Actuation of a technical system based on solutions of relaxed abduction

• US 9,449,275 B2
• Filed: 07/02/2012
• Issued: 09/20/2016
• Est. Priority Date: 07/12/2011
• Status: Active Grant

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Hubauer, Thomas, Lamparter, Steffen
• Primary Examiner(s): Chang, Li-Wu
• Application Number:
  US14/232,315
• Publication Number:
  US 20140149337A1
• Time in Patent Office: 1,541 Days
• Field of Search: None
• US Class Current: 1/1
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G05B 23/0221 Preprocessing measurements, e.g. data collection rate adjustment; Standardization of measurements; Time series or signal analysis, e.g. frequency analysis or wavelets; Trustworthiness of measurements; Indexes therefor; Measurements using easily measured parameters to estimate parameters difficult to measure; Virtual sensor creation; De-noising; Sensor fusion; Unconventional preprocessing inherently present in specific fault detection methods like PCA-based methods
• CPC Class Codes: G05B 23/0278 Qualitative, e.g. if-then rules; Fuzzy logic; Lookup tables; Symptomatic search; FMEA
• CPC Class Codes: G06F 11/004 Error avoidance G06F11/07 and subgroups take precedence
• CPC Class Codes: G06F 17/00 Digital computing or data processing equipment or methods, specially adapted for specific functions information retrieval, database structures or file system structures therefor G06F16/00
• CPC Class Codes: G06N 5/02 Knowledge representation; Symbolic representation

Abstract

To enable efficient abduction even for observations that are faulty or inadequately modeled, a relaxed abduction problem is proposed in order to explain the largest possible part of the observations with as few assumptions as possible. On the basis of two preference orders over a subset of observations and a subset of assumptions, tuples can therefore be determined such that the theory, together with the subset of assumptions, explains the subset of observations. The formulation as a multi-criteria optimization problem eliminates the need to offset assumptions made and explained observations against one another. Due to the technical soundness of the approach, specific properties of the set of results (such as correctness, completeness etc.), can be checked, which is particularly advantageous in safety-critical applications. The complexity of the problem-solving process can be influenced and therefore flexibly adapted in terms of domain requirements through the selection of the underlying representation language and preference relations. The invention can be applied to any technical system, e.g. plants or power stations.

Claims

1. A method of actuating a technical system, the method comprising:

receiving at least one observation from at least one sensor;

determining, by a computer which is configured to execute program code stored on a non-transitory computer-readable medium, a relaxed abduction problem;

solving, by the computer, the relaxed abduction problem, by determining tuples that are optimal with respect to two preference orders over subsets of assumptions and observations, wherein the determined optimal tuples comprise a subset of observations smaller than a complete set of observations, respectively, that concurrently minimize the subset of assumptions to explain the observations comprising the at least one observation received from the at least one sensor and maximize the subset of observations abductively explained by the subset of assumptions given a theory T, with the objective of determining a causal consequence of the largest possible portion of observations with as few assumptions as possible; and

actuating the technical system according to the solution of the relaxed abduction problem by communicating at least one actuator signal.

2. The method as claimed in claim 1, in which the relaxed abduction problem is determined to be RAP=(T,A,O,∘

_A,∘

_O),

wherein;

a set of abducible axioms is A,

a set of observations is O

with

T′

/O; and

further comprising taking orders of preference

∘

_A⊂

P(A)×

P(A) and

∘

_O⊂

P(O)×

P(O)

as a basis for determining ∘

-minimal tuples (A,O)ε

P(A)×

P(O),

so that T∪

A is consistent and T∪

A′

O holds.

3. The method as claimed in claim 1, wherein the relaxed abduction problem is solved by transforming the relaxed abduction problem into a hypergraph, so that the tuples (A,O) are encoded by pareto-optimal paths in the hypergraph.

4. The method as claimed in claim 3, wherein the pareto-optimal paths are determined via a label approach.

5. The method as claimed in claim 3, further comprising inducing hyperedges of the hypergraph by transcriptions of prescribed rules.

