Optimization Of Nonlinear Processes Research Articles

Data-driven distributionally robust chance-constrained optimization with large data set and outliers: Sequential sample removal algorithm for solution improvement

Data-driven distributionally robust chance-constrained optimization (DRCCP) is a powerful technique to handle optimization problems involving uncertainty in constraint functions. However, the outliers and extreme samples in the data set may deteriorate the decision quality of DRCCP. Although there are numerous outlier detection techniques, they are either unable to pinpoint the samples causing overly conservative solutions, or incompatible with DRCCP models. This work proposes a novel and widely compatible algorithm that generates a representative subset of the original data set and removes samples causing overly conservative solutions for the DRCCP problem. With the proposed approach, the DRCCP solution quality can be enhanced while simultaneously ensuring the solution feasibility. To illustrate its effectiveness, we examine two numerical examples and a nonlinear process optimization problem in our study.

Kernel distributionally robust chance-constrained process optimization

A kernel distributionally robust chance-constrained optimization (DRCCP) method is proposed in this study based on the kernel ambiguity set. The kernel ambiguity set is established via the kernel mean embedding (KME) and the maximum mean discrepancy (MMD) between distributions. The proposed approach can be formulated as two different models. The first one is a mixed-integer model employing the indicator function for handling the joint chance constraint. The second one is a continuous optimization model using the Conditional Value-at-Risk (CVaR) approximation to approximate the indicator function. The proposed method is compared with the popular Wasserstein ambiguity set based approach. A numerical example and a nonlinear process optimization problem are studied to demonstrate its efficacy.

Nonlinear dynamic of picosecond pulse propagation in atmospheric air-filled hollow core fibers

Atmospheric air-filled hollow core (HC) fibers, representing the simplest yet reliable form of gas-filled hollow core fiber, show remarkable nonlinear properties and have several interesting applications such as pulse compression, frequency conversion and supercontinuum generation. Although the propagation of sub-picosecond and few hundred picosecond pulses are well-studied in air-filled fibers, the nonlinear response of air to pulses with a duration of a few picoseconds has interesting features that have not yet been explored fully. Here, we experimentally and theoretically study the nonlinear propagation of ~6 ps pulses in three different types of atmospheric air-filled HC fiber. With this pulse length, we were able to explore different nonlinear characteristics of air at different power levels. Using in-house-fabricated, state-of-the-art HC photonic bandgap, HC tubular and HC Kagomé fibers, we were able to associate the origin of the initial pulse broadening process in these fibers to rotational Raman scattering (RRS) at low power levels. Due to the broadband and low loss transmission window of the HC Kagomé fiber we used, we observed the transition from initial pulse broadening (by RRS) at lower powers, through long-range frequency conversion (2330 cm-1) with the help of vibrational Raman scattering, to broadband (~700 nm) supercontinuum generation at high power levels. To model such a wide range of nonlinear processes in a unified approach, we have implemented a semi-quantum model for air into the generalized nonlinear Schrodinger equation, which surpasses the limits of the common single damping oscillator model in this pulse length regime. The model has been validated by comparison with experimental results and provides a powerful tool for the design, modeling and optimization of nonlinear processes in air-filled HC fibers.

Optimization of nonlinear process based on sequential extreme learning machine

In this paper, a new approach to the optimal control with constraints is proposed to achieve a desired end product quality for nonlinear processes based on new kernel extreme learning machine (KELM). The contributions of the paper are as follows: (1) In existing ILC algorithm, the model was built only between manipulated input variables U and output variables Y without considering the state variables. However, the states variables X state are important in the industrial processes, which are usually constrained. In this paper, the variables are divided into state variables X state , manipulated input variables U and output Y in the process of modeling. Then Δ U can be obtained by batch-to-batch iterative learning control separately. Kernel algorithm is added to ELM. (2) Constraints of state variables X state and the input variables U are considered in the current version. PSO is used to solve the optimization problem. (3) Kernel trick is introduced to improve accuracy of ELM modeling. New KELM algorithm is proposed in the current version. The input trajectory for the next batch is accommodated by searching for the optimal value through the error feedback at a minimum cost. The particle swarm optimization algorithm is used to search for the optimal value based on the iterative learning control (ILC). The proposed approach has been shown to be effective and feasible by applying bulk polymerization of the styrene batch process and fused magnesium furnace.

