Integration of Design and Control under Uncertainty: A New Back-off Approach using PSE Approximations

Chemical process design is still an active area of research since it largely determines the optimal and safe operation of a new process under various conditions. The design process involves a series of steps that aims to identify the most economically attractive design typically using steady-state optimization. However, optimal steady-state designs may fail to comply with the process constraints when the system under analysis is subject to process disturbances (e.g. the composition of a reactant in a feed stream) or parameter uncertainty (e.g. the activation energy in a chemical reaction). Moreover, the practice of overdesigning a process to ensure feasibility under process disturbances and parameter uncertainty has been proven to be costly. Therefore, a new methodology for simultaneous design and control for dynamic systems under uncertainty has been proposed. The proposed methodology uses Power Series Expansions (PSE) to obtain analytical expressions for the process constrains and cost function. The key idea is to use the back off approach from the optimal steady state design to address the simultaneous process and design problem in an efficient systematic manner using PSE approximations. The challenge in this method is to determine the magnitude of the back-off needed to accommodate the transient and feasible operation of the process in presence of disturbances and parameter uncertainty. In this approach, PSE functions are used to obtain analytical expressions of the actual process constraints and are explicitly defined in terms of system’s uncertain parameter and the largest variability in a constraint function due to time-varying changes in the disturbances. Also, the PSE approximation for each constraint is developed around a nominal point in the optimization variables and for each realization considered for the uncertain parameters. The PSE-based constraint represents the actual process constraint and can be evaluated faster since it is explicitly defined in the terms of the optimization variables. The work focuses on calculating various optimal design and control parameters by solving various sets of optimization problems using mathematical expressions obtained from power series expansions. These approximations are used to determine the direction in the search of optimal design parameters and operating conditions required for an economically attractive, dynamically feasible process. The proposed methodology was tested on an isothermal storage tank and a step by step procedure to develop the methodology has been presented. The methodology was also tested on a non-isothermal CSTR and the results were compared with the formal integration process. Effect of tuning parameter, which is a key parameter in the methodology, have been studied and the results show that the quality of the results improves when smaller values of tuning parameter are used but at the expense of higher computational costs. The effect of the order of the PSE approximation used in the calculations has also been studied and it shows that the quality in the results is improved when higher orders in the PSE approximations are used at the expense of higher computational costs. The methodology was also tested on a large-scale Waste Water treatment plant. A comparison was made for different values of tuning parameters and the most feasible value was chosen for the case study. Effects of different disturbances profiles such as step and ramp changes were also studied. The studies concluded that a lower cost value is obtained when ramps are used as disturbance profile when compared with step changes. The methodology was also tested when parameter uncertainty was introduced and the results show a higher cost is required when uncertainty is present in the system when compared with no uncertainty. The results show that this method has the potential to address the integration of design and control of dynamic systems under uncertainty at low computational costs

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Stochastic optimization methods for the simultaneous control of parameter-dependent systems

We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the recently developed Continuous Stochastic Gradient (CSG) algorithm. We consider the problem of computing simultaneous controls through the minimization of a cost functional defined as the superposition of individual costs for each realization of the system. We compare the performances of these stochastic approaches, in terms of their computational complexity, with those of the more classical Gradient Descent (GD) and Conjugate Gradient (CG) algorithms, and we discuss the advantages and disadvantages of each methodology. In agreement with well-established results in the machine learning context, we show how the SGD and CSG algorithms can significantly reduce the computational burden when treating control problems depending on a large amount of parameters. This is corroborated by numerical experiments

