## 1 Introduction  
There has been a constant focus on the characteristic of near-fault earthquake motion since the Northridge event in the U.S., the Kobe event in Japan, and the Chi-Chi event in Taiwan [1]. The increased availability of recorded ground motions from these seismic events suggests that the dynamic characteristics of ground shaking can significantly vary as a function of the recording station's location with respect to the fault and evolution of the rupture process [2]. The long pulse period and large velocity amplitude of the near-fault earthquake motion may cause severe damage to massive engineering structures [3]. The empirical mode decomposition (EMD) is used to identify and separate the dominant pulse [4]. [PERSON] et al. [5] found that the pulse-like near-fault ground motions can significantly increase the displacement demand of structures under a medium period. The near-fault earthquake motion is roughly defined by the record whose closest distance-to-fault is within 20-30 km. The effect of rupture direction and the permanent ground displacement, are two significant features of the near-fault earthquake motion [6]. Larger pulse motions exist in the direction normal to the fault than that parallel to it, due to the radiation pattern of shear dislocation on the fault [7]. The rupture source propagates into the surrounding medium at a speed close to shear velocity, which causes rupture energy arrival in a few pulse patterns. The horizontal component, perpendicular to the fault, contains the long period pulse-like motion [8]. This type of phenomenon is very similar to the Doppler Effect concept in acoustics. The peak ground acceleration, velocity, and displacement are the critical parameters that influence the structural seismic response [9]. Near-fault recordings from recent earthquakes indicate that the pulse is a narrow band waveform, whose period increases with magnitude [10]. The closest distance-to-fault (R) is just a convenient engineering parameter that roughly identifies the pulse-like motion. A more rigorous identification and representation approach should be considered to quantitatively classify the near-fault pulse-like motions. No universal accepted criteria exist regarding how to identify the most unfavorable seismic input direction with the largest pulse energy, and the knowledge about the characteristic of the seismic signal in that unfavorable direction is limited. Many researchers have investigated the characteristic of the pulse-like earthquake motion, and its influence on the seismic response of structures: [PERSON] et al., input the equivalent pulse into the elastic and elastic-plastic frame structure to investigate the influence of pulse motion on frame structure. They found that frame structures behave differently depending on whether their base frequency is smaller or larger than pulse frequency [11]. [PERSON] et al. investigated the influence of bidirectional near-fault excitations on reinforced concrete (RC) bridge piers. The influence of bidirectional shaking is accounted for by using a simplified 30% rule. Bidirectional interaction under near-fault motion is observed to substantially amplify damage, particularly for a stiff system [12]. [PERSON] et al. studied the effect of near-fault ground motions on the multi-story structures. They found that pulse-like forward-directivity ground motions impose a larger ductility demand on the structure compared to ordinary ground motions [13]. Based on the value of maximum fractional signal energy contribution by any half-cycle of the velocity time-history, [PERSON] et al. proposed an objective criterion to differentiate directivity pulse-like motions from the available suite of recorded ground motions [14]. [PERSON] et al. utilized the moving average filtering with appropriate cut-off frequency to decompose the near-fault ground motions into two components: Pulse-Type record and BackGround record.