Fault diagnosis

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1. A diagnosis engine for estimating a status of an entity with a plurality of components which each is assumed to be in a faultfree mode or be in exactly one of at least one fault mode, the diagnosis engine comprising:
 a processing unit adapted to analyze test results; and
at least one storage area adapted to store diagnostic data in respect of the entity, wherein said processing unit is adapted to;
receive an original disjunction of diagnostic expressions indicating at least one of said modes for at least one of said components, receive first test results of a set of diagnostic tests in respect of the entity, the result of each test being a disjunction of statements wherein each statement indicates at least one of said modes for one of said components, store the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area, investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result;
if not so, remove the expression from the temporary disjunction of diagnostic expressions; and
, for each statement in the first test result, generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression, compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression, and, discard the joint diagnostic expression, if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, or, add the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area, if an original diagnostic expression is not found, the updated disjunction of diagnostic expressions representing an estimated status of the entity, thereafter add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions, and produce a status report based on the updated disjunction of diagnostic expressions.
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Abstract
Status estimation is determined for an entity having a plurality of components. An original disjunction of diagnostic expressions indicating at least one of a faultfree or at least one fault mode for at least one of the components is determined, which is then investigated against a set of diagnostic test results, and expressions that do not imply the test result are discarded. Further, for each statement in the test result, a joint diagnostic expression is generated representing a conjunction of the statement and the currently investigated diagnostic expression. Joint diagnostic expressions that imply one of the original diagnosis expressions are discarded. Otherwise, they are added to an updated disjunction of diagnostic expressions. All remaining diagnostic expressions in the temporary disjunction of diagnostic expressions are then added to the updated disjunction of diagnostic expressions, and a status report is produced.
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9 Claims
 1. A diagnosis engine for estimating a status of an entity with a plurality of components which each is assumed to be in a faultfree mode or be in exactly one of at least one fault mode, the diagnosis engine comprising:
 a processing unit adapted to analyze test results; and
at least one storage area adapted to store diagnostic data in respect of the entity, wherein said processing unit is adapted to;
receive an original disjunction of diagnostic expressions indicating at least one of said modes for at least one of said components, receive first test results of a set of diagnostic tests in respect of the entity, the result of each test being a disjunction of statements wherein each statement indicates at least one of said modes for one of said components, store the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area, investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result;
if not so, remove the expression from the temporary disjunction of diagnostic expressions; and
, for each statement in the first test result, generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression, compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression, and, discard the joint diagnostic expression, if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, or, add the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area, if an original diagnostic expression is not found, the updated disjunction of diagnostic expressions representing an estimated status of the entity, thereafter add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions, and produce a status report based on the updated disjunction of diagnostic expressions.  View Dependent Claims (2)
 a processing unit adapted to analyze test results; and
 3. A motor vehicle comprising a plurality of components and a diagnosis system adapted to estimate a status of at least a subgroup of said components, wherein the diagnosis system comprises a diagnosis engine comprising:
 a processing unit adapted to analyze test results; and
at least one storage area adapted to store diagnostic data in respect of the motor vehicle, wherein said processing unit is adapted to;
receive an original disjunction of diagnostic expressions indicating at least one mode for at least one of said components, wherein the at least one mode is a faultfree mode or one of at least one fault mode, receive first test results of a set of diagnostic tests in respect of the motor vehicle, the result of each test being a disjunction of statements, wherein each statement indicates at least one of said modes for one of said components, store the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area, investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result, if not so, remove the expression from the temporary disjunction of diagnostic expressions, and, for each statement in the first test result, generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression, compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression, and, discard the joint diagnostic expression if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, or, add the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area, if an original diagnostic expression is not found, the updated disjunction of diagnostic expressions representing an estimated status of the entity, thereafter add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions, and produce a status report based on the updated disjunction of diagnostic expressions.
 a processing unit adapted to analyze test results; and
 4. A method of diagnosing an entity with a plurality of components which each is assumed to be in a faultfree mode or be in exactly one of at least one fault mode, said method comprising:
 receiving an original disjunction of diagnostic expressions indicating at least one of said modes for at least one of said components, receiving a first test result of a set of diagnostic tests in respect of the entity, the result of each test being a disjunction of statements wherein each statement indicates at least one of said modes for one of said components, storing the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area, investigating, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result;
if not so, remove the expression from the temporary disjunction of diagnostic expressions; and
, for each statement in the first test result, generating a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression, comparing the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression, and, discarding the joint diagnostic expression if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, or, adding the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area, if an original diagnostic expression is not found, the updated disjunction of diagnostic expressions representing an estimated status of the entity, thereafter adding all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions, and producing a status report based on the updated disjunction of diagnostic expressions.  View Dependent Claims (5, 6)
 receiving an original disjunction of diagnostic expressions indicating at least one of said modes for at least one of said components, receiving a first test result of a set of diagnostic tests in respect of the entity, the result of each test being a disjunction of statements wherein each statement indicates at least one of said modes for one of said components, storing the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area, investigating, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result;
 7. A computer program product, comprising:
 a computerreadable medium comprising;
a first set of codes for causing a computer to receive an original disjunction of diagnostic expressions indicating at least one mode for at least one of a plurality of components including in an entity, wherein the at least one mode is a faultfree mode or one of at least one fault modes;
a second set of codes for causing the computer to receive first test results of a set of diagnostic tests in respect of the entity, the result of each test being a disjunction of statements, wherein each statement indicates at least one of the modes for one of said components;
a third set of codes for causing the computer to store the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area;
a fourth set of codes for causing the computer to investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether a currently investigated diagnostic expression implies the first test result;
a fifth set of codes for causing the computer, if the currently investigated diagnostic expression does not imply the first test result, to remove the expression from the temporary disjunction of diagnostic expressions and, for each statement in the test result;
a sixth set of codes for causing the computer to generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression;
a seventh set of codes for causing the computer to compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression;
a eighth set of codes for causing the computer, to discard the joint diagnostic expression, if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, or add the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area, if an original diagnostic is not found, the updated disjunction of diagnostic expressions representing an estimated status of the entity;
a ninth set of codes for causing the computer to add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions; and
a tenth set of codes for causing the computer to produce a status report based on the updated disjunction of diagnostic expressions.  View Dependent Claims (8, 9)
 a computerreadable medium comprising;
1 Specification
The present invention relates generally to diagnosing complex systems and devices including a large number of parts and components.
As today's technical systems generally become increasingly complex, efficient monitoring and detection of malfunctioning components is an area that gains progressive importance. Fault diagnosis algorithms may be applied to determine why an entity does not behave as intended. Typically, “diagnosing” the entity means selecting a subset of a predetermined set of causes responsible for the entity's incorrect behavior. A diagnosis must both explain the incorrect behavior and optimize some objective function, such as probability of correctness or cost of incorrect diagnosis. The need to diagnose is a common reason to measure or to test the entity. It is assumed that the entity consists of a finite number of diagnosed components. Further, failures of the entity are caused only by faults in one of these components.
In Reiter, R., “A theory of diagnosis from first principles”, Artificial Intelligence, 32(1):57.95, April, 1987 and deKleer, J. and Williams, B. C., “Diagnosing multiple faults” Artificial Intelligence, Issue 1, Volume 32:pp. 97.130, 1987, algorithms for finding all socalled minimal diagnoses are presented. Later, various improvements of these algorithms have also been described. The abovementioned original algorithm and its associated framework as presented by deKleer and Williams presumes that the system to be diagnosed includes a number of components being represented by a set C. Here, a conflict is represented as a set C<u style="single">⊂</u>C. A conflict C is understood to mean that not all components in C can be in the faultfree mode. Moreover, a conflict C<sub>1 </sub>is said to be minimal if there is no other conflict C<sub>2 </sub>such that C<sub>2</sub>⊂C<sub>1</sub>.
A diagnosis δ is also represented as a set δ<u style="single">⊂</u>C. The meaning of a diagnosis δ is that the components contained in δ are faulty and the components not contained in δ are faultfree. A diagnosis δ<sub>1 </sub>is said to be minimal if there is no other diagnosis δ<sub>2 </sub>such that δ<sub>2</sub>⊂δ<sub>1</sub>.
One fundamental relation between conflicts and diagnoses is that if <img id="CUSTOMCHARACTER00001" he="3.13mm" wi="2.46mm" file="US0752964320090505P00001.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> is the set of all minimal conflicts, then δ is a diagnosis if and only if for all conflicts Cε<img id="CUSTOMCHARACTER00002" he="3.13mm" wi="2.46mm" file="US0752964320090505P00002.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> it holds that δ∩C≠Ø.
