連続ウェーブレット変換を用いたDuffing系の不規則応答におけるジャンプ現象の解析 (第2報，複素ウェーブレット変換による解析)

狭帯域不規則励振を受けるDuffing系は，応答の標本関数において振幅が急激に変化す る確率論的ジャンプ現象を生じることがある.この現象は，調和励振におけるジャン プ現象と同様に応答振幅の大/小，励振と応答の同位相/逆位相の2つの安定状態が 存在することに対応する.本研究では，狭帯域不規則励振を受けるDuffing系の確率論 的ジャンプ現象に対し，励振と応答の複素ウェーブレット変換を用いて励振と応答の 位相差を求め，調和励振に対する周波数応答関数より応答の状態を判別する方法を提 案する.提案した指標と前報で示した指標を比較した結果，両者とも同等に応答の状 態を判別できることが分かった.

Stochastic jump phenomena in the random responses of a Duffing oscillator subjected to narrow band excitation are investigated. The stochastic jump phenomena correspond to the existence of multiple stationary responses, which differ in phase to the excitation. In our previous paper, the product of each real wavelet of response and excitation is proposed as the phase of each frequency component. But taking the moving average of the product over one period is necessary because of pulsation. In this paper, the product of the complex wavelet transform of the response and the complex conjugate of that of the excitation is used to evaluate phase of each frequency component. The central value of unstable region of the phase in the frequency response function is used as the center of the range of the principal value of the complex argument, and the value and bounds of unstable region are taken as the threshold for phase obtained from the wavelet transforms. Using this range of principal value of complex argument and thresholds, two states of the response are successfully identified, as well as the previously proposed criterion using real wavelet transform.