Diseño para operabilidad: Una revisión de enfoques y estrategias de solución

In the last decades the chemical engineering scientific research community has largely addressed the design-foroperability problem. Such an interest responds to the fact that the operability quality of a process is determined by design, becoming evident the convenience of considering operability issues in early design stages rather than later when the impact of modifications is less effective and more expensive. The necessity of integrating design and operability is dictated by the increasing complexity of the processes as result of progressively stringent economic, quality, safety and environmental constraints. Although the design-for-operability problem concerns to practically every technical discipline, it has achieved a particular identity within the chemical engineering field due to the economic magnitude of the involved processes. The work on design and analysis for operability in chemical engineering is really vast and a complete review in terms of papers is beyond the scope of this contribution. Instead, two major approaches will be addressed and those papers that in our belief had the most significance to the development of the field will be described in some detail.En las últimas décadas, la comunidad científica de ingeniería química ha abordado intensamente el problema de diseño-para-operabilidad. Tal interés responde al hecho de que la calidad operativa de un proceso esta determinada por diseño, resultando evidente la conveniencia de considerar aspectos operativos en las etapas tempranas del diseño y no luego, cuando el impacto de las modificaciones es menos efectivo y más costoso. La necesidad de integrar diseño y operabilidad esta dictada por la creciente complejidad de los procesos como resultado de las cada vez mayores restricciones económicas, de calidad de seguridad y medioambientales. Aunque el problema de diseño para operabilidad concierne a prácticamente toda disciplina, ha adquirido una identidad particular dentro de la ingeniería química debido a la magnitud económica de los procesos involucrados. El trabajo sobre diseño y análisis para operabilidad es realmente vasto y una revisión completa en términos de artículos supera los alcances de este trabajo. En su lugar, se discutirán los dos enfoques principales y aquellos artículos que en nuestra opinión han tenido mayor impacto para el desarrollo de la disciplina serán descriptos con cierto detalle.Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin

Short-Term Robustness of Production Management Systems: New Methodology

This paper investigates the short-term robustness of production planning and control systems. This robustness is defined here as the systems ability to maintain short-term service probabilities (i.e., the probability that the fill rate remains within a prespecified range), in a variety of environments (scenarios). For this investigation, the paper introduces a heuristic, stagewise methodology that combines the techniques of discrete-event simulation, heuristic optimization, risk or uncertainty analysis, and bootstrapping. This methodology compares production control systems, subject to a short-term fill-rate constraint while minimizing long- term work-in-process (WIP). This provides a new tool for performance analysis in operations management. The methodology is illustrated via the example of a production line with four stations and a single product; it compares Kanban, Conwip, Hybrid, and Generic production control schemes.manufacturing;inventory;risk analysis;robustness and sensitivity analysis;scenarios

Millimeter wave satellite concepts. Volume 1: Executive summary

The objectives of the program were: (1) development of methodology based on the technical requirements of potential services that might be assigned to millimeter wave bands for identifying the viable and appropriate technologies for future NASA millimeter research and development programs, and (2) testing of this methodology with user applications and services. The scope of the program included the entire communications network, both ground and space subsystems. The reports include: (1) cost, weight, and performance models for the subsystems, (2) conceptual design for point-to-point and broadcast communications satellites, (3) analytic relationships between subsystem parameters and an overall link performance, (4) baseline conceptual systems, (5) sensitivity studies, (6) model adjustment analyses, (7) identification of critical technologies and their risks, (8) brief R&D program scenarios for the technologies judged to be moderate or extensive risks

Sample Approximation-Based Deflation Approaches for Chance SINR Constrained Joint Power and Admission Control

Consider the joint power and admission control (JPAC) problem for a multi-user single-input single-output (SISO) interference channel. Most existing works on JPAC assume the perfect instantaneous channel state information (CSI). In this paper, we consider the JPAC problem with the imperfect CSI, that is, we assume that only the channel distribution information (CDI) is available. We formulate the JPAC problem into a chance (probabilistic) constrained program, where each link's SINR outage probability is enforced to be less than or equal to a specified tolerance. To circumvent the computational difficulty of the chance SINR constraints, we propose to use the sample (scenario) approximation scheme to convert them into finitely many simple linear constraints. Furthermore, we reformulate the sample approximation of the chance SINR constrained JPAC problem as a composite group sparse minimization problem and then approximate it by a second-order cone program (SOCP). The solution of the SOCP approximation can be used to check the simultaneous supportability of all links in the network and to guide an iterative link removal procedure (the deflation approach). We exploit the special structure of the SOCP approximation and custom-design an efficient algorithm for solving it. Finally, we illustrate the effectiveness and efficiency of the proposed sample approximation-based deflation approaches by simulations.Comment: The paper has been accepted for publication in IEEE Transactions on Wireless Communication

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks