Project Ideas
Here I list all the ideas for future BTech/MTech/PhD projects. Ideas are expressed in general terms and the specific techniques and methods to be used are not specified. The ideas are meant to be starting points for discussion and can be modified and refined as needed. Feel free to contact me if you are interested in any of these ideas or if you have your own ideas that are related to my research interests.
Project Ideas
PINNs for Multi-objective Multi-fidelity Surrogate Models
Physics-informed neural networks (PINNs) are a class of machine learning algorithms that are used to solve partial differential equations. PINNs are trained to satisfy the governing equations of the problem as well as the boundary conditions. PINNs have been used to solve a wide range of problems in fluid dynamics, heat transfer, and structural mechanics.
The aim of this project is to investigate possible application of PINNs to develop a single multi-fidelity surrogate model for multiple objective functions. The idea is to use PINNs to combine data from multiple sources, each with different levels of fidelity, to develop a surrogate model that is accurate and computationally efficient.
Willingness to learn and code in Python is a must for this project.
ML for potential flow solution over an airfoil
Given the geometry of an airfoil, the free stream conditions, and the angle of attack, we aim to estimate the lift over the airfoil using potential flow theory.
There are essentially three different routes to solving this problem in the classical setup:
Conformal mapping where we map the airfoil geometry to a circle and solve the potential flow problem over the circle. The lift is then calculated using conformal mapping.
Boundary element method (BEM) where we introduce singularities (vortices, sources, and doublets) on the airfoil surface in the form of panels and solve the resulting system of linear equations to obtain the velocity potential in the entire flow domain. Then, the lift is calculated using Kutta-Joukowski theorem.
Flow domain discretization where we discretize the flow domain using a structured or unstructured grid and solve the potential flow problem using finite difference or finite volume methods. The lift is then calculated using the pressure distribution on the airfoil surface.
The first two methods are computationally efficient but are limited to simple geometries. The third method is computationally expensive but can handle complex geometries. The accuracy of the lift estimation is expected to improve as we move from the first to the third method.
With the availability of the computing resources these days, all methods can be used to estimate the lift over an airfoil with equal ease. But the aim of the project is to develop new machine learning techniques that can combine the information from the three methods to estimate the lift accurately and efficiently.
The project will involve the following steps:
Choose a parametric representation of the airfoil geometry. The parameterisation should be such that it can represent a wide range of airfoil shapes. The simplest example is NACA four digit parameterisation. But something more sophisticated will be required in this case.
Develop (adapt an existing) conformal mapping code to estimate the lift over the selected set of airfoils.
This results in a multi-fidelity model where the first method is the low-fidelity model and the third method is the high-fidelity model. The aim is to use machine learning to develop a surrogate model that can predict the lift accurately and efficiently using data from the low-fidelity and high-fidelity models.
This is a test problem that aims to explore the use of machine learning in multi-fidelity modeling of fluid flow problems. The ideas developed in this project can be easily extended to more realistic problems in aerodynamics.
Hessian based UAV conceptual design
At present the lab has a simple UAV design code with four disciplines written in C. It has been differentiated using Tapenade in the forward as well as reverse mode to calculate the gradient of the objective function. However, it lacks realistic constraints and the fidelity of some of the disciplines can be improved further. Also, Hessian calculation (second order derivative) can be implemented for this MDO code and used for gradient based optimisation.
This project aims to showcase AD methodology for MDO using a simple test case of UAV design. Interest in automatic differentiation and programming essential for the project. You will start with the existing code and develop it further.
Orbital Uncertainty Propagation for Collision Probability Computation
Past Students
2020
Neelappagouda V Hiregoudar
(MTech Aerospace Engineering)
Project Title: Multimodal optimization of NACA0012 wing with diffential evolution based parallel niching algorithm and reduced-order modeling technique
Abstract: A test problem for multi-modal aerodynamics optimisation (Problem 6 from Aerodynamic design optimisaiton discussion group (ADODG)) is solved using a parallel niching differential evolution algorithm. Principal Component Analysis (PCA) is used for reduced order modelling on top of the Free Form Deformation (FFD) based geometric parameterisation. The entire project was implemented using Python, and .
Past Projects
Orbital uncertainty Propagation for Collision Probability Computation
In the context of space situational awareness, in particular, the conjunction assessment and collision avoidance maneuver, it is important to compute the collision probability between two space objects accurately and efficiently.
The problem would be straight forward to solve if we could accurately predict the position of any space object at all times. However, the reality is that the position of any space object is uncertain due to various reasons such as:
- Inaccurate knowledge of the initial state of the object
- Uncertainty in the atmospheric density
Hence, accurate position of any space object is unavailable due to inherited errors in orbit determination process. Usually, any space object position is available with mean and its uncertainty. In earlier days, the Monte Carlo simulations were used to propagate these uncertainities and the collision probability was calculated with high accuracy.
The number of space objects have increased greatly due to large number of satellites as well as non-operational spacecraft in a constellation. Monte Carlo simulations are prohibitively expensive in such a scenario.
Hence there is a need to develop a computationally efficient method to propagate the uncertainty in the position of space objects and compute the collision probability accurately.
The primary objective is to develop the mathematical tool for propagating complex dynamics of the near-Earth spacecraft with realistic perturbations (up to J4, SRP) and computationally efficient propagation of uncertainty to compute accurate collision probability of two objects in conjunction. The performance of this method should be superior in terms of computational speed to standard Monte Carlo simulations/methods with minimum loss of accuracy.
The uncertainty arising from the variation in atmospheric density plays a major role in predicting the near-Earth orbit. Therefore, accurate estimation of atmospheric density and quantification of uncertainty is important.
Hence, computation of collision probability between two space objects should include the propagation of uncertainty in position as well as atmospheric density.
This task is split into two projects:
Investigation of various methods to propagate the uncertainty in the position of space objects. The performance of these methods should be compared in terms of computational speed and accuracy. This will involve trajectory calculation and uncertainty propagation for a large number of space objects.
Investigation of various uncertainty quantification and propagation methods for variation in the atmospheric density.
These are preliminary thoughts and the exact nature of the project will be decided based on the literature survey and the interest of the student.
These two projects are in collaboration with VSSC, ISRO.
Multi-discipilinary Optimization of winged UAV using PINNs
In this project, aim to investigate possible use of PINNs for multi-disciplinary optimization. Initially, simple algebraically coupled problems will be solved using PINNs to demonstrate the capability of PINNs to solve multi-disciplinary optimization problems. If successful, we will move on to the actual problem.
This is an open ended project where I am not clear which direction we will go. But it will be exciting!
You can refer to this paper as a starting point.
Willingness to learn and code in Python is a must for this project.
Launch Vehicle Trajectory Optimization using PINNs
Retropropulsion is a technique used in space exploration to slow down a vehicle as it approaches a planetary surface. The technique is used in the final stages of descent to reduce the velocity of the vehicle and allow it to land safely on the surface. The aim of this project is to use physics-informed neural networks (PINNs) to optimize the trajectory of a launch vehicle using retropropulsion.
A similar project was attempted earlier with just the neural networks. That did not work out well. Hence, the idea is to use PINNs to solve the problem.
Willingness to learn and code in Python is a must for this project.