Using Sparse-Grid Methods To Improve Computation Efficiency in Solving Dynamic Nonlinear Chance-Constrained Optimization Problems

Chance-constrained programming is known as a suitable approach to optimization under uncertainty. However, a serious difficulty is the requirement of evaluating the probability of holding inequality constraints through the numerical computation of multidimensional integrals. If a nonlinear system with many uncertain variables is considered, the computational load will be prohibitive when using a full-grid integration method. Thus our aim is to investigate a method to decrease the computation expense in solving nonlinear chance-constrained optimization problems with many uncertain variables. In particular, we consider dynamic nonlinear process optimization under uncertainty, which will be transferred into a nonlinear chance-constrained optimization problem by a discretization scheme. To solve this problem, we propose to use sparse-grid methods for the evaluation of the objective function, the probability of constraint satisfaction, and their gradients. These components are implemented in a nonlinear progra...

Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

Dynamic Optimization of Nonlinear Processes with an Enhanced Scatter Search Method

An enhanced scatter search method for the global dynamic optimization of nonlinear processes using the control vector parametrization (CVP) approach is presented. Sharing some features of the scatter search metaheuristic, this new method presents a simpler but more effective design which helps to overcome typical difficulties of nonlinear dynamic systems optimization such as noise, flat areas, nonsmoothness, and/or discontinuities. This new algorithm provides a good balance between robustness and efficiency in the global phase, and couples a local search procedure to accelerate the convergence to optimal solutions. Its application to four multimodal dynamic optimization problems, compared with other state-of-the-art global optimization algorithms, including an advanced scatter search design, proves its efficiency and robustness, showing a very good scalability.

Integrating relevance vector machines and genetic algorithms for optimization of seed-separating process

A hybrid intelligent approach based on relevance vector machines (RVMs) and genetic algorithms (GAs) has been developed for optimal control of parameters of nonlinear manufacturing processes. It concerns the finding of the near-optimal control parameters of the nonlinear discrete manufacturing process with a specific objective. First, the nonlinear process with measurement noise is regressed by the relevance vector learning mechanism based on a kernel-based Bayesian framework. For minimizing the approximate error, uniform design sampling, online incremental learning and cross-validation are used in the learning process of RVMs. Such well-trained models become a specialized process simulation tool, which is valuable in prediction and optimization of nonlinear processes. Next, the near-optimal setpoints of the control system, which maximize the objective function, are sought by GAs from the numerous values of the objective function obtained from the simulation. As a case study, the seed separator system (5XZW-1.5) is used for evaluating the proposed intelligent approach. The control parameters to reach the maximum weighted objective, which combine the system output and evaluation functions, are optimized. The experimental results show the effectiveness of the proposed hybrid approach.

FEM-based optimum design of multi-stage deep drawing process of molybdenum sheet

Molybdenum, one of the refractory metals, has high heat and electrical conductivity while remaining strong, mechanically, at high, as well as low, temperatures. Therefore, it is a technologically very useful material, especially for high temperature applications. However, due to its very low drawability, a multi-stage process is necessary to make a deep drawn part from the molybdenum sheet. In this study, a multi-stage circular cup deep drawing process for a molybdenum sheet was designed by including ironing, which was effective in increasing drawability. A parametric study by finite element analysis of deep drawing was conducted to evaluate the effect of die design variables. From parametric study results, the design variables of the multi-stage deep drawing process were selected. Then, nonlinear process optimization, based on finite element simulation, was conducted to obtain the optimum multi-stage deep drawing process, using a global, as well as a local, optimum search algorithm.

