Accurate and reliable arcing fault identification in distribution systems ensures the safety of personnel and equipment during operations and maintenance works. However, the different configurations of circuit components, under various operating scenes, may distort the fault dynamics inconsistently and continuously impact to the representation form of the faults’ signature characteristics, which poses substantial challenges to arc fault identification. This paper proposed various operating scenes adapted robust arc identification approach, incorporating the Hilbert Transform (HT) based nonlinear circuit impedance representation and chaotic characteristic analysis of fault circuit. With establish the equivalent variable coefficient differential equation based impedance model of arc faults, the mechanism of how circuit parameters impact the representation of arc fault dynamic has been revealed. Then, to decouple the correlation between arc fault features and circuits parameters, meanwhile obtaining the signature feature set, HT based modulus of voltage and current dynamic phasor ratio (MVCR) has been calculated, which directly represents the fault dynamic in time/frequency domain. Meanwhile, to enhance the robustness of feature selection, chaotic features of fault signals have been studied and extracted in phase space. In addition, LSTM based classification algorithm has been designed for arc fault identification with the distinction of time-series features. With the series of actual arc fault cases under different configurations, the effectiveness and robustness of the proposed method have been thoroughly validated.