Multiple Objective Function Optimization and Trade Space Analysis

Author

Yifan XuFollow

Date of Award

12-2022

Document Type

Thesis

Degree Name

Master of Engineering (ME)

Department

Mechanical Engineering

Committee Chair/Advisor

John Wagner

Committee Member

Cameron Turner

Committee Member

Todd Schweisinger

Abstract

Optimization can assist in obtaining the best possible solution to a design problem by varying related variables under given constraints. It can be applied in many practical applications, including engineering, during the design process. The design time can be further reduced by the application of automated optimization methods. Since the required resource and desired benefit can be translated to a function of variables, optimization can be viewed as the process of finding the variable values to reach the function maxima or minima. A Multiple Objective Optimization (MOO) problem is when there is more than one desired function that needs to be minimized concurrently. In MOO, Pareto Solutions are defined as the set of solutions that are not worse than any single solution of all objective functions simultaneously. In other words, MOO is a process of applying algorithms to find Pareto solutions to a certain problem. Using Tradespace analysis, we can further identify the optimal Pareto Solution with the highest utility at a fixed cost. The combination of MOO and tradespace analysis can evaluate hundreds of designs simultaneously to select the optimal one.

Mechanical system design is the process of devising a procedure to accomplish the given task, for which a design engineer's role is to optimize resource consumption. With recent advancements in multi-functional systems, the complexity of machines has been increasing. This presents a great challenge for design engineers, who must contend with optimizing systems with several functions in tandem. It is thus essential to develop methods that can simplify the design process. Tower clocks, as a classical type of machine, were extensively used for public time display during the period when watches and home clocks iii were rare. These mechanical movements once played essential roles in society and industry. They could be found at churches, courthouses, and universities/schools to visually and auditorily record the passage of time for residents and students. They were also used to regulate railroad schedules and workforce hours for the emerging industrial sector. Although mainly used for decorative purposes today, the components of such movement, including the assembled gears, escapement, and pendulum with weight drive, provide insight into optimization and tradespace analysis problems.

In this research, computational methods plus experimental observations were used to investigate the optimal designs of the E. Howard Clock Model 00 - a movement was manufactured by E. Howard Clock Company. First, A computer-aided-design (CAD) model of this movement was created using the SolidWorks® software package to illustrate the working principle of the pendulum clock and facilitate engineering optimization studies. Next, the mathematical model of this clock was developed and simulated to explore the operation behaviors and conversion of potential-to-kinetic energy. The experimental process to validate this model was also described in detail. After that, A Single Objective Optimization (SOO) algorithm (i.e., simulated annealing) was applied to the model to optimize the pendulum subsystem for accuracy, quality factor, and mass. Numerical results show the desired quality factor can be achieved by varying the pendulum length and bob radius/thickness. Compared to the original, the optimized design added 15% to the mass of the pendulum while maintaining the clock's accuracy. Tradeoffs between quality factor, pendulum properties, and period were investigated and discussed with representative experimental and computational results. Lastly, two Multiple Objective Optimization iv (MOO) approaches (i.e., Multi-objective Genetic Algorithm (MOGA-II) and Multiobjective Simulated Annealing (MOSA) were applied to the developed mathematic model. The optimal movement designs in terms of pendulum mass and time accuracy were further explored for a range of clock periods. Numerical results demonstrated a 0.7% increase in the quality factor and a 0.56% reduction in the mass while maintaining the designed period by modifying the above-mentioned pendulum's parameters. More importantly, these changes can provide material cost savings in a mass production scenario. Overall, this study highlighted the optimization design engineers have considered for decades which can now be visualized using computer tools for greater insight. This methodology has the potential to be applied in the designing of other complex systems as well.

Recommended Citation

Xu, Yifan, "Multiple Objective Function Optimization and Trade Space Analysis" (2022). All Theses. 3922.
https://open.clemson.edu/all_theses/3922