Computational methods for solving optimal industrial process control problems

In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem involving systems with both input and output delays, and subject to continuous inequality state constraints; and (iii) a max-min optimal control problem arising in gradient elution chromatography.In the first problem, we consider a parameter identification problem involving a general nonlinear time-delay system, where the unknown time delays and system parameters are to be identified. This problem is posed as a dynamic optimization problem, where its cost function is to measure the discrepancy between predicted output and observed system output. The aim is to find unknown time-delays and system parameters such that the cost function is minimized. We develop a gradient-based computational method for solving this dynamic optimization problem. We show that the gradients of the cost function with respect to these unknown parameters can be obtained via solving a set of auxiliary time-delay differential systems from t = 0 to t = T. On this basis, the parameter identification problem can be solved as a nonlinear optimization problem and existing optimization techniques can be used. Two numerical examples are solved using the proposed computational method. Simulation results show that the proposed computational method is highly effective. In particular, the convergence is very fast even when the initial guess of the parameter values is far away from the optimal values.Unlike the first problem, in the second problem, we consider a time delay identification problem, where the input function for the nonlinear time-delay system is piecewise-constant. We assume that the time-delays—one involving the state variables and the other involving the input variables—are unknown and need to be estimated using experimental data. We also formulate the problem of estimating the unknown delays as a nonlinear optimization problem in which the cost function measures the least-squares error between predicted output and measured system output. This estimation problem can be viewed as a switched system optimal control problem with time-delays. We show that the gradient of the cost function with respect to the unknown state delay can be obtained via solving a auxiliary time-delay differential system. Furthermore, the gradient of the cost function with respect to the unknown input delay can be obtained via solving an auxiliary time-delay differential system with jump conditions at the delayed control switching time points. On this basis, we develop a heuristic computational algorithm for solving this problem using gradient based optimization algorithms. Time-delays in two industrial processes are estimated using the proposed computational method. Simulation results show that the proposed computational method is highly effective.For the third problem, we consider a general optimal control problem governed by a system with input and output delays, and subject to continuous inequality constraints on the state and control. We focus on developing an effective computational method for solving this constrained time delay optimal control problem. For this, the control parameterization technique is used to approximate the time planning horizon [0, T] into N subintervals. Then, the control is approximated by a piecewise constant function with possible discontinuities at the pre-assigned partition points, which are also called the switching time points. The heights of the piecewise constant function are decision variables which are to be chosen such that a given cost function is minimized. For the continuous inequality constraints on the state, we construct approximating smooth functions in integral form. Then, the summation of these approximating smooth functions in integral form, which is called the constraint violation, is appended to the cost function to form a new augmented cost function. In this way, we obtain a sequence of approximate optimization problems subject to only boundedness constraints on the decision variables. Then, the gradient of the augmented cost function is derived. On this basis, we develop an effective computational method for solving the time-delay optimal control problem with continuous inequality constraints on the state and control via solving a sequence of approximate optimization problems, each of which can be solved as a nonlinear optimization problem by using existing gradient-based optimization techniques. This proposed method is then used to solve a practical optimal control problem arising in the study of a real evaporation process. The results obtained are highly satisfactory, showing that the proposed method is highly effective.The fourth problem that we consider is a max-min optimal control problem arising in the study of gradient elution chromatography, where the manipulative variables in the chromatographic process are to be chosen such that the separation efficiency is maximized. This problem has three non-standard characteristics: (i) The objective function is nonsmooth; (ii) each state variable is defined over a different time horizon; and (iii) the order of the final times for the state variable, the so-called retention times, are not fixed. To solve this problem, we first introduce a set of auxiliary decision variables to govern the ordering of the retention times. The integer constraints on these auxiliary decision variables are approximated by continuous boundedness constraints. Then, we approximate the control by a piecewise constant function, and apply a novel time-scaling transformation to map the retention times and control switching times to fixed points in a new time horizon. The retention times and control switching times become decision variables in the new time horizon. In addition, the max-min objective function is approximated by a minimization problem subject to an additional constraint. On this basis, the optimal control problem is reduced to an approximate nonlinear optimization problem subject to smooth constraints, which is then solved using a recently developed exact penalty function method. Numerical results obtained show that this approach is highly effective.Finally, some concluding remarks and suggestions for further study are made in the conclusion chapter

In Situ Remediation Technology for Heavy Metal Contaminated Sediment: A Review

Sediment is an important part of the aquatic ecosystem, which involves material storage and energy exchange. However, heavy metal pollution in sediment is on the increase, becoming an important concern for the world. In this paper, the state-of-art in situ remediation technology for contaminated sediment was elaborated, including water diversion, capping, electrokinetic remediation, chemical amendments, bioremediation and combined remediation. The mechanisms for these techniques to reduce/immobilize heavy metals include physical, electrical, chemical and biological processes. Furthermore, application principle, efficiency and scope, advantages and disadvantages, as well as the latest research progress for each restoration technology, are systematically reviewed. This information will benefit in selecting appropriate and effective remediation techniques for heavy metal-contaminated sediment in specific scenarios

Optimal control for zinc solution purification based on interacting CSTR models

In zinc solution purification process, zinc dust is used to remove impurity ions in several serial stirred tank reactors. It is modelled by using several interacting continuously stirred tank reactor (ICSTR) systems with multiple time delays. Some unknown parameters of the ICSTR model are identified based on experimental data collected from a zinc production factory in China. Then a time delayed optimal control problem with continuous inequality constraints is constructed for the zinc solution purification. A numerical computational algorithm is developed, based on the control parameterization method, to design an optimal control law to ensure that a sufficiently low level of effluent impurities is achieved with the least zinc dust consumption. Finally, numerical simulation is carried out. The results obtained indicate that the effect of the optimal control for zinc solution purification is highly satisfactory

