Prasanth B. Nair

Max-min surrogate-assisted evolutionary algorithm for robust design

Solving design optimization problems using evolutionary algorithms has always been perceived as finding the optimal solution over the entire search space. However, the global optima may not always be the most desirable solution in many real-world engineering design problems. In practice, if the global optimal solution is very sensitive to uncertainties, for example, small changes in design variables or operating conditions, then it may not be appropriate to use this highly sensitive solution. In this paper, we focus on combining evolutionary algorithms with function approximation techniques for robust design. In particular, we investigate the application of robust genetic algorithms to problems with high dimensions. Subsequently, we present a novel evolutionary algorithm based on the combination of a max-min optimization strategy with a Baldwinian trust-region framework employing local surrogate models for reducing the computational cost associated with robust design problems. Empirical results are presented for synthetic test functions and aerodynamic shape design problems to demonstrate that the proposed algorithm converges to robust optimum designs on a limited computational budget

Efficient computational method for assessing the effects of implant positioning in cementless total hip replacements

The present work describes a statistical investigation into the effects of implant positioning on the initial stability of a cementless total hip replacement (THR). Mesh morphing was combined with design of computer experiments to automatically construct Finite Element (FE) meshes for a range of pre-defined femur-implant configurations and to predict implant micromotions under joint contact and muscle loading. Computed micromotions, in turn, are postprocessed using a Bayesian approach to: (a) compute the main effects of implant orientation angles, (b) predict the sensitivities of the considered implant performance metrics with respect to implant ante-retroversion, varus-valgus and antero-posterior orientation angles and (c) identify implant positions that maximise and minimise each metric. It is found that the percentage of implant area with micromotion greater than 50 μm, average and maximum micromotions are all more sensitive to antero-posterior orientation than ante-retroversion and varus-valgus orientation. Sensitivities, combined with the main effect results, suggest that bone is less likely to grow if the implant is increasingly moved from the neutral position towards the anterior part of the femur, where the highest micromotions occur. The computed implant best position leads to a percentage of implant area with micromotion greater than 50 μm of 1.14 when using this metric compared to 14.6 and 5.95 in the worst and neutrally positioned implant cases. In contrast, when the implant average/maximum micromotion is used to assess the THR performance, the implant best position corresponds to average/maximum micromotion of 9 μm/59 μm, compared to 20 μm/114 μm and 13 μm/71 μm in the worst and neutral positions, respectively. The proposed computational framework can be extended further to study the effects of uncertainty and variability in anatomy, bone mechanical properties, loading or bone-implant interface contact conditions.

Mining data from hemodynamic simulations via Bayesian emulation

Background:Arterial geometry variability is inevitable both within and across individuals. To ensure realistic prediction of cardiovascular flows, there is a need for efficient numerical methods that can systematically account for geometric uncertainty.Methods and results:A statistical framework based on Bayesian Gaussian process modeling was proposed for mining data generated from computer simulations. The proposed approach was applied to analyze the influence of geometric parameters on hemodynamics in the human carotid artery bifurcation. A parametric model in conjunction with a design of computer experiments strategy was used for generating a set of observational data that contains the maximum wall shear stress values for a range of probable arterial geometries. The dataset was mined via a Bayesian Gaussian process emulator to estimate: (a) the influence of key parameters on the output via sensitivity analysis, (b) uncertainty in output as a function of uncertainty in input, and (c) which settings of the input parameters result in maximum and minimum values of the output. Finally, potential diagnostic indicators were proposed that can be used to aid the assessment of stroke risk for a given patients geometry.

Genetic Programming Approaches for Solving Elliptic Partial Differential Equations

In this paper, we propose a technique based on genetic programming (GP) for meshfree solution of elliptic partial differential equations. We employ the least-squares collocation principle to define an appropriate objective function, which is optimized using GP. Two approaches are presented for the repair of the symbolic expression for the field variables evolved by the GP algorithm to ensure that the governing equations as well as the boundary conditions are satisfied. In the case of problems defined on geometrically simple domains, we augment the solution evolved by GP with additional terms, such that the boundary conditions are satisfied by construction. To satisfy the boundary conditions for geometrically irregular domains, we combine the GP model with a radial basis function network. We improve the computational efficiency and accuracy of both techniques with gradient boosting, a technique originally developed by the machine learning community. Numerical studies are presented for operator problems on regular and irregular boundaries to illustrate the performance of the proposed algorithms.

