Optimization of Production, Maintenance, Design and Reliability for Multipurpose Process Plants: an Analysis and Revision of Models

The successful design of multipurpose process plants, which are characterized by their flexibility, is accomplished by maximizing the availability of process units and therefore, the profitability of the process. Maximum availability is achieved through the optimization of the design and production scheduling of a process under constraints relating to equipment maintenance and failure. Mathematical models that incorporate the production scheduling, maintenance scheduling, process design and initial reliability aspects of a process can be optimized in order to maximize availability. These mathematical models are solved through the use of computers. Mathematical process models, presented in the literature and containing the aforementioned components, were replicated and analyzed in this research; the simplest was replicated first and additional complexity was added thereafter. The last model replicated from the literature, the one containing the initial reliability component, is revised and improved. Specifically, the mathematics of the model are altered and simplified. Analysis reveals that as the models became more complex the harder it was to replicate the results provided in the literature. However, the revisionist model significantly improved upon the literature initial reliability model; it was solved faster and with greater accuracy. At the beginning of this report, a review of the mathematical and theoretical framework for this type of process optimization research is provided. The models of the multipurpose process plants are formulated as mixed-integer linear programming (MILP) problems in the General Algebraic Modeling System and solved using the XPRESS and CPLEX solvers

Discretization of Fractional Differential Equations by a Piecewise Constant Approximation

There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a dynamical systems analysis. Unfortunately, due to mistakes in the fundamental papers, the difference equations formulated through this process do not capture the dynamics of the fractional order equations. We show that the correct application of this nonstandard piecewise approximation leads to a one parameter family of fractional order differential equations that converges to the original equation as the parameter tends to zero. A closed formed solution exists for each member of this family and leads to the formulation of a difference equation that is of increasing order as time steps are taken. Whilst this does not lead to a simplified dynamical analysis it does lead to a numerical method for solving the fractional order differential equation. The method is shown to be equivalent to a quadrature based method, despite the fact that it has not been derived from a quadrature. The method can be implemented with non-uniform time steps. An example is provided showing that the difference equation can correctly capture the dynamics of the underlying fractional differential equation

Bridge Foundation Pinning Resistance Implied by Simplefied Equivalent Static Analysis Procedure for Lateral Spreading

Liquefaction-induced lateral spreading is a critical design case for many bridges located in high-seismicity regions of the Pacific Northwest. The design procedures currently used in the region tend to rely upon a simplified 2D plane strain analytical approach, and as a result may result in overly conservative and expensive design solutions. In some cases this over-conservatism has limited the feasibility of entire bridge projects. Given the shortcomings of the current design procedure, a modified design framework has been proposed to supplant the existing approach. This modified procedure takes an equivalent static approach (ESA) that makes consideration for 3D effects and foundation pinning through the combination of a foundation pushover analysis with a pseudo-static slope stability analysis to find a compatible foundation displacement as shown below