Identification technique for impulsive seismic motions based on the combination of EAMRCM and SVM

Abstract

This study proposes a novel method for identifying impulsive seismic motions by integrating the Enhanced Adaptive Multi-Resolution Chirplet Method (EAMRCM) with a Support Vector Machine (SVM) classifier. EAMRCM provides refined time-frequency representations that effectively extract intricate pulse characteristics from near-fault seismic motion records, thereby enhancing both the accuracy and robustness of the extraction process. Principal Component Analysis (PCA) is employed to distill key features from the seismic data, which is subsequently coupled with an SVM classifier to automatically distinguish between impulsive and non-impulsive events. Compared to existing approaches, the proposed method effectively adapts to complex seismic motion patterns, significantly reduces manual intervention, and enhances both automation and classification accuracy. Simulation tests performed in MATLAB demonstrate that this approach markedly improves the identification accuracy for impulsive seismic events, offering a novel tool and methodological foundation for seismic analysis and disaster mitigation engineering.

Keywords

multi-pulse seismic motion velocity pulse asymmetric Gaussian linear Chirplet model support vector machine near-fault seismic motion

Introduction

In recent years, near-fault ground motions have garnered increasing attention from seismologists and earthquake engineers, owing to the growing understanding of seismic phenomena. These ground motions are often characterized by long-duration, high-energy velocity pulses, primarily induced by forward directivity and fling-step effects (Kalkan and Kunnath, 2006; Somerville et al., 1997; Spudich et al., 2004). Such phenomena can significantly prolong ground motion duration and exert considerable influence on the seismic response of structures (Chen et al., 2023a; Chen et al., 2022; Wang et al., 2024; Srivastava et al., 2024). When a fault rupture propagates toward a site, forward directivity amplifies the amplitude of velocity pulses, while the fling-step effect results from permanent displacements along the fault trace. Compared to non-pulse-like motions, pulse-like ground motions impose more demanding requirements on structural performance. With the continued expansion of transportation infrastructure, an increasing number of engineering structures are inevitably located in close proximity to active faults, thereby elevating the expectations for seismic ductility and strength. Furthermore, although much of the existing research has focused on the impact of a single dominant pulse on structural response, multiple embedded pulses frequently appear in velocity records, potentially leading to misinterpretation of the ground motion characteristics (Jia et al., 2024b, 2024a; Zhang et al., 2024).

In recent years, significant progress has been made in the extraction and identification of pulse-like features in ground motion records. (Bray and Rodriguez-Marek, 2004) proposed a parameterization method based on velocity amplitude, pulse period, and the number of prominent pulses to identify pulse-like motions. However, their approach relies heavily on manual interpretation, rendering it labor-intensive and susceptible to subjective bias. To address this limitation (Baker, 2007), introduced a wavelet transform-based technique to automate the extraction process, thereby enhancing analytical efficiency. Building upon this work, (Shahi and Baker, 2014) developed a refined algorithm capable of extracting pulses from both horizontal components of ground motion, and made the tool publicly available as an open-source resource. Alternatively, (Feng et al., 2021) employed the Variational Mode Decomposition (VMD) method to detect pulse characteristics. While these approaches have demonstrated effectiveness in capturing single dominant pulses, their performance tends to degrade when applied to complex ground motions containing multiple embedded pulses, often resulting in limited identification accuracy and a higher incidence of false classifications.

To address the limitations of single-pulse extraction methods, (Chen and Wang, 2020; Chen et al., 2023b) proposed an automated preliminary pulse detection algorithm based on the Hilbert-Huang Transform (HHT), and further advanced a Generalized Continuous Wavelet Transform (GCWT) approach. By integrating convolutional analysis with parameter evaluation, this method enables effective identification of ground motions containing multiple embedded pulses. (Feng et al., 2024) employed a non-causal fourth-order low-pass Butterworth filter to extract velocity pulses. However, due to the inherent filtering characteristics, the method often neglects critical pulse components. In parallel, (Boßmann and Ma, 2015; Sharbati et al., 2020) utilized a Gaussian Chirplet model to capture and model pulses in recorded ground motions, demonstrating promising accuracy. Nevertheless, their reliance on fixed window lengths for feature extraction limits adaptability to nonstationary signals. Moreover, their parameter estimation procedures, which depend on initial guess values and basic statistical measures, are prone to convergence issues and may easily become trapped in local optima.

In the domain of ground motion classification, (Baker, 2007) pioneered the use of pulse indices, arrival time, and peak velocity as key metrics to distinguish pulse-like motions. Building upon this framework, (Shahi and Baker, 2014) enhanced classification performance by integrating Principal Component Analysis (PCA) with a second-order polynomial kernel in a Support Vector Machine (SVM) classifier. Subsequent studies by (Chen et al., 2023a; Feng et al., 2024), and other researchers (Liu et al., 2020; Mukhopadhyay and Gupta, 2013; Panella et al., 2017; Tang and Zhang, 2011; Yu et al., 2024) incorporated additional features such as peak velocity and energy ratios to refine classification schemes. In particular, (Wang and Huang, 2024) introduced a wavelet packet–based decomposition method that explicitly separates the primary pulse component from the residual motion, thereby enabling more robust extraction of pulse parameters and mitigating distortions caused by multi-pulse phenomena. However, the presence of multiple pulses within a single ground motion record may distort energy ratio calculations, leading to increased misclassification and undermining the robustness of such methods.

