Kathleen Fowler

Estimating the Resuspension Rate and Residence Time of Indoor Particles

Abstract Resuspension experiments were performed in a single-family residence. Resuspension by human activity was found to elevate the mass concentration of indoor particulate matter with an aerodynamic diameter less than 10 µm (PM10) an average of 2.5 times as high as the background level. As summarized from 14 experiments, the average estimated PM10 resuspension rate by a person walking on a carpeted floor was (1.4 ± 0.6) × 10−4 hr−1. The estimated residence time for PM in the indoor air following resuspension was less than 2 hr for PM10 and less than 3 hr for 2-μm tracer particles. However, experimental results show that the 2-μm tracer particles stayed in the combined indoor air and surface compartments much longer (»19 days). Using a two-compartment model to simulate a regular deposition and resuspension cycle by normal human activity (e.g., walking and sitting on furniture), we estimated residence time for 2-μm conservative particulate pollutants to be more than 7 decades without vacuum cleaning, and months if vacuum cleaning was done once per week. This finding supports the observed long residence time of persistent organic pollutants in indoor environments. This study introduces a method to evaluate the particle resuspension rate from semicontinuous concentration data of particulate matter (PM). It reveals that resuspension and subsequent exfiltration does not strongly affect the overall residence time of PM pollutants when compared with surface cleaning. However, resuspension substantially increases PM concentration, and thus increases short-term inhalation exposure to indoor PM pollutants.

Pseudo-Transient Continuation for Nonsmooth Nonlinear Equations

Pseudo-transient continuation is a Newton-like iterative method for computing steady-state solutions of differential equations in cases where the initial data are far from a steady state. The iteration mimics a temporal integration scheme, with the time step being increased as steady state is approached. The iteration is an inexact Newton iteration in the terminal phase. In this paper we show how steady-state solutions to certain ordinary and differential algebraic equations with nonsmooth dynamics can be computed with the method of pseudo-transient continuation. An example of such a case is a discretized PDE with a Lipschitz continuous, but nondifferentiable, constitutive relation as part of the nonlinearity. In this case we can approximate a generalized derivative with a difference quotient. The existing theory for pseudo-transient continuation requires Lipschitz continuity of the Jacobian. Newton-like methods for nonsmooth equations have been globalized by trust-region methods, smooth approximations, and splitting methods in the past, but these approaches are not designed to find steady-state solutions of time-dependent problems. The method in this paper synthesizes the ideas from nonsmooth calculus and the method of pseudo-transient continuation.

A hydraulic capture application for optimal remediation design

The goal of a hydraulic capture model for remediation purposes is to design a well field so that the direction of groundwater flow is altered, thereby halting or reversing the migration of a contaminant plume. Management strategies typically require a well design that will contain or shrink a plume at minimum cost. Objective functions and constraints can be nonlinear, non-convex, non-differentiable, or even discontinuous. The solution uses optimization algorithms with groundwater flow and possibly transport simulators. The formulation of the objective function dictates possible optimization algorithms that can be used. For example, a gradient based method is likely to fail on a discontinuous objective function or gradient information may not be available. Computational efficiency as well as accuracy is desirable and often influences the choice of solution method. In this paper we present three hydraulic capture models. Our motivation is a hydraulic capture application proposed in the literature for benchmarking purposes. We present numerical results for the three models using the implicit filtering algorithm.

Hybrid optimization schemes for simulation-based problems

The inclusion of computer simulations in the study and design of complex engineering systems has created a need for efficient approaches to simulation-based optimization. For example, in water resources management problems, optimization problems regularly consist of objective functions and constraints that rely on output from a PDE-based simulator. Various assumptions can be made to simplify either the objective function or the physical system so that gradient-based methods apply, however the incorporation of realistic objection functions can be accomplished given the availability of derivative-free optimization methods. A wide variety of derivative-free methods exist and each method has both advantages and disadvantages. Therefore, to address such problems, we propose a hybrid approach, which allows the combining of beneficial elements of multiple methods in order to more efficiently search the design space. Specifically, in this paper, we illustrate the capabilities of two novel algorithms; one which hybridizes pattern search optimization with Gaussian Process emulation and the other which hybridizes pattern search and a genetic algorithm. We describe the hybrid methods and give some numerical results for a hydrological application which illustrate that the hybrids find an optimal solution under conditions for which traditional optimal search methods fail.