6. The method as claimed in claim 5, wherein the prescribed rules are determined as follows:

7. The method as claimed in claim 3, wherein a weighted hypergraph H_RAP=(V,E) which is induced by the relaxed abduction problem, is determined by

V={(Aô

B),(A∃

r.B)|A,Bε

N_C^T,rε

N_R},

wherein

V_T={(Aô

A),(Aô

T)|Aε

N_C¹}⊂

V

denotes a set of final states and E denotes a set of the hyperedges

e=(T(e),h(e),w(e)),

so that the following holds;

an axiom aε

T∪

A exists that justifies derivation h(e)ε

V from T(e)⊂

V based on one of the prescribed rules,

wherein the edge weight w(e) is determined according to

8. The method as claimed in claim 7, wherein p_X,t=(V_X,t,E_X,t) is determined as a hyperpath in H=(V,E) from X to t if

(1) tε

X and p_X,t=({t},0) or

(2) there is an edge eε

E, so that h(e)=t,T(e)=(y₁, . . . , y_k) holds.

9. The method as claimed in claim 8, wherein shortest hyperpaths are determined by taking account of two preferences.

10. The method as claimed in claim 9, wherein the shortest hyperpaths are determined by taking account of the two preferences via a label correction algorithm.

11. The method as claimed in claim 10, wherein the labels encode pareto-optimal paths to the hitherto found nodes of the hypergraph.

12. The method as claimed in claim 11, wherein alterations along the hyperedges are propagated by a meet operator and/or by a join operator.

13. The method as claimed in claim 1, wherein the relaxed abduction problem is determined via a piece of description logic.

14. A computer system for actuating a technical system, comprising:

a processor configured to automatically execute program code stored on a non-transitory computer-readable medium, to;

control receipt of at least one observation from at least one sensor;

determine a relaxed abduction problem;

solve the relaxed abduction problem by determining tuples that are optimal with respect to two preference orders over subsets of assumptions and observations, wherein the determined optimal tuples comprise a subset of observations smaller than a complete set of observations, respectively, that concurrently minimize the subset of assumptions to explain the observations comprising the at least one observation received from the at least one sensor and maximize the subset of observations abductively explained by the subset of assumptions given a theory T, with the objective of determining a causal consequence of the largest possible portion of observations with as few assumptions as possible; and

an actuator output port configured to actuate the technical system according to the solution of the relaxed abduction problem.

15. The computer as claimed in claim 14, in which the relaxed abduction problem is determined to be:

RAP=(T,A,O,∘

_A,∘

_O),

wherein;

a set of abducible axioms is A,

a set of observations is O

with T′

/O; and

further comprising taking orders of preference

∘

_A⊂

P(A)×

P(A) and

∘

_O⊂

P(O)×

P(O)

as a basis for determining ∘

-minimal tuples (A,O)ε

P(A)×

P(O),

so that T∪

A is consistent and T∪

A′

O holds.

16. The computer as claimed in claim 14, wherein the processor is configured to solve the relaxed abduction problem by transforming the relaxed abduction problem into a hypergraph, so that the tuples (A,O) are encoded by pareto-optimal paths in the hypergraph.

17. The computer as claimed in claim 16, wherein the processor is further configured to automatically induce hyperedges of the hypergraph by transcriptions of prescribed rules determined as follows:

18. The computer as claimed in claim 16, wherein the processor is further configured to determine a weighted hypergraph H_RAP=(V,E) induced by the relaxed abduction problem:

V={(Aô

B),(A,∃

r.B)|A,Bε

N_C^T,rε

N_R},

wherein;

V_T={(Aô

A), (Aô

T)|Aε

N_C¹}⊂

V denotes a set of final states, and

E denotes a set of the hyperedges e=(T(e),h(e),w(e)),

so that the following holds;

an axiom aε

T∪

A exists that justifies derivation h(e)ε

V from T(e)⊂

V based on one of the prescribed rules,

wherein the edge weight w(e) is determined according to

19. A method of controlling a technical system, comprising:

receiving at least one observation from at least one sensor;

determining a relaxed abduction problem;

determining a pareto-optimum set of tuples (A,O) by taking as a basis two orders of preference over a subset of observations (O) smaller than a complete set of observations, and a subset of assumptions (A), so that a theory (T) together with a minimized subset of the assumptions (A) explains a maximized subset of the observations (O) comprising the at least one observation (O) received from the at least one sensor, with the objective of determining a causal consequence of the largest possible portion of subset of observations (O) with as few members of the subset of assumptions (A) as possible;

defining a solution to the determined relaxed abduction problem, by an automated computer which executes program code stored on a non-transitory computer-readable medium; and

actuating the technical system in accordance with the defined solution.

20. The method according to claim 19, further comprising transforming the relaxed abduction problem into a hypergraph, so that the tuples (A,O) are encoded by pareto-optimal paths in the hypergraph.