Support Vector Machine (SVM), a machine learning algorithm capable of both linear and nonlinear classification, has found widespread applications in diverse domains such as image recognition and system monitoring. Its fundamental principle lies in maximizing the margin between classes to minimize structural risk (Vapnik, 2013). In recent years, (Sun et al., 2016) combined compressed dictionary techniques with the Least Squares Support Vector Machine (LS-SVM) to alleviate the computational burden associated with high-dimensional and large-scale datasets, thereby enhancing training efficiency and model sparsity. The continued evolution of SVM has not only advanced theoretical developments but also facilitated its integration into complex decision-making tasks such as autonomous driving, medical diagnostics, and seismic motion identification (Banerjee and Bhowmik, 2024; Liu et al., 2024; Mohammadi et al., 2024; Pundir et al., 2024).

To address the key challenges in identifying multi-pulse ground motions—such as the inability of conventional methods to capture nonstationary features, interference of multiple pulses with classification parameters, and limited generalization capability of existing classifiers—this study proposes an Enhanced Adaptive Multi-Resolution Chirplet Method (EAMRCM). This method synergistically integrates an asymmetric Gaussian Chirplet model, adaptive parameter adjustment, regularization-based optimization, and multi-resolution analysis to improve modeling fidelity, parameter estimation, and feature extraction. Furthermore, by incorporating the SVM classifier, the proposed framework enables automated, accurate, and efficient identification of pulse-like ground motions. This research aims to establish a robust and high-precision identification framework tailored to complex multi-pulse seismic records, thereby contributing both theoretical insight and practical value to the advancement of pulse extraction methodologies and seismic motion classification techniques.

Enhanced adaptive multi-resolution Gaussian Chirplet wavelet method

Mathematical formulation of the asymmetric Gaussian linear Chirplet model (AGCM)

At the core of EAMRCM lies the Asymmetric Gaussian Linear Chirplet Model (AGCM), which represents the various components or “atoms” of a seismic signal. The model is defined by a set of parameters that describe the time shape and amplitude modulation of Chirplet atoms, making the AGCM a powerful tool for simulating various seismic pulse shapes. The AGCM serves as the foundation of EAMRCM, aiming to model the components or “atoms” of the seismic signal. Each atom is expressed in a mathematical form through its basis function:

A_{k} (t) = E_{p} (t) F_{k} (t)

(1)

where

A_{k} (t)

represents the k-th Chirplet atom, which corresponds to a specific feature within the signal.

The envelope function $E_{p} (t)$ determines the time shape and amplitude modulation of the Chirplet atom, and can be expressed as:

E_{p} (t) = \exp (- α_{k} (1 - β_{k} \tanh (C (t - τ_{k}))) {(t - τ_{k})}^{2})

(2)

where

α_{k}

denotes the bandwidth or spread of the atom,

β_{k}

introduces asymmetry to simulate skewed pulse shapes,

τ_{k}

represents the time offset of the atom, determining its position in the time domain, and C is a constant used to control the hyperbolic tangent function.

The frequency modulation function $F_{k} (t)$ governs the oscillatory behavior within the envelope and can be expressed as:

F_{k} (t) = \cos (f_{k} (t - τ_{k}) + γ_{k} {(t - τ_{k})}^{2} + θ)

(3)

where

f_{k}

indicates the center frequency of the Chirplet,

γ_{k}

represents the Chirplet’s rate, allowing for time-dependent frequency modulation, and

θ

is the initial phase.

In the formulas above, $\tanh (C t) = - i \tanh (i C t)$ is the hyperbolic tangent function. For larger values of C, when $t > 0$ , the function approximates 1; when $t < 0$ , it approximates −1. The value of C is a predetermined constant. The AGCM function $A_{k} (t)$ is defined by a parameter set $p = (α_{k}, β_{k}, τ_{k}, f_{k}, γ_{k}, θ_{k})$ , where the bandwidth factor $α > 0$ , asymmetry factor $β \in (- 1, 1)$ , time offset $τ > 0$ , center frequency $f \in [0, 2 π)$ , frequency modulation rate $γ \in [0, 2 π)$ , and phase angle $θ \in [0, 2 π)$ . The combination of the envelope and frequency modulation functions allows the AGCM to flexibly simulate various seismic pulse shapes, making $A_{k} (t)$ a powerful tool for accurately representing the components of seismic signals.

