An unconditionally sound algorithm for testability analysis in linear time-invariant electrical networks

• Published in: International journal of circuit theory and applications Vol. 44; no. 6; pp. 1308 - 1340
• Main Authors: Fontana, G., Luchetta, A., Manetti, S., Piccirilli, M. C.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.06.2016; Wiley Subscription Services, Inc
• Subjects: Algorithms; analog system testing; circuit theory; Complexity; Computation; Computer programs; Electric networks; electrical networks; parametric fault detection; Robustness; Roundoff error; symbolic analysis; Testability; testability analysis
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.2164

Summary The issue of testability, intended as a measure of solvability of the parametric fault diagnosis problem in analog linear time‐invariant electrical networks, is addressed in this paper. Independently of the considered fault location method, such important metric provides information as to how many and which components can be diagnosed. For the reader's convenience and to set up an appropriate framework for our main achievements, our first concern is to rederive fundamental results concerning analog linear time‐invariant electrical network testability hinging on multifrequency measurements. Then a novel algorithm for testability analysis is proposed, which is straightforward and able to circumvent the main drawbacks of formerly proposed methods, such as computational and conceptual complexities, proneness to roundoff errors, and vulnerability to particular cases. A computer program that implements such algorithm is also described. Moreover, the possibility of employing further simplified versions of the latter and their links with a previously proposed approach are discussed on rigorous bases. Finally, examples are provided, which show the effectiveness and robustness of the new algorithms, also by means of a comparison with the old ones. Copyright © 2015 John Wiley & Sons, Ltd. A novel approach to testability analysis in analog linear time‐invariant electrical networks is proposed. It is quite straightforward, both conceptually and computationally, and capable to circumvent the main shortcomings of formerly proposed methods, such as calculation complexities, roundoff errors, and failures in the presence of degeneracy. A computer program that implements the approach in questions is described as well. Moreover, further simplified versions are discussed and compared with previous approaches. Thoroughly discussed examples of application are also given.