## 4 Case Simulation and Result Analysis  
### Harmonic Signal Detection Experiment  
The power system's harmonic simulation signal from the study [20] is used for simulation, and the target harmonic signal is  
\[s(t)=A_{1}\sin(2\pi f_{1}t)+A_{2}\sin(2\pi f_{2}t)+A_{3}\sin(2\pi f_{3}t)+A_{4} \sin(2\pi f_{4}t)+A_{5}\sin(2\pi f_{5}t) \tag{45}\]  
Which \(A_{1}=1\), \(A_{2}=0.15\), \(A_{3}=0.25\), \(A_{4}=0.2\), \(A_{5}=0.1\), \(f_{0}=50\) Hz, \(f_{1}=f_{0}\), \(f_{2}=2.2f_{0}\), \(f_{3}=3f_{0}\), \(f_{4}=5f_{0}\), \(f_{5}=7f_{0}\). For easy understanding, in the simulation experiments of this paper, \(s(t)\) values all denote the ideal target signal contained in the noise-containing signal of the input stochastic resonance system, \(n(t)\) values all denote the random noise contained in the noise-containing signal of the input stochastic resonance system, \(S(f)\) values denote the amplitude-frequency spectral value of the ideal target signal, and \(N(f)\) values denote the amplitude-frequency spectral value of the random noise. \(x(t)\) denotes the output signal of the stochastic resonance detection system, which is essentially a time course of the characteristic displacements of the bistable system, and \(X(f)\) is the amplitude-frequency spectral value of the output signal of the stochastic resonance system. which is essentially the time course of the characteristic displacements of the bistable system, and \(X(f)\) is the amplitude-frequency spectral value of the output signal of the stochastic resonance system. Setting the system parameters as \(a=1.5\), \(b=1\), \(c=2\), Gaussian white noise with noise intensity \(D\) of 1 is mixed with the harmonic signals of Equation (45) through the secondary sampling process [21] and inputted to the classical stochastic resonance detection system, the unsaturated stochastic resonance detection system, and the accelerated stochastic resonance detection system, and the fourth-order Runge-Kutta algorithm is utilized for the calculation of Langevin equation [22]. The mixed signal waveforms and spectra are shown in Figure 11, and the experimental results are shown in Figures 12-14. Figure 11: Input noise signal waveform and spectrum at \(D=1\). (**a**) Time domain waveform. (**b**) Spectral amplitude. Figure 12: SR detection system output signal waveform and spectrum at \(D=1\). **(a)** Time domain waveform. **(b)** Spectral amplitude. Figure 13: UBSR detection system output signal waveform and spectrum at \(D=1\). **(a)** Time domain waveform. **(b)** Spectral amplitude. Comparing Figure 11 with Figures 12-14, it can be seen that all three stochastic resonance detection models can realize the conversion of noise energy to signal energy, which in turn suppresses the noise and improves the signal-to-noise ratio. Comparing the output signals of Figures 12-14, it can be seen that under the low-intensity noise interference, the non-saturated stochastic resonance improves the amplitude of the output of the system and has the highest output signal-to-noise ratio, the classical stochastic resonance system has an intermediate output signal-to-noise ratio, and the accelerated stochastic resonance system has the lowest output signal-to-noise ratio, which is in line with the conclusions of the previous derivation. The Gaussian white noise with a noise intensity \(D\) of 5 is mixed with the harmonic signals of Equation (45) through the secondary sampling process and then input to the classical stochastic resonance detection system, unsaturated stochastic resonance detection system, and accelerated stochastic resonance detection system, and the subsequent signals are all processed by the secondary sampling process, and the fourth-order Runge-Kutta algorithm is used to calculate the Langevin equations. The waveforms and spectra of the mixed signals are shown in Figure 15, and the experiment results are shown in Figures 16-18. The results are shown in Figures 16-18.