Electronics system thermal management optimization using finite element and Nelder-Mead method

The demand for high-performance, smaller-sized, and multi-functional electronics component poses a great challenge to the thermal management issues in a printed circuit board (PCB) design. Moreover, this thermal problem can affect the lifespan, performance, and the reliability of the electronic system. This project presents the simulation of an optimal thermal distribution for various samples of electronics components arrangement on PCB. The objectives are to find the optimum components arrangement with minimal heat dissipation and cover small PCB area. Nelder-Mead Optimization (NMO) with Finite Element method has been used to solve these multi-objective problems. The results show that with the proper arrangement of electronics components, the area of PCB has been reduced by 26% while the temperature of components is able to reduce up to 40%. Therefore, this study significantly benefits for the case of thermal management and performance improvement onto the electronic product and system.


Electronics system thermal management optimization using… (Nurul Kausar Ab Majid)
2269 selected for multi-objective optimization, which are average temperature of components and area of PCB.

Model Development
Nelder-Mead algorithm is a simplex search algorithm, where it is also known as one of the best-known algorithms for multidimension unconstrained optimization without derivatives [19]. The basic algorithm is simple to understand and easy to use. That is the reason, why it is very popular in many fields of science and technology. This method does not require any derivative information, which makes it suitable for non-smooth function problem. It is used to solve parameters estimation where the function values are subjected to noise [20]. Finate Element Method (FEM) and Nelder-Mead optimization (NMO) solver from COMSOL Multiphysics was use to solve single objective function for the temperature and multi-objective functions for temperature of the components and area of PCB.
Model of component on PCB has been developed following a few steps as shown in Figure 1. The initial arrangement of the component is created. Next, the other parameters such as thermal conductivity, material, initial temperature, and boundary temperature are set. Afterwards, the process of generating the finite element mesh has been conducted for optimization process. Figure 2 shows the Nelder Mead Optimization (NMO) solver process that has been selected to solve for single objective and multi-objective problem. This method has an ability to solve for the worse point on the control variable for proposing the optimal solution [13,[20][21][22][23][24]. Model of celectronics component on PCB from optimization solver for a single objective function has been developed using Test sample, which consist of 3 components as listed in Table 1. Based on this result, a multi-objectives optimization model is designed and tested. Finally, comparative analysis from published samples by [2] and [10] is conducted and the optimal design of those samples is proposed.
Firstly, single objective function has been tested, where the temperature (T) of each component is optimized, hence the fitness function is given in (1). (1) where i is the current number of components and n is total number of components. Secondly, multi-objective functions, which minimize the temperature of each components and area of PCB have been developed. The total fitness function is given by (2): where; ( ) : average Temperature of Components ( ) : area of PCB fitness function for area of PCB is given in (3) where: In order to achieve an optimal fitness function ( ), the solver will rearrange the position of each component on the PCB until the minimum average temperature is achieved. These control variables, which are the position of all components are evaluated. Fitness function for area of PCB, ( ) is calculated from the length (PCB_L) and width (PCB_W) of PCB. By adjusting and reducing these parameters, it will able to minimise the size of PCB. Table 2 shows all the control parameters for sample Model. During evaluation process, the fitness function must satisfy all the constraint parameters such as maximum temperature allowed, maximum area of PCB, components overlapping, and all the components must be within set range [25]. All the constraints are listed in Table 3. Optimizer setting has been selected based on several trials and analysis such as maximum number of iterations is 500 and maximum number of populations is 100. While the number of optimality tolerance is 0.01. These set up are applicable for all simulation work in this paper.

Results and Analysis 3.1. Single Objective Temperature Optimization
Average temperature of components from Test sample has been simulated and optimized based on the given initial design. The variation of an average temperature versus the number of iterations are plotted in Figure 3. The details average optimal temperature for each component are shown in Figures 4 (a) and 4 (b), which comparing thermal profile of initial design and proposed optimal design. Table 4 shows the results of the temperature for all components have reduced as compared to the initial setting. While the location of all components relocates to the edge of the PCB and non-overlap occurred. This new arrangement has more space for a heat to dissipate by conduction within components and PCB or via convection to surrounding. This process has minimized the temperature of each components.

Multi-objective Temperature and Area Optimization
The same Test sample is used for multi-objective optimization algorithm, which is to minimize the average temperature of components and area of PCB. Figure 5 presents the result of multi-objective optimization process where the area of PCB is minimized to 16 cm 2 and the average of temperature on the PCB reduces up to 2°C. In this case, the process stops after the 80 th iteration since the stationary point is reached. The thermal profile for the proposed optimal design is presented in Figure 6, while the initial design as in Figure 4. All results are recorded in Table 5. It can be seen that, even the area of the components is reduced about 34% to 16.4 cm 2 . The temperature of components is reduced up to 16%. The components are moving towards the edge of PCB and located away from each other. It will help all the components to have better heat dissipation to the PCB and surrounding.

Comparative Analysis using Sample [2]
The dimension of Sample [2] is a 5x5 cm PCB and consist of 8 same size components with various power dissipation. By using the same optimization parameters from Test sample, the result of optimal solution is plotted in Figure 7. Thermal profile for initial design and final design are presented in Figures 8 (a) and 8 (b) respectively. By using NMO, the optimization algorithm is able to solve for worse point. The optimal design shows the temperature of the components has been minimized up to 22.8%. While the area of PCB reduced from 25cm 2 to 18.5cm 2 , which is about 26.2%. All the results are recorded in Table 6.

Comparative Analysis using Sample [10]
Sample [10], Multi-voltage regulator (MVR) is a multipurpose signal conditioning circuits for laboratory equipment, especially for data acquisition and measurement system. This sample consists of 9 components with unequal power dissipation and the PCB area is 198 cm 2 . There are also others non-heated components that was grouped together. The result of optimization is presented in Figure 9 and thermal profile for initial and optimal design can be seen in Figures 10 (a) and 10 (b) respectively. Figure 9. Graph for area of PCB vs average temperature of sample [10] From the initial design as shown by Figure 10 (a), there are two high power components located near to each other. However, after optimization arrangement, the result shows that it is able to reduce the temperature up to 40%. Although this is the high-power dissipation components, when it placed at the edge of PCB, it will have more space for convection process, hence the reducing in temperature. At the same time, 16.67% area of PCB has been reduced. All the results of temperature and percentage of area reduction are presented in Table 7. The results show that the proposed approch in this work are better than using evaluationary Genetic Algorithm obtanied by [10].

Conclusion
This paper has presented optimization thermal management based on electronics components arrangement using Finite Element Method and Nelder-Mead optimization (NMO) solver. In general, when the size of packaging is reduced, it will contribute to the increment of power density. However, from the result of the sample showed that when the area of PCB is reduced by 26.2%, the highest temperature of component also has reduced by 22%. For sample the area of PCB is reduced by 16.67% and the temperature of components are able to reduce up to 40%. These results have confirmed that, with the proper arrangement of the components, the temperature of distribution can be maintained or reduce although the area of PCB is decreased. This optimization algorithm will help the designer to predict the temperature of components on PCB before the fabrication process. It will help to reduce the cost of development by enabling the optimization to be performed at the design stage to meet the customer satisfactions.