Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

Engineering knowledge-based variance-reduction simulation and G-dominance for structural frame robust optimization

[EN] This paper proposes the incorporation of engineering knowledge through both (a) advanced state-of-the-art preference handling decision-making tools integrated in multiobjective evolutionary algorithms and (b) engineering knowledge-based variance reduction simulation as enhancing tools for the robust optimum design of structural frames taking uncertainties into consideration in the design variables.The simultaneous minimization of the constrained weight (adding structuralweight and average distribution of constraint violations) on the one hand and the standard deviation of the distribution of constraint violation on the other are handled with multiobjective optimization-based evolutionary computation in two different multiobjective algorithms. The optimum design values of the deterministic structural problem in question are proposed as a reference point (the aspiration level) in reference-point-based evolutionary multiobjective algorithms (here g-dominance is used). Results including

Variance-Reduced Particle Filters for Structural System Identification Problems

A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. DOI: 10.1061/(ASCE)EM.1943-7889.0000480. (C) 2013 American Society of Civil Engineers.

The (de)merits of minimum-variance hedging: application to the crack spread

We study the empirical performance of the classical minimum-variance hedging strategy, comparing several econometric models for estimating hedge ratios of crude oil, gasoline and heating oil crack spreads. Given the great variability and large jumps in both spot and futures prices, considerable care is required when processing the relevant data and accounting for the costs of maintaining and re-balancing the hedge position. We find that the variance reduction produced by all models is statistically and economically indistinguishable from the one-for-one “naïve” hedge. However, minimum-variance hedging models, especially those based on GARCH, generate much greater margin and transaction costs than the naïve hedge. Therefore we encourage hedgers to use a naïve hedging strategy on the crack spread bundles now offered by the exchange; this strategy is the cheapest and easiest to implement. Our conclusion contradicts the majority of the existing literature, which favours the implementation of GARCH-based hedging strategies.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Estimation of time variant reliability of randomly parametered non-linear vibrating systems

The problem of time variant reliability analysis of randomly parametered and randomly driven nonlinear vibrating systems is considered. The study combines two Monte Carlo variance reduction strategies into a single framework to tackle the problem. The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations, and the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. Illustrative examples include study of single/multi degree of freedom linear/non-linear inelastic randomly parametered building frame models driven by stationary/non-stationary, white/filtered white noise support acceleration. The estimated reliability measures are demonstrated to compare well with results from direct Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Girsanov Transformation-Based Reliability Modeling and Testing of Actively Controlled Structures

The problem of estimation of the time-variant reliability of actively controlled structural dynamical systems under stochastic excitations is considered. Monte Carlo simulations, reinforced with Girsanov transformation-based sampling variance reduction, are used to tackle the problem. In this approach, the external excitations are biased by an additional artificial control force. The conflicting objectives of the two control forces-one designed to reduce structural responses and the other to promote limit-state violations (but to reduce sampling variance)-are noted. The control for variance reduction is fashioned after design-point oscillations based on a first-order reliability method. It is shown that for structures that are amenable to laboratory testing, the reliability can be estimated experimentally with reduced testing times by devising a procedure based on the ideas of the Girsanov transformation. Illustrative examples include studies on a building frame with a magnetorheologic damper-based isolation system subject to nonstationary random earthquake excitations. (C) 2014 American Society of Civil Engineers.

Latin hypercube sampling used in the calculation of the fracture probability

The paper proposes Latin hypercube sampling combined with the stratified sampling of variance reduction technique to calculate accurate fracture probability. In the compound sampling, the number of simulations is relatively small and the calculation error is satisfactory.

Simulation de centres de contacts

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Méthode de simulation avec les variables antithétiques

Les fichiers qui accompagnent mon document ont été réalisés avec le logiciel Latex et les simulations ont été réalisés par Splus(R).

Modeling of carrier transport in nanowires

We consider a physical model of ultrafast evolution of an initial electron distribution in a quantum wire. The electron evolution is described by a quantum-kinetic equation accounting for the interaction with phonons. A Monte Carlo approach has been developed for solving the equation. The corresponding Monte Carlo algorithm is NP-hard problem concerning the evolution time. To obtain solutions for long evolution times with small stochastic error we combine both variance reduction techniques and distributed computations. Grid technologies are implemented due to the large computational efforts imposed by the quantum character of the model.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.