Damage-sensitive Features Research Articles

Highly nonlinear solitary waves for the detection of localized corrosion

This paper investigates the application of highly nonlinear solitary waves as a nondestructive evaluation method to detect localized corrosion in metallic structures. An experiment was conducted by using chains of monoperiodic particles in contact with a steel plate subjected to localized accelerated corrosion. A few damage-sensitive features were extracted from the time waveforms and fed into a multivariate statistical analysis to enhance the sensitivity of the proposed non-invasive monitoring approach. The experiment was complemented by a finite element model to quantify the effects of localized corrosion on certain features of the solitary waves propagating along the chain. Both the numerical and the experimental results show that the solitary waves reflected at the chain-plate interface are affected by the presence and progression of corrosion. Furthermore, the multivariate statistical analysis improved the sensitivity of the proposed approach. In the future, the proposed method may be implemented in those applications in which high temperature or radioactive environments are detrimental for the use of piezoelectric based ultrasonic testing.

An innovative hybrid strategy for structural health monitoring by modal flexibility and clustering methods

Structural health monitoring is usually implemented by model-driven or data-driven methods. Both of them have their advantages and disadvantages. This article proposes an innovative hybrid strategy as a combination of model-driven and data-driven approaches to detecting and locating damage in civil structures. In this regard, modal flexibility matrices of the undamaged and damaged conditions are initially derived from their modal frequencies and mode shapes. Subsequently, the discrepancy between these matrices is proposed as a damage-sensitive feature. To increase damage detectability and localizability, the modal flexibility discrepancy matrix is expanded by the Kronecker product and then converted into a vector by a simple vectorization algorithm yielding vector-style feature samples. To detect and locate damage, this article introduces the k-medoids and density-based spatial clustering of applications with noise techniques. The vector-style feature samples are incorporated into these clustering methods to obtain two different damage indices including the direct clustering outputs and their Frobenius norms. The great novelty of this article is to develop an innovative hybrid strategy for damage detection and localization under noise-free and noisy conditions so that the damage-sensitive feature is obtained from a model-driven scheme and the decision-making is carried out by a data-driven strategy. A shear-building frame and the numerical model of the ASCE benchmark structure are used to validate the accuracy and performance of the proposed methods. Results demonstrate that the hybrid strategy presented here is influentially able to detect and locate damage in the presence of noisy modal data.

Structural damage assessment through features in quefrency domain

The difficulties in dynamic system modeling and the recently developed machine learning tools have moved the attention of the structural damage assessment community towards a new direction. Attention is now placed on the immediate extraction of damage sensitive features directly from the monitored dynamic response of the structure, allowing engineers by-pass the creation of complex and sophisticated structural models. It is in this framework that the work presented in this paper has to be considered: the extraction of new damage sensitive features in the quefrency domain is discussed in the context of a vibration based analysis. Despite such a domain has been fully explored in acoustics, it represents an uncommon approach for the civil engineering community. In this paper, some variables characterizing the system dynamic response in the quefrency domain, referred to as cepstral coefficients, have been derived as functions of the structural characteristics and used in a damage assessment strategy. The main advantage of the quefrency domain over the frequency domain consists in a massive dimensionality reduction and, when dealing with real data, in a simplification of the extraction of cepstral coefficients versus that of natural frequencies. In this paper, the analytical expression of cepstral coefficients of the structural acceleration response has been derived and the statistical distribution of such coefficients has been investigated in a pattern recognition approach. In addition, a damage assessment strategy has been proposed by extracting, through a Principal Component Analysis (PCA), the projections of the cepstral coefficients with the lowest variances so to minimize the effect of external disturbances. The effectiveness of the proposed damage assessment strategy has been validated through numerical simulations and experimental data.

