Optimizing spatiotemporal sensors placement for nutrient monitoring: a stochastic optimization framework

Nutrient monitoring is very important for the area of food–energy–water nexus. The sensor network for nutrient monitoring requires dynamic sensing where the positions of the sensors change with time. In this work, we have proposed a methodology to optimize a dynamic sensor network which can address the spatiotemporal aspect of nutrient movement in a watershed. This is a first paper in the series where an algorithmic and methodological framework for spatiotemporal sensor placement problem is proposed. Dynamic sensing is widely used in wireless sensors, and the current approaches to solving this problem are data intensive. This is the first time we are introducing a stochastic optimization approach to dynamic sensing which is efficient. This framework is based on a novel stochastic optimization algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). A small case study of the dynamic sensor placement problem is presented to illustrate the approach. In the second paper of this series, we will present a detailed case study of nutrient monitoring in a watershed.     

Drinking Water Treatment Plant Design Incorporating Variability and Uncertainty

Both inherent natural variability and model parameter uncertainty must be considered in the development of robust and reliable designs for drinking water treatment. This study presents an optimization framework for investigating the effects of five variable influent parameters and three uncertain model parameters on the least-cost treatment plant configuration (contact, direct, or nonsweep conventional filtration) that reliably satisfies an effluent particulate matter concentration constraint. Incorporating variability and uncertainty within the decision-making framework generates information for investigating: (1) impacts on total cost and treatment reliability; (2) shifts on the least-cost treatment configuration for providing reliable treatment; and (3) the importance of the individual variable and uncertain parameter distributions for reliably satisfying an effluent water quality constraint. Increasing the magnitude of influent variability and model parameter uncertainty results in a greater expected design cost due, generally, to increases in process sizing required to reliably satisfy the effluent concentration constraint. The inclusion of variability and uncertainty can also produce a shift in the locations of the least-cost configuration regions, which are dependent on the expected influent water quality and the magnitude of variability and uncertainty. The additional information provided by incorporating the variable and uncertain parameters illustrates that parameter distributions related to the primary removal mechanism are critical, and that contact and direct filtration are more sensitive to variability and uncertainty than conventional filtration.     

Stability of matrix second-order systems: new conditions andperspectives

Modeling of many dynamic systems results in matrix second-order differential equations. In the paper, the stability issues of matrix second-order dynamical systems are discussed. In the literature, only sufficient conditions of stability and/or instability for a system in matrix second-order form are available. In this paper, necessary and sufficient conditions of asymptotic stability for time-invariant systems in matrix second-order form under different types of dynamic loadings (conservative/nonconservative) are derived and a physical interpretation is carried out. The stability conditions in the sense of Lyapunov (the jw-axis behavior of eigenvalues) are also analyzed. As the conditions are gained directly in terms of physical parameters of the system, the effect of different loadings on the system stability is made transparent by dealing with the stability issues directly in matrix second-order form     

Minimization of water consumption under uncertainty for a pulverized coal power plant

Coal-fired power plants are large water consumers. Water consumption in thermoelectric generation is strongly associated with evaporation losses and makeup streams on cooling and contaminant removal systems. Thus, minimization of water consumption requires optimal operating conditions and parameters, while fulfilling the environmental constraints. Several uncertainties affect the operation of the plants, and this work studies those associated with weather. Air conditions (temperature and humidity) were included as uncertain factors for pulverized coal (PC) power plants. Optimization under uncertainty for these large-scale complex processes with black-box models cannot be solved with conventional stochastic programming algorithms because of the large computational expense. Employment of the novel better optimization of nonlinear uncertain systems (BONUS) algorithm, dramatically decreased the computational requirements of the stochastic optimization. Operating conditions including reactor temperatures and pressures; reactant ratios and conditions; and steam flow rates and conditions were calculated to obtain the minimum water consumption under the above-mentioned uncertainties. Reductions of up to 6.3% in water consumption were obtained for the fall season when process variables were set to optimal values. Additionally, the proposed methodology allowed the analysis of other performance parameters like gas emissions and cycle efficiency which were also improved.     