Adaptive windowing in seismic signal analysis

In previous studies, using a fixed window size has often proven insufficient for analyzing seismic signals, particularly due to the highly time-variant nature of seismic data. A window that is too narrow may miss important features, while a window that is too wide may introduce noise. Building on the limitations highlighted by (Boßmann and Ma, 2015; Sharbati et al., 2020), this paper introduces an adaptive windowing mechanism that dynamically adjusts the window size based on the local variance of the signal, thereby enhancing the focus and efficiency of the analysis. The adaptive window can be expressed as:

W s = \max (a, \min (b, \frac{c}{\sqrt{V a r (y (t))}}))

(4)

where Ws represents the size of the analysis window, while a and b are predefined minimum and maximum window sizes, ensuring that the window remains within practical limits. The parameter c is a scaling factor that adjusts the window size according to the local variance of the signal, Var(y(t)) which measures the fluctuation of the signal within the window. This adaptive strategy ensures that the window size is optimized to capture the most relevant features of the signal while minimizing the influence of irrelevant noise, thereby improving the accuracy of pulse extraction.

Adaptive orthogonal matching pursuit (ADOMP) for seismic signal analysis

The Adaptive Orthogonal Matching Pursuit (ADOMP) method aims to iteratively decompose seismic signals into sparse representations using Chirplet atoms, thereby accommodating the dynamic characteristics of seismic data (Sharbati et al., 2020). Traditional fixed-parameter models often fail to capture the complexity of seismic signals, necessitating the use of adaptive methods like ADOMP.

Initialization

The initial residual is set to the input seismic signal, expressed as:

R_{0} (t) = y (t)

(5)

where

y (t)

represents the recorded seismic motion.

Iterative process

Time Offset Selection $τ_{k}$ : In each iteration, the algorithm determines the time offset $τ_{k}$ that maximizes the correlation between the current residual $R_{k - 1} (t)$ and the candidate Chirplet atom $A_{k} (t)$ . The time shift is determined by:

τ_{k} = \arg \max_{τ} | \int R_{k - 1} (t) E_{p} (t) d t |

(6)

Parameter Estimation: After determining $τ_{k}$ , the parameter set $p = (α_{k}, β_{k}, τ_{k}, f_{k}, γ_{k}, θ_{k})$ is estimated based on the local statistical characteristics of the signal. This ensures that each Chirplet atom $A_{k} (t)$ is finely tuned to match the specific features of the signal.

Amplitude Optimization: The amplitude $α_{k}$ of the Chirplet atom is optimized to minimize the residual. The amplitude is calculated as:

a_{k} = \frac{R_{k - 1} (t) A_{k} (t)}{A_{k} (t) A_{k} (t)}

(7)

This optimization ensures that the selected atom maximally reduces the residual.

Residual Update: Once the best-fitting Chirplet atom and its amplitude are determined, the residual is updated by subtracting the contribution of the selected atom:

R_{k} (t) = R_{k - 1} (t) - α_{k} A_{k} (t)

(8)

Stopping Criteria: The iteration continues until the norm of the residual $‖ R_{k} (t) ‖$ falls below a predefined threshold $ε$ or the maximum number of iterations is reached. This criterion ensures that the decomposition process captures the essential features of the signal without overfitting. The stopping condition can be expressed as:

\frac{‖ R_{k} ‖}{‖ y (t) ‖} < ε or maximun iterations reached

(9)

This adaptive method enables a more precise and flexible analysis of seismic signals, potentially leading to a better understanding and prediction of seismic activity.

Regularized newton method

To precisely refine the frequency parameters of Chirplet atoms, this study employs the regularized Newton method. This approach minimizes the residual error based on the least squares method and incorporates a regularization term to enhance the stability and robustness of the optimization process. The selection of the regularization parameter is crucial for balancing the goodness of fit and smoothness. An adaptive method is used to determine this parameter, ensuring optimal updates and preventing overfitting. The residual calculation can be expressed as:

R (t) = y (t) - \sum_{k = 1}^{n} a_{k} A_{k} (t)

(10)

The regularization parameter update can be formulated as:

Δ P = - {(J_{R}^{T} J_{R} + λ I)}^{- 1} J_{R}^{T} R

(11)

P_{n e w} = P_{o l d} + h Δ P

(12)

where

J_{R}

represents the Jacobian matrix of the residual with respect to the frequency parameters.

λ

is the regularization parameter that controls the trade-off between fitting the data and maintaining the smoothness of parameter updates. The dynamic step size h is adjusted based on the gradient norm.

The dynamic step size is given by:

h = \min (h_{\max}, \frac{1}{‖ Δ P ‖})

(13)

This method ensures the optimization process remains stable and adaptive, allowing for more precise adjustment of the Chirplet atom parameters while avoiding overfitting.

Multi-resolution analysis

The EAMRCM framework employs multi-resolution analysis to effectively capture seismic characteristics at different scales. By decomposing the signal into multiple resolution levels, the framework applies the ADOMP algorithm at each level, enhancing the accuracy of feature representation while balancing computational requirements. This method enables detailed yet computationally efficient analysis, accommodating both coarse and fine-scale features within seismic data.

The decomposition of seismic data can be expressed as:

y (t) = \sum_{s = 1}^{n} y_{s} (t)

(14)

where

y_{s} (t)

represents the signal at the s-th resolution level.

Pulse Extraction

A_{p} (t) = \sum_{s = 1}^{n} A_{p, s} (t)

(15)

where

A_{p, s} (t)

denotes the pulse component extracted at the s-th resolution level.