Unsupervised deep learning approach using a deep auto-encoder with a one-class support vector machine to detect damage

This article proposes an unsupervised deep learning–based approach to detect structural damage. Supervised deep learning methods have been proposed in recent years, but they require data from an intact structure and various damage scenarios of monitored structures for their training processes. However, the labeling work on the training data is typically time-consuming and costly, and sometimes collecting sufficient training data from various damage scenarios of infrastructures in service is impractical. In this article, the proposed unsupervised deep learning method based on a deep auto-encoder with an one-class support vector machine only uses the measured acceleration response data acquired from intact or baseline structures as training data, which enables future structural damage to be detected. The major contributions and novelties of the proposed method are as follows. First, an appropriate deep auto-encoder is carefully designed through comparative studies on the depth of neural networks. Second, the designed deep auto-encoder is taken as an extractor to obtain damage-sensitive features from the measured acceleration response data, and an one-class support vector machine is used as a damage detector. Third, experimental and numerical studies validate the high accuracy of the proposed method for damage detection: a 97.4% mean average for a 12-story numerical building model and a 91.0% accuracy for a laboratory-scaled steel bridge. Fourth, the proposed method also detects light damage (i.e. a 10% reduction in stiffness) with 96.9% to 99.0% accuracy, which shows its superior performance compared with the current state of the art. Fifth, it provides stable and more robust damage detection performance with reduced tuning parameters.

Deep neural networks–based damage detection using vibration signals of finite element model and real intact state: An evaluation via a lab-scale offshore jacket structure

Structural health monitoring of mechanical systems is essential to avoid their catastrophic failure. In this article, an effective deep neural network is developed for extracting the damage-sensitive features from frequency data of vibration signals to damage detection of mechanical systems in the presence of the uncertainties such as modeling errors, measurement errors, and environmental noises. For this purpose, the finite element method is used to analyze a mechanical system (finite element model). Then, vibration experiments are carried out on the laboratory-scale model. Vibration signals of real intact system are used to updating the finite element model and minimizing the disparities between the natural frequencies of the finite element model and real system. Some parts of the signals that are not related to the nature of the system are removed using the complete ensemble empirical mode decomposition technique. Frequency domain decomposition method is used to extract frequency data. The proposed deep neural network is trained using frequency data of the finite element model and real intact state and then is tested using frequency data of the real system. The proposed network is designed in two stages, namely, the pre-training classification based on deep auto-encoder and Softmax layer (first stage), and the re-training classification based on backpropagation algorithm for fine tuning of the network (second stage). The proposed method is validated using a lab-scale offshore jacket structure. The results show that the proposed method can learn features from the frequency data and achieve higher accuracy than other comparative methods.

Unsupervised Damage Identification Scheme Using PCA-Reduced Frequency Response Function and Waveform Chain Code Analysis

Mechanical machines face structural damage problems during their service life. Structural damage can severely affect safety and functionality of the structure and lead to economic loss. In this work, a damage identification scheme is developed by combining waveform chain code (WCC) analysis and hierarchical cluster analysis based on complex network theory. Waveform chain code analysis was carried out using the principal component analysis reduced frequency response function (PCA-reduced FRF), and the areas under the slope differential value curves were calculated as damage-sensitive WCC features. Unsupervised machine learning using hierarchical cluster analysis was then conducted on these damage-sensitive features. A rectangular Perspex plate was studied using the newly developed damage identification scheme as an example. Experimental results showed that the proposed scheme can successfully separate all the damage conditions from the undamaged state with 100% accuracy. In terms of damage severity and location identification, the proposed scheme is sensitive to detect damage severity with damage index as low as 0.17. In addition, combination of PCA-reduced FRF and mode shapes showed positive correlation between the magnitude of the resonant peak and the displacement of the impact point in identifying different damage locations of the plate.

Autoregressive Model-Based Structural Damage Identification and Localization Using Convolutional Neural Networks

Traditional autoregressive (AR) model-based damage identification methods construct structural damage sensitive features by trial and error, which are time-consuming, laborious and may lead to poor recognition effect. This study applies convolutional neural networks (CNNs) to quickly and automatically extract high-dimensional features of autoregressive model coefficients (ARMCs). In this research, AR model was utilized to fit the acceleration time series. The input matrices marked with damage location were produced by ARMCs, and then those matrices were sent to the proposed CNN for training. The trained CNN was employed for damage identification and localization. The effectiveness of the proposed method was verified by the damage identification and localization of a three-storied frame structure. The performance of the proposed CNN was compared with multilayer perception (MLP), random forest, and support vector machine (SVM). Meanwhile, the prediction results from different sample types were also discussed. Furthermore, parametric study in relation to the number of accelerometers and ARMCs used is conducted. These analyses demonstrate that the accuracy of CNN tests results reach 100%, 6.67%, 20%, and 25% higher than that of MLP, random forest, and SVM, respectively. Besides, other metrics calculated in this paper (e.g., precision, recall) further indicate that the proposed CNN performs well. The combination of AR and CNN does show excellent performance in damage identification and localization, which seems to be able to resist external excitation changes and accurately identify the multi-location damage and minor damage using limited accelerometers and ARMCs.

