## 3 Optimization Strategies and Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of Grid** & **Final Value of** & **Total Execution** & **Number of** & **Number of Grid** \\
**Points of Coarse** & **Objective** & **Time, s** & **Iterations** & **Points of Fine** \\
**LHS Grid** & **Function 1 mW** & & & **LHS Grid** \\ \hline
25 & 6.95 & 3660 & 14 & 155 \\
50 & 6.95 & 2466 & 6 & 100 \\
75 & 6.94 & 3253 & 7 & 135 \\ \hline \hline \end{tabular}  
* Values obtained from computer model.  
\end{table} 
Table 3: Results of optimization using Strategy III. wires over the cross section of a single coil of the twin-coil armature corresponding with the above solution. It should be noted that this result can easily be accomplished in the physical system, as shown in Figure 4c. Figure 5 displays the laboratory test-stand for validation of the obtained results. The comparison of powers measured for the systems with initially designed cylindrical coils with area w \(\times\) h (dashed line in Figure 4) filled uniformly with 2000 turns (Figure 4a) and for that with the optimized racetrack coils (Figure 4b). As shown in Figure 5, the output power increased as much as by 300%. The slight (14 percent) differences between the results in Table 3 and the maximum power measured for the optimized system are most likely due to complex (non-straight line) motional effects of magnets 3 on the induced emf in the physical harvester, which is a specific feature of the considered system that we identified and analyzed in [20], and is also due to inaccuracy of manufacturing of physical coils where the turn distribution does not match exactly one presented in Figure 4b. Though, the values of total coil resistance and inductance \(R_{c}\) and \(L_{c}\) measured using the laboratory multimeter agree to those calculated from formulas (3)-(9) within 2 and 6 percent, respectively (see Table 4). Figure 4: Results of optimization: distribution of turns over coil cross-section plane (see Figure 2) before (**a**) and after optimization (**b**). Dashed line denotes assumed area \(w\times h\) with \(r_{c}\) = 2 mm, and \(w\), \(h\) and \(\delta\) equal to 22, 33 and 0.01 mm, respectively. Colormap displays distribution of quantity (2) in V-s/m. c) Assembled armature using a 3d-printed coil carcass including formed bobbin and flat lid so as to obtain the distribution of turns shown in Figure 4b. The coils in the physical system are connected in parallel. Figure 5: Measurements: (**a**) laboratory test-stand; (**b**) output powers vs. load resistance for initial and optimized designs at a vibration frequency equal to 34.5 Hz; (**c**) frequency characteristics for increasing and decreasing frequency of vibrations for load resistance \(R_{l}\) equal to 1824 \(\Omega\). The results are obtained at accelerations applied to the system base equal to 1 g.  
Figure 5c presents the measured characteristics of output power vs. frequency for the initial and optimal designs. The maximum power is reached at 35.5 Hz and is equal to 6.46 mW. Due to nonlinear magnetic force caused by interaction between moving magnets (magnets 3 in Figure 1a) and stationary magnets (magnets 2 in Figure 1a), the proposed energy harvester operates in the wide range of vibration frequency (around 10 Hz) providing output power sufficient to charge small Li-Ion battery in a power supply of a wireless sensor network. In comparison to reference systems of similar size operating at the same value of acceleration our converter has very similar range of operation frequency (7.8 Hz in [31] and 10 Hz in [32]), although it provides significantly higher output power (1.18 mW in [31] and 2.5 mW in [32]). The latter confirms the applicability and novelty of the proposed method for maximization of the output power of such systems.