Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion PDE system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns

Techniques for the Tuning of Helicopter Multivariable Flight Control Systems and Handling Qualities

Helicopter flight control systems are often developed using low order linear descriptions of the plant. Unfortunately, unmodelled high order dynamics, such as those of the actuators and the main rotor, can have an adverse effect on stability and cross couplings when the design is tested on the aircraft. Hence, the flight controller may require tuning during commissioning trials in order to yield a system with acceptable handling qualities. As the sophistication of flight control systems is enhanced, the currently used trial and error optimization techniques will lose effectiveness. Anticipating the difficulties which will arise in the implementation of active control technology to helicopters, a study has been made of systematic procedures for adjusting the control system gains. The tuning processes which have been developed rely upon the signal convolution method to generate sensitivity functions of the state variables with respect to control system gains. State variable sensitivities allow one to predict what effects changing a controller gain will have on the system response. The beauty of the signal convolution method is that the sensitivity information is generated without knowledge of the helicopter plant. Therefore, by using data collected during flight trials, it is possible to calculate the sensitivity functions with respect to the dynamics of the actual system plant, including the unmodelled modes. The sensitivity information is used by an adjustment algorithm which employs Newton-Raphson techniques to predict how the system response will change with a trial set of perturbations to the controller gains. For each set of perturbations, an estimate is made of the modifed response which, in turn, is assigned a figure of merit. The set of perturbation values which yields the best figure of merit is then used to update the initial values of the control system gains. Since the characteristics of the optimized system response are determined by the type of figure of merit used in the adjustment algorithm, two distinct performance indices have been evaluated during the study. In model reference tuning, the Least Integral Error Square Performance Index is calculated to provide the figure of merit for each projected system response. The controller gains are altered to minimize the difference between the response of the actual system and a desirable response which is generated by a computer simulation model. However, in using a reference model, care must be taken to ensure that the desirable response is consistent with a Level 1 handling qualities rating so that pilots find the tuned system acceptable to fly. In contrast, the Handling Qualities Performance Index allows system responses to be compared explicitly in terms of whether or not they satisfy the handling quality requirements. As these requirements form the starting point for many control system designs, the use of the Handling Qualities Performance Index should guarantee an improvement in system response. This new performance index uniquely links the values of control system gains to the helicopter's handling quality ratings. Computer simulation has been used to validate both the application of the signal convolution method to multivariable control systems and the ability of the two performance indices to tune a helicopter's flight controller. The flight control systems considered during these simulations were developed using modal control theory and have been used with both linear and nonlinear representations of the helicopter plant. The results of a real-time simulation have reinforced the notion that the flight controller's structure and parameter values must be determined with respect to desirable flight handling qualities rather than purely on the basis of mathematical control system design techniques

A multiple objective optimization approach to quality control

The use of product quality as the performance criteria for manufacturing system control is explored. The goal in manufacturing, for economic reasons, is to optimize product quality. The problem is that since quality is a rather nebulous product characteristic, there is seldom an analytic function that can be used as a measure. Therefore standard control approaches, such as optimal control, cannot readily be applied. A second problem with optimizing product quality is that it is typically measured along many dimensions: there are many apsects of quality which must be optimized simultaneously. Very often these different aspects are incommensurate and competing. The concept of optimality must now include accepting tradeoffs among the different quality characteristics. These problems are addressed using multiple objective optimization. It is shown that the quality control problem can be defined as a multiple objective optimization problem. A controller structure is defined using this as the basis. Then, an algorithm is presented which can be used by an operator to interactively find the best operating point. Essentially, the algorithm uses process data to provide the operator with two pieces of information: (1) if it is possible to simultaneously improve all quality criteria, then determine what changes to the process input or controller parameters should be made to do this; and (2) if it is not possible to improve all criteria, and the current operating point is not a desirable one, select a criteria in which a tradeoff should be made, and make input changes to improve all other criteria. The process is not operating at an optimal point in any sense if no tradeoff has to be made to move to a new operating point. This algorithm ensures that operating points are optimal in some sense and provides the operator with information about tradeoffs when seeking the best operating point. The multiobjective algorithm was implemented in two different injection molding scenarios: tuning of process controllers to meet specified performance objectives and tuning of process inputs to meet specified quality objectives. Five case studies are presented