Developing deep neural network for damage detection of beam-like structures using dynamic response based on FE model and real healthy state

Fundamentally, Structural Health Monitoring (SHM) of mechanical systems is essential to avoid their catastrophic failure. The first key contribution of this paper is presenting a new method for damage detection of mechanical systems in presence of the uncertainties such as modeling errors, measurement errors, varying loading conditions and environmental noises based on Finite Element (FE) model and real healthy state. On the other hand, deep learning has been widely used in image and signal analyses with great success. According to this enhancement, the second key contribution of this paper is designing a developed Deep Convolutional Neural Network (DCNN) with training interference and customized architecture to learn the features. In industrial environments, most structures are exposed to varying environmental conditions and it is difficult to collect data containing real damages, and generally, only the data of a real healthy system is available; therefore, it is necessary to have an effective method for damage detection of real systems based on the artificial damages and real healthy data. From this standpoint, the third key contribution of this paper is training process of the proposed DCNN using raw frequency data of the FE model and real healthy state, which is then tested using the raw frequency data of the real system. The proposed DCNN can directly learn the features from raw frequency data of the FE model and real healthy state and discover the damage-sensitive features in order to damage detection of a real system. In this method, only dynamic responses of real healthy system are used to updating the FE model and minimizing the errors. The efficacy of the proposed method is validated using the experimental beam structure. Time data and several manual features from time and frequency data as well as two intelligent methods are used as comparisons. The results show that the proposed method can learn the features from raw frequency data and achieve higher accuracy than other comparative methods.

Feature extraction of wood-hole defects using empirical mode decomposition of ultrasonic signals

Holes and knots are common defects that occur in wood that affect its value for both structural and high-end aesthetic applications. When these defects are internal to wood they are rarely evident from visual inspection. It is therefore important to develop techniques to detect and analyse these defects both in standing trees prior to harvesting them and in processed timber and/or completed wooden structures. This paper presents an effective method to detect and analyse hole defects in wood. The method uses the recorded output wave signal from an ultrasonic device tested on rectangular wood samples. The ultrasonic wave signal is decomposed into its constructive modes using Empirical Mode Decomposition (EMD). This process decomposes a non-stationary non-linear wave signal into its semi-orthogonal bases known as intrinsic mode functions (IMFs). A matrix of all IMFs (except the residual IMF) is then assembled and its covariance matrix derived. The research demonstrates through several experimental studies that the maximum eigenvalue of the proposed covariance matrix is more sensitive to hole defects in wood than traditionally used measures such as time-of-flight. The results provide evidence that the proposed damage sensitive feature (DSF) can successfully detect hole defects in hardwood samples but further work is recommended on its application to other materials. It is anticipated that this method will have wide applicability in the forestry and timber industries for aiding in product value determination.

Structural damage identification based on unsupervised feature-extraction via Variational Auto-encoder

Abstract Structural health monitoring (SHM) is a practical tool for assessing the safety and system performance of existing structures. And structural damage identification has become the core of a SHM system. However, how to extract damage-sensitive features from structural response has become a challenging problem. Thus deep learning methods have attracted increasing attention for its ability to effectively extract high-level abstract features form raw data. This paper presents a damage detection method based on Variational Auto-encoder (VAE), one of the most important generative models in unsupervised deep learning. In this paper, VAE is used to process responses of the structure, which reduces the high-dimensional data to low-dimensional feature space, and then restores the original data from the low-dimensional representations. This structure forces the VAE to learn the essential features hidden behind the complex data. Taking advantage of this characteristic, we apply the VAE to damage identification task of a bridge under moving vehicle. The results of both numerical simulation and experiment are proved that the proposed method can accurately identify the structural damage/s. This method directly analyzes the measured responses of the structure without the structural element model and baseline data. It is a baseline-free data driven method, which is suitable for real engineering application in SHM.

