Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Surrogate-based-optimization methods provide a means to achieve high-fidelity design optimization at reduced computational cost by using a high-fidelity model in combination with lower-fidelity models that are less expensive to evaluate. This paper presents a provably convergent trust-region model-management methodology for variableparameterization design models: that is, models for which the design parameters are defined over different spaces. Corrected space mapping is introduced as a method to map between the variable-parameterization design spaces. It is then used with a sequential-quadratic-programming-like trust-region method for two aerospace-related design optimization problems. Results for a wing design problem and a flapping-flight problem show that the method outperforms direct optimization in the high-fidelity space. On the wing design problem, the new method achieves 76% savings in high-fidelity function calls. On a bat-flight design problem, it achieves approximately 45% time savings, although it converges to a different local minimum than did the benchmark.

Determining the parametric effectiveness of a CAD model

The motivation for this paper is to present an approach for rating the quality of the parameters in a computer-aided design model for use as optimization variables. Parametric Effectiveness is computed as the ratio of change in performance achieved by perturbing the parameters in the optimum way, to the change in performance that would be achieved by allowing the boundary of the model to move without the constraint on shape change enforced by the CAD parameterization. The approach is applied in this paper to optimization based on adjoint shape sensitivity analyses. The derivation of parametric effectiveness is presented for optimization both with and without the constraint of constant volume. In both cases, the movement of the boundary is normalized with respect to a small root mean squared movement of the boundary. The approach can be used to select an initial search direction in parameter space, or to select sets of model parameters which have the greatest ability to improve model performance. The approach is applied to a number of example 2D and 3D FEA and CFD problems.

Strategies for adding features to CAD models in order to optimize performance

This paper presents an approach which enables new parameters to be added to a CAD model for optimization purposes. It aims to remove a common roadblock to CAD based optimization, where the parameterization of the model does not offer the shape sufficient flexibility for a truly optimized shape to be created. A technique has been developed which uses adjoint based sensitivity maps to predict
the sensitivity of performance to the addition to a model of four different feature types, allowing the feature providing the greatest benefit to be selected. The optimum position to add the feature is also discussed. It is anticipated that the approach could be used to iteratively add features to a model, providing greater flexibility to the shape of the model, and allowing the newly-added parameters to be used as design variables in a subsequent shape optimization.

Rapid design of discrete orthonormal wavelet transforms

A methodology which allows a non-specialist to rapidly design silicon wavelet transform cores has been developed. This methodology is based on a generic architecture utilizing time-interleaved coefficients for the wavelet transform filters. The architecture is scaleable and it has been parameterized in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is designed in such a way that the cores can also be cascaded without any interface glue logic for any desired level of decomposition. This parameterization allows the use of any orthonormal wavelet family thereby extending the design space for improved transformation from algorithm to silicon. Case studies for stand alone and cascaded silicon cores for single and multi-stage analysis respectively are reported. The typical design time to produce silicon layout of a wavelet based system has been reduced by an order of magnitude. The cores are comparable in area and performance to hand-crafted designs. The designs have been captured in VHDL so they are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Multi-Fidelity Multidisciplinary Whole Engine Thermo-Mechanical Design Optimization

Traditionally, the optimization of a turbomachinery engine casing for tip clearance has involved either twodimensional transient thermomechanical simulations or three-dimensional mechanical simulations. This paper illustrates that three-dimensional transient whole-engine thermomechanical simulations can be used within tip clearance optimizations and that the efficiency of such optimizations can be improved when a multifidelity surrogate modeling approach is employed. These simulations are employed in conjunction with a rotor suboptimization using surrogate models of rotor-dynamics performance, stress, mass and transient displacements, and an engine parameterization.

Biofilm Complexity Controls Fine Particle Dynamics in Streams

Most models of riverine eco-hydrology and biogeochemistry rely upon bulk parameterization of fluxes. However, the transport and retention of carbon and nutrients in headwater streams is strongly influenced by biofilms (surface-attached microbial communities), which results in strong feedbacks between stream hydrodynamics and biogeochemistry. Mechanistic understanding of the interactions between streambed biofilms and nutrient dynamics is lacking. Here we present experimental results linking microscale observations of biofilm community structure to the deposition and resuspension of clay-sized mineral particles in streams. Biofilms were grown in identical 3 m recirculating flumes over periods of 14-50 days. Fluorescent particles were introduced to each flume, and their deposition was traced over 30 minutes. Particle resuspension from the biofilms was then observed under an increased stream flow, mimicking a flood event. We quantified particle fluxes using flow cytometry and epifluorescence microscopy. We directly observed particle adhesion to the biofilm using a confocal laser scanning microscope. 3-D Optical Coherence Tomography was used to determine biofilm roughness, areal coverage and void space in each flume. These measurements allow us to link biofilm complexity to particle retention during both baseflow and floodflow. The results suggest that increased biofilm complexity favors deposition and retention of fine particles in streams.