物理学报
物理學報
물이학보
2013年
9期
49-61
,共13页
分数阶非线性系统%Duffing振子%弱信号检测
分數階非線性繫統%Duffing振子%弱信號檢測
분수계비선성계통%Duffing진자%약신호검측
fractional nonlinear system%duffing oscillator%weak signal detection
本文建立了分数阶可停振动系统,其可停振动状态的改变对周期策动力敏感,对零均值随机微小扰动不敏感,这事实上为周期未知微弱信号检测提供了一种新的高效检测方法和判别标准.与现有的利用混沌系统的大尺度周期状态变化检测周期未知弱信号的方法需逐一尝试设置不同频率内置信号以便期望与待检周期信号发生共振不同,利用分数阶可停振动系统的可停振动状态变化检测周期未知微弱信号的方法,除了同样具有因为状态变化对周期信号的敏感性而能够实现极低检测门限的特点外,还具有混沌系统信号检测所不具有的优点:1)无需预先估计待检信号的周期;2)无需计算系统状态的临界阈值;3)可停振动状态可由本文设计的指数波动函数可靠地进行判断;4)通过系统微分阶数的变化,将检测系统层次化,从而可得到比整数阶检测系统更低的检测门限,特别是在色噪声环境下,通过选取合适的微分阶数,基于分数阶可停振动系统的微弱周期信号检测法能够大幅度的降低检测门限,在本文的仿真试验中,检测门限可达–182 dB.
本文建立瞭分數階可停振動繫統,其可停振動狀態的改變對週期策動力敏感,對零均值隨機微小擾動不敏感,這事實上為週期未知微弱信號檢測提供瞭一種新的高效檢測方法和判彆標準.與現有的利用混沌繫統的大呎度週期狀態變化檢測週期未知弱信號的方法需逐一嘗試設置不同頻率內置信號以便期望與待檢週期信號髮生共振不同,利用分數階可停振動繫統的可停振動狀態變化檢測週期未知微弱信號的方法,除瞭同樣具有因為狀態變化對週期信號的敏感性而能夠實現極低檢測門限的特點外,還具有混沌繫統信號檢測所不具有的優點:1)無需預先估計待檢信號的週期;2)無需計算繫統狀態的臨界閾值;3)可停振動狀態可由本文設計的指數波動函數可靠地進行判斷;4)通過繫統微分階數的變化,將檢測繫統層次化,從而可得到比整數階檢測繫統更低的檢測門限,特彆是在色譟聲環境下,通過選取閤適的微分階數,基于分數階可停振動繫統的微弱週期信號檢測法能夠大幅度的降低檢測門限,在本文的倣真試驗中,檢測門限可達–182 dB.
본문건립료분수계가정진동계통,기가정진동상태적개변대주기책동력민감,대령균치수궤미소우동불민감,저사실상위주기미지미약신호검측제공료일충신적고효검측방법화판별표준.여현유적이용혼돈계통적대척도주기상태변화검측주기미지약신호적방법수축일상시설치불동빈솔내치신호이편기망여대검주기신호발생공진불동,이용분수계가정진동계통적가정진동상태변화검측주기미지미약신호적방법,제료동양구유인위상태변화대주기신호적민감성이능구실현겁저검측문한적특점외,환구유혼돈계통신호검측소불구유적우점:1)무수예선고계대검신호적주기;2)무수계산계통상태적림계역치;3)가정진동상태가유본문설계적지수파동함수가고지진행판단;4)통과계통미분계수적변화,장검측계통층차화,종이가득도비정수계검측계통경저적검측문한,특별시재색조성배경하,통과선취합괄적미분계수,기우분수계가정진동계통적미약주기신호검측법능구대폭도적강저검측문한,재본문적방진시험중,검측문한가체–182 dB.
In this paper, a new detecting method for weak periodic signals with unknown periods and unknown forms, the so-called fractional stopping oscillation method, is presented. This new detecting method, which is based on the research of some dissipative system of single degree of freedom, is sensitive to periodic signal—even with unknown period and unknown form—and insensitive to noise. Compared with the known chaotic detections in which a built-in signal must be pre-set with the same frequency and the same form as the detected periodic signal, the fractional stopping oscillation method can not only be used even at lower SNR than chaotic detection, but also has some other notable advantages as follows: (1) it need not get the period and the form of detected signal before hand or pre-estimate them; (2) it need not pre-calculate the chaotic threshold value; (3) the existence of periodic signal in system input can be reliably and quantitatively judged by volatility index function, designed in this paper, for stopping oscillation method;(4) a more sensitive detection method can be achieved by the fractionalization of the detection system, especially, the detection threshold can reach–182 dB when the background noise is colored Gaussian noise.