Post-smoothing

To mitigate high-frequency noise and irregular fluctuations inherent in the original seismic pulse signal, a Gaussian smoothing operation is applied to the signal $A p (t)$ , as defined in equation (16). This technique performs a weighted average over a window of $ω$ sampling points centered at time $t$ , thereby generating a smoothed signal $A_{s m o o t h e d} (t)$ . The smoothing process effectively preserves the principal characteristics and energy distribution of the signal, while suppressing high-frequency disturbances arising from instrumental inaccuracies or numerical artifacts. This denoising step facilitates the subsequent extraction and classification of salient features in the seismic motion.

The post-smoothing process can be expressed as:

A_{s m o o t h e d} (t) = \frac{1}{2 ω + 1} \sum_{k = - ω}^{ω} A_{p} (t + k δ_{t})

(16)

where

ω

is the window size of the smoothing filter, and

δ_{t}

represents the time step interval.

Application and refinement of EAMRCM

Implementation process of EAMRCM

Table 1 provides an overview of the Enhanced Adaptive Multi-Resolution Chirplet Method (EAMRCM) for extracting velocity pulses from near-fault ground motion data. The process begins by initializing the residual signal, envelope matrix, and iteration index. Using an adaptive Chirplet basis, the algorithm iteratively refines the residual, identifies the most significant contributions, and adjusts the Chirplet atoms based on multi-resolution analysis.

Table 1.

Algorithm for extracting velocity pulses using EAMRCM.

Input of algorithm: Ground motion

v (t)

, stopping parameter m Ground motion

y (t)

, stopping parameter m, initial guess for Chirplet parameters

G_{0}

, initial residual

R_{0} = y (t)

Initial assumption: Residual

R_{0} = y (t)

, Chirplet atom matrix

G_{0} = ϕ

,Iteration

J = 0

While

{‖ R_{J} ‖}_{\infty} \geq m {‖ E n v (y) ‖}_{\infty}

Increment iteration index

J = J + 1

Calculate

τ_{J} = argmax R_{J} (t), a_{J} = R_{J} (τ_{J})

Choose M sample points

(t_{1}, t_{2}, . . ., t_{m})

around

τ_{J}

and extract the envelope atom

g_{J} (t)

based on the multiresolution analysis

Orthogonalize the extracted atom

g_{J} (t)

Extend the atom matrix

G_{J} = G_{J - 1} \cup {g_{J}}

Optimize the amplitude coefficient matrix

A_{J} = {(G_{J}^{T} G_{J})}^{- 1} G_{J}^{T} R_{J}

Update the residual

R_{J} = y (t) - A_{t} G_{J} (t)

End

Output of algorithm:

R_{J}, G_{J}, A_{J}, G_{J}

In each iteration, the algorithm calculates the maximum residual, selects sample points for extracting the envelope atoms, orthogonalizes them, and optimizes the amplitude coefficients using the least squares method. This iterative process continues until the maximum residual value drops below the specified stopping parameter, ensuring accurate pulse extraction and minimal residual errors.

To further enhance the accuracy of frequency parameters within the EAMRCM framework, Table 2 describes an optimization algorithm that employs the regularized Newton method. Starting with an initial guess for the frequency parameters, the algorithm iteratively updates these parameters by solving a linearized system, optimizing the amplitude coefficients, and calculating the step size to ensure stable convergence. The regularization term improves the stability of the optimization process and prevents overfitting. This iterative process continues until the maximum number of iterations is reached or the convergence criterion is satisfied, resulting in optimized frequency parameters that improve the representativeness of the extracted velocity pulses.

Table 2.

Algorithm for optimizing frequency parameters in EAMRCM.

Input of algorithm: Signal

y (t)

, Chirplet matrix

G_{J}

, maximum iterations

N

, initial frequency guess

P

Initial assumption: Iteration

n = 0

, initial parameter guess

P

While

n \leq N

Solve

R (P) = - J_{R} (P) Δ P

using the linearized Chirplet model

Calculate step size

h

using a line search method for stable convergence

Update

P \leftarrow P + h Δ P

Solve for amplitude coefficients

{\tilde{a}}_{j}^{J} = argmin {∥ y - \sum_{j = 1}^{J} {\tilde{a}}_{j}^{J} E_{j} F_{j} ∥}_{2}^{2}

Update iteration

n = n + 1

End

Output of algorithm: Optimized frequency parameters

P

, updated amplitude coefficients

{\tilde{a}}_{j}^{J}

The flowchart in Figure 1 provides a visual representation of the entire EAMRCM implementation process, highlighting key steps such as adaptive window application, multi-resolution analysis, and the use of post-smoothing filters.

Figure 1.

Flowchart of the EAMRCM implementation process.