Given a set of diagnoses Δ and a conflict C the minimal hitting set algorithm according to deKleer and Williams finds an updated set of minimal diagnoses. Specifically, the algorithm as described by deKleer and Williams, can be written as follows.
<tables id="TABLEUS00001" num="00001"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="3"><colspec colname="offset" colwidth="14pt" align="left"/><colspec colname="1" colwidth="189pt" align="left"/><colspec colname="2" colwidth="14pt" align="left"/><thead><row><entry/><entry namest="offset" nameend="2" align="center" rowsep="1"/></row></thead><tbody valign="top"><row><entry/><entry>Input: a set of minimal diagnoses Δ, and a conflict set C.</entry><entry/></row><row><entry/><entry>Output: an updated set of minimal diagnoses Θ.</entry></row><row><entry/><entry>Δ<sub>old </sub>= Δ</entry></row><row><entry/><entry>for all δ<sub>i </sub>ε Δ do</entry></row><row><entry/><entry> if δ<sub>i </sub>∩ C ≠ Ø; then</entry></row><row><entry/><entry> Remove δ<sub>i </sub>from Δ<sub>old</sub></entry></row><row><entry/><entry> for all c ε C do</entry></row><row><entry/><entry> δ<sub>new </sub>:= δ<sub>i </sub>∪ {c}</entry></row><row><entry/><entry> for all δ<sub>k </sub>ε Δ, δ<sub>k </sub>≠ δ<sub>i </sub>do</entry></row><row><entry/><entry> if δ<sub>k </sub><u style="single">⊂</u> δ<sub>new</sub>; then</entry></row><row><entry/><entry> go to LABEL1</entry></row><row><entry/><entry> end if</entry></row><row><entry/><entry> next</entry></row><row><entry/><entry> Δ<sub>add </sub>:= Δ<sub>add </sub>∪ {δ<sub>new</sub>}</entry></row><row><entry/><entry> LABEL1</entry></row><row><entry/><entry> next</entry></row><row><entry/><entry> end if</entry></row><row><entry/><entry>next</entry></row><row><entry/><entry>Θ := Δ<sub>old </sub>∪ Δ<sub>add</sub></entry></row><row><entry/><entry namest="offset" nameend="2" align="center" rowsep="1"/></row></tbody></tgroup></table></tables>
The algorithm has the properties that if Δ is the set of all minimal diagnoses, the algorithm output Θ will contain all minimal diagnoses with respect to also the new conflict C. Further, it holds that Θ will contain only minimal diagnoses.
These are certainly useful properties when monitoring and testing an entity. However, when determining the status of a complex entity, it is a severe limitation that each tested component may only have two possible behavioral modes, i.e. either be faultfree or be faulty. Instead, more specific fault statuses are desirable for improved diagnosis quality.
SUMMARY OF THE INVENTIONThe object of the present invention is therefore to provide a solution, which solves the problem above, and thus offers distinction between more than two behavioral modes.
According to one aspect of the invention, the object is achieved by the initially described diagnosis engine, wherein the processing unit is adapted to receive an original disjunction of diagnostic expressions indicating at least one of said modes for at least one of said components, i.e. whether the component is in the faultfree mode or if it has attained exactly one of at least one fault mode. The processing unit is also adapted to receive test results of diagnostic tests in respect of the entity. In each processing cycle of the proposed processing, however, only one test result is processed. Here, each test result is a disjunction of statements, wherein each statement indicates at least one of said modes for one of said components. Further, the processing unit is adapted to copy the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area. Preferably, the original disjunction of diagnostic expressions is empty prior to receiving a first test result in respect of the entity. Nevertheless, for each diagnostic expression in the temporary disjunction of diagnostic expressions, the processing unit is adapted to investigate whether or not a currently investigated diagnostic expression implies the test result. If this is found not to be the case, the processing unit is adapted to remove the diagnostic expression from the temporary disjunction of diagnostic expressions. Moreover, for each statement in the test result, the processing unit is adapted to generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression. Then, the processing unit is adapted to compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except the currently investigated diagnostic expression. If an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, the processing unit is adapted to discard the joint diagnostic expression. Otherwise, the processing unit adds the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area. Here, the updated disjunction of diagnostic expressions represents an estimated status of the entity. After having processed the test result and all received diagnostic expressions, the processing unit is adapted to also add any remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions. Finally, the processing unit is adapted to produce a status report based on the updated disjunction of diagnostic expressions.
Important advantages by this diagnosis engine is that it allows multiple behavioral modes essentially without increasing the algorithm complexity relative to the original algorithm of deKleer and Williams.
According to one embodiment of this aspect of the invention, after having processed a result of a first test of the tests, the processing unit is adapted to, for each result of at least one second test of the tests, investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions, whether or not a currently investigated diagnostic expression implies the second test result. If this is found not to be the case, the expression is removed from the temporary disjunction of diagnostic expressions. When in a first step, only one test result is considered, the diagnoses are already described by this result. Thus, the algorithm is not needed. Analogous to the above, the processing unit is adapted to, for each statement in the second test result, generate a joint diagnostic expression representing a conjunction of the statement and the currently investigated diagnostic expression. The processing unit is adapted to compare the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression, and if an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, the processing unit is adapted to discard the joint diagnostic expression. Otherwise, the joint diagnostic expression is added to an updated disjunction of diagnostic expressions in the second storage area. After having processed the test result and all received diagnostic expressions, the processing unit is adapted to add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions. Subsequently, the processing unit is adapted to produce an updated status report based on the updated disjunction of diagnostic expressions. A gradually improved status report can then be generated as further test results are received.
According to another aspect of the invention, the object is achieved by the motor vehicle described initially, wherein the diagnosis system includes the aboveproposed diagnosis engine.
According to another aspect of the invention, the object is achieved by the method described initially, wherein an original disjunction of diagnostic expressions is received and copied into a temporary disjunction of diagnostic expressions in a first storage area. The original disjunction of diagnostic expressions indicates at least one of said modes for at least one of said components. A test result is also received, where the result reflects tests performed in respect of the entity. Here, each test result is a disjunction of statements, wherein each statement indicates at least one of said modes for one of said components. For each diagnostic expression in the temporary disjunction of diagnostic expressions, it is investigated whether or not a currently investigated diagnostic expression implies the test result. If not so, the expression is removed from the temporary disjunction of diagnostic expressions. For each statement in the test result, the method involves, generating a joint diagnostic expression that represents a conjunction of the statement and the currently investigated diagnostic expression. The joint diagnostic expression is compared with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression. If an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, the method involves discarding the joint diagnostic expression. Otherwise, the joint diagnostic expression is added to an updated disjunction of diagnostic expressions in a second storage area. After having processed the test result and all received diagnostic expressions, all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions are added to the updated disjunction of diagnostic expressions. Finally, a status report is produced based on the updated disjunction of diagnostic expressions.
The advantages of this method, as well as the preferred embodiments thereof, are apparent from the discussion hereinabove with reference to the proposed diagnosis engine.
According to a further aspect of the invention the object is achieved by a computer program product directly loadable into the internal memory of a computer, comprising software for controlling the above proposed method when said program is run on a computer.
According to another aspect of the invention the object is achieved by a computer readable medium, having a program recorded thereon, where the program is to make a computer control the above proposed method.
BRIEF DESCRIPTION OF THE DRAWINGSThe present invention is now to be explained more closely by means of embodiments, which are disclosed as examples, and with reference to the attached drawings.
FIG. 1 shows a block diagram over the diagnosis engine according to one embodiment of the invention,
FIG. 2 schematically depicts a motor vehicle equipped with the proposed diagnosis engine, and
FIG. 3 shows a flow diagram illustrating the general method according to the invention.
DESCRIPTION OF EMBODIMENTS OF THE INVENTIONWe will describe a diagnosis algorithm that unlike the deKleer/Williams algorithm can handle also the case of more than two behavioral modes per component. In the original algorithm, conflicts and diagnoses were represented as sets. For a more efficient representation in the case of more than two behavioral modes, we will here use a framework where conflicts and diagnoses are represented by logical formulas.
