Adjoint-based Optimization Technique Research Articles

Adjoint-based optimization of dielectric coatings for refractory metals to achieve broadband spectral reflection

Refractory metals, which include niobium, tantalum, molybdenum, and tungsten, are critical components in applications in extreme environments due to their attractive thermomechanical properties. However, their low reflectivity below 1500 nm has prompted researchers to focus on increasing their reflection at shorter wavelengths. In this study, we applied an adjoint-based optimization technique to improve the spectral reflectivity of refractory metals in the broadband spectrum (300–3000 nm). An optimized periodic multilayer consisting of SiO2/TiO2 is selected as a starting point for the process. Then, the adjoint-based method is implemented to enhance the reflection of the surfaces. This approach involves an iterative procedure that guarantees improvement in every iteration. In every iteration, both the direct and adjoint solutions of Maxwell’s equations are computed to predict the scattering characteristics of a particular microstructure on a surface and measure its effectiveness. The results of our study indicate that the final designs not only increase reflectivity to over 90% but also have thermomechanical benefits that make them suitable for use in harsh environments. We also explored the effect of initial geometry on the results. Overall, our study shows that the adjoint-based optimization technique is an effective method for creating high-performing broadband reflectors with refractory metal substrates coated with dielectric multilayers.

Shape Optimization of an Asymmetric Airfoil for Low Wind Speed Region having Adjoint-Based Optimization Technique

The land needed to install wind turbines is shrinking as power generation from renewable energy sources increases significantly. A large number of studies are being conducted to maximize the power extraction from wind turbines in areas with low wind speeds. Wind turbine blades play a significant role in utilizing the maximum amount of energy from the wind. The aerodynamic performance of a wind turbine blade depends on the airfoil shape. The shape optimization of an asymmetric S2027 airfoil for a low wind speed region was investigated using the adjoint-based optimization technique. The primary objectives of this study were to maximize the lift coefficient, minimize the drag coefficient, and maximize the lift-to-drag ratio. The optimization is based on the adjoint method for Reynolds number variation in the range of 2 × 105 to 5 × 105 and an angle of attack variation from 0° to 12°. A two-dimensional Reynolds–Averaged Navier–Strokes Computational Fluid Dynamics model was created with all the operating parameters and used for optimization. The aerodynamic performance was validated experimentally. For each optimization function, approximately 16 shapes were obtained. The aerodynamic performance for each optimized shape was determined under different operating conditions. Different airfoil shapes with a specific chord, leading and trailing edges, and span arrangement was obtained. The drag coefficient was reduced by 2%–30%; the lift coefficient was improved by 2%–35%, and the lift-to-drag ratio was improved up to 40%.

Finite-fault source inversion using adjoint methods in 3-D heterogeneous media

Accounting for lateral heterogeneities in the 3-D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1-D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3-D heterogeneity in source inversion involves pre-computing 3-D Green’s functions, which requires a number of 3-D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense data sets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green’s functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green’s functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3-D heterogeneous velocity model. The velocity model comprises a uniform background and a 3-D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3-D velocity model are performed for two different station configurations, a dense and a sparse network with 1 and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak-slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect, homogeneous velocity model. We find that, for velocity uncertainties that have standard deviation and correlation length typical of available 3-D crustal models, the inverted sources can be severely contaminated by spurious features even if the station density is high. When data from thousand or more receivers is used in source inversions in 3-D heterogeneous media, the computational cost of the method proposed in this work is at least two orders of magnitude lower than source inversion based on pre-computed Green’s functions.

Achievements and challenges in automated parameter, shape and topology optimization for divertor design

Plasma edge transport codes play a key role in the design of future divertor concepts. Their long simulation times in combination with a large number of control parameters turn the design into a challenging task. In aerodynamics and structural mechanics, adjoint-based optimization techniques have proven successful to tackle similar design challenges. This paper provides an overview of achievements and remaining challenges with these techniques for complex divertor design. It is shown how these developments pave the way for fast sensitivity analysis and improved design from different perspectives.

Interval-Based Approach for Uncertainty Propagation in Inverse Problems

AbstractA new class of interval-based computational algorithms for parameter identification under uncertainty in structural engineering problems is presented. The iterative method allows passing directly from uncertain raw measurements to sharp (tight) bound estimates of the unknown parameters by exploiting interval FEMs and adjoint-based optimization techniques. Overestimation in interval width is handled successfully using the inclusion isotonicity property of interval arithmetic. First, an update of the iterative solution proceeds in a degenerated interval form until it becomes insignificant, and then the update is switched to full interval form, allowing uncertainty propagation and sensitivity analysis. A new containment-stopping criterion, which is intrinsic to intervals, is used. Example problems are then presented and discussed to show the effectiveness of the proposed inverse method in estimating the range of Young’s moduli from given ranges in displacements.