Validation of the AGCM method

Figure 2 illustrates the time-frequency analysis using the Asymmetric Gaussian Chirplet Model (AGCM). Each subplot demonstrates the energy distribution across time and frequency, highlighting how different parameter sets affect the Chirplet atom representation of seismic pulses. Figure 2(a) shows the time-frequency diagram with the parameter set $p = (0.01, 0, 0, 0.5, 0, 0)$ . This plot reveals a narrow bandwidth Chirplet centered around a specific time and frequency. Under this parameter set, the low-frequency pulse exhibits no chirp (constant frequency) and has a symmetric distribution in both time and frequency domains. Figure 2(b) presents a phase difference of $π / 4$ compared to Figure 2(a). This phase shift causes a rotation or tilt in the time-frequency distribution, affecting the energy’s position in the plot. While the overall structure is similar to that in Figure 2(a), the phase difference results in a waveform shift. Figure 2(c) reduces the atom’s bandwidth from 0.1 to 0.0025, resulting in a broader time-frequency distribution. The energy is spread over a wider range, thereby decreasing the resolution in both time and frequency. The concentration of peak energy is less pronounced than in Figure 2(a). Figure 2(d) sets the asymmetry factor to 0.8. The non-zero asymmetry factor introduces a change in frequency over time, creating a slanted pattern in the time-frequency diagram. Additionally, the presence of a $π / 4$ phase difference increases the complexity of the pulse wave. Figure 2(e) further introduces a frequency modulation rate, resulting in multiple peaks in the time-frequency plot. The combination of parameters creates a more intricate time-frequency structure, where multiple pulse-like components can be observed. Figure 2(f) displays the composite 2D projection of the five time-frequency plots from Figure 2(a)–(e). This provides an overall comparison of how different parameter sets influence the energy distribution in the time-frequency domain and clearly illustrates the impact of each parameter on the Chirplet atoms.

Figure 2.

Time-frequency analysis based on AGCM with different parameter sets. (a) $p = (0.01, 0, 0, 0.5, 0, 0)$ ; (b) $p = (0.01, 0, 0, 0.5, 0, \frac{π}{4})$ ; (c) $p = (0.0025, 0, 0, 0.5, 0, 0)$ ; (d) $p = (0.0025, 0.8, 0, 0.5, 0, 0)$ ; (e) $p = (0.0025, 0.8, 0, 0.5, 0.015, 0)$ ; (f) Composite 2D Time-Frequency Projection.

AGCM Envelope calculation

The envelope function of the recorded seismic motions was calculated using the formula described in equation (2). The seismic data were obtained from the Pacific Earthquake Engineering Research Center (PEER), with detailed information on the recorded earthquakes listed in Table 3. The results of the envelope calculation are presented in Figure 3.

Table 3.

Near-fault seismic records used to validate the proposed method.

Number	Name	Earthquake name	Magnitude	Mechanism
1	RSN143	Tabas_ Iran	7.35	Reverse
2	RSN149	Coyote Lake	5.74	Strike slip
3	RSN566	Kalamata_Greece-02	5.4	Normal
4	RSN1013	Northridge-01	6.69	Reverse
5	RSN1480	Chi-Chi_ Taiwan	7.62	Reverse oblique
6	RSN1531	Chi-Chi_ Taiwan	7.62	Reverse oblique
7	RSN1602	Duzce_ Turkey	7.14	Strike slip
8	RSN2114	Denali_ Alaska	7.9	Strike slip
9	RSN4097	Slack Canyon	6.0	Strike slip
10	RSN4480	L'Aquila_ Italy	6.3	Normal
11	RSN6887	Darfield_ New Zealand	7	Strike slip
12	RSN8119	Christchurch_New Zealand	6.2	Reverse oblique

Figure 3.

Velocity pulse envelopes derived using AGCM.

Figure 3 displays the velocity pulse envelopes derived from the recorded seismic motions using the AGCM analysis. A comparison of different seismic records reveals the diversity of earthquake pulses. The time of energy concentration and the attenuation process of pulses vary significantly across different seismic records. For example, RSN1480, RSN1531, and RSN6887 have longer durations of energy concentration and slower attenuation, whereas RSN566 and RSN4097 exhibit shorter durations of energy concentration with rapid attenuation. The envelope plays an intuitive role in pulse energy analysis, enabling a quick assessment of the energy concentration and attenuation rate in different seismic records.

Comparison of pulse extraction techniques: EAMRCM vs Baker method

Pulse identification accuracy comparison

Figure 4 compares the EAMRCM and Baker methods in extracting pulses from measured seismic velocity waveforms. EAMRCM captures pulse details more effectively, especially in records with abrupt waveform changes, such as RSN143 and RSN1013. A key advantage of EAMRCM is its ability to handle multi-pulse phenomena, accurately extracting multiple pulse components in records like RSN1480 and RSN4097, where the Baker method typically identifies only one. Additionally, EAMRCM excels in low-amplitude regions, as seen in RSN1531 and RSN6887, and performs well even in waveforms with small amplitudes but distinct frequency characteristics. Overall, EAMRCM outperforms the Baker method in extracting complex and multi-pulse structures, offering a more accurate reflection of real seismic motions.

Figure 4.

Comparison of velocity pulses extracted using the EAMRCM and Baker methods.

Residual seismic motion analysis

Figure 5 presents a comparison of the residual seismic motions extracted by the EAMRCM and Baker methods. As shown in the figure, most seismic records exhibit similar residual seismic motion patterns for both methods, particularly in the lower frequency range. This similarity suggests that both methods have a certain level of consistency when extracting the primary pulse features.

Figure 5.