Identification of Dynamic Characterization Parameters of Agitated Pulp Chests Using Hybrid Genetic Algorithm

Pulp suspensions are non-Newtonian and possess a significant yield stress, which creates considerable deviations from ideal mixing as demonstrated by dynamic tests made on both industrial and scale-model pulp chests. Due to the existence of non-ideal flows in agitated pulp chests, the determination of their discrete-time characterization parameters is very challenging. This paper optimally determines these parameters using a multi-parameter hybrid genetic algorithm specially developed to generate robust and high quality results. The algorithm integrates the genetic operations of selection, crossover and mutation with gradient search inside successively expanding and contracting parameter domains using alternating logarithmic and linear mappings. The algorithm is successfully tested on three different sets of simulated data, and it is found to retrieve the model parameters with high accuracy. Three sets of experimental data are then processed by the algorithm for the optimal determination of their characterization parameters. The corresponding optimal outputs match well with their experimental counterparts. The results indicate the potential application of the algorithm to solve non-linear process optimization problems with high accuracies.

Design for model parameter uncertainty using nonlinear confidence regions

AbstractAn accurate method presented accounts for uncertain model parameters in nonlinear process optimization problems. The model representation is considered in terms of algebraic equations. Uncertain quantity parameters are often discretized into a number of finite values that are then used in multiperiod optimization problems. These discrete values usually range between some lower and upper bound that can be derived from individual confidence intervals. Frequently, more than one uncertain parameter is estimated at a time from a single set of experiments. Thus, using simple lower and upper bounds to describe these parameters may not be accurate, since it assumes the parameters are uncorrelated. In 1999 Rooney and Biegler showed the importance of including parameter correlation in design problems by using elliptical joint confidence regions to describe the correlation among the uncertain model parameters. In chemical engineering systems, however, the parameter estimation problem is often highly nonlinear, and the elliptical confidence regions derived from these problems may not be accurate enough to capture the actual model parameter uncertainty. In this work, the description of model parameter uncertainty is improved by using confidence regions derived from the likelihood ratio test. It captures the nonlinearities efficiently and accurately in the parameter estimation problem. Several examples solved show the importance of accurately capturing the actual model parameter uncertainty at the design stage.

計装 紙パルプ製造工程における多変数プロセスの最適化

The economic cycle for the industry is becoming much less predictable than it was ten to twenty years ago. The ways in which we communicate and use paper are changing. Finally, with the construction of mills all over the world, the pulp and paper industry has truly become a global market. Every mill executive's current objectives are to increase productivity while decreasing costs and delivering added value to their customers, in turn, generating added value for their shareholders.For the past five years, software products utilizing adaptive technologies have been introduced for solving process modeling/control applications in the pulp and paper industry. These adaptive algorithms (Neural Nets, Chaos Theory, Fuzzy Logic) have provided the unique ability to build accurate non-linear process models based on enormous historical data sets. These models are then put on-line using on-line software for continuous real time savings. Over twenty pulp and paper companies are currently using these products with resulting increases in yield, efficiency and throughput.This paper describes a new product that represents the next step in process optimization and its use for paper machine control. The Process PerfecterTM enables closed-loop control and optimization of nonlinear processes. The benefits of this system over traditional techniques delivers increased profitability by 1) the true unification of optimization and control into one discipline, 2) enabling nonlinear control in processes where traditional linear control is not applicable, 3) reducing the plant testing time for identification of process dynamics resulting in significantly reduced installation and process disruption, 4) by reducing maintenance cost and re-identification, and 5) improving quality through the implementation of statistically smart controls. This standard product, built upon and enhancing the previous products, provides a total solution that can be applied to significant pulp and paper unit.

