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Figure 2.16 RF network comprising an RF pad, and a tuning inductor of an RF circuit, with an ESD element represented as a shunt capacitor element and shunt resistor element

1 2 3

10

Preparation of this chapter was supported in part by grants from the National Institute of Mental Health (MH55469) and by the Medical Research Council of Canada (MT-14039).

P(Y = y) =

Fuzzy rule-based models are a highly modular and easily expandable form of fuzzy models They support the principle of locality and the distributed nature of modeling as each rule can be viewed as a local descriptor of a system regime [25] Fuzzy rule-based models effectively combine and interpolate different operating regimes to describe general behavior [15] One of the major dif culties in developing rule-based models is the proper, adequate, and expedient generation of their structure, especially the rule base, rule semantics, membership functions, and parameters A trend until the early 1990s was to rely on existing expert knowledge and to tune fuzzy membership function parameters using gradient-based methods or genetic algorithms (GAs) using problem-speci c data [1] During the late 1990s, data-driven rule/ knowledge extraction methods were intensively investigated and developed [5, 13, 14].

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Data-driven methods attempt to identify model structure and model parameters based on data and uses expert knowledge as complementary information The main techniques used during this period include clustering, linear least squares, and nonlinear optimization to ne tune rule antecedent and consequent membership function parameters [13, 14] As the modeling complexity increases, however, the information required to develop fuzzy rule bases may not be easily available and experts may be unable to extract all relevant knowledge Genetic fuzzy systems appeared during the past few years as one of the few techniques capable of developing complex fuzzy system models [24] Genetic fuzzy systems constitute a powerful approach to the design of fuzzy models Basically, these are fuzzy systems augmented by learning mechanisms based on genetic algorithms Essentially, genetic fuzzy systems approaches use evolutionary techniques to adjust the components of fuzzy models.

Gallium arsenide (GaAs) technology has been pervasive in semiconductor technology where power, speed, and reliability are necessary [1 4]. GaAs has advantages over other competing technologies, such as RF CMOS and RF silicon germanium because of its performance [5 8]. In recent times, GaAs technology has been dominating telecommunications, optical interconnect systems, cell phones, as well as space and military applications in the sectors where performance is needed [6 9]. Because reliability is important in these applications, electrostatic discharge (ESD) has been an issue since the early usage of GaAs semiconductor products [9 39]. Additionally, gallium-based and indium-based technologies [40 42] also have growing interest in the area of reliability and ESD protection [40 50]. Presently, the ESD protection is being pursued from on-chip ESD power clamps [50,51], on-chip spark gaps and eld emission devices (FEDs) [35], separate GaAs ESD chips [9] to off-chip protection surge protection devices [52,53].

Evaluation of complete solutions is one of the features of traditional evolutionary approaches In contrast with evolutionary approaches, incremental or growing algorithms developed local models using heuristic search for rule antecedents and corresponding rule consequents optimized by local weighted least-squares technique [11, 23] Fuzzy neural networks with evolving structures have been developed as an alternative to fuzzy rule-based modeling [22] This modeling approach constitutes evolving connectionist systems whose structure and functionality are continuously adapted using incoming information [17] They adopt different mechanisms for network updating, but basically parameter learning and self-organization are based on clustering and error of previous steps Evolving connectionist systems learn local models from data using clustering and a local output function for each cluster [6] The concept of evolving fuzzy systems introduced the idea of gradual self-organization and parameter learning in fuzzy rule-based models [2].

Evolving fuzzy systems uses information streams to continuously adapt the structure and functionality of fuzzy rule-based models The basic learning mechanisms rely on online clustering and parameter estimation using least squares algorithms Online clustering is based on the idea of data potential or data density The evolving mechanism ensures greater generality of the structural changes because rules are able to describe a number of data samples Evolving fuzzy rule-based models include mechanisms for rule modi cation to replace a less informative rule with a more informative one [2] Overall, evolution guarantees.

16.6.3.2 16.6.4

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