A Lamb wave quantification model for inclined cracks with experimental validation

This paper investigates the influence of crack orientation on damage quantification using Lamb wave in plate structures. Finite element simulation is performed to acquire Lamb wave signal responses for different configurations of crack orientations and crack lengths. Two Lamb wave features, namely the normalized amplitude and the phase change, are used as damage sensitive features to develop a crack size quantification model. A hypothesis based on the geometrical influence on signal features is proposed, and the crack size quantification model incorporating the orientation angle is established using the hypothesis. An index of Probability of Reliable Quantification (PRQ) is proposed to evaluate the performance of the model. The index can be used to determine the sizing risk in terms of probabilities. A realistic aluminum plate is used to obtain the experimental data using piezoelectric (PZT) wafer-type sensors around a center through crack. The experimental data are used to validate the overall method. Results indicate that the proposed model can yield reliable results for size quantification of inclined cracks.

Seismic damage assessment using improved wavelet-based damage-sensitive features

In this paper, acceleration responses of steel MRFs under different ground motions using incremental dynamic analysis (IDA) are used for nonlinear damage diagnosis. In the first step, auto-regressive moving-average with exogenous input (ARX) model, along with stabilization diagram, is utilized to assess the natural frequencies of MRFs. In the second step, complex Morlet (cmorfb-fc) wavelet-based refined damage-sensitive features (rDSFs), as new DSFs considering higher mode contributions and end-effect modifications, are proposed. Improved efficiency and accuracy of the proposed rDSFs are presented through benchmark steel MRFs. Results indicate that the damage pattern (DP) causing first plastic hinge formation and also the damaged story can be accurately recognized using the proposed wavelet-based rDSFs. In addition, the damage extent (severity) for each DP at each story can be assessed using the cumulative sum of wavelet energy at time-shift b (or sum of scalogram for each time) over the refined effective time of vibration (refined ETV) for each output acceleration when compared with that over the refined ETV for the input ground acceleration. Finally, results also indicate improvement over the DSFs existing in the technical literature.

A Multi-Model Based Approach for the Detection of Subtle Structural Damage Considering Environmental Variability

Minor structural damages like incipient cracks are difficult to detect as they alter the structural stiffness marginally. It is difficult to extract the features of minor damage, from the measured time history responses, which are usually contaminated by measurement noise. Also, the effect of environmental/operational variabilities often misleads the damage diagnostic process, especially for subtle damages. To tackle all the above challenges in detecting and locating the minor incipient damage, an automated multi-model based data-driven technique is proposed in this paper. It is based on the fact that a subtle damage alters only some structural modes, while the others remain unaltered. Hence, the proposal here is to decompose the measured time-history response into the modal components and then reconstruct the signal using only the modal components with the damage sensitive features. The reconstructed signal is used in damage diagnosis. As an improved version of the second-order blind identification, the blind source separation technique is proposed in this paper for signal decomposition and a crisp automated algorithm is presented for isolating the modal components with damage sensitive features. The autoregressive moving average with exogenous input model with the cepstral distance as the damage index is employed for localizing the damage. The proposed multi-model approach is completely automated. Numerical studies have been carried out to demonstrate the effectiveness of the proposed algorithm. Also, experimental studies have been conducted to ensure the practicality of the proposed technique.

A Data-Driven Damage Identification Framework Based on Transmissibility Function Datasets and One-Dimensional Convolutional Neural Networks: Verification on a Structural Health Monitoring Benchmark Structure.

Vibration-based data-driven structural damage identification methods have gained large popularity because of their independence of high-fidelity models of target systems. However, the effectiveness of existing methods is constrained by critical shortcomings. For example, the measured vibration responses may contain insufficient damage-sensitive features and suffer from high instability under the interference of random excitations. Moreover, the capability of conventional intelligent algorithms in damage feature extraction and noise influence suppression is limited. To address the above issues, a novel damage identification framework was established in this study by integrating massive datasets constructed by structural transmissibility functions (TFs) and a deep learning strategy based on one-dimensional convolutional neural networks (1D CNNs). The effectiveness and efficiency of the TF-1D CNN framework were verified using an American Society of Civil Engineers (ASCE) structural health monitoring benchmark structure, from which dynamic responses were captured, subject to white noise random excitations and a number of different damage scenarios. The damage identification accuracy of the framework was examined and compared with others by using different dataset types and intelligent algorithms. Specifically, compared with time series (TS) and fast Fourier transform (FFT)-based frequency-domain signals, the TF signals exhibited more significant damage-sensitive features and stronger stability under excitation interference. The utilization of 1D CNN, on the other hand, exhibited some unique advantages over other machine learning algorithms (e.g., traditional artificial neural networks (ANNs)), particularly in aspects of computation efficiency, generalization ability, and noise immunity when treating massive, high-dimensional datasets. The developed TF-1D CNN damage identification framework was demonstrated to have practical value in future applications.