Dynamic optimization of nonlinear processes by combining neural net model with UDMC

AbstractA new dynamic optimization technique presented combines a neural network model with a universal dynamic matrix control (UDMC) algorithm. This technique utilizes a nonlinear‐model‐predictive control technique for on‐line optimization and feedback control by using a dynamic neural net model. This approach offers two important advantages over conventional UDMC. One is that a dynamic neural net model can be developed from process data and used for optimization calculations, thus achieving optimization without a first principle model. This neural‐network‐based optimization approach also produces good performance even with processmodel mismatch. The other is that our neural‐net‐model‐based UDMC algorithm greatly reduces the computation time required for the nonlinear dynamic matrix used for the successive quadratic programming algorithm. The development of this technique also involved an analysis of the effect of network structure on dynamic optimization. A state‐space‐based neural network model which utilizes a priori process knowledge is best suited for optimization calculations. Advantages of this technique are illustrated by simulation for two chemical processes.

Coordinated design and control optimization of nonlinear processes

On a small time-scale, disturbances to a process can lead to off-spec production, decreased profitability and the violation of hard process constraints, creating unsafe conditions. A strategy is presented for the design of processes that are operationally optimal, as well as steady-state optimal, and that operate prudently far from hard constraints. In addition to the evaluation of an economic objective, each potential design is evaluated for its controllability, using the closed-loop response to several disturbances, simulated with model predictive control (MPC) algorithms. These algorithms provide excellent responses to unmeasured disturbances, allow for the inclusion of constraints and are fairly insensitive to the tuning parameters, allowing for an evaluation of the inherent controllability of a process. This strategy has been applied to a fermentation process with complex chemical and physical interactions and characterized by hysteresis and periodic behavior for some ranges of its design parameters. A simple optimization of venture profit leads to a design that is highly constrained and unstable. Using the above strategy, it is demonstrated that alternative designs exist with improved controllability, but without retreating from the design constraints. This is counterintuitive and contrary to the results of several case studies. Furthermore, the design remains unstable.

Large-scale decomposition for successive quadratic programming

Successive quadratic programming (SQP) has emerged as the algorithm of choice for solving moderately-sized nonlinear process optimization problems. However, as the nonlinear programming problem becomes large (over 100 variables, say) storage requirements for the Hessian matrix and the computational expense of solving large quadratic programs can become prohibitive. To overcome this problem, Westerberg and coworkers proposed two SQP decomposition strategies in 1980 and 1983. The first strategy overcomes this problem but is difficult to implement, while the second has been observed to give inconsistent results. The strategy in this paper uses range and null space projections to develop a decomposition algorithm that is both easy to implement and performs as well as the full SQP algorithm on small problems. This range and null space decomposition (RND) allows for sparse implementations and thus solves large problems easily and reliably. Theoretical development of the RND method is presented as well as a geometric interpretation of this approach compared to others. Finally, a thorough numerical comparison of SQP strategies is presented on a battery of nonlinear programming and process optimization test problems.

Simultaneous optimization and heat integration of chemical processes

AbstractA procedure is proposed for simultaneously handling the problem of optimal heat integration while performing the optimization of process flow sheets. The method is based on including a set of constraints into the nonlinear process optimization problem so as to insure that the minimum utility target for heat recovery networks is featured. These heat integration constraints, which do not require temperature intervals for their definition, are based on a proposed representation for locating pinch points that can vary according to every set of process stream conditions (flow rates and temperatures) selected in the optimization path. The underlying mathematical formulations correspond to nondifferentiable optimization problems, and an efficient smooth approximation method is proposed for their solution. An example problem on a chemical process is presented to illustrate the economic savings that can be obtained with the proposed simultaneous approach. The method reduces to simple models for the case of fixed flow rates and temperatures.

On Multilevel Optimization of Nonconvex Static Problems - Application to Water Distribution of a River System

The paper deals with theoretical and computational problems of multilevel optimization of nonlinear processes. After having proved some theorems concerning relations between local and global minima of the subsystems, the coordinator, and the overall problem, a method is presented for getting the global minimum of a multimodal subproblem. A three-level optimization for multistage processes with feedbacks is proposed thereafter, using discrete dynamic programming on the lowest level and primal coordination on the 2nd and the 3rd level. The method is applied to the distribution of water-flow towards industrial and agricultural users situated along two rivers having connection with each other.