When describing the invention, we define the term “diagnostic expression” to designate a conjunction of statements relating to a diagnosed entity, which reflect faulty or faultfree statuses of one or more components. Thus, the diagnostic expression is a conjunction of statements. One example of a diagnostic expression is:
 “the intake pressure sensor is faultfree or has a bias, and the exhaust gas regulator valve has jammed in a closed position or has an unknown error.”
A “test result” is understood to mean a set of statements, wherein at least one statement is true. Thus a test result is a disjunction of statements. One example of a test result is:
 “the intake pressure sensor is faultfree or has a bias, or the exhaust gas regulator valve has jammed in a closed position or has an unknown error.”
Of course, given these definitions, a diagnostic expression is generally more informative (or contains information of a higher quality) than a test result.
Moreover, a first diagnostic expression may logically “imply” a second diagnostic expression. One example of such an implication is:
 “the intake pressure sensor is faultfree” implies that
 “the intake pressure sensor is faultfree or has a bias.”
Another example is:
 “the intake pressure sensor is faultfree or has a bias, and the exhaust gas regulator valve has jammed in a closed position” implies that
 “the intake pressure sensor is faultfree or has a bias.”
Formally, each component is assumed to be in exactly one out of several behavioral modes. A behavioral mode can be for example nofault, abbreviated NF, gainfault G, bias B, open circuit OC, short circuit SC, unknown fault UF, or just faulty F. For our purposes, each component is abstracted to a variable specifying the mode of that component. Let now C denote the set of such variables. For each component variable c let R<sub>c </sub>denote the domain of possible behavioral modes, i.e. cεR<sub>c</sub>.
To reason about the behavioral modes of different components, we use the following formal language. The expression cεM, where cεC and M<u style="single">⊂</u>R<sub>c </sub>is a formula. For example, if p is a pressure sensor, the formula pε{NF, G, UF} means that the pressure sensor p is in mode NF, G or UF. If M is a singleton, e.g. M={NF}, this may also be expressed c=NF. Further, the constant ⊥ with value false, is a formula. If φ and γ are formulas, then φ<img id="CUSTOMCHARACTER00003" he="2.79mm" wi="2.12mm" file="US0752964320090505P00003.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>γ, φ<img id="CUSTOMCHARACTER00004" he="2.79mm" wi="2.12mm" file="US0752964320090505P00004.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>γ, and <img id="CUSTOMCHARACTER00005" he="2.12mm" wi="2.12mm" file="US0752964320090505P00005.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>φ are also formulas. In accordance with the theory of first order logic, we say that a formula φ is implied by another formula γ, and write γ=φ, if all assignments of the variables C that make γ true also make φ true. This can be generalized to sets of formulas, i.e. {γ<sub>1</sub>, . . . , γ<sub>n</sub>}={φ<sub>1</sub>, . . . , φ<sub>m</sub>} if and only if γ<sub>1</sub>^ . . . ^γ<sub>n</sub>=1φ<sub>1</sub>^ . . . ^φ<sub>m</sub>. If it holds that Γ=Φ and Φ=Γ, where Φ and Γ are formulas or sets of formulas, Φ and Γ are said to be equivalent and we write Γ≅Φ.
For conjunctions (c<sub>i1</sub>εM<sub>i1</sub>^ εM<sub>i2</sub>^ . . . c<sub>ini</sub>εM<sub>ini</sub>), we will often use the notation D<sub>i</sub>. We will say that a formula is in maximal normal form (MNF) if it is written on the form<FORM>(c<sub>11</sub>εM<sub>11</sub>^c<sub>12</sub>εM<sub>12</sub>^ . . . c<sub>1n1</sub>εM<sub>1n1</sub>)v . . . v(c<sub>m1</sub>εM<sub>m1</sub>^ . . . ^c<sub>mnm</sub>εM<sub>mnm</sub>) where c<sub>ij</sub>≠c<sub>ik </sub>if j≠k, and</FORM>
 1) no conjunction is implied by another conjunction, i.e. for each conjunction D<sub>i</sub>, there is no conjunction D<sub>j</sub>, j≠i, for which it holds that D<sub>j</sub>=D<sub>i</sub>, and
 2) each M<sub>ij </sub>is a nonempty proper subset of R<sub>cij</sub>, i.e.; Ø≠M<sub>ij</sub>⊂R<sub>c</sub>.
Note that the purpose of using formulas in MNF is that the two MNFrequirements guarantee that a formula is relatively compact in the sense that it does not contain redundant conjunctions and that each conjunction does not contain redundant assignments.
For example consider the following two formulas containing pressure sensors p<sub>1</sub>, p<sub>2 </sub>and p<sub>3</sub>, where all have the behavioral modes R<sub>pi</sub>={NF, G, B, UF}.<FORM>p<sub>1</sub>ε{UF}^p<sub>2</sub>ε{B, UF}vp<sub>3</sub>ε{UF}</FORM><FORM>p<sub>1</sub>ε{UF}^p<sub>2</sub>ε{B, UF}vp<sub>1</sub>ε{G, UF}</FORM>
The first formula is in MNF, however not the second formula, since p<sub>1</sub>ε{(UF)}^p<sub>2</sub>ε{B, UF}/=p<sub>1</sub>ε{G, UF}.
Using the logical language defined above, a conflict can be expressed as follows. For example, if it has been found that the pressure sensor p<sub>1 </sub>cannot be in the mode NF at the same time as p<sub>2 </sub>is in the mode B or NF, this gives the conflict<FORM>H=p<sub>1</sub>ε{NF}^p<sub>2</sub>ε{B, NF} (1)</FORM>
This definition of conflict can be compared with the previously mentioned conflict C={a, b, c}. Using the logical language, we can write this conflict as aε{NF}^bε{NF}^cε{NF}
Instead of conflicts, the invention will primarily be described with reference to negated conflicts. Therefore, as an alternative to H, we consider <img id="CUSTOMCHARACTER00006" he="2.12mm" wi="3.89mm" file="US0752964320090505P00006.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>H. In particular we will use negated conflicts written in MNF. For an example, the negated conflict <img id="CUSTOMCHARACTER00007" he="2.12mm" wi="3.89mm" file="US0752964320090505P00007.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>H, where H is defined in (1), can be written in MNF as:<FORM>p<sub>1</sub>ε{G, B, UF}vp<sub>2</sub>ε{G, UF}</FORM>
In this context, the negated conflict is equivalent to the abovementioned test result. Without loss of generality, we will from now on assume that all negated conflicts are written on the form:<FORM>c<sub>1</sub>εM<sub>1</sub>vc<sub>2</sub>εM<sub>2</sub>v . . . vc<sub>n</sub>εM<sub>n</sub> (2)</FORM>where c<sub>j</sub>≠c<sub>k </sub>if j≠k and Ø≠M<sub>i</sub>⊂R<sub>ci</sub>. This means that (2) is in MNF.
A system behavioral mode is defined as a conjunction containing a unique assignment of all components in C. For example if C={p<sub>1</sub>, p<sub>2</sub>, p<sub>3</sub>}, a system behavioral mode could be:<FORM>p<sub>1</sub>=UF^p<sub>2</sub>=B^p<sub>3</sub>=NF</FORM>
We consider the term diagnosis to refer to a system behavioral mode consistent with all negated conflicts. More formally, if <img id="CUSTOMCHARACTER00008" he="3.13mm" wi="2.12mm" file="US0752964320090505P00008.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> is the set of all negated conflicts, a system behavioral mode d is a diagnosis if {d}∪<img id="CUSTOMCHARACTER00009" he="3.13mm" wi="2.12mm" file="US0752964320090505P00009.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>≠⊥ or equivalently d=<img id="CUSTOMCHARACTER00010" he="3.13mm" wi="2.79mm" file="US0752964320090505P00010.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>.
To relate this definition of diagnosis to the definition used by deKleer and Williams, assume that C={a, b, c, d} and consider the diagnosis δ={a, b}. With the logical language, we can write this diagnosis as a=F^b=F^c=NF^d=NF.
The algorithm according to the present invention is capable of handling more than two behavioral modes per component. As inputs, the algorithm takes a formula D and a negated conflict P, which are both written in MNF. The purpose of the algorithm is then to derive a new formula Q in MNF such that Q≅D^P.