A decision making framework with MODFLOW-FMP2 via optimization

Farmers in regions experiencing water stress or drought conditions can struggle to balance their crop portfolios. Periods of low precipitation often lead to increased, unsustainable reliance on groundwater-supplied irrigation. As a result, regional water management agencies place limits on the amount of water which can be obtained from groundwater, requiring farmers to reduce acreage for more water-intensive crops or remove them from the portfolio entirely. Real-time decisions must be made by the farmer to ensure viability of their farming operation and reduce the impacts associated with limited water resources. Evolutionary algorithms, coupled with accurate, flexible, realistic simulation tools, are ideal mechanisms to allow farmers to assess scenarios with regard to multiple, competing objectives. In order to effective, however, one must be able to select among a variety of simulation tools and optimization algorithms. Many simulation tools allow no access to the source code, and many optimization algorithms are now packaged as part of a suite of tools available to a user. In this work, we describe a framework for integrating these different software components using only their associated input and output streams. We analyze our strategy by coupling a multi-objective genetic algorithm available in the DAKOTA optimization suite (developed and distributed by Sandia National Laboratory) with the MODFLOW-FMP2 simulation tool (developed and distributed by the United States Geological Survey). MODFLOW-FMP2 has been used extensively to model hydrological and farming processes in agriculture-dominated regions, allowing us to represent both farming and conservation interests. We evaluate our integration by considering a case study related to planting decisions facing farmers experiencing water stress. We present numerical results for three competing objectives associated with stakeholders in a given region (i.e., profitability, meeting demand targets, and water conservation). The data obtained from the optimization are robust with respect to algorithmic parameter choices, validating the ability of the associated evolutionary algorithm to perform well without expert guidance. This is integral to our approach, as a motivation for this work is providing decision-making tools. In addition, the results from this study demonstrate that output from the chosen evolutionary algorithm provides a suite of feasible planting scenarios, giving farmers and policy makers the ability to compromise solutions based on realistic simulation data.

Approaching the Groundwater Remediation Problem Using Multifidelity Optimization.

The objective of the hydraulic capture method for optimal groundwater remediation design is containment of a contaminant plume using barrier wells to reverse the direction of groundwater flow. Finding a solution involves applying optimization algorithms in conjunction with simulators for groundwater flow and possibly for contaminant transport. The formulation of the objective function and its corresponding constraints dictates which optimization algorithms are appropriate and usually eliminates gradient based approaches from consideration. In addition, objective functions and constraints can be nonlinear, non-convex, non- differentiable, or even discontinuous, and the simulations involved can be computationally expensive. Both computational efficiency and accuracy are important, and this further influences the choice of solution method. With the advent and increasing availability of massively parallel computers, computational speed has increased tremendously. Unfortunately, the numerical and model complexities of problems like groundwater remediation still demand significant computational resources. Moreover, these expenses can be a limiting factor of optimization since obtaining solutions often requires the completion of numerous computationally intensive jobs. Therefore, we propose an algorithm designed to improve the computational efficiency of an optimization method for a wide range of applications and apply it to groundwater remediation. Our approach takes advantage of the interactions between multifidelity models and is applicable to problems for which models of varying fidelity are available. The method can be described as follows: First, a direct search method is applied to the high fidelity model over a reduced design space. In conjunction with this search, a specialized oracle is employed to map the design space of this high fidelity model to that of a computationally cheaper low fidelity model using space mapping techniques. Then, in the low fidelity space, an optimum is obtained using gradient based optimization, and it is mapped back to the high fidelity space. To motivate this work, we consider a hydraulic capture problem proposed in the literature for benchmarking purposes. The problem is to minimize the cost to install and operate a set of wells subject to constraints on the concentration of a contaminant at specified locations in the physical domain. We solve the problem by applying the multifidelity approach described above using only flow information for the low fidelity model and using concentration based constraints for the high fidelity model. We present some promising results for this preliminary problem, and explain how we plan to extend our study by considering more representative physical models, simulators, objective function formulations, and by incorporating real-site data.

