基于卡尔曼增益的Duffing系统状态预测算法

A Predictive Algorithm for Duffing System State Based on Kalman Gain

传统的Duffing系统检测算法主要基于相图的变化,通常需要大量的循环采样点数来激励系统从混沌态转移到大尺度周期态,极大地限制了Duffing振子的应用。本文提出一种新型的基于卡尔曼增益的预测算法,通过建立Duffing系统状态方程并设定量测方程的控制条件,得到Duffing系统的卡尔曼增益改进形式,根据增益的变化可以实现Duffing系统状态的预判,从而降低了系统的输入采样。谐波信号检测实验表明,相比传统算法,预测方法不仅可以减少至少50%的循环采样点数,而且检测的精度也得到了显著的提高。

Traditional identification algorithms for Duffing oscillator are mainly based on the transitions of phase diagram, and they need a large number of cumulative inputs to transform the system from chaos to the large-scale periodic state, and these limit their applications of Dulling oscillator. A new algorithm based on Kalman gain is proposed in the paper to predict state transitions of the Duffing oscillator before transitions in the phase diagram. By the establishing of Dulling state equations and setting the control condition of measurement equations, an improved form of Kalman gain c-an be obtained to effectively predict the state changes of the Duffing oscillator, experiments of harmonic signal detections show that the predictive algorithm can not only reduce at least 50% input points to identify the phase transitions of oscillator, but also the detection accuracy is obviously improved.