In the algorithm, we use the notation D<sub>i</sub>εD to denote the fact D<sub>i </sub>is a conjunction in D. Hence, the algorithm can be expressed as follows:
<tables id="TABLEUS00002" num="00002"><table frame="none" colsep="0" rowsep="0"><tgroup align="left" colsep="0" rowsep="0" cols="2"><colspec colname="offset" colwidth="21pt" align="left"/><colspec colname="1" colwidth="196pt" align="left"/><thead><row><entry/><entry namest="offset" nameend="1" align="center" rowsep="1"/></row></thead><tbody valign="top"><row><entry/><entry>Input: a formula D in MNF, and a negated conflict P in MNF</entry></row><row><entry/><entry>Output: Q</entry></row><row><entry/><entry>D<sub>old </sub>= D</entry></row><row><entry/><entry>for all D<sub>i </sub>ε D do</entry></row><row><entry/><entry> if D<sub>i </sub>≠ P then</entry></row><row><entry/><entry> Remove D<sub>i </sub>from D<sub>old</sub></entry></row><row><entry/><entry> for all P<sub>j </sub>ε P do</entry></row><row><entry/><entry> Let D<sub>new </sub>be a conjunction in MNF such</entry></row><row><entry/><entry> that D<sub>new </sub>≅ D<sub>i </sub><img id="CUSTOMCHARACTER00011" he="2.46mm" wi="2.12mm" file="US0752964320090505P00011.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> P<sub>j</sub></entry></row><row><entry/><entry> for all D<sub>k </sub>ε D, D<sub>k </sub>≠ D<sub>i </sub>do</entry></row><row><entry/><entry> if D<sub>new </sub>= D<sub>k </sub>then</entry></row><row><entry/><entry> go to LABEL1</entry></row><row><entry/><entry> end if</entry></row><row><entry/><entry> next</entry></row><row><entry/><entry> D<sub>add </sub>:= D<sub>add </sub><img id="CUSTOMCHARACTER00012" he="2.12mm" wi="1.78mm" file="US0752964320090505P00012.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> D<sub>new</sub></entry></row><row><entry/><entry> LABEL1</entry></row><row><entry/><entry> next</entry></row><row><entry/><entry> end if</entry></row><row><entry/><entry>next</entry></row><row><entry/><entry>Q := D<sub>old </sub><img id="CUSTOMCHARACTER00013" he="2.12mm" wi="1.78mm" file="US0752964320090505P00012.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> D<sub>add</sub></entry></row><row><entry/><entry namest="offset" nameend="1" align="center" rowsep="1"/></row></tbody></tgroup></table></tables>
According to one embodiment of the invention, the algorithm is implemented as follows. To illustrate how the condition D<sub>i</sub>=P may be checked, we will consider an example where D<sub>i </sub>contains components c<sub>1</sub>, c<sub>2 </sub>and c<sub>3 </sub>and P contains components c<sub>2</sub>, c<sub>3 </sub>and c<sub>4</sub>. Since D is in MNF and P is in the form (2), D<sub>i </sub>and P will have the form<FORM>D<sub>i</sub>c<sub>1</sub>εM<sub>1</sub><sup>D</sup>^c<sub>2</sub>εM<sub>2</sub><sup>D</sup>^c<sub>3</sub>εM<sub>3</sub><sup>D</sup> (3)</FORM><FORM>P=c<sub>2</sub>εM<sub>2</sub><sup>P</sup>vc<sub>3</sub>εM<sub>3</sub><sup>P</sup>vc<sub>4</sub>εM<sub>4</sub><sup>P</sup> (4)</FORM>
We realize that the condition D<sub>i</sub>=P holds if and only if M<sub>2</sub><sup>D</sup><u style="single">⊂</u>M<sub>2</sub><sup>P </sup>or M<sub>3</sub><sup>D</sup><u style="single">⊂</u>M<sub>3</sub><sup>P</sup>. Thus, this example shows that in general, D<sub>i</sub>=P holds if and only if D<sub>i </sub>and P contain at least one common component c<sub>i </sub>where M<sub>i</sub><sup>D</sup><u style="single">⊂</u>M<sub>i</sub><sup>P</sup>.
An expression Q<sub>new </sub>in MNF must be found such that D<sub>new</sub>≅D<sub>i</sub>^P<sub>j</sub>. To illustrate this, consider an example where D<sub>i </sub>contains components c<sub>1 </sub>and c<sub>2</sub>, and P<sub>j </sub>contains the component c<sub>2</sub>. Since D is in MNF and P is in the form (2), D<sub>i </sub>and P<sub>j </sub>will have the form<FORM>D<sub>i</sub>=c<sub>1</sub>εM<sub>1</sub><sup>D</sup>^c<sub>2</sub>εM<sub>2</sub><sup>D</sup> (5a)</FORM><FORM>P<sub>j</sub>=c<sub>2</sub>εM<sub>2</sub><sup>P</sup> (5b)</FORM>
Then Q<sub>new </sub>will be formed as<FORM>D<sub>new</sub>=c<sub>1</sub>εM<sub>1</sub><sup>D</sup>^c<sub>2</sub>εM<sub>2</sub><sup>D</sup>∩M<sub>2</sub><sup>P</sup></FORM>which means that D<sub>new</sub>≅D<sub>i</sub>^P<sub>j</sub>. If it holds that M<sub>2</sub><sup>P</sup>≠Ø, D<sub>new </sub>will be in MNF. Otherwise let D<sub>new</sub>=⊥.
The condition D<sub>new</sub>=D<sub>k </sub>must be checked. To illustrate this, consider an example where D<sub>new </sub>contains components c<sub>1 </sub>and c<sub>2 </sub>and D<sub>k </sub>contains the components c<sub>2 </sub>and c<sub>3</sub>. Since D<sub>new </sub>and D are both in MNF, D<sub>new </sub>and D<sub>k </sub>will have the form<FORM>D<sub>new</sub>=c<sub>1</sub>ε(M<sub>1</sub><sup>n</sup>^c<sub>2</sub>εM<sub>2</sub><sup>n</sup> (6a)</FORM><FORM>D<sub>k</sub>=c<sub>2</sub>εM<sub>2</sub><sup>D</sup>^c<sub>3</sub>εM<sub>3</sub><sup>D</sup> (6b)</FORM>
Without changing their meanings, these expressions can be expanded so that they contain the same set of components:<FORM>D′<sub>new</sub>=c<sub>1</sub>εM<sub>1</sub><sup>n</sup>^c<sub>2</sub>εM<sub>2</sub><sup>n</sup>^c<sub>3</sub>εR<sub>c3</sub> (7)</FORM><FORM>D′<sub>k</sub>=c<sub>1</sub>εR<sub>c1</sub>^c<sub>2</sub>εM<sub>2</sub><sup>D</sup>^c<sub>3</sub>εM<sub>3</sub><sup>D</sup> (8)</FORM>
Now we see that the condition D<sub>new</sub>=D<sub>k </sub>holds if and only if M<sub>1</sub><sup>n</sup><u style="single">⊂</u>R<sub>c1</sub>, M<sub>2</sub><sup>n </sup><u style="single">⊂</u>M<sub>2</sub><sup>D </sup>and R<sub>c3</sub><u style="single">⊂</u>M<sub>3</sub><sup>D</sup>. The first of these three conditions is always fulfilled and the third can never be fulfilled since, by definition of MNF, M<sub>3</sub><sup>D</sup><u style="single">⊂</u>R<sub>c3</sub>. Thus, this example shows that D<sub>new</sub>=D<sub>k </sub>holds if and only if (1) D<sub>k </sub>contains only components that are also contained in D<sub>new</sub>, and (2) for all components c<sub>i </sub>contained in both D<sub>new </sub>and D<sub>k </sub>it holds that M<sub>i</sub><sup>n</sup><u style="single">⊂</u>M<sub>i</sub><sup>D</sup>.
The expression D<sub>add</sub>:=D<sub>add</sub>vD<sub>new </sub>must be considered. Since D<sub>add </sub>is not assigned from the beginning, this expression is to be read as D<sub>add</sub>:=D<sub>new </sub>when D<sub>add </sub>is unassigned.
We must also consider the expression Q:=D<sub>old</sub>vD<sub>add</sub>. Note that after several removals, D<sub>old </sub>may become empty. It may therefore happen that either D<sub>old </sub>or D<sub>add </sub>is unassigned. Therefore the expression Q:=D<sub>old</sub>vD<sub>add </sub>should be read as Q:=D<sub>old </sub>if D<sub>add </sub>is unassigned, and Q:=D<sub>add </sub>if D<sub>old </sub>is unassigned. A safe way to avoid this is to always include a UF mode in all sets M<sub>i </sub>in (2).