Fractal analysis of nonlinear ultrasonic waves in phase-space domain as a quantitative method for damage assessment of concrete structures

The present paper applies fractal dimension as a mathematical tool to extract a quantitative geometric feature from nonlinear ultrasonic waves in phase-space domain. The feature is then used for damage assessment of concrete material under different service loads after experiencing extreme compressive loads. For this purpose, concrete samples are loaded in two different scenarios: the first loading part is set to initiate micro cracks and generate macro cracks, while the second loading procedure is set to simulate service loads and change the cracks' boundary conditions. Due to nonlinear ultrasonic waves’ sensitivity to cracks in early stages, nonlinear ultrasound test is performed. In contrast to traditional approaches which analyze nonlinear ultrasound waves in frequency domain, in this paper, nonlinear ultrasonic waves in phase-space domain are studied. Phase-space domain is a powerful mathematical tool that allows researchers to analyze data quantitatively and qualitatively using different signal processing techniques like fractal dimension. For the first time, fractal analysis of nonlinear ultrasound waves in phase-space domain is performed to measure the nonlinearity of the waves due to interactions with loaded-induced cracks in concrete materials. In general, fractal analysis makes it possible to assign dimension for sets that do not have integer dimension. To calculate fractal dimension, the box-counting method, as a pragmatic method, is used. A two-dimensional (2D) and three-dimensional (3D) box-counting method for calculating the fractal dimension of nonlinear ultrasonic waves in phase-space domain are utilized. It is shown that fractal dimension is a powerful signal processing tool for analyzing nonlinear ultrasonic signals in phase-space domain and extracting quantitative damage-sensitive features in presence of service load. In contrast, results of frequency domain analysis show a lack of noticeable trend, especially for large service loads. This observation indicates that features extracted in frequency domain may not be reliably used as damage-sensitive features for evaluating the level of cracking in concrete material under service load.

Vibration-based health monitoring of ball screw in changing operational conditions

Structural health monitoring (SHM) of the ball screw of machine tools relies on the repeated observation of the damage-sensitive features. The natural frequency is a characteristic inherent to the structure that is more robust than other signal features as a SHM index. However, a major problem is that regular changes in the operating conditions, such as the feed speeds, the worktable positions and other uncertain complex boundary conditions, also affect the natural frequencies, and these factors may mask the subtle variations induced by structural damage. Therefore, it is necessary to adopt an effective method to eliminate those effects to avoid false alarms during structural damage monitoring.In this article, Bayesian ridge regression modelling methods are developed to eliminate the effects of the worktable different positions and feed speeds on the natural frequencies. The proposed method can model the natural frequencies that are simultaneously affected by two dimensional operational factors and provide a rigorous quantitative assessment of the uncertainties associated with the complex boundary conditions of the ball screw drive system and the inevitable estimation errors. First, the different worktable positions and feed speeds were tested on the experimental bench to verify the proposed method. Then, two novel criteria were used as damage warning signals, which can reduce false alarm. Finally, this method was applied to monitor the wear of a ball screw of a CNC machining centre in an automobile factory. The validity of the method was provend using actual monitoring results.

Model-free damage detection of a laboratory bridge using artificial neural networks

This paper investigates a model-free damage detection method using a laboratory model of a steel arch bridge with a five-metre span. The efficiency of the algorithm was studied for various damage cases. The structure was excited with a rolling mass and seven accelerometers were used to record its response. An artificial neural network (ANN) was trained to predict the bridge accelerations based on data collected from the undamaged structure. Damage-sensitive features were defined as the root mean squared errors between the measured data and the ANN predictions. A baseline healthy state was established with which new data could be compared to. Outliers from the reference state were taken as an indication of damage. Two outlier detection methods were used: Mahalanobis distance and the Kolmogorov–Smirnov test. The method showed promising results and damage was successfully detected for four out of the five single damage cases. The gradual damage case was also detected, however, for some instances, greater damage did not result in an increase in the damage index. The Kolmogorov–Smirnov test performed best at detecting small single damage cases, while Mahalanobis distance was better at tracking gradual damage.