Assessment of Heavy Metal Pollution in Suburban River Sediment of Nantong (China) and Preliminary Exploration of Solidification/Stabilization Scheme

Sediments are sinks and sources of pollutants, playing a rather important role in metal migration and transformation. A set of toxic metals of Hg, Pb, Zn, Cr, Cu, Ni and Cd in a suburban river sediment was investigated in the Yangtze River Delta of China, Nantong, and then, the solidification/stabilization scheme and resource-oriented utilization for heavy metal-contaminated sediment were explored. The results showed that all of the metals were apparently higher than the background values. The geo-accumulation index indicated that Ni, Cr, Pb, Cu, Zn and Cd exhibited a none–moderately polluted degree, while Hg corresponded to the moderately contaminated grade. A correlation analysis showed that the contents of metals were not strongly affected by the pH and organic matter content (p > 0.05), but they were associated with each other (p < 0.05) and might have common natural and anthropogenic sources. Moreover, the leaching experiment revealed that the concentration of Ni exceeded the national standard of China for groundwater, which might cause environmental contamination. Thus, three effective solidification/stabilization formulations for amendments were developed: (1) zero valent iron (9.5% w.w.) and sodium carboxymethylcellulose (0.5% w.w.); (2) sulphate aluminum cement (1% d.w.) and sodium carboxymethylcellulose (0.3% d.w.) and (3) sulphate aluminum cement (1% d.w.), zero valent iron (0.5% d.w.) and sodium carboxymethylcellulose (0.3% d.w.). The findings can provide an effective approach and theoretical basis for the treatment of heavy metal pollution in river sediments

A Review of the Discriminant Analysis Methods for Food Quality Based on Near-Infrared Spectroscopy and Pattern Recognition

Near-infrared spectroscopy (NIRS) combined with pattern recognition technique has become an important type of non-destructive discriminant method. This review first introduces the basic structure of the qualitative analysis process based on near-infrared spectroscopy. Then, the main pretreatment methods of NIRS data processing are investigated. Principles and recent developments of traditional pattern recognition methods based on NIRS are introduced, including some shallow learning machines and clustering analysis methods. Moreover, the newly developed deep learning methods and their applications of food quality analysis are surveyed, including convolutional neural network (CNN), one-dimensional CNN, and two-dimensional CNN. Finally, several applications of these pattern recognition techniques based on NIRS are compared. The deficiencies of the existing pattern recognition methods and future research directions are also reviewed

Light-Induced TaHY5-7A and TaBBX-3B Physically Interact to Promote <i>PURPLE PERICARP-MYB 1</i> Expression in Purple-Grained Wheat

Purple-grained wheat (Triticum aestivum L.) is an important germplasm source in crop breeding. Anthocyanin biosynthesis in the pericarps of purple-grained wheat is largely light-dependent; however, the regulatory mechanisms underlying light-induced anthocyanin accumulation in the wheat pericarp remain unknown. Here we determined that anthocyanins rapidly accumulate in the pericarps of the purple-grained wheat cultivar Heixiaomai 76 (H76) at 16 days after pollination under light treatment. Using transcriptome sequencing, differential gene expression analysis, and phylogenetic analysis, we identified two key genes involved in light signaling in wheat: ELONGATED HYPOCOTYL 5-7A (TaHY5-7A) and B-BOX-3B (TaBBX-3B). TaHY5-7A and TaBBX-3B were highly expressed in purple-grained wheat pericarps. The heterologous expression of TaHY5-7A partially restored the phenotype of the Arabidopsis (Arabidopsis thaliana) hy5 mutant, resulting in increased anthocyanin accumulation and a shortened hypocotyl. The heterologous expression of TaBBX-3B in wild-type Arabidopsis had similar effects. TaHY5-7A and TaBBX-3B were nucleus-localized, consistent with a function in transcription regulation. However, TaHY5-7A, which lacks a transactivation domain, was not sufficient to activate the expression of PURPLE PERICARP-MYB 1 (TaPpm1), the key anthocyanin biosynthesis regulator in purple pericarps of wheat. TaHY5-7A physically interacted with TaBBX-3B in yeast two-hybrid and bimolecular fluorescence complementation assays. Additionally, TaHY5-7A, together with TaBBX-3B, greatly enhanced the promoter activity of TaPpm1 in a dual luciferase assay. Overall, our results suggest that TaHY5-7A and TaBBX-3B collaboratively activate TaPpm1 expression to promote light-induced anthocyanin biosynthesis in purple-pericarp wheat

A Max–Min Control Problem Arising in Gradient Elution Chromatography

Gradient elution chromatography is an industrial process used to separate and purify multi-component chemical mixtures. In this article, we consider an optimal control problem in which manipulative variables in the chromatographic process need to be determined to maximize separation efficiency. This problem has two nonstandard characteristics: (i) the objective function is nonsmooth, and (ii) each state variable is defined over a different time horizon. The final time for each state variable, the so-called retention time, is not fixed and actually depends on the control variables. To solve this optimal control problem, we first introduce a set of auxiliary decision variables to govern the ordering of the retention times. Then, we approximate the control by a piecewise-constant function and apply a novel time-scaling transformation to map the retention times and control switching times to fixed points in a new time horizon. The retention times and control switching times become decision variables in the new time horizon. On this basis, the optimal control problem is reduced to an approximate nonlinear optimization problem that can be solved using a recently developed exact penalty method. Numerical results show that our approach is both accurate and efficient