Preferably, the algorithm is used in an iterative manner as follows. First, when only one negated conflict P<sub>1 </sub>is considered, the diagnoses are already described by P<sub>1</sub>. Thus, the algorithm is not needed. When a second negated conflict P<sub>2 </sub>is considered, the algorithm is fed with D=P<sub>1 </sub>and P=P<sub>2</sub>, and produces the output Q such that Q≅P<sub>1</sub>^P<sub>2</sub>. Then, for each additional negated conflict P<sub>n </sub>that is considered, the input D is the old output Q.
When the algorithm is used in this way, the following results can be guaranteed.
Theorem 1 Let <img id="CUSTOMCHARACTER00014" he="3.13mm" wi="2.12mm" file="US0752964320090505P00013.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> be a set of negated conflicts and let Q be the output from the proposed algorithm after processing all negated conflicts in <img id="CUSTOMCHARACTER00015" he="3.13mm" wi="2.79mm" file="US0752964320090505P00014.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>. Then it holds that Q≅<img id="CUSTOMCHARACTER00016" he="3.13mm" wi="2.79mm" file="US0752964320090505P00015.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>.
PROOF. Let P be the negated conflict in a last application of the algorithm, and let <img id="CUSTOMCHARACTER00017" he="3.13mm" wi="2.12mm" file="US0752964320090505P00016.TIF" alt="custom character" imgcontent="character" imgformat="tif"/><sub>n−1 </sub>denote the set of all negated conflicts in <img id="CUSTOMCHARACTER00018" he="3.13mm" wi="2.12mm" file="US0752964320090505P00017.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> except P. Then it holds that <img id="CUSTOMCHARACTER00019" he="3.13mm" wi="2.12mm" file="US0752964320090505P00018.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>≅<img id="CUSTOMCHARACTER00020" he="3.13mm" wi="2.12mm" file="US0752964320090505P00019.TIF" alt="custom character" imgcontent="character" imgformat="tif"/><sub>n−1</sub>∪{P}≅D^P. Lemma 4 below implies that D^P=Q. Left to prove is Q=D^P. Take an arbitrary conjunction Q<sub>k </sub>in the output Q. If Q<sub>k </sub>is in D<sub>old</sub>, then it must be in also D, i.e. Q<sub>k</sub>=D<sub>i </sub>for some conjunction D<sub>i </sub>in D. The fact that D<sub>i </sub>is in D<sub>old </sub>means also that D<sub>i</sub>=P. Thus Q<sub>k</sub>=D<sub>i</sub>=D^P. If Q<sub>k </sub>instead is in D<sub>add</sub>, there is a D<sub>i </sub>in D and a P<sub>j </sub>in P such that Q<sub>k</sub>≅D<sub>i</sub>^P<sub>j </sub>which implies Q<sub>k</sub>=D^P.
Lemma 1 The output Q from the proposed algorithm fulfills MNF requirement 1.
PROOF. Assume the contrary, that Q<sub>1 </sub>and Q<sub>2 </sub>are two conjunctions in Q and Q<sub>2</sub>=Q<sub>1</sub>. There are three cases that need to be investigated: (1) Q<sub>1</sub>εD<sub>old</sub>, Q<sub>2</sub>εD<sub>add</sub>, (2) Q<sub>2</sub>εD<sub>old</sub>, Q<sub>1</sub>εD<sub>add</sub>, (3) Q<sub>1</sub>εD<sub>add</sub>, Q<sub>2</sub>εD<sub>add</sub>.
1) The fact Q<sub>2</sub>εD<sub>add </sub>means that D<sub>new</sub>=Q<sub>2 </sub>at some point. Since Q<sub>1</sub>εD<sub>old</sub>, D<sub>new </sub>must then have been compared to Q<sub>1</sub>. Since Q<sub>2 </sub>has really been added, it cannot have been the case that Q<sub>2</sub>=Q<sub>1</sub>.
2) Since Q<sub>1</sub>εD<sub>add</sub>, it holds that Q<sub>1</sub>=D<sub>i</sub>^P<sub>j </sub>for some Q<sub>i</sub>εD. The fact Q<sub>2</sub>=Q<sub>1 </sub>implies that Q<sub>2</sub>=D<sub>i</sub>^P<sub>j</sub>=D<sub>i</sub>. This is a contradiction since Q<sub>2</sub>εD, and D fulfills the MNFrequirement 1.
3) There are three cases: (a) Q<sub>2</sub>=D<sub>i</sub>^P<sub>j2</sub>=D<sub>i</sub>^P<sub>j1</sub>=Q<sub>1</sub>, (b) Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j</sub>=D<sub>i</sub>^P<sub>j</sub>=Q<sub>1</sub>, (c) Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j2</sub>=D<sub>i1</sub>^P<sub>j1</sub>=Q<sub>1</sub>, where in all cases, P<sub>j1</sub>≠P<sub>j2 </sub>and D<sub>11</sub>≠D<sub>i2</sub>.
 a) We know that D<sub>i </sub>and P are formulas on forms like D<sub>i</sub>=aεA^bεB^cεC and P=aεA<sub>p</sub>vbεB<sub>p </sub>respectively. This means that Q<sub>1</sub>=aεA∩A<sub>p</sub>^bεB^cεC and Q<sub>1</sub>=aεA^bεB∩B<sub>p</sub>^cεC. The fact Q<sub>2</sub>=Q<sub>1 </sub>implies that A<u style="single">⊂</u>A∩A<sub>p</sub>, which further means that A<u style="single">⊂</u>A<sub>p</sub>. This implies Di=aεA^bεB^cεC=aεA<sub>p</sub>=P. Thus, Q<sub>1 </sub>and Q<sub>2 </sub>are never subject to be added to D<sub>add</sub>.
 b) We have that Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j</sub>=D<sub>i1</sub>^P<sub>j</sub>=D<sub>i1</sub>εD. This means that Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j </sub>cannot have been added to D<sub>add</sub>.
 c) We have that Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j2</sub>=D<sub>i1</sub>^P<sub>j</sub>=D<sub>i1</sub>εD. This means that Q<sub>2</sub>=D<sub>i2</sub>^P<sub>j2 </sub>cannot have been added to D<sub>add</sub>.
All these investigations show that it impossible that Q<sub>2</sub>=Q<sub>1</sub>.
Lemma 2 Let Q be the output from the proposed algorithm after processing all negated conflicts in <img id="CUSTOMCHARACTER00021" he="3.13mm" wi="2.79mm" file="US0752964320090505P00020.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> For any two conjunctions Q<sub>1 </sub>and Q<sub>2 </sub>in Q, there is no component c and conjunction <o ostyle="single">D</o>, not containing c, such that Q<sub>1</sub>≅ <o ostyle="single">D</o>^ <o ostyle="single">c</o>εM<sub>1 </sub>and Q<sub>2</sub>≅ <o ostyle="single">D</o>^ <o ostyle="single">c</o>εM<sub>2</sub>.
PROOF. Assume that there is a component c and conjunction <o ostyle="single">D</o> such that Q<sub>1</sub>≅ <o ostyle="single">D</o>^ <o ostyle="single">c</o>εM<sub>1 </sub>and Q<sub>2</sub>≅ <o ostyle="single">D</o>^ <o ostyle="single">c</o>εM<sub>2</sub>. We can write Q<sub>1 </sub>as cεΩ<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>1</sup2></sup>^ <o ostyle="single">D</o><sub>1 </sub>where Ω<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>1 </sup2></sup>is the intersection of the sets M<sub>c</sub><sup>P </sup>obtained from all Pεφ<sub>c</sub><sup>1</sup><u style="single">⊂</u><img id="CUSTOMCHARACTER00022" he="3.56mm" wi="3.13mm" file="US0752964320090505P00021.TIF" alt="custom character" imgcontent="character" imgformat="tif"/> and <o ostyle="single">D</o> is the conjunction of one P<sub>j </sub>obtained from every Pε<img id="CUSTOMCHARACTER00023" he="3.13mm" wi="2.12mm" file="US0752964320090505P00022.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>\φ<sub>c</sub><sup>1</sup>. Similarly we write Q<sub>2 </sub>as cεΩ<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>2</sup2></sup>^ <o ostyle="single">D</o><sub>2</sub>.
