# Parameter Identification of Lithium Battery Model Based on Chaotic Quantum Sparrow Search Algorithm
## 4 Improvements on the Sparrow Search Algorithm
### Simulation and Verification
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & & **PSO** & **GA** & **GWO** & **DOA** & **SSA** & **CQSSA** \\ \hline F1 & Best & \(1.6792\times 10^{-1}\) & \(8.0814\times 10^{-5}\) & \(6.2782\times 10^{-5}\) & \(4.7453\times 10^{-6}\) & \(9.2096\times 10^{-6}\) & \(\mathbf{4.2640\times 10^{-6}}\) \\  & Ave & \(7.1141\times 10^{-1}\) & \(1.3028\times 10^{-3}\) & \(4.8361\times 10^{-4}\) & \(1.0664\times 10^{-4}\) & \(8.1352\times 10^{-5}\) & \(\mathbf{7.5527\times 10^{-5}}\) \\  & Std & \(3.0420\times 10^{-1}\) & \(1.3417\times 10^{-3}\) & \(6.0031\times 10^{-4}\) & \(1.3815\times 10^{-4}\) & \(7.6052\times 10^{-5}\) & \(\mathbf{5.3268\times 10^{-5}}\) \\ F2 & Best & \(-9.29\times 10^{3}\) & \(\mathbf{-1.25\times 10^{4}}\) & \(-1.25\times 10^{4}\) & \(-8.39\times 10^{3}\) & \(-9.61\times 10^{3}\) & \(-1.04\times 10^{4}\) \\  & Ave & \(-7.31\times 10^{3}\) & \(\mathbf{-1.24\times 10^{4}}\) & \(-1.19\times 10^{4}\) & \(-6.53\times 10^{3}\) & \(-8.67\times 10^{3}\) & \(-9.47\times 10^{3}\) \\  & Std & \(8.78\times 10^{2}\) & \(\mathbf{2.64\times 10^{2}}\) & \(7.71\times 10^{2}\) & \(9.58\times 10^{2}\) & \(5.08\times 10^{2}\) & \(4.65\times 10^{2}\) \\ F3 & Best & \(1.4081\times 10^{2}\) & \(6.3677\times 10^{2}\) & \(2.5251\times 10^{1}\) & \(2.8700\times 10^{1}\) & \(2.4401\times 10^{-10}\) & \(\mathbf{9.1537\times 10^{-11}}\) \\  & Ave & \(6.0121\times 10^{2}\) & \(1.3177\times 10^{3}\) & \(2.5889\times 10^{1}\) & \(2.8829\times 10^{1}\) & \(4.3553\times 10^{-6}\) & \(\mathbf{5.9915\times 10^{-7}}\) \\  & Std & \(4.3758\times 10^{2}\) & \(3.0390\times 10^{3}\) & \(1.8254\times 10^{-1}\) & \(4.5647\times 10^{-2}\) & \(1.7396\times 10^{-5}\) & \(\mathbf{1.5278\times 10^{-6}}\) \\ F4 & Best & \(6.3826\times 10^{-1}\) & \(1.6803\times 10^{3}\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(\mathbf{0.0000}\) \\  & Ave & \(1.1170\times 10^{0}\) & \(1.7286\times 10^{0}\) & \(2.1608\times 10^{-3}\) & \(0.0000\) & \(0.0000\) & \(\mathbf{0.0000}\) \\  & Std & \(1.4760\times 10^{-1}\) & \(2.0729\times 10^{-1}\) & \(5.6434\times 10^{-3}\) & \(0.0000\) & \(0.0000\) & \(\mathbf{0.0000}\) \\ F5 & Best & \(3.9496\times 10^{0}\) & \(4.2819\times 10^{0}\) & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) & \(\mathbf{8.8818\times 10^{-16}}\) \\  & Ave & \(5.3482\times 10^{0}\) & \(4.4290\times 10^{0}\) & \(3.9672\times 10^{-15}\) & \(1.4803\times 10^{-15}\) & \(8.8818\times 10^{-16}\) & \(\mathbf{8.8818\times 10^{-16}}\) \\  & Std & \(1.0122\times 10^{0}\) & \(3.094\times 10^{-1}\) & \(2.0298\times 10^{-15}\) & \(1.3467\times 10^{-5}\) & \(0.0000\) & \(\mathbf{0.0000}\) \\ F6 & Best & \(1.3308\times 10^{0}\) & \(5.0399\times 10^{-1}\) & \(1.9654\times 10^{-5}\) & \(4.4535\times 10^{-2}\) & \(7.1302\times 10^{-19}\) & \(\mathbf{1.5705\times 10^{-32}}\) \\  & Ave & \(6.3947\times 10^{0}\) & \(1.3249\times 10^{0}\) & \(2.7880\times 10^{-4}\) & \(1.9846\times 10^{-1}\) & \(2.7284\times 10^{-14}\) & \(\mathbf{1.5705\times 10^{-32}}\) \\  & Std & \(3.6420\times 10^{0}\) & \(1.2239\times 10^{0}\) & \(1.2421\times 10^{-3}\) & \(1.3124\times 10^{-1}\) & \(5.0740\times 10^{-14}\) & \(\mathbf{5.5674\times 10^{-48}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The simulation results of the six algorithms on different test functions. iteration, they fall into local optimal solutions after that. However, CQSSA finally achieves the best convergence accuracy. Different than F3 and F6, the convergence processes of the CQSSA and SSA are almost the same under F4 and F5. The best convergence results are observed for both. In general, compared to SSA, CQSSA uses an improved strategy to make a more intelligent search and jump out of the local optimal solutions in time. This allows CQSSA to exhibit good convergence accuracy on both unimodal and multimodal test functions in high dimensions. Figure 3: The convergence characteristics of the six algorithms under six test functions. (**a**) The convergence curve of algorithms on F1. (**b**) The convergence curve of algorithms on F2.