Passive Micromixers

Micro-total analysis systems and lab-on-a-chip platforms are widely used for sample preparation and analysis, drug delivery, and biological and chemical syntheses. A micromixer is an important component in these applications. Rapid and efficient mixing is a challenging task in the design and development of micromixers. The flow in micromixers is laminar, and, thus, the mixing is primarily dominated by diffusion. Recently, diverse techniques have been developed to promote mixing by enlarging the interfacial area between the fluids or by increasing the residential time of fluids in the micromixer. Based on their mixing mechanism, micromixers are classified into two types: active and passive. Passive micromixers are easy to fabricate and generally use geometry modification to cause chaotic advection or lamination to promote the mixing of the fluid samples, unlike active micromixers, which use moving parts or some external agitation/energy for the mixing. Many researchers have studied various geometries to design efficient passive micromixers. Recently, numerical optimization techniques based on computational fluid dynamic analysis have been proven to be efficient tools in the design of micromixers. The current Special Issue covers new mechanisms, design, numerical and/or experimental mixing analysis, and design optimization of various passive micromixers

Design And Optimization Of Nanostructured Optical Filters

Optical filters encompass a vast array of devices and structures for a wide variety of applications. Generally speaking, an optical filter is some structure that applies a designed amplitude and phase transform to an incident signal. Different classes of filters have vastly divergent characteristics, and one of the challenges in the optical design process is identifying the ideal filter for a given application and optimizing it to obtain a specific response. In particular, it is highly advantageous to obtain a filter that can be seamlessly integrated into an overall device package without requiring exotic fabrication steps, extremely sensitive alignments, or complicated conversions between optical and electrical signals. This dissertation explores three classes of nano-scale optical filters in an effort to obtain different types of dispersive response functions. First, dispersive waveguides are designed using a sub-wavelength periodic structure to transmit a single TE propagating mode with very high second order dispersion. Next, an innovative approach for decoupling waveguide trajectories from Bragg gratings is outlined and used to obtain a uniform second-order dispersion response while minimizing fabrication limitations. Finally, high Q-factor microcavities are coupled into axisymmetric pillar structures that offer extremely high group delay over very narrow transmission bandwidths. While these three novel filters are quite diverse in their operation and target applications, they offer extremely compact structures given the magnitude of the dispersion or group delay they introduce to an incident signal. They are also designed and structured as to be formed on an optical wafer scale using standard integrated circuit fabrication techniques. A number of frequency-domain numerical simulation methods are developed to fully characterize and model each of the different filters. The complete filter response, which includes the dispersion and delay characteristics and optical coupling, is used to evaluate each filter design concept. However, due to the complex nature of the structure geometries and electromagnetic interactions, an iterative optimization approach is required to improve the structure designs and obtain a suitable response. To this end, a Particle Swarm Optimization algorithm is developed and applied to the simulated filter responses to generate optimal filter designs

Multiscale Modeling and Gaussian Process Regression for Applications in Composite Materials

An ongoing challenge in advanced materials design is the development of accurate multiscale models that consider uncertainty while establishing a link between knowledge or information about constituent materials to overall composite properties. Successful models can accurately predict composite properties, reducing the high financial and labor costs associated with experimental determination and accelerating material innovation. Whereas early pioneers in micromechanics developed simplistic theoretical models to map these relationships, modern advances in computer technology have enabled detailed simulators capable of accurately predicting complex and multiscale phenomena. This work advances domain knowledge via two means: firstly, through the development of high-fidelity, physics-based finite element (FE) models of composite microstructures that incorporate uncertainty in predictions, and secondly, through the development of a novel inverse analysis framework that enables the discovery of unknown or obscure constituent properties using literature data and Gaussian process (GP) surrogate models trained on FE model predictions. This work presents a generalizable approach to modeling a diverse array of composite subtypes, from a simple particulate system to a complex commercial composite. The inverse analysis framework was demonstrated for a thermoplastic composite reinforced by spherical fillers with unknown interphase properties. The framework leverages computer model simulations with easily obtainable macroscale elastic property measurements to infer interphase properties that are otherwise challenging to measure. The interphase modulus and thickness were determined for six different thermoplastic composites; four were reinforced by micron-scale particles and two with nano-scale particles. An alginate fiber embedded with a helically symmetric arrangement of cellulose nanocrystals (CNCs) was investigated using multiscale FE analysis to quantify microstructural uncertainty and the subsequent effect on macroscopic behavior. The macroscale uniaxial tensile simulation revealed that the microstructure induces internal stresses sufficient to rotate or twist the fiber about its axis. The reduction in axial elastic modulus for increases in CNC spiral angle was quantified in a sensitivity analysis using a GP surrogate modeling approach. A predictive model using GP regression was employed to investigate the link between input features and the mechanical properties of fiberglass-reinforced magnesium oxychloride (MOC) cement boards produced from a commercial process. The model evaluated the effect of formulation, crystalline phase compositions, and process control parameters on various mechanical performance metrics