Overall comparison of residual seismic motions extracted by the EAMRCM and Baker methods.

However, the residual seismic motion from the EAMRCM method contains more high-frequency components, whereas the residual from the Baker method appears relatively smoother. This difference likely arises because the EAMRCM method captures more complex pulse structures and details, leaving behind more high-frequency residual signals after pulse extraction. This effect is especially noticeable in the later stages of the seismic records.

Overall, the EAMRCM method demonstrates a clearer advantage over the Baker method in processing complex seismic motions, particularly in capturing Low-frequency pulse features and residual vibrations. For seismic motion records with complex pulse characteristics, the EAMRCM method retains more high-frequency information in the residual seismic motion, while the Baker method tends to produce a smoother outcome. Given these characteristics, the EAMRCM method has a significant advantage in identifying complex and multiple pulse structures, especially in seismic motions containing intricate Low-frequency components.

Response spectrum analysis comparison

Figure 6 compares the response spectra of the RSN2114 seismic record after pulse extraction using the EAMRCM method and the Baker method. From the response spectra, it can be observed that the residual ground motion extracted by the EAMRCM method is primarily concentrated within a 0∼1 second period. In contrast, the residual ground motion extracted using the Baker method is distributed over a broader 0∼2 second period. This indicates that the Baker method may fail to effectively extract the pulse components of the actual seismic motion in certain records.

Figure 6.

Response spectra of the residual ground motion for RSN2114.

Additionally, the pulses extracted by the EAMRCM method are more concentrated in the high-frequency region, suggesting that this method has greater sensitivity and adaptability when capturing low-frequency pulses. On the other hand, the Baker method may exhibit limitations when dealing with complex seismic records, resulting in incomplete pulse extraction. This observation further implies that using the Baker method could lead to incomplete pulse extraction, potentially affecting the identification and analysis of near-fault seismic motions. Therefore, the EAMRCM method demonstrates significant advantages in extracting complex pulse-type seismic motions and effectively addresses the limitations of the Baker method in certain scenarios.

Automatic identification method for pulse-type seismic motions

Application of support vector machine (SVM) in seismic classification

In the context of seismic motion identification, SVM is employed to distinguish between pulse-type and non-pulse-type seismic events. This study uses MATLAB’s fitcsvm function to train the model with an RBF kernel. Before training, the data is standardized to ensure that the model exhibits good generalization ability and stability across various seismic datasets. The decision function in SVM is based on a linear combination of support vectors and can be expressed as:

f (x) = \sum_{i = 1}^{n} α_{i} y_{i} K (x_{i}, x) + b

(17)

where

x

represents the input features to be predicted,

x_{i}

are the support vectors,

a_{i}

are the Lagrange multipliers obtained during training (non-zero for support vectors),

y_{i}

are the labels of the support vectors,

K (x_{i}, x)

is the kernel function (RBF in this study),

b

is the bias term, and

n

is the number of support vectors. The decision boundary is defined by setting

f (x) = 0

The Radial Basis Function (RBF) kernel is given by:

K (x_{i}, x_{j}) = \exp (- γ {‖ x_{i} - x_{j} ‖}^{2})

(18)

where

γ

controls the influence of each training example. A larger value of

γ

makes the decision boundary more tightly fitted around the support vectors.

Near-fault seismic motion identification method

To identify near-fault seismic motions, the Peak Ground Velocity ratio (PGV ratio) and the pulse energy ratio are introduced as key indicators. These metrics reflect the significance of pulse components in the seismic motion and serve as effective tools to distinguish between pulse-type and non-pulse-type seismic events. The PGV ratio is calculated as follows (Baker, 2007):

V_{PR} = \frac{\max (| V_{p} (t) |)}{\max (| V (t) |)}

(19)

where

V_{p} (t)

represents the extracted velocity pulse time history, and

V (t)

denotes the recorded seismic velocity time history.

The pulse energy ratio is given by (Feng et al., 2024):

E_{r} = \frac{\int_{0}^{T} {V_{p}}^{2} (t) d t}{\int_{0}^{T} V^{2} (t) d t}

(20)

where T is the duration of the seismic motion,

V_{p}

is the extracted velocity pulse time history, and

V

is the recorded seismic signal.

The PGV ratio is defined as the ratio of the peak velocity of the extracted pulse to the maximum velocity in the recorded seismic motion. The pulse energy ratio, on the other hand, quantifies the proportion of energy in the extracted pulse relative to the total seismic motion energy over the entire duration. A higher PGV ratio and pulse energy ratio indicate a more pronounced velocity pulse in the recorded seismic data, while lower values suggest a minimal pulse contribution. Furthermore, the pulse energy ratio and PGV ratio are linearly correlated, with most of their variance aligning along the same axis, as shown in Figure 7. To capture this relationship, principal component analysis (PCA) was performed using MATLAB, and the first principal component was computed as a linear combination of the PGV ratio ( $V_{PR}$ ) and the energy ratio ( $E_{r}$ ). The expression for the principal component (PC) is given by equation (21):

P C = 0.80 \times V_{PR} + 0.60 \times E_{r}

(21)

Figure 7.