We can find a D′ such that D′≅ <o ostyle="single">D</o><sub>1</sub>≅ <o ostyle="single">D</o><sub>2 </sub>and where D′ is the conjunction of one P<sub>j </sub>obtained from every Pε<img id="CUSTOMCHARACTER00024" he="3.13mm" wi="2.12mm" file="US0752964320090505P00023.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>\(φ<sub>c</sub><sup>1</sup>∩φ<sub>c</sub><sup>2</sup>). Then let D*=cεΩ<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>1</sup2></sup><sup>∩φ</sup><sup><sub2>c</sub2></sup><sup><sup2>2</sup2></sup>^D′ which means that Q<sub>1</sub>=cεΩ<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>1</sup2></sup><sup>∩φ</sup><sup><sub2>c</sub2></sup><sup><sup2>2</sup2></sup>^ <o ostyle="single">D</o><sub>1</sub>≅D*. Similarly we can obtain the relation Q<sub>2</sub>=cεΩ<sup>φ</sup><sup><sub2>c</sub2></sup><sup><sup2>1</sup2></sup><sup>∩φ</sup><sup><sub2>c</sub2></sup><sup><sup2>2</sup2></sup>^ <o ostyle="single">D</o><sub>2</sub>≅D*. By construction of D* it can be realized that D*=Q<sub>k </sub>for some conjunction Q<sub>k </sub>in Q. Thus Q<sub>1</sub>=Q<sub>k </sub>and according to Theorem 2, the only possibility is that Q<sub>k</sub>≡Q<sub>1</sub>, which is a contradiction. This means that there can not be a component c and conjunction <o ostyle="single">D</o> such that Q<sub>1</sub>≅ <o ostyle="single">D</o>^cεM<sub>1 </sub>and Q<sub>2</sub>≅ <o ostyle="single">D</o>^cεM<sub>2</sub>.
Lemma 3 Let Q=D<sub>old</sub>^D<sub>add </sub>be the output from the proposed algorithm after processing all negated conflicts in <img id="CUSTOMCHARACTER00025" he="3.13mm" wi="2.79mm" file="US0752964320090505P00024.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>. If D<sub>im </sub>is not contained in D<sub>old</sub>, and the set D<sub>im</sub>^P<sub>j </sub>is not contained in D<sub>add</sub>, after running the algorithm, then there is a D<sub>im+1 </sub>in D such that D<sub>im</sub>^P<sub>j</sub>=D<sub>im+1 </sub>and D<sub>im+1</sub>^P<sub>j</sub>≠D<sub>im</sub>^P<sub>j</sub>.
PROOF. The fact that D<sub>im </sub>is not contained in D<sub>old </sub>means that the inner loop of the algorithm must have been entered when D<sub>i</sub>=D<sub>im</sub>. Then the fact that D<sub>im</sub>^P<sub>j </sub>is not contained in D<sub>add</sub>, means that D<sub>im</sub>^P<sub>j</sub>=D<sub>k </sub>for some D<sub>k</sub>, k≠i<sub>m</sub>. By choosing i<sub>m+1</sub>=k, this gives D<sub>im</sub>^P<sub>j</sub>=D<sub>im+1</sub>.
Next we prove that D<sub>k</sub>^P<sub>j</sub>≠D<sub>i</sub>^P<sub>j</sub>. Let the single assignment in P<sub>j </sub>be aεA<sub>p</sub>, and let comps D<sub>i </sub>denote the set of comps in D<sub>i</sub>. We will divide the proof into four cases: (1) a∉comps D<sub>i</sub>, a∉comps D<sub>k</sub>, (2) aεcomps D<sub>i</sub>, a∉comps D<sub>k</sub>, (3) aεcomps D<sub>i</sub>, aεcomps D<sub>k</sub>, and (4) aεcomps D<sub>i</sub>, aεcomps D<sub>k</sub>.
1) The fact D<sub>i</sub>^P<sub>j</sub>=D<sub>k </sub>would imply D<sub>i</sub>=D<sub>k </sub>which is impossible because D is in MNF.
2) This case means that D<sub>i </sub>can be written as D<sub>i</sub>=D′^aεA<sub>i</sub>. The fact D<sub>i</sub>^P<sub>j</sub>=D′^aεA<sub>i</sub>∩A<sub>p</sub>=D<sub>k</sub>, together with the fact that a∉comps D<sub>k</sub>, would then imply that D′=D<sub>k </sub>and consequently that D<sub>i</sub>=D<sub>k</sub>, which is impossible because D is in MNF.
3) Assume that D<sub>k</sub>^P<sub>j</sub>=D<sub>i</sub>^P<sub>j</sub>. This relation can be written D′<sub>k</sub>^aεA<sub>p</sub>∩A<sub>k</sub>=D<sub>i</sub>^aεA<sub>p </sub>where D′<sub>k </sub>is a conjunction not containing component a. For this relation to hold it must hold that D′<sub>k</sub>=D<sub>i</sub>. This means that D<sub>k</sub>=aεA<sub>k</sub>^D′<sub>k</sub>=D<sub>i </sub>which is impossible because D is in MNF.
4) Assume that D<sub>k</sub>^P<sub>j</sub>=D<sub>i</sub>^P<sub>j</sub>. This relation can be written D′<sub>k</sub>^aεA<sub>p</sub>∩A<sub>k</sub>=D′<sub>i</sub>^aεA<sub>p</sub>∩A<sub>i </sub>where D′<sub>k </sub>and D′<sub>i </sub>are conjunctions not containing component a. This relation would imply D′<sub>k</sub>32 D′<sub>i</sub>. Further on, the fact D<sub>i</sub>^P<sub>j</sub>=D<sub>k </sub>can be written aεA<sub>p</sub>∩A<sub>i</sub>^D′<sub>i</sub>=aεA<sub>k</sub>^D′<sub>k</sub>, which implies that D′<sub>i</sub>=D′<sub>k</sub>. Thus we have D′<sub>i</sub>≅D′<sub>k </sub>and the only possible difference between D<sub>i </sub>and D<sub>k </sub>is the assignment of component a. Lemma 2 says this is impossible.
With i=i<sub>m </sub>and k=i<sub>m+1</sub>, these four cases have shown that D<sub>im+1</sub>^P<sub>j</sub>≠D<sub>im</sub>^P<sub>j</sub>.
Lemma 4 Let D be the output from the proposed algorithm after processing all negated conflicts in <img id="CUSTOMCHARACTER00026" he="3.13mm" wi="2.12mm" file="US0752964320090505P00025.TIF" alt="custom character" imgcontent="character" imgformat="tif"/><sub>n−1</sub>, and Q the output given D and P as inputs. For each conjunction D<sub>i </sub>in D and P<sub>j </sub>in P it holds that there is a conjunction Q<sub>k </sub>in Q such that D<sub>i</sub>^P<sub>j</sub>.
PROOF. If, after running the algorithm, D<sub>i </sub>is contained in D<sub>old</sub>, then the lemma is trivially fulfilled. If instead D<sub>i</sub>^P<sub>i </sub>is contained in D<sub>add</sub>, then the lemma is also trivially fulfilled. Study now the case where D<sub>i </sub>is not contained in D<sub>old </sub>and D<sub>i</sub>^P<sub>j </sub>is not contained in D<sub>add</sub>. We can then apply Lemma 3 with <img id="CUSTOMCHARACTER00027" he="3.13mm" wi="2.12mm" file="US0752964320090505P00026.TIF" alt="custom character" imgcontent="character" imgformat="tif"/>=<img id="CUSTOMCHARACTER00028" he="3.13mm" wi="2.12mm" file="US0752964320090505P00027.TIF" alt="custom character" imgcontent="character" imgformat="tif"/><sub>n−1</sub>∩{P} and i<sub>m</sub>=i. This gives us a D<sub>im+1 </sub>such that D<sub>im</sub>^P<sub>j</sub>=D<sub>im </sub>and D<sub>im+1</sub>^P<sub>j</sub>≠D<sub>im</sub>^P<sub>j</sub>.
If D<sub>im+1 </sub>is contained in D<sub>old</sub>, then the lemma is fulfilled. If instead D<sub>im+i</sub>^P<sub>j </sub>is contained in D<sub>add</sub>, note that D<sub>im</sub>^P<sub>j</sub>=D<sub>im+1 </sub>implies D<sub>im</sub>^P<sub>j</sub>=D<sub>im+1</sub>^P<sub>j</sub>. This means that the lemma is fulfilled. In this way we can repeatedly apply Lemma 3 as long as the new D<sub>im+1 </sub>obtained is not contained in D<sub>old </sub>and D<sub>im+i</sub>^P<sub>j </sub>is not contained in D<sub>add</sub>.
