Frequency- and time-domain stochastic analysis of lossy and dispersive interconnects in a SPICE-like environment

This paper presents an improvement of the state-of-the-art polynomial chaos (PC) modeling of high-speed interconnects with parameter uncertainties via SPICE-like tools. While the previous model, due to its mathematical formulation, was limited to lossless lines, the introduction of modified classes of polynomials yields a formulation that allows to account for lossess and dispersion as well. Thanks to this, the new implementation can also take full advantage of the combination of the PC technique with macromodels that accurately describe the interconnect properties. An application example, i.e. the stochastic analysis of an on-chip line, validates and demonstrates the improved method

Sample-path solutions for simulation optimization problems and stochastic variational inequalities

inequality;simulation;optimization

Seismic Risk Analysis of Revenue Losses, Gross Regional Product and transportation systems.

Natural threats like earthquakes, hurricanes or tsunamis have shown seri- ous impacts on communities. In the past, major earthquakes in the United States like Loma Prieta 1989, Northridge 1994, or recent events in Italy like L’Aquila 2009 or Emilia 2012 earthquake emphasized the importance of pre- paredness and awareness to reduce social impacts. Earthquakes impacted businesses and dramatically reduced the gross regional product. Seismic Hazard is traditionally assessed using Probabilistic Seismic Hazard Anal- ysis (PSHA). PSHA well represents the hazard at a specific location, but it’s unsatisfactory for spatially distributed systems. Scenario earthquakes overcome the problem representing the actual distribution of shaking over a spatially distributed system. The performance of distributed productive systems during the recovery process needs to be explored. Scenario earthquakes have been used to assess the risk in bridge networks and the social losses in terms of gross regional product reduction. The proposed method for scenario earthquakes has been applied to a real case study: Treviso, a city in the North East of Italy. The proposed method for scenario earthquakes requires three models: one representation of the sources (Italian Seismogenic Zonation 9), one attenuation relationship (Sa- betta and Pugliese 1996) and a model of the occurrence rate of magnitudes (Gutenberg Richter). A methodology has been proposed to reduce thou- sands of scenarios to a subset consistent with the hazard at each location. Earthquake scenarios, along with Mote Carlo method, have been used to simulate business damage. The response of business facilities to earthquake has been obtained from fragility curves for precast industrial building. Fur- thermore, from business damage the reduction of productivity has been simulated using economic data from the National statistical service and a proposed piecewise “loss of functionality model”. To simulate the economic process in the time domain, an innovative businesses recovery function has been proposed. The proposed method has been applied to generate scenarios earthquakes at the location of bridges and business areas. The proposed selection method- ology has been applied to reduce 8000 scenarios to a subset of 60. Subse- quently, these scenario earthquakes have been used to calculate three system performance parameters: the risk in transportation networks, the risk in terms of business damage and the losses of gross regional product. A novel model for business recovery process has been tested. The proposed model has been used to represent the business recovery process and simulate the effects of government aids allocated for reconstruction. The proposed method has efficiently modeled the seismic hazard using scenario earthquakes. The scenario earthquakes presented have been used to assess possible consequences of earthquakes in seismic prone zones and to increase the preparedness. Scenario earthquakes have been used to sim- ulate the effects to economy of the impacted area; a significant Gross Regional Product reduction has been shown, up to 77% with an earthquake with 0.0003 probability of occurrence. The results showed that limited funds available after the disaster can be distributed in a more efficient way

Adaptive Transmission Planning: Implementing a New Paradigm for Managing Economic Risks in Grid Expansion

The problem of whether, where, when, and what types of transmission facilities to build in terms of minimizing costs and maximizing net economic benefits has been a challenge for the power industry from the beginning-ever since Thomas Edison debated whether to create longer dc distribution lines (with their high losses) or build new power stations in expanding his urban markets. Today?s planning decisions are far more complex, as grids cover the continent and new transmission, generation, and demand-side technologies emerge

Response statistics and failure probability determination of nonlinear stochastic structural dynamical systems