Process design for the environment: A multi-objective framework under uncertainty

 Designing chemical processes for the environment requires consideration of several indexes of environmental impact including ozone depletion, global warming potentials, human and aquatic toxicity, photochemical oxidation, and acid rain potentials. Current methodologies, such as the generalized waste reduction algorithm (WAR), provide a first step towards evaluating these impacts. However, to address the issues of accuracy and the relative weights of these impact indexes, one must consider the problem of uncertainties. Environmental impacts must also be weighted and balanced against other concerns, such as their cost and long-term sustainability. These multiple, often conflicting, goals pose a challenging and complex optimization problem, requiring multi-objective optimization under uncertainty. This paper will address the problem of quantifying and analyzing the various objectives involved in process design for the environment. Towards this goal, we proposed a novel multi-objective optimization framework under uncertainty. This framework is based on new and efficient algorithms for multi-objective optimization and for uncertainty analysis. This approach finds a set of potentially optimal designs where trade-offs can be explicitly identified, unlike cost-benefit analysis, which deals with multiple objectives by identifying a single fundamental objective and then converting all the other objectives into this single currency. A benchmark process for hydrodealkylation (HDA) of toluene to produce benzene modeled in the ASPEN simulator is used to illustrate the usefulness of the approach in finding environmentally friendly and cost-effective designs under uncertainty. Received: 8 February 2000 / Accepted: 10 March 2000     

Model-based approach to study the impact of biofuels on the sustainability of an ecological system

The importance and complexity of sustainability have been well recognized and a formal study of sustainability based on system theory approaches is imperative as many of the relationships between various components of the ecosystem could be nonlinear, intertwined and non-intuitive. A mathematical model capable of yielding qualitative inferences can serve as an important tool for policy makers as it can be simulated under various important scenarios and also help in evaluating different strategies and technologies. In this article, we consider a simplified ecological food web which comprises a macro-economic system, an industrial production sector, an energy generation sector, and elements of a human society along with a rudimentary legal system. The energy sector is designed to supply energy to the other components of the ecosystem either by using a finite, non-renewable energy source or by a combination of non-renewable source and biomass. Many of the components of the ecosystem depend directly or indirectly on the biomass used for energy production. Subsequently, this model is used to study the impact of using biomass for the production of energy on the sustainability of other components of ecosystem. We have also simulated the model under two commonly foreseen scenarios of population explosion and consumption increase to understand the effect of using biomass for the production of energy on the sustainability of the various components of the system.     

Optimal reflux rate policy determination for multicomponent batch distillation columns

This paper describes a procedure to obtain optimal reflux or optimal distillate rate policy for multicomponent batch distillation columns using the Pontryagin's continuous maximum principle. For application to multicomponent systems, a reduced order model is used using short-cut procedure developed specifically for analysis and design of batch columns.     

Stochastic maximum principle for optimal control under uncertainty

Optimal control problems involve the difficult task of determining time-varying profiles through dynamic optimization. Such problems become even more complex in practical situations where handling time dependent uncertainties becomes an important issue. Approaches to stochastic optimal control problems have been reported in the finance literature and are based on real option theory, combining Ito’s Lemma and the dynamic programming formulation. This paper describes a new approach to stochastic optimal control problems in which the stochastic dynamic programming formulation is converted into a stochastic maximum principle formulation. An application of such method has been reported by Rico-Ramirez et al. (Computers and Chemical Engineering, 2003, 27, 1867) but no details of the derivation were provided. The main significance of this approach is that the solution to the partial differential equations involved in the dynamic programming formulation is avoided. The classical isoperimetric problem illustrates this approach.     

Integrating product and process design with optimal control: A case study of solvent recycling

This paper proposes the simultaneous integration of environmentally benign solvent selection (product design), solvent recycling (process design) and optimal control for the separation of azeotropic systems using batch distillation. The previous work performed by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606-1633) combines the chemical synthesis and process synthesis under uncertainty. For batch distillation, optimal operation is also important due to the unsteady state nature of the process and high operating costs. Optimal control allows us to optimize the column operating policy by selecting a trajectory for the reflux ratio. However, there are time-dependent uncertainties in thermodynamic models of batch distillation due to the assumption of constant relative volatility. In this paper, the uncertainties in relative volatility were modeled using Ito processes and the stochastic optimal control problem was solved by combined maximum principle and non-linear programming (NLP) techniques. Then the previous work of optimal solvent selection and recycling was coupled with optimal control. As a real world example for this integrated approach, a waste stream containing acetonitrile-water was studied. The optimal design parameters obtained by Kim et al. (2004. Entrainer selection and solvent recycling in complex batch distillation. Chemical Engineering Communications 191(12), 1606-1633), for this separation were used and the optimal control policy is computed first without considering uncertainties by variable transformation technique. The deterministic optimal control policy improves the product yield by 4.0% as compared to the base case, verified using a rigorous simulator for batch distillation. When the stochastic optimal control policy was computed representing the relative volatility as an Ito process, a similar recovery rate was obtained from simulations, but the batch time was reduced significantly, producing the most profitable operation.