Adaptive Control Method Of Stochastic Resonance Based On Improved Potential Function And Its Application

Signal detection,industrial equipment detection,biomedicine,materials science,etc.,many research fields need to use weak signal detection technology.Traditional detection techniques improve the signal-to-noise ratio(SNR)by suppressing noise.These methods and technologies may eliminate weak useful signals together while suppressing noise.A nonlinear system solves this problem perfectly that can produce stochastic resonance(SR)phenomenon.To obtain the SR phenomenon,it is necessary for the three elements of the nonlinear system,signal,and noise to achieve a coordinated state.At this time,energy of the noise is transformed,so that the noise is weakened and the useful signal is strengthened.It is meaningful because of this characteristic of the nonlinear stochastic resonance system that it has attracted many scholars to study it,and it has been widely used in various fields using weak signal detection technology.This thesis first introduces the development process of stochastic resonance theory,and the corresponding basic theory.On the basis of the existing theory,we focus on the transformation and application of nonlinear system.The main work and innovation of the thesis are as follows:(1)Based on the structural characteristics of the stochastic resonance system and its optimization principle,a piecewise linear bistable stochastic resonance system with asymmetric structure and unsaturated characteristics is constructed.The SNR formula is deduced and compared with the SNR formulas of the classical bistable system and the symmetric linear bistable system.First,it theoretically explains that the constructed asymmetric system has good performance.Then,the form of numerical simulation is used to verify the excellent performance of the construction system,and at the same time,it shows that the theoretical analysis and formula derivation are correct.(2)Because the bistable system and the tristable system have their own advantages and disadvantages.Therefore,it is necessary to improve the potential function of the tristable system.Aiming at the problems that the classic three-stable model is not ideal,the correlation between parameters is too big to realize the optimization of parameters with algorithms,a novel structure of the three-stable system model was constructed.The formula of output SNR is deduced,and the influence of its parameters on the model is explained.Then in the numerical simulation experiment,it is compared with the piecewise linear model,which verifies the correctness of the formula and shows that the model has good system performance.(3)By retrieving the literature,it is found that most of the single stochastic resonance systems with different potential functions are used in engineering.The stochastic resonance system is a system whose performance is affected by system parameters.If two complex systems are coupled together,many parameters will be introduced,and the correlation between parameters is too complex to find appropriate parameters to obtain better system performance.Based on this,a simple monostable system coupled with a stochastic resonance system with good performance but a large number of parameters is proposed.A controllable stochastic resonance coupled system is formed.By comparing with the first two newly constructed stochastic resonance systems,a new coupled control system can be obtained.In the derivation of the signal-to-noise ratio formula,it is compared with the uncoupled system,and it is theoretically demonstrated that this method can effectively improve system performance.Then,it was compared and analyzed with the results obtained from the numerical simulation experiment,and it was found to be the same as the theoretical analysis,thus verifying the correctness of the theoretical analysis.(4)Due to a large number of parameters of the new potential function constructed,the general iterative optimization algorithm will spend a lot of time in parameter optimization,and it is difficult to obtain better system parameters.The practical value of the stochastic resonance system will also be reduced due to the difficulty of parameter optimization.In order to solve this problem,an algorithm for adaptive parameter optimization is proposed.Because this algorithm optimizes parameters by simulating biological genetics,it is also called genetic algorithm.The actual use of the genetic algorithm to search the optimal parameter shows that the goal can be achieved successfully.The actual application results show that the improved potential function has excellent system performance and fully conforms to the conclusions of theoretical derivation and numerical simulation.