Novel approximation techniques are proposed for the analysis and evaluation of nonlinear dynamical systems in the field of stochastic dynamics. Efficient determination of response statistics and reliability estimates for nonlinear systems remains challenging, especially those with singular matrices or endowed with fractional derivative elements. This thesis addresses the challenges of three main topics. The first topic relates to the determination of response statistics of multi-degree-of-freedom nonlinear systems with singular matrices subject to combined deterministic and stochastic excitations. Notably, singular matrices can appear in the governing equations of motion of engineering systems for various reasons, such as due to a redundant coordinates modeling or due to modeling with additional constraint equations. Moreover, it is common for nonlinear systems to experience both stochastic and deterministic excitations simultaneously. In this context, first, a novel solution framework is developed for determining the response of such systems subject to combined deterministic and stochastic excitation of the stationary kind. This is achieved by using the harmonic balance method and the generalized statistical linearization method. An over-determined system of equations is generated and solved by resorting to generalized matrix inverse theory. Subsequently, the developed framework is appropriately extended to systems subject to a mixture of deterministic and stochastic excitations of the non-stationary kind. The generalized statistical linearization method is used to handle the nonlinear subsystem subject to non-stationary stochastic excitation, which, in conjunction with a state space formulation, forms a matrix differential equation governing the stochastic response. Then, the developed equations are solved by numerical methods. The accuracy for the proposed techniques has been demonstrated by considering nonlinear structural systems with redundant coordinates modeling, as well as a piezoelectric vibration energy harvesting device have been employed in the relevant application part. The second topic relates to code-compliant stochastic dynamic analysis of nonlinear structural systems with fractional derivative elements. First, a novel approximation method is proposed to efficiently determine the peak response of nonlinear structural systems with fractional derivative elements subject to excitation compatible with a given seismic design spectrum. The proposed methods involve deriving an excitation evolutionary power spectrum that matches the design spectrum in a stochastic sense. The peak response is approximated by utilizing equivalent linear elements, in conjunction with code-compliant design spectra, hopefully rendering it favorable to engineers of practice. Nonlinear structural systems endowed with fractional derivative terms in the governing equations of motion have been considered. A particular attribute pertains to utilizing localized time-dependent equivalent linear elements, which is superior to classical approaches utilizing standard time-invariant statistical linearization method. Then, the approximation method is extended to perform stochastic incremental dynamical analysis for nonlinear structural systems with fractional derivative elements exposed to stochastic excitations aligned with contemporary aseismic codes. The proposed method is achieved by resorting to the combination of stochastic averaging and statistical linearization methods, resulting in an efficient and comprehensive way to obtain the response displacement probability density function. A stochastic incremental dynamical analysis surface is generated instead of the traditional curves, leading to a reliable higher order statistics of the system response. Lastly, the problem of the first excursion probability of nonlinear dynamic systems subject to imprecisely defined stochastic Gaussian loads is considered. This involves solving a nested double-loop problem, generally intractable without resorting to surrogate modeling schemes. To overcome these challenges, this thesis first proposes a generalized operator norm framework based on statistical linearization method. Its efficiency is achieved by breaking the double loop and determining the values of the epistemic uncertain parameters that produce bounds on the probability of failure a priori. The proposed framework can significantly reduce the computational burden and provide a reliable estimate of the probability of failure

Risk Hedging Strategies under Energy System and Climate Policy Uncertainties

The future development of the energy sector is rife with uncertainties. They concern virtually the entire energy chain, from resource extraction to conversion technologies, energy demand, and the stringency of future environmental policies. Investment decisions today need thus not only to be cost-effective from the present perspective, but have to take into account also the imputed future risks of above uncertainties. This paper introduces a newly developed modeling decision framework with endogenous representation of above uncertainties. We employ stochastic modeling techniques within a system engineering model of the global energy system and implement several alternative representations of risk. We aim to identify salient characteristics of least-cost risk hedging strategies that are adapted to considerably reduce future risks and are hence robust against a wide range of future uncertainties. These lead to significant changes in response to energy system and carbon price uncertainties, in particular, (i) higher short- to medium-term investments into advanced technologies, (ii) pronounced emissions reductions, and (iii) diversification of the technology portfolio. From a methodological perspective, we find that there are strong interactions and synergies between different types of uncertainties. Cost-effective risk hedging strategies thus need to take a holistic view and comprehensively account for all uncertainties jointly. With respect to costs, relatively modest risk premiums (or hedging investments) can significantly reduce the vulnerability of the energy system against the associated uncertainties. The extent of early investments, diversification and emissions reductions, however, depends on the risk premium that decision makers are willing to pay to respond to prevailing uncertainties, and remains thus one of the key policy variables

A Simulation-Based Optimization Framework for Urban Transportation Problems

This paper proposes a simulation-based optimization (SO) method that enables the efficient use of complex stochastic urban traffic simulators to address various transportation problems. It presents a metamodel that integrates information from a simulator with an analytical queueing network model. The proposed metamodel combines a general-purpose component (a quadratic polynomial), which provides a detailed local approximation, with a physical component (the analytical queueing network model), which provides tractable analytical and global information. This combination leads to an SO framework that is computationally efficient and suitable for complex problems with very tight computational budgets. We integrate this metamodel within a derivative-free trust region algorithm. We evaluate the performance of this method considering a traffic signal control problem for the Swiss city of Lausanne, different demand scenarios, and tight computational budgets. The method leads to well-performing signal plans. It leads to reduced, as well as more reliable, average travel times