Data science and aircraft design
As an aspiring data scientist I looked back to my previous experiences in search for topics that I learned earlier which can be useful for my new career. Few years ago I finished my studies in Aeronautical Engineering at Warsaw University of Technology. I realized that algorithms that we used for optimization of aircraft design are the same algorithms that I will be using in my (hopefully) upcoming career. I haven’t thought about them at that time as ‘data science’. For me they were mathematical approaches to finding the best design. Based on Wikipedia’s definition “Data Science” is a multidisciplinary field using scientific methods and algorithms to extract knowledge from data. So it turns out that I was using data science a few years ago and I didn’t see that. In this post I would like to zoom in on the subject of aircraft design process and few optimization algorithms used in this field.
Aircraft Design Process
During the aircraft design process different approach to complexity and cost is taken. As the design progresses, there is growth in decision variables, constraints and the change in objectives.
This process can be divided into three main stages:
- Conceptual Design
- Preliminary Design
- Detail Design
First phase — Conceptual Design is focused on collecting all requirements. The decisions about configuration, performance and mission are made. Here starts the initial sizing of the aircraft — many alternative designs are taken into consideration in response to requirements. Optimization methods are used at this step to find a design that will fulfill all of them and to estimate the lowest weight that will meet the mission. During this phase, the work is focused on research to find the best configuration at lowest cost.
Next phase — Preliminary design — is where the main configuration is already established and no bigger changes are made. Each subsystem is considered separately and the impact on structural and aerodynamic performance is identified. Optimization at this stage continues for the most important parameters as wing loading or thrust to weight ratio.
Third stage is called Detail Design. At this point every part is defined and the analysis of all of them are taken into account. During this phase, the optimization is considered for single parts or subsystems and the main emphasis is on reducing their weight.
Multidisciplinary Optimization
In general optimization is the selection of best result from a set of alternatives. In optimization process we are looking for minimizing or maximizing specific parameter what we call an objective function. This function is described by many constraints, because we want our design to be feasible to produce and to fulfill our requirements. Using numerical approach can help reduce the cost of building many different designs on our way to find the optimal one. But the more parameters we want to include in optimization calculations the more time consuming and complicated are the calculations itself.
In aircraft design we want to optimize design with respect to many different variables. For example in wing design we want to take into account aerodynamics, structures and controls. Choosing the best result by changing design looking only at one of those will result in worse performance and not optimal design whatsoever. Like changes in geometrical variables will affect aerodynamics and structural strength. This is where Multidisciplinary Optimization comes in. MDO is a methodology which uses a collection of multivariable optimization methods to solve design problems crossing a number of disciplines simultaneously.
Optimization algorithms
Solving multidisciplinary optimization problems cad be done using a wide variety of different approaches. Many times our objective function has many local minimums and using gradient methods is too complicated. For solving such problems non-deterministic methods come in handy. Some of the algorithms used in optimization are the following:
- Stepping searches
- Evolutionary Algorithms
- Monte Carlo
Stepping searches
Many different optimization methods can be described as Stepping searches methods. In general in those methods for each design the objective function is calculated. The decision of the new design direction is made based on the local improvement of the objective function in the next step. This step is a predefined change in a variable and the new design becomes the new origin for the next calculations. The directions can be found using derivatives or finite difference methods. Among stepping search algorithms we can distinguish steepest descent algorithm, where we are focusing on minimizing the gradient of considered function. In aircraft design this algorithm can be used, for example, to find the most optimum wing design minimizing the drag in cruise conditions while changing wing parameters.
Another algorithm in this family is orthogonal steepest descent in which the direction of change is investigated only along the variables’ axes. One other example of searching by steps is a random walk. In this method there is no preferred direction to search for the optimum design. Next step is verified at random direction and if it leads to a better design then the step is taken.
Evolutionary Algorithms
Evolutionary algorithms, as the name may suggest, are using techniques inspired by natural evolution to solve optimization problems. Those algorithms are applying process of “survival of the fittest” to the population of possible outcomes. Genetic algorithms belong to the evolutionary algorithms family. Those algorithms use such natural techniques as inheritance, mutation, selection and crossover for solving optimization issue. We are starting with a random set of initial designs. The optimum design is found by an iterative process of selection the best “parents” for the next generation based on evaluation for each outcome with respect to required solution. The selection can be done either by tournament selection or roulette wheel selection. After selecting best individuals the process of creating new generation is starting. Offsprings are created basing on the parents genes but the new chromosome is the combination of both of them through a crossover and mutation. The genetic algorithms were used in aircraft design for optimizing the aircraft range based on major aircraft characteristics. [3]
Monte Carlo
All of the variables in the optimization problem, as there are many uncertainties in inputs that need to be taken into consideration, can be mathematically represented. Probabilistic methods are based on analytical simplifications or are simulation based. Monte Carlo experiments approach is a general name for a class of algorithms using random sampling for solving problems not possible to solve in analytical approach. Those methods use probability and statistics to determine the best result. Monte Carlo algorithms are used for simulations of physical and mathematical systems. Can be used in risk management in business, as well as in determining the design space for physical designs. In aircraft design can be used, for example, to collect all possible scenarios of assembly process including geometric dimensioning and tolerancing to verify the outcomes.
Summary
As you can see optimization algorithms can be used in various different disciplines ranging from business to rocket science. If you want to deep dive into the optimization topic here you can find some useful links:
Gradient descent and other optimization methods used in machine learning:
Great article explaining Genetic Algorithms in details:
More details on Monte Carlo simulations can be found in this post:
Sources:
[1] Raymer, Daniel; Enhancing Aircraft Conceptual Design Using Multidisciplinary Optimization; Doctoral Thesis
[2] Hoburg, Warren; Aircraft Design Optimization as a Geometric Program; Dissertation
[3] Chaundhry, Imran, Ahmed, Al; Preliminary Aircraft Design Optimization Using Genetic Algorithims
