Simbolic function approaches for analogue fault diagnosis

In analogue circuits or in the analogue part of mixed digital–analogue systems, fault diagnosis is a very complex task due to the lack of simple fault models and the presence of component tolerances and circuit non-linearities. For these reasons, the automation level of fault diagnosis procedures in the analogue field has not yet achieved the development level achieved in the digital field, in which well-consolidated techniques for automated test and fault diagnosis are commonly used. Analogue fault diagnosis procedures are usually classified into two categories: the simulation-after-test approach (SAT) and the simulation-before-test approach (SBT). The techniques presented in this chapter are of the SAT type and are devoted to parametric (soft) faults, that is, it is assumed that all faults are expressed as parameter variations, without influencing the circuit topology. In this class of problems, the use of the symbolic approach can be very useful to develop efficient testing methodologies and design for testability tools. The chapter is organized as follows: in Section 2.2, a brief review on symbolic analysis is reported. Section 2.3 is dedicated to symbolic procedures for testability analysis, that is, testability evaluation and ambiguity group determination. In Section 2.4 fault diagnosis procedures based on the use of symbolic techniques are reported. Both Sections 2.3 and 2.4 refer to analogue linear or linearized circuits. This is not a big restriction, because, the analogue part of modern complex systems is almost all linear, while the non-linear functions are moved toward the digital part. However, in Section 2.5 a brief description of a possible use of symbolic methods for testability analysis and fault diagnosis of non-linear analogue circuits is reported.