Problem solving environments in aerospace design

Abstract Recent developments in aerospace design systems are being driven by studies in a number of areas including new software methodologies, advanced approximation techniques, data archiving and fusion methods, artificial intelligence, and the natural biology and socio-economic behaviour of species together with the continuing developments in computational hardware. Advances in these areas are leading to interesting new ways of managing the design process when dealing with increasingly complex systems and also increasingly complex design organizations. This work covers topics as diverse as the formal optimisation of differential equation models, the management of workstation clusters in design offices and the re-use of linguistically formulated knowledge. Collectively, such studies allow the production of problem solving environments, where a wide range of approaches can be readily integrated by the design team to suit the problem in hand. The ideas discussed in this paper have been formed by the authors experiences gained in aero-engine, aircraft and satellite design optimisation. They are not meant to be exhaustive or prescriptive, but instead present a personal view of some of the challenges that lie ahead.

Forced response statistics of mistuned bladed disks: a stochastic reduced basis approach

This paper presents a stochastic reduced basis approach for predicting the forced response statistics of mistuned bladed-disk assemblies. In this approach, the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors with undermined coefficients. The terms of the preconditioned stochastic Krylov subspace are used here as basis vectors. Two variants of the stochastic Bubnov–Galerkin scheme are employed for computing the undetermined terms in the reduced basis representation, which arise from how the condition for orthogonality between two random vectors is interpreted. Explicit expressions for the response quantities can then be derived in terms of the random system parameters, which allow for the possibility of efficiently computing the response statistics in the post-processing stage. Numerical studies are presented for mistuned cyclic assemblies of mono-coupled single-mode components. It is demonstrated that the accuracy of the response statistical moments computed using stochastic reduced basis methods can be orders of magnitude better than classical perturbation methods.

Robust Design of Compressor Blades Against Manufacturing Variations

The aim of this paper is to develop and illustrate an efficient methodology to design blades with robust aerodynamic performance in the presence of manufacturing uncertainties. A novel geometry parametrization technique is developed to represent manufacturing variations due to tolerancing. A Gaussian Stochastic Process Model is trained using DOE techniques in conjunction with a high fidelity CFD solver. Bayesian Monte Carlo Simulation is then employed to obtain the statistics of the performance at each design point. A multiobjective optimizer is used to search the design space for robust designs. The multiobjective formulation allows explicit trade-off between the mean and variance of the performance. A design, selected from the robust design set is compared with a deterministic optimal design. The results demonstrate an effective method to obtain compressor blade designs which have reduced sensitivity to manufacturing variations with significant savings in computational effort.Copyright

Efficient Genetic Algoritm Based Robust Design Method for Compressor Fan Blades

This paper presents an efficient genetic algorithm based methodology for robust design that produces compressor fan blades tolerant against erosion. A novel geometry modeling method is employed to create eroded compressor fan blade sections. A multigrid Reynolds-Averaged Navier Stokes (RANS) solver HYDRA with Spalart Allmaras turbulence model is used for CFD simulations to calculate the pressure losses. This is used in conjunction with Design of Experiment techniques to create Gaussian stochastic process surrogate models to predict the mean and variance of the performance. The Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed for the multiobjective optimization to find the global Pareto-optimal front. This enables the designer to trade off between mean and variance of performance to propose robust designs.Copyright

Statistical analysis of the forced response of mistuned bladed disks using stochastic reduced basis methods

This paper is concerned with the forced response statistics of mistuned bladed disk assemblies subjected to a deterministic sinusoidal excitation. A stochastic reduced basis method (SRBM) is used to compute the statistics of the system component amplitudes. In this approach, the system response in the frequency domain is represented using a linear combination of stochastic basis vectors with undermined coefficients. The three terms of the second-order perturbation approximation (which span the stochastic Krylov subspace) are used as basis vectors and the undetermined coefficients arenevaluated using stochastic variants of the Bubnov- Galerkin Scheme. This results in explicit expressions for the response quantities in terms of the random system parameters. The statistics of the system response can hence be efficiently computed in the post-processing stage. Numerical results are presented for a model problem to demonstrate that the stochastic reduced basis formulation gives highly accurate results for the response statistical moments.

Bayesian surrogate modeling of deterministic simulation codes for probablistic analysis

A Bayesian Gaussian process modeling framework is presented for uncertainty analysis of systems using existing deterministic black-box simulation codes. It is argued that the Bayesian modeling approach is statistically more meaningful as compared to response surface methods which use least-square regression techniques. Further, the present framework allows for the possibility of computing error estimates of the computed statistics. An adaptive design of experiments strategy is also presented for improving the accuracy of the model. Numerical studies are presented for a structural reliability analysis problem. The results indicate that the Bayesian approach holds promise for significantly reducing the computational cost of simulation based approaches. Further, the error estimates computed using the Bayesian approach are shown to become reasonably tighter with increase in the number of design points.