## 3 Simulated Results and Error Analysis
### Discussion and Analysis of Reconstruction Simulation Results
#### 3.3.2 Non-Axisymmetric Simulation Distribution  
In this section, the effect of different noise levels on the reconstruction of non-axisymmetric temperature and concentration distributions is analyzed to assess the robustness of the  
Figure 8: Effect of noise in axisymmetric distribution on various algorithms. (**a**) ARE and standard deviation of temperature reconstruction results; (**b**) ARE and standard deviation of concentration reconstruction results. Figure 9: Effect of noise in axisymmetric distribution on various algorithms. (**a**) ARMSE and standard deviation of temperature reconstruction results; (**b**) ARMSE and standard deviation of concentration reconstruction results. algorithms under such conditions. In industries, non-axisymmetric distributions do occur. Figure 10 depicts the reconstruction results of the temperature and concentration fields with non-axisymmetric distributions using the four algorithms. Similar to the conclusion drawn with the axisymmetric distributions, the MIARO algorithm achieved the best results with the smallest error and the mildest fluctuations at the edges of the field. Taking a cross-section at y = 14 cm, where temperature peaks appear when using the axisymmetrical settings, the reconstruction results over this plane are shown in Figure 11. Comparing the different algorithms, it can be found that the temperature and concentration reconstruction errors with the MIARO algorithm are much smaller than those obtained with the other algorithms. In fact, the maximum error of temperature is within 8%, the error for concentration is within 6%, and the fluctuations at the edges of the cross-section are lower than those obtained with the other algorithms, which further proves the superiority of MIARO. To further assess the noise immunity of the reconstruction algorithm for complex distributions, random noises at levels of 2%, 4%, 6% and 8% were applied to the LOS measurement \(A\) database again. Figures 12 and 13 show the reconstructed temperature and concentration at 4% and 8% noise levels. The characteristic peaks are clearly visible in the temperature reconstruction results for all four algorithms at the 4% noise level, but only  
Figure 11: Comparison of cross-section center reconstruction results: (**a**) temperature reconstruction values; (**b**) concentration reconstruction values. Figure 10: Temperature and concentration field reconstruction results and errors for different algorithms non-axisymmetric model: (**a,b**) ART iterative algorithm, (**c,d**) [PERSON] iterative algorithm, (**e,f**) MAART iterative algorithm, (**g,h**) MIARO iterative algorithm. with the MIARO algorithm are the characteristic peaks in the concentration reconstruction distinguishable. At the 8% noise level, only MIARO provides recognizable characteristic peaks in the reconstructed results, showing the robustness of this algorithm over the other three. In the non-axisymmetric distribution setup, two types of errors (ARE and ARMSE) were also calculated for the four algorithms, which are shown in Figures 14 and 15. Clearly, both ARE and ARMSE become greater with the increased noise level. The overall trends of ARE and ARMSE are the same, though ARMSE is higher. The ratio ARE/ARMSE of different reconstruction algorithms is slightly different in some noise conditions, which reflects the different natures of these two error criteria. The temperature reconstruction ARE is below 0.05, and ARMSE is better than 0.06 at 8% random noise; the concentration reconstruction ARE is no larger than 0.04, and ARMSE is under 0.06. The figure shows that the temperature reconstruction errors in terms of ART do not have specific patterns with noise levels for the Landweber and MAART algorithms. Figure 12: Temperature reconstruction results for non-axisymmetric distribution with different noise levels. Figure 13: Concentration reconstruction results for non-axisymmetric distribution with different noise levels. However, in the concentration reconstruction, the MAART algorithm produces significant errors.