Then we create the rule for element Ek: Figure 3: Gamma type membership function for "high". Premises. Conclusions measurement. SJk>O. SkO. VI is.
Analog Fault AC Dictionary Creation - The Fuzzy Set Approach Damian Grzechca, Tomasz Golonek, Jerzy Rutkowski Institute of Electronics Silesian University of Technology Gliwice, Poland e-mail: Damian.Grzechcagpolsl.pl
Abstract-This paper discusses the basic concept of analog functional test approach. Recently, most on going research has been focused on distinguishing faulty or healthy circuit - from the manufacturer's point of view, this is more important than locating particular faulty element. The article shows the concept of fuzzy theory approach to functional test creation. To find and locate faulty circuit (system) the sensitivity matrix can be used. It has been observed that for most practical circuits the sensitivity matrix is sparse. This observation has been utilized in the fuzzy expert system and the system modification based on the reduction of the sensitivity matrix size has been proposed. The modified system can effectively decide whether the system is faulty or healthy. The results obtained and presented here are promising and tend to prove that the proposed strategy can improve fault detection on a production line.
I. INTRODUCTION Two different approaches to analogue circuit testing can be distinguished: specification driven testing and component fault driven testing. In the advance of integrated circuit (IC) technology, access to internal nodes is limited and specification driven testing seems to be the most practical. Nevertheless, diagnosing component failures is still important. Many circuits are still designed with discrete components, and failures on the board should be quickly corrected. Moreover, integrated circuits must be characterized before production runs. This involves determining any systematic sources of yield loss, including components whose performances may fluctuate significantly due to the variations in manufacturing [1]. For fault driven testing two different techniques are possible: Simulation Before Test (SBT) and Simulation After Test (SAT). In the simulation-before-test (SBT) approach a fault dictionary is constructed, i.e. the circuit is simulated for hypothesized faulty cases and signatures are stored. At the time of testing the signatures obtained are compared with those stored and a final decision is taken. Classical SBT techniques, based on mathematical methods (pattern
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recognition techniques), have been known for almost 20 years, however their practical utilization is of no great importance [1]. Limitation to catastrophic faults and fault masking by design tolerances are among the main problems faced by the SBT approach. The fuzzy rule system discussed here is the first attempt to solve these problems by means of the fuzzy sets.
In the following sections we briefly describe how to create a fuzzy expert system taking into account the sparsity of the sensitivity matrix, such that the location of hard and even parametric faults is possible. 1.
Fuzzy ANALOGFAULTDiCTIONARY
The process of creating fuzzy fault dictionary is well described in [2]. From now let us call it standard fuzzy dictionary (SFD). To create SFD it is necessary to calculate voltage sensitivity matrix at the beginning (with respect to all parameters and frequency). Depending on a possible number of faults in the circuit under test (CUT) fuzzy sets and rules are created as shown in fig. 1-3. Three fuzzy sets and their corresponding three basic shapes are chosen. At first, it has been determined frequencies FQ for the maximum voltage deviation with respect to all elements.
5744
g(VAit 0.5-
I_._\_V_
/
Vvan Figure 1: Triangle membership function for "normal" j
AO'(V)
measurement.
0.5-
vj
/
Vj
Figure 2: Reversed-gamma type membership function for "low" measurement.
ISCAS 2006
'/(VJA
Then, the rules have to be constructed. Rules depend on sensitivity matrix sign. Let us assume that we have a following row in sensitivity matrix:
the
0.5L-
o SikO v|Slt
X
Vill
Then we create the rule for element Ek: Premises Conclusions SkO SJk>O 4 Ek is "low"-er j is VI is Vj is IF "low" then nominal "low" "high" V is Vjjis i Ekis"high"-er VI is then nominal "low" ."high" "'high",
i
Figure 3: Gamma type membership function for "high" measurement
The FQ vector includes maximum frequency for each
measurement:
FQ = [fq VI , fq VI
2
...
fq vJ]
r
2
'/The
____St_o_
algorithm presented above is changed if the sensitivity matrix is sparse. Crisp membership functions instead of fuzzy ones are chosen.
(1)
If the frequencies are determined, the following calculation must be performed. For each measurement, boundary values can be calculated as:
III.
ALGORITHM OF ANALOG FAULT DETECTION
The following issues have been assumed: 1. 500 tolerance of fault free elements with normal distribution. It leads to linear sensitivity function. K where: AV = E ~SkAEk and SIk = (avj /aEk )n is the 2. Only one fault can exist at a time i.e. algorithm is k=1 terminated after locating the first fault. . first order sensitivity of measurement Vj with respect to 3. Parametric faults have a uniform distribution within deviation of parameter AEk, k=l,...,K calculated at the selected regions. nominal point. Generally, E is the impedance of capacitor or inductor. It also can be resistance. 4. Sensitivity functions are linear (1st order approximation) within a range given by design tolerance of 500. / To determinethe boundary value V or Vh V, first we 5. yFor . . J. given measurements V=[V1,..., VK] and tested have to find the minimum acceptable partial deviation: parameters E=[E,,...,En] elements of the sensitivity matrix, Sjk; k=l,..,K, j=l,..,J, as well as the nominal V,'7n =minl SIk AEk}> 0 j1=1,...,................... ,(3)J measurements Vn have been calculated. V =EV-AL§ andLV+ =En+AI\V,
(2)
.
Many circuits have a sparse sensitivity matrix or some sensitivity values are by one or more orders smaller than the others. If in column of the matrix a ratio of
The total maximum deviation caused by all fault free elements, is equal to:
sensitivity any the sum of the smallest sensitivities to the maximum one is I smaller than a given coefficient (e.g. 1%), then (4) corresponding entries can be treated as zeros. The coefficient AV1 = SjkAEk k=1 must be chosen very carefully because it can cause empty rows. Moreover, some of elements are passed over due to Thus, the maximum value of "low" measurement, due to small influence on corresponding voltage. The equation is a single fault iS given as: presented below:
VJ
Vn
+/AVJ'-/VJ V+A-2AV¶n
M
(5)
,sSJ ax
The boundary (minimum) value of "high" measurement
where sma = max