Principal component analysis. (a) Formula calculation for PCA; (b) PGV Ratio vs. Pulse energy ratio.

The principal components (PC) derived from the analysis are subsequently combined with the PGV ratio to serve as input features for training a support vector machine (SVM) classifier, aiming to identify near-fault seismic motions. A crucial step in this classification process is the computation of the decision value, also referred to as the pulse index (PI value), which reflects the distance of a data point from the SVM decision boundary. A positive PI value indicates that the corresponding seismic event is classified as pulse-type. The mathematical expression for the PI value is given by equation (22):

P I = f (x) (f o r e a c h t e s t p o i n t x)

(22)

This PI value helps further assess the confidence of the classification. Points with larger positive PI values are classified as pulse-type with higher confidence.

Figure 8 compares the results of pulse-type seismic motion identification using Baker’s method and the SVM-based classifier. In Figure 8(a), the classification results show that using the PGV ratio and pulse energy ratio as features for automatic identification can lead to some misclassifications: some non-pulse-type seismic events are incorrectly classified as pulse-type, and vice versa. This limitation often requires manual adjustment, increasing the complexity of pulse-type seismic motion identification. In contrast, Figure 8(b) presents the results of the proposed SVM-based method, which effectively reduces identification errors without the need for manual intervention. The SVM classifier can more accurately distinguish between pulse-type and non-pulse-type seismic motions, clearly delineating the classification boundary, thereby improving the automation and accuracy of seismic motion identification.

Figure 8.

Pulse-type seismic motion identification results. (a) Classification results using Baker’s method. (b) Classification using the SVM-based method.

Implementation process of SVM classifier for pulse-type seismic motion identification

The flowchart of the proposed pulse-type seismic motion identification method is shown in Figure 9. The step-by-step overview of the procedure is outlined as follows.

Figure 9.

Pulse-type seismic motion identification using the SVM classifier.

Step 1: Set the velocity threshold, $P G V_{\min}$

One of the main characteristics of pulse-type seismic motions is the presence of a significant peak ground velocity (PGV) in the seismic record. Using PGV as a criterion for identifying pulse-type seismic motions is a direct and effective method. Therefore, setting an appropriate velocity threshold is the first step in the identification process. Based on previous research (Baker, 2007; Boßmann and Ma, 2015; Chen and Wang, 2020; Chen et al., 2023b; Liu et al., 2020; Mukhopadhyay and Gupta, 2013; Panella et al., 2017; Shahi and Baker, 2014; Sharbati et al., 2020; Tang and Zhang, 2011; Yu et al., 2024), this study sets the velocity threshold at 30 cm/s.

Step 2: Pulse extraction

Apply the Enhanced Adaptive Multi-Resolution Chirplet Method (EAMRCM) to extract pulses from the seismic record. This method accurately characterizes the pulse patterns within the seismic motion.

Step 3: Feature calculation and principal component analysis (PCA)

The relative energy ratio and peak velocity ratio are key indicators for determining whether a seismic motion exhibits pulse characteristics. The magnitudes of these ratios directly influence the classification of the seismic motion. In this study, these ratios are calculated, and the principal components (PC) are extracted as critical features for subsequent classification.

Step 4: SVM classification

Use the trained SVM model to automatically identify pulse-type seismic motions by combining the principal components with the peak velocity.

Comparison of methods

The 142 ground motion sets used in this study were identified based on the classification methods described in references [], which sourced data from the Pacific Earthquake Engineering Research Center (PEER) database. These sets were selected by integrating ground motions recognized in the three referenced studies. Each set consists of three components: longitudinal, transverse, and vertical, resulting in 426 individual ground motion records. However, some records lacked vertical components, reducing the total to 423. After excluding aftershocks, the dataset includes only mainshock recordings. Additionally, using the maximum pulse direction method proposed by (Shahi and Baker, 2014), the strongest pulse direction was determined for each set, yielding 141 strong pulse records. In total, the dataset comprises 564 ground motion records, corresponding to 142 earthquakes worldwide with magnitudes ranging from 5.5 to 7.9. The data were sourced from the PEER NGA-West2 database, with all records obtained from stations located within 30 km of the Joyner–Boore distance (Xiaofen et al., 2021).

This study reviews several pulse identification methods for ground motions. Baker’s method uses a wavelet-based approach, specifically the Daubechies wavelet, to extract the largest pulse and classifies motions based on the Peak Ground Velocity (PGV) ratio and energy ratio (Baker, 2007). Shahi and Baker improved upon this by incorporating Support Vector Machine (SVM) for nonlinear classification, utilizing wavelet transformation to extract pulses in any direction (Shahi and Baker, 2014). Chen’s method employs the Generalized Continuous Wavelet Transform (GCWT) and convolution analysis, using energy ratio and correlation coefficients to identify pulses (Chen et al., 2023a). Feng’s approach combines a non-causal Butterworth filter with an adaptive cutoff frequency, classifying ground motions based on relative energy and a Comprehensive Evaluation Index (CEI) (Feng et al., 2024). Panella’s method quantifies the velocity time history using development length (Ldv) and PGV, applying logistic regression to identify pulse characteristics (Panella et al., 2017). The pulse identification results obtained using the proposed EAMRCM method were validated by comparing them with five other identification methods across 564 recorded ground motions. The pulse identification results of the six methods are shown in Figure 10.