Shape Optimization of NREL S809 Airfoil for Wind Turbine Blades Using a Multiobjective Genetic Algorithm

The goal of this paper is to employ a multiobjective genetic algorithm (MOGA) to optimize the shape of a well-known wind turbine airfoil S809 to improve its lift and drag characteristics, in particular to achieve two objectives, that is, to increase its lift and its lift to drag ratio. The commercially available software FLUENT is employed to calculate the flow field on an adaptive structured mesh using the Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with a two-equationk-ωSST turbulence model. The results show significant improvement in both lift coefficient and lift to drag ratio of the optimized airfoil compared to the original S809 airfoil. In addition, MOGA results are in close agreement with those obtained by the adjoint-based optimization technique.

Adjoint-Based Aerodynamic Optimization of Supersonic Biplane Airfoils

This paper addresses the aerodynamic performance of Busemann type supersonic biplane at off-design conditions. An adjoint based optimization technique is used to optimize the aerodynamic shape of the biplane to reduce the wave drag at a series of Mach numbers ranging from 1.1 to 1.7, at both acceleration and deceleration conditions. The optimized biplane airfoils dramatically reduces the effects of the choked flow and flow-hysteresis phenomena, while maintaining a certain degree of favorable shockwave interaction effects at the design Mach number. Compared to a diamond shaped single airfoil of the same total thickness, the wave drag of our optimized biplane is lower at almost all Mach numbers, and is significantly lower at the design Mach number.

Adjoint-based optimization for understanding and suppressing jet noise

Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized. This paper, which follows from a presentation at the 2010 IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, reviews recent and ongoing efforts by the author and co-workers. It provides a new formulation of the basic approach and demonstrates the approach on a series of model flows, culminating with a preliminary result for a turbulent jet.

A semi-coupled solution algorithm in aerodynamic inverse shape design

The numerical solution of an inverse airfoil design problem requires computational tools for grid generation, flow solution and the geometry update to provide the desirable shape corresponding to a given surface target pressure. Un-coupled as well as fully and semi-coupled shape design strategies have already been developed and employed. The target pressure is directly imposed in the fully coupled approach in contrast to un-coupled methods. Available semi-coupled methods use additional computational tools to couple the flow solver and the shape updater to directly impose the target pressure. In this article, a semi-coupled numerical shape design strategy is introduced, in the context of an ideal flow model, in which the target tangential velocity is directly imposed while no additional computational tool is employed. Numerical test cases, implemented on both structured and unstructured grids, are carried out to compare the performance of the proposed method with an adjoint-based optimization technique. Results show that the semi-coupled method has a two to three times faster convergence rate as compared to the adjoint approach. However, the semi-coupled solution convergence rate usually stalls after three orders of magnitude reduction of the objective function, while the un-coupled optimization method provides a more accurate solution. Therefore, a hybrid solution methodology is also advised, which provides faster convergence as well as lower computational errors as compared to both semi and un-coupled methods.

Adjoint-based optimization for understanding and suppressing jet noise

Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not of themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized.

Reprint of: Adjoint-based optimization for understanding and suppressing jet noise

Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not of themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized.

Computational Techniques for Closed–loop Reservoir Modeling with Application to a Realistic Reservoir

Real-time model-based reservoir management requires efficient computational techniques for optimizing reservoir performance under uncertainty. A variety of algorithms addressing various aspects of this “closed-loop” methodology have been presented by various investigators, but substantial effort is still needed to make the entire process robust and efficient. In our recent work, we introduced an approximate feasible direction optimization algorithm for treating nonlinear path constraints (which are constraints such as maximum liquid production rate, which must be satisfied at every time step) and a new parameterization based on kernel principal component analysis (KPCA) for multipoint geostatistical models. The KPCA representation allows for the use of a gradient-based history-matching procedure that is able to maintain a higher degree of geological realism in the history-matched model. In this article, we combine these procedures with our general adjoint-based optimization technique to provide a full closed-loop capability. This integrated set of algorithms is then applied to a realistic field case. Specifically, we describe the key computational procedures and highlight the linkages required to provide the closed-loop capability. The example case considered is based on a Gulf of Mexico reservoir and involves three injection wells and four production wells operating under bottom hole pressure, total injection rate, and maximum water cut constraints. For this case, it is demonstrated that application of the closed-loop methodology provides a 25% increase in the net present value (NPV) over predictions for a realistic base case. This improvement is almost the same as that achieved using an open-loop approach, which is an idealized formulation in which the geological model is assumed to be known. These results demonstrate that the overall closed-loop procedure will indeed be applicable for practical cases with uncertain geology.