## Engineering Optimization

This constitutes a bulk of my past work at General Electric Global Research (GRC) as well as my doctoral dissertation work. The focus of this research is to employ optimization and machine learning techniques for aerodynamic design of Turbomachinery components. Turbomachinery design is a complex problem that does not have a closed form solution. Such designs are done using an iterative process where the design is incrementally changed where the impact of the previous change is used for determining the next change. This process has traditionally been done manually where a designer uses his skills to determine the design changes. This research entails automating the manual process by using optimization algorithms to drive the design and achieve the objectives. This work was done in collaboration with engineers at GE Power Systems and GE Aircraft Engines, the Engineous team at GRC, as well as my advisor Prabhat Hajela at RPI.

### Machine Learning Algorithms for Turbomachinery Design

Two different approaches were used in this work. In the first approach a neural network was used for learning and mimicking the analysis code. Rules for optimization of Turbomachinery configuration were then reverse-engineered from the weight matrices of the neural network. The second approach involved use of learning classifier systems in which design rules are gradually evolved using genetic operators of crossover and mutation. In this rules can either trigger other rules or result in the changes to the design. Based on the rule performance and its frequency of usage, credit is apportioned to the rules. The better rules flourish and propagate and the weaker rules atrophy and eventually perish. This scheme was applied to optimize Turbomachinery airfoils. Two papers on reengineering and automation of the turbine design process have been published in the AIAA Journal of Propulsion and Power and in the Journal of Engineering Optimization. Optimization Algorithms for Turbomachinery Design

This work involved use of optimization algorithms for performance optimization of turbines and to transform the manual labor-intensive process for design of airfoils into an optimization driven automated process. Multiple optimization algorithms including genetic algorithms; gradient-based search, and rule-based search were used in tandem to maximize performance. This work involved use of several innovative techniques from geometry and mathematics to model the problem. Steam and gas engine turbines throughout General Electric were used for the design. As a part of this work a new generation of steam turbines called Dense-Pack steam turbine was launched. This turbine had a radically different design from existing turbines and it improved performance by several percentage points making its products more competitive. Such techniques were also used for automation of the manual and cumbersome process of airfoil design. Bezier curves were used for modeling geometric shapes and metrics were defined to replicate the visual cues that the designer uses during manual design. This approach was used for design of high-pressure and low-pressure turbines for steam and gas turbines. Several publications have resulted from this work.

### Decision Support System for Turbine Design

Engineering design is quite complex and often involves multiple disciplines such as aerodynamics, structures, etc. To reduce the complexity of the problem design is often done sequentially for each discipline. However, sensitivities are computed at the design point for a discipline and are then used to modify the design to optimize or meet constraints in a different discipline. Tradeoffs between different competing objectives may however require large deviations from the optimum in the search space where the sensitivities computed at the optimum point are no longer accurate. This leads to suboptimum designs. This work involves analyzing the design a grid of points that span the entire search space and then using SQL based queries to generate sensitivity curves of loci of optimum points in the search space. This decision support system became the primary decision-making tool for designers and managers in the Steam Turbine operations. This coupled with Six Sigma statistical design tools resulted in most of the design work for steam turbines. This has resulted in several classified reports at General Electric Power Systems.

### Cellular Automata & Optimization

In this research, a novel optimization approach is developed that uses a grid of hyper-cubes in the search space. Each grid point has a set of local rules that allows it to compare itself to its neighbor and then adaptive changes its space. The grid points gradually coalesce with neighboring grid points based on the status of the constraint satisfaction. Once stabilized, the information on the topology of the search space can be used to prune the search space. This approach handles multimodal search spaces particularly well since multiple clusters are created based on local optima. This work was done in collaboration with Shashi Talya of GE Global Research.

### Related Publications

- Goel, S. 3D Turbine Airfoil Geometry Optimization using Quasi-3D Analysis, ASME Jounal of Turbomachinery). Under Review
- Goel S., & Talya, S. (August 2004). Constrained Optimization Using Cellular Automata. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY. (C)
- Goel, S., & Hajela, P. (2002). A Classifier Based Optimization Technique for Designing Turbine Airfoils. Eng. Opt., 34,195-218. (J)
- Goel S. (May 1998). Machine Learning Paradigms in Design Optimization. [Ph.D. thesis] Rensselear Polytechnic Institute.
- Goel, S., & Hajela, P. (1996). Identification of Parameter Couplings in Turbine Design using Neural Networks, AIAA Journal of Propulsion and Power, 12(3), 75-102. (J)
- Maughan, J.R., Hill, J.M., Willey, L.D., & Goel, S. (July 23-26 2000). Development of the Densepack Steam Turbine: A Design Methodology for Increased Efficiency. International Joint Power Generation Conference, FL. (C)
- Goel, S., & Embrechts M. (1996). Quantification of shape characteristics by using Neural Networks. ARTIFICIAL NEURAL NETWORKS IN ENGINEERING: Intelligent Systems through Artifical Neural Networks, Smart Engineering Systems, Neural Networks, Fuzzy Logic and Evolutionary Programming, 6, Ed. Dagli C. H., Akay M., Chen C. L. P., Fernandez B., and Ghosh J., 1996. (J)
- Goel, S., Cofer, J.I., & Singh H. (June 10-13 1996). Turbine Airfoil Design Optimization, International Gas Turbine and Aeroengine Congress and Exposition, Birmingham, UK. (C)
- Goel, S., & Lamson, S. (November 12-17 1995). Automating the Design Process for 3D Turbine Blades.ME 1995 International Mechanical Engineering Congress and Exposition, San Francisco, CA.
- Goel, S., & Hajela, P. (September 7-9 1994). Identification of Parameter Couplings in Turbine Design using Neural Networks. 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL. (C)
- Goel S., & Lamson, S.H. (April 1994). Knowledge Based System for Detailed Blade Design of Turbines. Applications of Artificial Intelligence XII:Knowledge-Based Systems in Aerospace and Industry, Orlando, FL. (C)
- Goel, S., Cherry, D., & Gregory, B. (April 1993). Knowledge-Based System for Preliminary Aerodynamic Design of Aircraft Engine Turbines. Applications of Artificial Intelligence XI: Knowledge-Based Systems in Aerospace and Industry, Orlando, FL. (C)
- Tong, S.S., Powell, D.J., & Goel, S. (February 1992). Integration of Artificial Intelligence and Numerical Optimization Techniques for the Design of Complex Aerospace Systems. American Institute of Aeronautics and Astronautics. (C) Lee, H., Goel, S., Hunter, S., Gregory, B., & Tong, S.S.(July 1993). Modeling for Concurrent Design of an Aircraft Engine Turbine. 38th ASME International Gas Turbine and Aeroengine Congress and Exposition, Cincinnati OH. (C)
- Goel, S., & Kwon, T.H. (August 1992). Geometric Reasoning for Automated Design of an Injection-Mold Cooling System. IAPR Workshop on Structural and Syntactic Pattern Recognition, Berne, Switzerland. (C)
- Rao, P.N., & Goel, S. (1988). A Study in Computer Aided Process Planning, Workshop on Computer Aided Manufacture. The Institution of Engineers (India). (C)