# A Spectrum Correction Method Based on Optimizing Turbulence Intensity
## 3 Results and Discussion
### Determine the Analog Frequency Range \([F_{max},F_{min}]\)
A one-dimensional simulation of three-dimensional wind speed is acquired, and the three-dimensional fluctuating wind velocity contour map and 3 d surface figure of simulation point 10 are shown in Figure 9.  
Figure 8: The contrast of standard deviation of simulated points between being corrected and uncorrected: (**a**) One-dimensional space; (**b**) Two-dimensional space; The contrast of standard deviation deviation of simulated points between being corrected and uncorrected: (**c**) One-dimensional space; (**d**) Two-dimensional space; The contrast of turbulence intensity of simulated points between being corrected and uncorrected: (**e**) One-dimensional space; (**f**) Two-dimensional space. The above results show that:  
1. The standard deviation \(\hat{\varepsilon}\) generated by the Kaimal spectrum simulation of a one-dimensional turbulent wind field decreases from 0.102 to 0.01, and the reduction is 9.2 times, and the error of truncation deviation \(\varepsilon\) is only 10%;
2. The numerical values of the Kaimal power density spectrum with a modified compensation coefficient \(\beta\) simulating the overall turbulence intensity \(\hat{I}_{T}\) of the spatial turbulent wind field are closer to the defined turbulence intensity \(I_{T}\), which is defined as the ratio of the fully defined standard deviation to the average wind speed \(I_{T}=\sigma/\overline{U}\). In the one-dimensional wind field, the corrected Kaimal spectrum can provide more simulated points that are conservative, according to Figure 8a,c, and the mean value of standard deviation has declined by 0.2 point while the standard deviation's deviation has dropped over 84.2%. Moreover, it can be drawn from Figure 8e that the turbulence intensity value of 45% (18/40) of the simulated points set in the simulation process finally reach the interval of [Referenced, Defined] after the spectrum is corrected, compared with that of the uncorrected spectrum simulation result, which has increased 35%. Therefore, the rate of efficient simulation points in the wind field has obtained a significant promotion. As can be seen from Figure 8e,f, the overall turbulence intensity of the compensated corrected turbulent wind field (referring to the \"corrected mean value\" line and \"Defined\" surface, respectively, in Figure 8) is very close to the turbulence intensity defined by the wind field;
3. The Kaimal power density spectrum simulation with the modified compensation coefficient \(\beta\) generates a more simulated point of fluctuating wind speed turbulence intensity that is distributed within the IEC reference turbulence intensity and defined turbulence intensity range, which can be effectively used in load design evaluation;
4. According to Figure 7, the line of the 'Corrected Spectrum Simulated' can always fit well with the line of the 'Corrected Spectrum', just like the line of the 'Original Simulated Spectrum' and the line of the 'Original Spectrum' does, which indicates that the fluctuating wind speed generated by the Kaimal power density spectrum simulation with the modified compensation coefficient \(\beta\) can perfectly fit the modified self-power spectrum and meet the requirements of engineering applications. Figure 9: (**a**) The three-dimensional fluctuating wind velocity contour map of point 10; (**b**) Standard The three-dimensional fluctuating wind velocity 3D surface of point 10.