts that hold for

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

the source of the analogy to its receiver. In this

example, a new fact about the recommendation

“Supply the pump TH11D01 with boric

concentrate 40g/kg caused by switching off ACS 1

due to closing the gates TH11S24 and TH11S25”

arises for Situation 4.

The methods of reasoning by analogy is more

general than on the bases of cases. Analogies are

used when it is impossible to find a suitable case in a

case library. The reasoning by analogy method can

be used independently from a case- based reasoning

method as well as for correction (adaptation) of the

nearest to a problem situation case to form a new

case for completing a case library. Further we shall

consider the case-based reasoning method and its

application.

7 CONCLUSIONS

The heuristic methods of finding the best current

measurement point based on environments of device

components work predictions are presented.

Practical experiments have confirmed the

greatest efficiency of current measurement point

choosing for the heuristic method based on the

knowledge about coincided assumptions of the

inconsistent environments SCAIEH.

Advantages of heuristic methods of the best

current measurement point choosing is the simplicity

of evaluations and lack of necessity to take into

consideration the internal structure interconnections

between components of the device.

The method of reasoning by analogy on the basis

of structural analogy was considered from the aspect

of its application in modern intelligent systems, in

particular, for a solution of problems of real-time

diagnostics and forecasting . The example of the

algorithm for solution search on the basis of

analogy of properties that takes into account the

context was proposed. This algorithm uses a

modified structure of analogy that is capable of

taking into account not one property (as in the base

algorithm), but a set of properties. These properties

determine the original context of analogy and

transfer from the source to the receiver only those

facts that are relevant in the context of the

constructed analogy.

The presented methods and tools were applied at

implementation of a prototype of Intelligent

Diagnosis System on the basis of non-classical

logics for monitoring and control of complex objects

like power units and electronic circuits (Eremeev et

al., 2007, 2009).

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