Figure 10.

Comparison of pulse-like ground motion identification. (a) Pulse-like ground motions; (b) Non-pulse-like ground motions.

Figure 10 shows the results of the six identification methods applied to 564 recorded ground motions, with pulse and non-pulse ground motions separated. The bar chart in Figure 10(a) reflects the number of pulse-like motions identified by each method. Panella’s method identified the most pulse-like motions (376), followed by the EAMRCM method with 371, and then Feng and Shahi’s methods, which identified 352 and 343 respectively. Chen and Baker’s methods identified fewer pulse-like motions, with 314 and 328 respectively. In Figure 10(b), the chart displays the number of non-pulse ground motions identified, with Chen’s method identifying the most (250), and Baker’s method identifying the fewest (81). Baker’s method had 155 unclassifiable results, leading to fewer definitive classifications. Overall, the pulse and non-pulse identification results vary across methods, but the EAMRCM method demonstrates high consistency with other methods, validating its effectiveness in pulse identification.

Conclusion

This study introduces an Enhanced Adaptive Multi-Resolution Chirplet Method (EAMRCM) for the identification of pulse-like ground motions, addressing critical limitations in existing pulse extraction and classification techniques. Compared with Baker’s wavelet-based method, EAMRCM demonstrates superior performance in accurately extracting multiple velocity pulses from complex seismic records, effectively resolving the long-standing challenge of single-pulse limitations.

(1) A key innovation of this work lies in the integration of an asymmetric Gaussian Chirplet model with adaptive decomposition, regularization-based optimization, and multi-resolution analysis. This framework enables precise modeling of time-varying pulse characteristics while preserving high-frequency seismic information often lost in traditional smoothing-based methods. Each stage of the EAMRCM—from signal decomposition to post-processing—is designed to accommodate the non-stationary and nonlinear nature of seismic velocity records, resulting in more reliable pulse characterization.

(2) Moreover, by incorporating Support Vector Machine (SVM) classification enhanced by Principal Component Analysis (PCA) and Radial Basis Function (RBF) kernels, the proposed method achieves high classification accuracy in identifying pulse-like ground motions. This automated identification framework reduces dependence on manual interpretation and mitigates misclassification, particularly in scenarios involving overlapping or hidden pulses.

(3) Comparative analysis with established methods—including Baker’s and Shahi’s wavelet techniques, Chen’s generalized continuous wavelet transform (GCWT), Feng’s non-causal Butterworth filtering, and Panella’s velocity quantification approach—demonstrates that EAMRCM consistently delivers more accurate and stable results across varied seismic datasets.

Despite its strong performance, the method is still with limitations. Its effectiveness depends on careful parameter tuning (e.g., cutoff frequency, iteration count), and the computational complexity introduced by the SVM-RBF structure may hinder real-time implementation. Additionally, while the asymmetric Gaussian Chirplet model captures most pulse behaviors, it may oversimplify the variability present in highly irregular seismic events.

Overall, EAMRCM provides a robust and scalable solution for pulse-like ground motion identification, laying a solid foundation for future developments in automated seismic data analysis and structural resilience assessment.

Footnotes

ORCID iDs

Liqiang Jiang

Jin Zhang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported by The research reported in this paper was supported by the National Natural Science Foundation of China (52378209), the Hunan Province Science and Technology Project Huxiang Young Talents Program (2023RC3057), the Sichuan Science and Technology Program (No. 2024NSFSC0932), and the Major science and technology project of Sichuan Province (No. 2023ZDZX0010). Their supports are gratefully acknowledged.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data will be made available on request.*

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Identification technique for impulsive seismic motions based on the combination of EAMRCM and SVM

Abstract

Keywords

Introduction

Enhanced adaptive multi-resolution Gaussian Chirplet wavelet method

Mathematical formulation of the asymmetric Gaussian linear Chirplet model (AGCM)

Adaptive windowing in seismic signal analysis

Adaptive orthogonal matching pursuit (ADOMP) for seismic signal analysis

Initialization

Iterative process

Regularized newton method

Multi-resolution analysis

Post-smoothing

Application and refinement of EAMRCM

Implementation process of EAMRCM

Validation of the AGCM method

AGCM Envelope calculation

Comparison of pulse extraction techniques: EAMRCM vs Baker method

Pulse identification accuracy comparison

Residual seismic motion analysis

Response spectrum analysis comparison

Automatic identification method for pulse-type seismic motions

Application of support vector machine (SVM) in seismic classification

Near-fault seismic motion identification method

Implementation process of SVM classifier for pulse-type seismic motion identification

Step 1: Set the velocity threshold, P G V min

Step 2: Pulse extraction

Step 3: Feature calculation and principal component analysis (PCA)

Step 4: SVM classification

Comparison of methods

Conclusion

Footnotes

ORCID iDs

Funding

Declaration of conflicting interests

Data Availability Statement

References

Step 1: Set the velocity threshold, $P G V_{\min}$