We will now prove that after a finite number of applications of Lemma 3 we obtain a D<sub>im+1 </sub>where D<sub>im+1 </sub>is contained in D<sub>old </sub>or D<sub>im+1</sub>^P<sub>j</sub>. is contained in D<sub>add</sub>. Note that that each application of Lemma 3 guarantees that D<sub>im</sub>^P<sub>j</sub>=D<sub>im+1</sub>^P<sub>j </sub>and D<sub>im+1</sub>^P<sub>j</sub>≈≠D<sub>im</sub>^P<sub>j</sub>. This fact itself implies that there cannot be an infinite number of applications of Lemma 3.
Theorem 2 The output Q from the proposed algorithm is in MNF.
PROOF. From Lemma 1 it follows that Q contains no two conjunctions such that Q<sub>2</sub>=Q<sub>1</sub>. All conjunctions in D<sub>old </sub>are trivially on the form specified by (1). All conjunctions in D<sub>add </sub>are also on the form (1) because of the requirement on D<sub>new</sub>. Thus Q is in MNF.
To illustrate the algorithm according to the invention, consider the following small example where C={p<sub>1</sub>, p<sub>2</sub>, p<sub>3</sub>} and the domain of behavioral modes for each component is R<sub>pi</sub>={NF, G. B, UF}.<FORM>D=D<sub>1</sub>vD<sub>2</sub>=p<sub>1</sub>ε{G, B, UF}vp<sub>3</sub>ε{G, UF}</FORM><FORM>P=P<sub>1</sub>vP<sub>2</sub>=p<sub>2</sub>ε{B, UF}vp<sub>3</sub>ε{G, B, UF}</FORM>
First the condition D<sub>1</sub>≠P is fulfilled, which means that D<sub>1 </sub>is removed from D<sub>old </sub>and the inner loop of the algorithm is entered. There a D<sub>new </sub>is created such that D<sub>new</sub>≅D<sub>1</sub>^P<sub>2</sub>=p<sub>1</sub>ε{G, B, UF}^p<sub>2</sub>ε{B, UF}. This D<sub>new </sub>is then compared to D<sub>2 </sub>in the checking the condition D<sub>new</sub>=D<sub>2</sub>. The condition is not fulfilled, which means that D<sub>new </sub>is added to D<sub>add</sub>. Next a D<sub>new </sub>is created such that D<sub>new</sub>≅D<sub>1</sub>^P<sub>2</sub>=p<sub>1</sub>ε{G, B, UF}^p<sub>3</sub>ε{G, B, UF}. Also this time, the condition D<sub>new</sub>=D<sub>2 </sub>is not fulfilled, implying that D<sub>new </sub>is added to D<sub>add</sub>. Next, the conjunction D<sub>2 </sub>is investigated. However, since D<sub>2</sub>=P holds, D<sub>2 </sub>is not removed from D<sub>old</sub>, and the inner loop is not entered. The algorithm output is finally formed as<FORM>Q:=D<sub>old</sub>vD<sub>add</sub>=D<sub>2</sub>v(D<sub>1</sub>^P<sub>1</sub>vD<sub>1</sub>^P<sub>2</sub>)=p<sub>3</sub>εE {G, UF}vp<sub>1</sub>ε{G, B, UF}^p<sub>2</sub>ε{B, UF}vp<sub>1</sub>ε{G, B, UF}^p<sub>3</sub>ε{G, B, UF}</FORM>
It can be verified that Q≅D^P. Also, it can be seen that Q is in MNF.
We now describe the algorithm with reference to FIG. 1, which shows a block diagram over diagnosis engine 100 for estimating a status of an entity 150 according to one embodiment of the invention. The entity 150, typically represented by a relatively complex system, has a plurality of components c<sub>1</sub>, . . . , c<sub>i</sub>, . . . , c<sub>n</sub>. Each of these components is assumed to either be in a faultfree mode, or be in exactly one of at least one fault mode.
The proposed diagnosis engine 100 includes a processing unit 110 that is adapted to analyze test results P<sup>1</sup>, . . . P<sup>J</sup>, . . . , P<sup>R </sup>produced by a set of diagnostic tests t<sub>1</sub>, . . . , t<sub>x </sub>in respect of the entity 150. Each test result, in turn, is a disjunction of statements P<sup>1</sup><sub>1</sub>v . . . vP<sup>1</sup><sub>x</sub>; . . . ; P<sup>J</sup><sub>1</sub>v . . . vP<sup>J</sup><sub>y</sub>; . . . ; P<sup>R</sup><sub>1</sub>v . . . vP<sup>R</sup><sub>z</sub>, wherein each statement P<sup>J</sup><sub>j </sub>indicates at least one of said modes for one of said components c<sub>1</sub>, . . . , c<sub>n</sub>.
The diagnosis engine 100 also includes at least one storage area adapted to store diagnostic data in respect of the entity 150. FIG. 1 illustrates three separate storage areas 120, 130 and 140. Naturally, in practice, these areas may be represented by different partitions of the same memory module.
The processing unit 110 is adapted to receive an original disjunction of diagnostic expressions D, which indicating at least one of said modes for at least one of said components c<sub>1</sub>, . . . , c<sub>n</sub>. I.e. original disjunction of diagnostic expressions D expresses whether one or more of the components c<sub>1</sub>, . . . , c<sub>n </sub>is faultfree or faulty, and if so, which respective fault mode it has. Additionally, the processing unit 110 is adapted to receive a test result P of a set of diagnostic tests t<sub>1</sub>, . . . , t<sub>x </sub>in respect of the entity 150. These tests are here collectively denoted T.
The processing unit 110 is further adapted to copy the expressions in the original disjunction of diagnostic expressions D to a temporary disjunction of diagnostic expressions D<sub>old </sub>in a first storage area 120.
For each diagnostic expression in the temporary disjunction of diagnostic expressions D<sub>old</sub>, the processing unit 110 is adapted to investigate whether or not a currently investigated diagnostic expression D<sub>i </sub>implies the test result P<sup>J</sup>. If this is found not to be the case, the processing unit 110 is adapted to remove the expression D<sub>i </sub>from the temporary disjunction of diagnostic expressions D<sub>old</sub>. For each statement P<sup>J</sup><sub>j </sub>in the test result, the processing unit 110 is adapted to generate a joint diagnostic expression D<sub>new </sub>representing a conjunction of the statement P<sup>J</sup><sub>j </sub>and the currently investigated diagnostic expression D<sub>i</sub>. Then, the joint diagnostic expression D<sub>new </sub>is compared the with each diagnostic expression in the original disjunction of diagnostic expressions D except for the currently investigated diagnostic expression D<sub>i</sub>.
If an original diagnostic expression D<sub>k </sub>is found, where the joint diagnostic expression D<sub>new </sub>implies the original diagnosis expression D<sub>k</sub>, the processing unit 110 is adapted to discard the joint diagnostic expression D<sub>new</sub>. Otherwise, the processing unit 110 is adapted to add the joint diagnostic expression D<sub>new </sub>to an updated disjunction of diagnostic expressions Q in a second storage area 130.
Subsequently (i.e. after having investigated all diagnostic expression D. in D<sub>old</sub>), the processing unit 110 is adapted to add all remaining diagnostic expressions in the temporary disjunction of diagnostic expressions D<sub>old </sub>to the updated disjunction of diagnostic expressions Q. The updated disjunction of diagnostic expressions Q represents an estimated status of the entity 150, i.e. typically an enhanced version of a status represented by the original disjunction of diagnostic expressions D.
Based on the updated disjunction of diagnostic expressions Q, the processing unit 110 is adapted to produce a status report R[Q], which can be studied by a service technician, an operator of the entity 150, or other personnel being involved in the operation and/or maintenance of the entity 150.
For example, the status report R[Q] may be generated as follows. Suppose that there is a probability associated with each mode of each component, say P(pressure_sensor=NF)=0,999, P(pressure_sensor=B)=0,0006, (pressure_sensor=UF)=0,0004. Let us further assume that the components may malfunction independently of one another. Then, the probability for one mode becomes equal to the product of the individual modes. For instance, for a system having two pressure sensors, we would have P(pressure_sensor_1=NF & pressure_sensor_1=B)=0,999×0,0006. The final diagnostic expression Q (e.g. Q=Q1 vQ2vQ3) obtained after having processed all test results is studied. Here, the most probable diagnoses are stored, which match Q1. Then, if there is another diagnosis matching Q2, which is even more probable, this diagnosis may be stored instead of Q1, and so on. In a system having three pressure sensors we may have the final diagnostic expression Q=Q1vQ2=P1<u style="single">⊂</u>{NF, B} & P2<u style="single">⊂</u>{UF}vP2<u style="single">⊂</u>{UF} & P3<u style="single">⊂</u>{B, UF}. The most probable diagnosis matching Q1 is <NF, UF, NF>, whereas the most probable diagnosis matching Q2 is <NF, NF, B>, which is somewhat more probable than <NF, UF, NF>. Therefore, <NF, NF, B> is stored and <NF, UF, NF> is discarded. Consequently, the status report may be R[Q]={<NF, NF, B>}.