Detection of Surface Breaking Cracks Filled With Solid Impurities Using a Baseline-Free NEWS-TR Method

The use of piezoceramic transducers for cracks identification via guided wave has attracted significant attention recently. Most studies assume that the medium in surface breaking cracks is only air. However, it is common that such cracks are filled with impurities (e.g. dust, grease) due to its exposure to the operational environment. The impurities may affect the propagation of the ultrasonic guided wave and hence it is of practical interest to develop detection methods for surface breaking cracks filled with impurities. This work investigates the possible effect of contact acoustic nonlinearity (CAN) on detecting surface breaking cracks filled with solid impurities. A baseline-free method is proposed to detect surface breaking cracks filled with solid impurities using the nonlinear elastic wave spectroscopy (NEWS) as a pre-treatment of time-reversal (TR). This method involves three key issues: selecting low-frequency swept signal modulated by Hanning window as an excitation signal, comparing the initial filtered response with the nonlinear time reversal response to determine the nonlinear feature related to such cracks, and determining the recommended low cut-off frequency to extract such nonlinear feature. The feasibility of the proposed method is experimentally and numerically verified using aluminum beams with surface breaking cracks. Results show that due to the existence of solid impurities, the crack interacts with low-frequency ultrasonic waves, which leads to nonlinear components in the response signal. It also indicates that after the time-reversal processing, the shifting of the maximum peak frequency from the second harmonic range to the third harmonic range can be used as a damage-sensitive nonlinear feature for detecting such cracks. The proposed method provides a promising way to identify surface breaking cracks filled with solid impurities without reference signal.

A data‐driven framework for near real‐time and robust damage diagnosis of building structures

Rapid condition monitoring of structural health is essential for post-earthquake safety assessment. Therefore, information about damage after extreme events could be of great value in resilient communities. This paper proposes a robust framework for the identification of the existence, probable location, and severity of damage using cumulative intensity-based damage features. Taken into account the seismic hazard uncertainties and the undesirable consequences of misclassification in data-driven methods, an objective function based on the confusion score matrix is optimized. This process can enhance the reliability of the prediction model in terms of two conflicting criteria, namely, the general accuracy and conservativeness. Support vector machines are utilized for the task of damage classification where Bayesian optimization is used to select the proper damage-sensitive input features and hyperparameters. A three-story reinforced concrete (RC) moment frame is designed and modeled in OpenSees to examine the performance of the proposed framework. For this purpose, 5,400 incrementally scaled nonlinear time history analyses are conducted considering 180 ground motions. Two different approaches are introduced to distort signals to simulate measurement noise. The robustness of models is also investigated with respect to different objective functions. Furthermore, in an independent experimental case study, the framework is evaluated on a dataset obtained from 44 shake table trials on a three-story RC frame with masonry infill. Given the results obtained from the two case studies, it is shown that the proposed framework is capable of robust and reliable identification of damage in near real-time whereas the concepts of hazard uncertainty and misclassification consequences are properly considered.

Selection of optimal wavelet-based damage-sensitive feature for seismic damage diagnosis

In this research work, a more efficient wavelet-based refined damage-sensitive feature (refined DSF1) is proposed for nonlinear damage diagnosis using acceleration responses extracted from steel moment resisting frames (MRFs), which are analyzed by incremental dynamic analysis (IDA) under various ground motion record sets (140 records in total). Auto-regressive moving-average with exogenous input (ARX) method and a stabilization diagram are employed to estimate the true modal parameters from noisy modes of each MRF using power spectral density. 64 real-valued and 103 complex-valued mother wavelets considering end-effects on the wavelet coefficients are examined and the best mother wavelet-based refined DSF1 is proposed. For this purpose, Shannon entropies and coefficient of determination (R2) are used for optimal selection of central frequency (fc) and bandwidth (fb) parameters of complex Morlet (cmorfb-fc) wavelet-based refined DSF1. Comparison of the results demonstrates that the cmorfb-fc wavelet-based refined DSF1 considering both real and imaginary parts of wavelet coefficients is well correlated with the maximum story drift ratio (SDR) and has more efficiency than the Morlet wavelet-based refined DSF1, introduced in the technical literature, especially for the high-rise structures.