This article proposes a three-level radial basis function (TLRBF)-assisted optimization algorithm for expensive optimization. It consists of three search procedures at each iteration: 1) the global exploration search is to find a solution by optimizing a global RBF approximation function subject to a distance constraint in the whole search space; 2) the subregion search is to generate a solution by minimizing an RBF approximation function in a subregion determined by fuzzy clustering; and 3) the local exploitation search is to generate a solution by solving a local RBF approximation model in the neighborhood of the current best solution. Compared with some other state-of-the-art algorithms on five commonly used scalable benchmark problems, ten CEC2015 computationally expensive problems, and a real-world airfoil design optimization problem, our proposed algorithm performs well for expensive optimization. 

A Three-Level Radial Basis Function Method for Expensive Optimization

Hard sail optimization and energy efficiency enhancement for sail-assisted vessel

New Hierarchical Genetic Algorithms (HGAs) mixing Nash game are presented to speed up the optimization of aerodynamic shapes. The approach of HGAs is a particular instance of Parallel GAs (PGAs) based on the notion of interconnected subpopulations evolving independently. To improve convergence history, the present study introduces a multilayered hierarchical topology in PGAs. Such a topology allows the use of multiple models for optimization problems, and shows that it is possible to mix fast Low Fidelity models for exploration and expensive High Fidelity models for exploitation. Finally, a new class of multiobjective optimizers mixing HGAs and Nash game is defined. These methods are tested for solving design optimization problems in Aerodynamics. A parallel version of this approach running on a cluster of PCs demonstrates the convergence speed up on an inverse nozzle problem and a high lift problem for a multiple element airfoil.

Parallel Evolutionary Algorithms for Optimization Problems in Aerospace Engineering

Ionosphere is the upper atmosphere region that contains sufficient number of electrons which disturb the propagation of radio signal travel from navigational satellite to ground/user receiver. Ionospheric delay in range measurement is related to its Total Electron Content (TEC). Ionospheric delay results in range error and degrades the user position accuracy of navigational satellite systems such as Global Positioning System (GPS) and Indian Regional Navigational Satellite System (IRNSS). Hence a suitable TEC prediction model to correct the range delay in single frequency range measurement is necessary. In dual frequency receiver, ionospheric delay is estimated and eliminated using the two range measurements performed at the same time. This paper describes the TEC prediction methodology using Ordinary Kriging based Surrogate Model (OKSM). OKSM is evaluated using the data received and collected from the IRNSS receiver station installed at ACS College of Engineering (ACSCE), Bengaluru (12.8913 °N, 77.4658 °E), India and other International GNSS Service (IGS) network stations. IRNSS TEC data (January 2018) is calculated by using dual frequency (L5 & S) pseudo range method and TEC is smoothed by normal cubic smoothing spline method. IRNSS Vertical TEC (VTEC) is predicted from 16 January 2018 to 26 January 2018 by using previous six days of estimated VTEC values. Similarly, GPS VTEC for IGS station at IISC, Bengaluru is also predicted for same duration to validate the developed OKSM. In order to evaluate the performance of the developed forecasting model for different geographic locations, solar activity conditions and seasons, the VTEC is predicted and analyzed for different latitude regions such as low-latitude PHON station (6.9599 °N, 158.2101 °E), mid-latitude ALGO station (45.9588 °N, −78.0714 °E) and high-latitude NRIL station (69.3618 °N, 88.3597 °E) during different solar activity conditions (Low-2008, Medium-2011 and High-2013 solar activity) and during different seasons (spring, summer, rainy and winter) in the year 2017. From the analysis of OKSM prediction results, it is observed that, RMSE of predicted TEC varies from 0.79 to 3.6 TECU, MAE is 0.4 to 3 TECU and MAPE is within 40% for ionospheric quiet days. VTEC is also predicted during storm days (26 October 2003 to 31 October 2003). To study the performance of the model, VTEC prediction results of OKSM are compared with prediction results from Standard Persistence Model (SPM) and VTEC derived from International Reference Ionosphere (IRI-2016) model. The RMSE of OKSM is 1.9679 TECU, MAE is 1.245 TECU and MAPE is 9%, whereas for SPM, RMSE is 4.8372 TECU, MAE is 3.7496 TECU and MAPE is 36%. Similarly, for IRI-2016 model, RMSE is 7.9 TECU, MAE is 7.1976 TECU and MAPE is 66%. Therefore, TEC predictions by OKSM are better than SPM and IRI-2016. The results show that the OKSM is useful for applications in ionospheric studies.

Forecasting of ionospheric TEC for different latitudes, seasons and solar activity conditions based on OKSM

Multi-condition multi-objective optimization using deep reinforcement learning

Computational fluid dynamics (CFD) is one of the computer-based solution methods which is more widely employed in aerospace engineering. The computational power and time required to carry out the analysis increase as the fidelity of the analysis increases. Aerodynamic shape optimization has become a vital part of aircraft design in the recent years. Generally if we want to optimize an airfoil we have to describe the airfoil and for that, we need to have at least hundred points of x and y co-ordinates. It is really difficult to optimize airfoils with this large number of co-ordinates. Nowadays many different schemes of parameter sets are used to describe general airfoil such as B-spline, and PARSEC. The main goal of these parameterization schemes is to reduce the number of needed parameters as few as possible while controlling the important aerodynamic features effectively. Here the work has been done on the PARSEC geometry representation method. The objective of this work is to introduce the knowledge of describing general airfoil using twelve parameters by representing its shape as a polynomial function. And also we have introduced the concept of Genetic Algorithm to optimize the aerodynamic characteristics of a general airfoil for specific conditions. A MATLAB program has been developed to implement PARSEC, Panel Technique, and Genetic Algorithm. This program has been tested for a standard NACA 2411 airfoil and optimized to improve its coefficient of lift. Pressure distribution and co-efficient of lift for airfoil geometries have been calculated using the Panel method. The optimized airfoil has improved co-efficient of lift compared to the original one. The optimized airfoil is validated using wind tunnel data.

Airfoil shape optimization using non-traditional optimization technique and its validation

In this paper, a computational fluid dynamics optimization strategy-based surrogate model, which is used for the predictions of vertical aerodynamic force (Cl), is proposed. An airfoil shape optimization problem has been formulated, and the particle swarm optimization algorithm technique is used to solve the problem along with the inclusion of constructed surrogate model. This is used to replace the actual CFD algorithms. Ordinary kriging and Hammersley sequence sampling approach are applied to construct and enhance the effectiveness of the constructed surrogate model, respectively. The geometry of the airfoils (NACA 2411 and 0012) is described with the help of parametric section method, and the flow around the airfoils is solved by using the Panel method. The constructed surrogate model is more accurate and limits their estimation error within the order of 10−2–10−6. The computational time required to solve the formulated ASO problem, which will take 630 s while using a normal optimization scheme in a computer system which has 2GB of DDR3 RAM, 2.0GHz of processor speed, and 1MB of L2 cache memory, is drastically reduced to 56.7 s while using the surrogate-based optimization, and also, the optimized airfoils have improved Cl when compared to the original airfoils. The optimized airfoils were validated using experimental data.

Kriging Methodology for Surrogate-Based Airfoil Shape Optimization

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Airfoil shape optimization using non-traditional optimization technique and its validation

Kriging Methodology for Surrogate-Based Airfoil Shape Optimization