According to one preferred embodiment of the invention, the processing unit 110 is adapted to gradually modify the updated disjunction of diagnostic expressions Q (and preferably also produce an improved status report R[Q]) in response to subsequent test results. To this aim, after having processed a result of a first test t<sub>1 </sub>in the test result P, the processing unit 110 is adapted to, for each result of at least one second test t<sub>x </sub>in the test result P, investigate, for each diagnostic expression in the temporary disjunction of diagnostic expressions D<sub>old</sub>, whether or not a currently investigated diagnostic expression D<sub>i </sub>implies the result of the second test t<sub>x</sub>. Analogous to the above, the processing unit 110 is adapted to remove the expression D<sub>i </sub>from the temporary disjunction of diagnostic expressions D<sub>old </sub>if the currently investigated diagnostic expression D<sub>i </sub>does not imply the result of the second test t<sub>x</sub>.
However, for each statement P<sup>J</sup><sub>j </sub>in the result of the second test t<sub>x </sub>that fulfills this requirement, the processing unit 110 is adapted to generate a joint diagnostic expression D<sub>new </sub>representing a conjunction of the statement P<sup>J</sup><sub>j </sub>and the currently investigated diagnostic expression D<sub>i</sub>. The joint diagnostic expression D<sub>new </sub>is compared with each diagnostic expression in the original disjunction of diagnostic expressions D except for the currently investigated diagnostic expression D<sub>i</sub>, and if an original diagnostic expression D<sub>k </sub>is found, where the joint diagnostic expression D<sub>new </sub>implies the original diagnosis expression D<sub>k</sub>, the joint diagnostic expression D<sub>new </sub>is discarded.
Otherwise, the processing unit 110 is adapted to add the joint diagnostic expression D<sub>new </sub>to an updated disjunction of diagnostic expressions Q in a second storage area 130. Thereafter, the processing unit 110 is adapted to also add any remaining diagnostic expressions in the temporary disjunction of diagnostic expressions D<sub>old </sub>to the updated disjunction of diagnostic expressions Q. Thus, the updated disjunction of diagnostic expressions Q represents an estimated status of the entity 150, whose merits constitutes yet an improvement relative to the previous version of Q. Naturally, the updated disjunction of diagnostic expressions Q may serve as a basis for an updated status report R[Q] produced by the processing unit 110.
Preferably, the diagnosis engine 100 includes, or is associated with, a computer readable medium 160 (e.g. a memory module) having a program recorded thereon, where the program is adapted to make the processing unit 110 control the steps of abovedescribed procedure.
FIG. 2 schematically depicts a motor vehicle 200 being equipped with the proposed diagnosis engine 100. Specifically, the vehicle 200 includes a number of components c<sub>1</sub>, c<sub>2</sub>, . . . , c<sub>n</sub>, . . . c<sub>s </sub>and a diagnosis system, which is adapted to estimate a status of at least a subgroup of its components, say c<sub>1</sub>, . . . , c<sub>n</sub>. The diagnosis engine 100, in turn, is included in the diagnosis system. Preferably, the diagnosis engine 100 is implemented in an ECU (electronic control unit) and test results in respect of one or more of the components in said subgroup c<sub>1</sub>, . . . , c<sub>n </sub>may be delivered to the diagnosis engine 100 via a data bus 210, e.g. adapted to the CAN format (CAN=Controller Area Network). However, the data bus 210 may equally well be adapted to any other standard, such as Time Triggered CAN (TTCAN), FlexRay, Media Oriented System Transport (MOST) or ByteFlight. These standards all represent efficient means of accomplishing networks in trucks, busses and other motor vehicles. By interconnecting various control units of a vehicle via a network, a very large number of vehicle functions may be accomplished based on relatively few ECUs. Namely, by combining resources from two or more ECUs a flexible and cost efficient overall vehicular design is obtained.
The test results may equally well be generated in an ECU being common to an ECU in which the proposed diagnosis engine is implemented. Naturally, in such a case, the test results do not need to be sent via an external data bus.
In order to sum up, the general method of diagnosing an entity including a plurality of components according to the invention will be described below with reference to the flow diagram in FIG. 3.
A first step 310 receives an original disjunction of diagnostic expressions, which for at least one of said components indicate a respective mode that reflects whether the component is faultfree, or has exactly one of at least one fault. A step 315, which may be parallel to, subsequent to or preceding the step 310, receives a test result in respect of the entity. The test result is a disjunction of statements, wherein each statement indicates at least one of said faultfree or fault modes for one of the entity's components.
A step 320 being subsequent to the step 310 copies the expressions in the original disjunction of diagnostic expressions to a temporary disjunction of diagnostic expressions in a first storage area.
Then, a step 325 selects a not yet tested diagnostic expression in a first storage area, where after a step 330 investigates whether or not a currently investigated diagnostic expression implies the test result. If this is found not to be the case, a step 335 follows. Otherwise, the procedure continues to a step 370.
The step 335 removes the stored diagnostic expression from the first storage area. Thereafter, a step 340 selects a not yet tested statement in the test result. Subsequently, a step 345 generates a joint diagnostic expression representing a conjunction of the selected test result statement and the currently investigated diagnostic expression from the first storage area. Then, a step 350 compares the joint diagnostic expression with each diagnostic expression in the original disjunction of diagnostic expressions except for the currently investigated diagnostic expression. If an original diagnostic expression is found, where the joint diagnostic expression implies the original diagnosis expression, a step 355 follows. Otherwise, the procedure continues to a step 360, which adds the joint diagnostic expression to an updated disjunction of diagnostic expressions in a second storage area. The updated disjunction of diagnostic expressions represents an estimated status of the entity. After the step 350, the procedure continues to a step 365.
The step 355 discards the joint diagnostic expression from the first storage area, and then the step 365 follows. This step checks whether all statements in the test result have been tested, and if so, a step 370 follows. Otherwise, the procedure loops back to the step 340. The step 370 checks whether all diagnostic expressions in the first storage area have been tested, and if so, a step 375 follows. Otherwise, the procedure loops back to the step 325.
The step 375 adds any remaining diagnostic expressions in the temporary disjunction of diagnostic expressions to the updated disjunction of diagnostic expressions in the second storage area. Thereafter, a step 380 produces a status report based on said updated disjunction of diagnostic expressions. Finally, the procedure may either end, or it may loop back to the step 310 and/or 315 for reception of further diagnostic expressions or test results respectively.
After the step 380, the procedure may either end, or loop back to the steps 310/315 for reception of any new diagnostic expressions or test results respectively.
All of the process steps, as well as any subsequence of steps, described with reference to the FIG. 3 above may be controlled by means of a programmed computer apparatus. Moreover, although the embodiments of the invention described above with reference to the drawings comprise computer apparatus and processes performed in computer apparatus, the invention thus also extends to computer programs, particularly computer programs on or in a carrier, adapted for putting the invention into practice. The program may be in the form of source code; object code, a code intermediate source and object code such as in partially compiled form, or in any other form suitable for use in the implementation of the process according to the invention. The carrier may be any entity or device capable of carrying the program. For example, the carrier may comprise a storage medium, such as a Flash memory, a ROM (Read Only Memory), for example a CD (Compact Disc) or a semiconductor ROM, an EPROM (Erasable Programmable ReadOnly Memory), an EEPROM (Electrically Erasable Programmable ReadOnly Memory), or a magnetic recording medium, for example a floppy disc or hard disc. Further, the carrier may be a transmissible carrier such as an electrical or optical signal, which may be conveyed via electrical or optical cable or by radio or by other means. When the program is embodied in a signal, which may be conveyed, directly by a cable or other device or means, the carrier may be constituted by such cable or device or means. Alternatively, the carrier may be an integrated circuit in which the program is embedded, the integrated circuit being adapted for performing, or for use in the performance of, the relevant processes.
The invention is not restricted to the described embodiments in the figures, but may be varied freely within the scope of the claims.