(4v) Global Optimization for System Identification and Green Engineering Applications

My Ph.D. research with Dr. Vasilios Manousiouthakis explored interval analysis-based branch-and-bound techniques for globally optimal parameter identification, a novel method for the assessment/synthesis of sustainable systems, graphical/analytical optimization techniques for the global solution of the TAC minimization problem for a series of compressors, and the introduction of the novel concept of the attainable region for separator networks. Throughout the course of my work, I have experienced first-hand the “curse of dimensionality” prevalent in non-linear optimization algorithms. Thus, I have applied analytical techniques, dimensionality reduction, convexification strategies, and functional analysis to identify global optima and to enhance the efficiency of their computation.

Interval Analysis-Based Branch-and-bound Methods for System Identification and Optimal Control

            Motivated by the lack of model validation and guarantee of global optimality in traditional non-linear regression techniques, I developed a method for parameter identification that couples finite-dimensional global optimization strategies with interval forms of numerical model approximations (e.g. Euler, 4^th order Runge Kutta). This method is guaranteed to identify the global optimum of the corresponding numerical non-linear regression problem. The method was employed in two case studies: (1) an ODE model aiming to identify the kinetic parameters of a Trambouze reaction scheme in a batch reactor based on experimental data related only to the reactant, and (2) a DAE model exhibiting trajectory discontinuities and infinite solutions. It was shown in both cases that the globally optimum objective function value was identified within the desired level of accuracy, and intervals were also identified, within which the globally optimal kinetic parameters must lie. These intervals were shown to be loose even though the associated collection of ODE trajectories tightly follows the experimental data, suggesting overparameterization with respect to the available data.

Infinite-Dimensional LPs for Process Synthesis and Attainable Region Identification

            Recently, I expanded the applicability of the Infinite DimEnsionAl State-space (IDEAS) framework to attainable region (AR) identification for separator networks. While extensive research has already been done on AR for reactive distillation (see [1] for a formal introduction, and [2], [3], [4], [5] for extension of the framework to more complex reaction schemes and azeotropic mixtures), and the application of IDEAS to separation network synthesis has been demonstrated ([6], [7], [8], [9], [10]), the AR concept for Separation networks has not even been defined in the literature. I have constructed the AR for a water/methanol/acetone mixture involving one network feed stream with known species molar fractions and three network outlet streams at 1 atm pressure. The binary methanol/acetone system exhibits a minimum-boiling azeotrope at 79.07% mole fraction of acetone at 328.5 K. The IDEAS-generated AR successfully identified that the binary methanol/acetone azeotrope was outside the AR.

Hydrogen Economy

            In my exploration of hydrogen as an alternative energy source, I formulated the minimum operating cost and minimum capital cost problems for a system of compressors and coolers in series that bring an ideal gas from a specified initial state  to a specified final state. Through mathematical proofs, I reduced the dimensionality of the optimization problems and established analytical properties of the compressor outlet temperatures when either operating costs or capital costs dominate. This allowed the development and Excel implementation of graphical/analytical solution strategies involving minimization of operating cost and capital cost for a given number of compressors and coolers. A case study involving hydrogen compression was done to illustrate the methods.

Sustainable System Assessment and Synthesis

            In my work, I proposed a novel global optimization approach that transforms basic indicator data in the form of intervals containing all possible basic indicator values, to an interval containing all possible values of the sustainability index, termed the “Sustainability Index Interval” (SII). The fuzzy-logic-based framework detailed in [11] was adapted for this work, since fuzzy logic is well-suited for simulating public opinions. Despite the nonconvexity of the underlying global optimization problems, I have proven that they possess a number of properties which can be utilized to reduce the burden associated with SII’s computation. Based on these properties, I developed a branch and bound algorithm exactly quantifying the SII in a finite number of iterations. The framework and results of case studies have been published in the AIChE Journal [12]. Further, to test the validity of the public opinion simulation of the framework, I supervised three high school students in conducting surveys of the public pertaining to the sustainability efforts of six leading aluminum-producing corporations.

References:

1. Nisoli, A., Malone, M. F., & Doherty, M. F. (1997). Attainable regions for reaction with separation. AIChE journal, 43(2), 374-387.
2. Agarwal, V., Thotla, S., & Mahajani, S. M. (2008). Attainable regions of reactive distillation—Part I. Single reactant non-azeotropic systems. Chemical Engineering Science, 63(11), 2946-2965.
3. Agarwal, V., Thotla, S., Kaur, R., & Mahajani, S. M. (2008). Attainable regions of reactive distillation. Part II: Single reactant azeotropic systems. Chemical Engineering Science, 63(11), 2928-2945.
4. Amte, V., Nistala, S., Malik, R., & Mahajani, S. (2011). Attainable regions of reactive distillation—Part III. Complex reaction scheme: Van de Vusse reaction.Chemical Engineering Science, 66(11), 2285-2297.
5. Amte, V., Gaikwad, R., Malik, R., & Mahajani, S. (2011). Attainable region of reactive distillation-part IV: Inclusion of multistage units for complex reaction schemes. Chemical Engineering Science.
6. Justanieah, A. M., & Manousiouthakis, V. (2003). IDEAS approach to the synthesis of globally optimal separation networks: application to chromium recovery from wastewater. Advances in Environmental Research, 7(2), 549-562.
7. Holiastos, K., & Manousiouthakis, V. (2004). Infinite-dimensional state-space (IDEAS) approach to globally optimal design of distillation networks featuring heat and power integration. Industrial & engineering chemistry research, 43(24), 7826-7842.
8. Drake, J. E., & Manousiouthakis, V. (2002). IDEAS approach to process network synthesis: minimum utility cost for complex distillation networks.Chemical engineering science, 57(15), 3095-3106.
9. Drake, J. E., & Manousiouthakis, V. (2002). IDEAS approach to process network synthesis: minimum plate area for complex distillation networks with fixed utility cost. Industrial & engineering chemistry research, 41(20), 4984-4992.
10. Ghougassian, P. G., & Manousiouthakis, V. (2012). Globally Optimal Networks for Multi-Pressure Distillation of Homogeneous Azeotropic Mixtures. Industrial & Engineering Chemistry Research.
11. Phillis, Y. A., & Davis, B. J. (2009). Assessment of corporate sustainability via fuzzy logic. Journal of intelligent & robotic systems, 55(1), 3-20.
12. Conner, J. A., Phillis, Y. A., & Manousiouthakis, V. I. (2012). On a sustainability interval index and its computation through global optimization.AIChE Journal, 58(9), 2743-2757.