Design Analysis of Polymer Filtration using a Multi‐Objective Genetic Algorithm

Abstract Filtration of particle debris is an important component of the polymer fiber melt‐spinning process. The filter lifespan is determined by the pressure drop across the filter, which increases as debris accumulates inside the filtration medium. The cost of filter replacement is high, as is the cost of a loss of the finished fiber product due to debris inclusion in the spun fiber. We use a multiobjective genetic algorithm to examine the trade‐off curve that evolves from these competing goals. A “blackbox” simulator models the debris deposition, and we choose filter porosity and pore diameter as the design variables. We provide numerical results and analysis for two sets of competing objectives.

Traditional and Hybrid Derivative-Free Optimization Approaches for Black Box Functions

Picking a suitable optimization solver for any optimization problem is quite challenging and has been the subject of many studies and much debate. This is due in part to each solver having its own inherent strengths and weaknesses. For example, one approach may be global but have slow local convergence properties, while another may have fast local convergence but is unable to globally search the entire feasible region. In order to take advantage of the benefits of more than one solver and to overcome any shortcomings, two or more methods may be combined, forming a hybrid. Hybrid optimization is a popular approach in the combinatorial optimization community, where metaheuristics (such as genetic algorithms, tabu search, ant colony, variable neighborhood search, etc.) are combined to improve robustness and blend the distinct strengths of different approaches. More recently, metaheuristics have been combined with deterministic methods to form hybrids that simultaneously perform global and local searches. In this Chapter, we will examine the hybridization of derivative-free methods to address black box, simulation-based optimization problems. In these applications, the optimization is guided solely by function values (i.e. not by derivative information), and the function values require the output of a computational model. Specifically, we will focus on improving derivative-free sampling methods through hybridization.We will review derivative-free optimization methods, discuss possible hybrids, describe intelligent hybrid approaches that properly utilize both methods, and give an examples of the successful application of hybrid optimization to a problem from the hydrological sciences.

Optimization of Anaerobic Digestion Model No. 1 (ADM1): Simulation of Dairy Manure Digestion

The operation and design of farm digesters has been primarily based on empirical models resulting in highly conservative (i.e. capital intensive) systems. In this research the Anaerobic Digestion Model No. 1 (ADM1), developed for municipal waste by the International Water Association, was used to simulate a mesophilic pilot scale digester treating dairy manure. The focus of this research was to develop a kinetic parameter set specific to dairy manure allowing for the simulation of digesters operated under transient conditions. Such a model could be used to evaluate changes in digester operation, feed stocks or assist in digester design. Model calibration was carried out by varying 32 biochemical parameters using Nedler-Mead optimization algorithm to fit the model to pilot plant data (COD, volatile fatty acids, biogas flow and biogas composition). The performance of the calibrated model was then compared with an empirically calibrated model. Results suggest that the calibrated model could simulate the dynamic behavior of the pilot scale digester reasonably well illustrating the potential use of the model to the agricultural community.

Analysis of model parameters for a polymer filtration simulator

We examine a simulation model for polymer extrusion filters and determine its sensitivity to filter parameters. The simulator is a three-dimensional, time-dependent discretization of a coupled system of nonlinear partial differential equations used to model fluid flow and debris transport, along with statistical relationships that define debris distributions and retention probabilities. The flow of polymer fluid, and suspended debris particles, is tracked to determine how well a filter performs and how long it operates before clogging. A filter may have multiple layers, characterized by thickness, porosity, and average pore diameter. In this work, the thickness of each layer is fixed, while the porosities and pore diameters vary for a two-layer and three-layer study. The effects of porosity and average pore diameter on the measures of filter quality are calculated. For the three layer model, these effects are tested for statistical significance using analysis of variance. Furthermore, the effects of each pair of interacting parameters are considered. This allows the detection of complexity, where in changing two aspects of a filter together may generate results substantially different from what occurs when those same aspects change separately. The principal findings indicate that the first layer of a filter is the most important.