Leakage current and process variations are two primary hurdles in modern VLSI design. It depends exponentially on process and environmental parameters and hence small variations in these result in a large spread in leakage current of manufactured dies. Traditionally, Exponential Quadratic(EQ) models have been used to model leakage current as a function of process parameters which can model limited non-linearity and hence become inaccurate for large process variations. Artificial Neural Networks (ANN) have shown great promise in modeling circuit parameters for CAD applications. We model leakage with ANN models which perform better than the EQ models for increased process variations. However, the complex nature of the ANN model, with the standard sigmoidal activation functions, does not allow analytical expressions for its mean and variance for the case of Gaussian process variations. We propose the use of a new activation function that allows us to derive an analytical expression for the mean and a semi-analytical expression for the variance of the ANN based leakage model. To the best of our knowledge this is the first result in this direction. All existing SLA frameworks are closely tied to the EQ leakage model and hence fail to work with sophisticated ANN models. We therefore set up an SLA framework that can efficiently work with these ANN models. Results show that the CDF of leakage current of ISCAS'85 circuits can be predicted accurately with the error in mean and standard deviation, compared to Monte Carlo based simulations, being less than 1\% and 2\% respectively across a range of voltage and temperature values. The complexity of our framework is similar to existing SLA frameworks yet more accurate over a larger range of variations. Ignoring the thermal profile of the chip leads to a gross error of nearly 50\% in the prediction of leakage yield. Our neural network model also includes the voltage and temperature as input parameters, thereby enabling voltage and temperature aware statistical leakage analysis (SLA). Similarly leakage CDF can be predicted across a range of supply and body voltages since they are both part of the model. Our framework used analytical techniques to account for local variations and Monte Carlo techniques for global variations and hence it can also be used for Non-Gaussian global variations.

Die vorliegende Dissertation hat die Bewertung und Modellierung der Exfiltration undichter Abwasserkanäle zum Thema. Verschiedene Methoden zur Bestimmung der Exfiltration werden ausführlich beschrieben. Es wurden Tracermethoden ausgewählt, in 5 Teileinzugsgebieten von Berlin und Dresden eingesetzt und bezüglich ihrer Anwendbarkeit in kommunalen Kanalnetzen bewertet. Tracermethoden ermitteln die Exfiltration mit einer Tracermassenbilanz über eine definierte Kanalstrecke. Ausgehend von diesen Messungen wurden Anforderungen an das Messen im Kanal und die Anwendung von Tracermassenbilanzen zur Bestimmung der Exfiltration formuliert. Ein anderer Schwerpunkt umfasst die Modellierung der Exfiltration mit der Identifizierung von Variablen, die Undichtigkeiten bzw. ungenügenden Kanalzustand signifikant beeinflussen sowie die Abbildung dieser Variablen in einem Model. Es wird die Verwendung eines auf dem Gesetz von Darcy basierenden Models vorgeschlagen. Darüber hinaus wurden Regressionsmodelle getestet und Signifikanztests durchgeführt. Die Dissertation schließt mit einer Diskussion über das Gefährdungspotential der Exfiltration von Abwasser aus undichten Kanälen insbesondere für Boden und Grundwasser. / The main goal of this dissertation is a comprehensive evaluation of exfiltration from leaky sewer pipes. Therefore, several methods for determining exfiltration are thoroughly described and two approaches are considered for extensive real sewer network testing in order to evaluate their application potential. These two methods estimate sewage loss by a tracer mass balance over a certain sewer distance. Exfiltration rates were estimated in 26 pipes located in 5 homogeneous subcatchments in Berlin and Dresden. Consequently analysing the experiences gained during the conducted measuring campaign, requirements on measurements in sewers in general and experimental design of the tracer tests in particular are discussed. A second focus was on modelling of sewer leakage and sewer deterioration. Variables which have significant effects on sewer leakage and deterioration have been identified according to the literature review and available data. Modelling approaches were proposed on the basis of (i) Darcy’s law and (ii) regression models for both data on sewer leakage derived from literature/tracer tests conducted within this work and data on sewer deterioration for the Dresden sewerage system. The dissertation concludes with a discussion on the relevance of sewer exfiltration, in particular its pollution potential for the environment is evaluated.