THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

An introduction to heat transfer

Advances in surrogate based modeling, feasibility analysis, and optimization: A review

A discrete technique of the Schwarz alternating method is presented in this last chapter, to combine the Ritz-Galerkin and finite element methods. This technique is well suited for solving singularity problems in parallel, and requires a little more computation for large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, will be studied. Also a balance strategy will be proposed to couple the iteration number with the element size used in the FEM. For the crack-infinity problem of singularity the total CPU time by the technique in this chapter is much less than that by the nonconforming combination in Chapter 12.

Schwarz Alternating Method

The tidal power available for electricity generation from in-stream turbines placed in the Minas Passage of the Bay of Fundy is examined. A previously derived theory is adapted to model the effect of turbine drag on the flow through the Minas Passage and the tidal amplitude in the Minas Basin. The theoretical maximum power production over a tidal cycle is determined by the product of the amplitude of the forcing tide in the Bay of Fundy and the undisturbed volumetric flowrate through the Minas Passage. Although the extraction of the maximum power will reduce the flowrate through the Minas Passage and the tides in the Minas Basin by over 30 per cent, a significant portion of the maximum power can be extracted with little change in tidal amplitude as the initial power generation causes only an increase in the phase lag of the basin tides. Two-dimensional, finite-element, numerical simulations of the Bay of Fundy—Gulf of Maine system agree remarkably well with the theory. The simulations suggest that...

Assessment of tidal current energy in the Minas Passage, Bay of Fundy:

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to n data points requires the computation of the inverse and determinant of n×n correlation matrices, R, that are sometimes computationally unstable due to near-singularity of R. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this article, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the inter...

/pdf/a-computationally-stable-approach-to-gaussian-process-36gdrzc8oq.pdf

A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data

For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to $n$ data points requires the computation of the inverse and determinant of $n \times n$ correlation matrices, $R$, that are sometimes computationally unstable due to near-singularity of $R$. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this paper, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator.

Determining optimal well placement and control is essential to maximizing production from an oil field. Most academic literature to date has treated optimal placement and control as two separate problems; well placement problems, in particular, are often solved assuming some fixed flow rate or bottom-hole pressure at injection and production wells. Optimal placement of wells, however, does depend on the control strategy being employed. Determining a truly optimal configuration of wells thus requires that the control parameters be allowed to vary as well. This presents a challenging optimization problem, since well location and control parameters have different properties from one another. In this paper, we address the placement and control optimization problem jointly using approaches that combine a global search strategy (particle swarm optimization, or PSO) with a local generalized pattern search (GPS) strategy. Using PSO promotes a full, semi-random exploration of the search space, while GPS allows us to locally optimize parameters in a systematic way. We focus primarily on two approaches combining these two algorithms. The first is to hybridize them into a single algorithm that acts on all variables simultaneously, while the second is to apply them sequentially to decoupled well placement and well control problems. We find that although the best method for a given problem is context-specific, decoupling the problem may provide benefits over a fully simultaneous approach.

/pdf/simultaneous-and-sequential-approaches-to-joint-optimization-1gpqgf31qa.pdf

Simultaneous and sequential approaches to joint optimization of well placement and control

https://ir.library.oregonstate.edu/downloads/3r074x04z

Ronald D. Haynes

Papers

Assessment of tidal current energy in the Minas Passage, Bay of Fundy:

A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data

A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data

Simultaneous and sequential approaches to joint optimization of well placement and control

Joint optimization of well placement and control for nonconventional well types