Continuous Wavelet Coefficients Research Articles

Three-dimensional reconstruction method for layered structures based on a frequency modulated continuous wave terahertz radar

The feasibility of employing a continuous-wave terahertz detection system for non-contact and non-destructive testing (NDT) in multi-layered bonding structures is assessed in this study. The paper introduces the detection principle of terahertz frequency modulated continuous wave (FMCW) radar and outlines the two-dimensional (2D) scanning platform, which integrates optical lenses, three linear actuators, a control platform, and data acquisition units. Experimental results on two types of insulation with prefabricated defects demonstrate the capability of terahertz waves for transparent inspection imaging. These results confirm the viability of terahertz FMCW detection technology as an advanced NDT tool for multi-layered bonding structures. However, the inherent limitations of terahertz wavelength and hardware systems pose challenges in discriminating reflection peaks on upper and lower surfaces. To address this issue, a local adaptive empirical wavelet coefficient modal decomposition (LAEWCMD) method is proposed to enhance the longitudinal discrimination ability of terahertz detection. The proposed method involves segmenting the 2D terahertz detection image into regions to differentiate between defective and non-defective areas. Continuous wavelet transforms (CWT) are then applied to the range signals of each region to derive continuous wavelet coefficients (CWCs). Subsequently, empirical mode decomposition (EMD) is performed on the CWCs to decompose them into intrinsic mode functions (IMFs) and residual signals. The 1st IMF is utilized for three-dimensional (3D) reconstruction, and the regions are fused to generate the final output. The effectiveness of the proposed method is validated on aircraft thermal protection structures (TPS), achieving high-precision 3D reconstruction. This offers a novel approach for the application of terahertz computed tomography imaging and NDT.

The potential of optical and SAR time-series data for the improvement of aboveground biomass carbon estimation in Southwestern China’s evergreen coniferous forests

ABSTRACT Accurate assessments of forest biomass carbon are invaluable for managing forest resources, evaluating effects on ecological protection, and achieving goals related to climate change and sustainable development. Currently, the integration of optical and synthetic aperture radar (SAR) data has been extensively utilized in estimating forest aboveground biomass carbon (AGC), while it is limited by using single-phase remote sensing images. Time-series data, which capture the interannual dynamic growth and seasonal variations of photosynthetic phenology in forests, can sufficiently describe forest growth characteristics. However, there remains a gap in research focusing on utilizing satellite-based time-series data for AGC estimation, especially for SAR sensors. This study investigated the potential of satellite-based optical and SAR time-series data for estimating AGC. Here, we undertook nine quantitative experiments of AGC estimation from Landsat 8 and Sentinel-1 and tested several regression algorithms (including multiple linear regression (MLR), random forests (RF), artificial neural network (ANN), and extreme gradient boosting (XGBoost)) to explore the contributions of spatiotemporal features to AGC estimation. The results suggested that the XGBoost algorithm was suitable for AGC estimation with explanatory solid power and stable performance. The temporal features representing forest growth trends and periodic change characteristics (such as coefficients of continuous wavelet transform) were more valuable for AGC estimation than spatial features for both sensor types, accounting for around 40% ~50% of the variance compared to 17% ~25%. The combination of optical and SAR time-series data produced the best performance (R2 = 0.814, RMSE = 18.789 Mg C/ha, rRMSE = 26.235%), compared with when utilizing optical or SAR time-series data alone (optical: R2 of 0.657 and rRMSE of 35.317%; SAR: R2 of 0.672 and rRMSE of 34.701%). Feature importance analysis also verified that temporal features of optical vegetation indices, SWIR 1/2 bands, and SAR backscatter from VV polarization were the most critical variables for AGC estimation. Furthermore, incorporating temporal features into the modeling is illustrated to be effective in reducing saturation effects within high-biomass forests. This study demonstrated the superiority of time-series data for forest carbon estimation. While the applicability of this methodology has only been investigated in evergreen coniferous forests, it may provide a viable approach needed to make full use of increasingly better and free satellite time-series data to estimate forest AGC with high accuracy, supporting policy making of forest management and sustainable development.

Optimizing spectral index to estimate the relative chlorophyll content of the forest under the damage of Erannis jacobsoni Djak in Mongolia

Jas's Larch Inchworm (Erannis jacobsoni Djak) is a Lepidopteran insect pest that seriously threatens larch forest ecosystems in Mongolia. Damage caused by E. jacobsoni changes the chlorophyll content of forest trees, leading to significant changes in the color of the larch canopy. Chlorophyll content, an important parameter that reflects the physiological state of plants, is expressed as the relative chlorophyll content (RCC) evaluated using a chlorophyll meter. In this study, we estimate the relative chlorophyll content of forest trees damaged by E. jacobsoni by optimizing the spectral index. Four larch forest areas affected by outbreaks of this pest in Ikhtamir, Battsengel, and Tsenkher in the Mongolia Houhangai Province and Binder in the Khentii Province were selected as study areas. Based on the RCC and measured hyperspectral data of forest trees, hyperspectral features such as spectral index (SI) and continuous wavelet coefficients were analyzed. Partial least squares regression (PLSR), support vector machine regression (SVMR), and stepwise multiple linear regression (SMLR) were used to estimate the RCC of the total damage process and different degrees of damage. The optimized spectral index (OSI) showed the highest potential for estimating the total damage process, exhibiting good estimation accuracy and model stability. For example, in the SVMR model, the R2A of OSI-39 SVMR was 0.077, 0.074, 0.014, and 0.115 higher than those of the traditional spectral index (TSI), bior1.5, coif1, and sym3, respectively, while the RMSE was 0.017, 0.021, 0.014, and 0.048 lower than those of TSI, bior1.5, coif1, and sym3, respectively. In the estimation of different degrees of damage, the estimation performance of OSI was significantly improved compared with that of TSI and had the same potential as that of coif1. TSI, OSI, and coif1 showed the best estimation potential in a moderate degree of damage, of which OSI-SVMR had the best effect (R2A = 0.710 44 and RMSE = 0. 137).The optimization and combination method of SI used in this study will help to facilitate future research. Our findings provide insights into the estimation of RCC at the regional scale and for the effective monitoring of forest pest severity.

Detection of Larch Forest Stress from Jas’s Larch Inchworm (Erannis jacobsoni Djak) Attack Using Hyperspectral Remote Sensing

Detection of forest pest outbreaks can help in controlling outbreaks and provide accurate information for forest management decision-making. Although some needle injuries occur at the beginning of the attack, the appearance of the trees does not change significantly from the condition before the attack. These subtle changes cannot be observed with the naked eye, but usually manifest as small changes in leaf reflectance. Therefore, hyperspectral remote sensing can be used to detect the different stages of pest infection as it offers high-resolution reflectance. Accordingly, this study investigated the response of a larch forest to Jas’s Larch Inchworm (Erannis jacobsoni Djak) and performed the different infection stages detection and identification using ground hyperspectral data and data on the forest biochemical components (chlorophyll content, fresh weight moisture content and dry weight moisture content). A total of 80 sample trees were selected from the test area, covering the following three stages: before attack, early-stage infection and middle- to late-stage infection. Combined with the Findpeaks-SPA function, the response relationship between biochemical components and spectral continuous wavelet coefficients was analyzed. The support vector machine classification algorithm was used for detection infection. The results showed that there was no significant difference in the biochemical composition between healthy and early-stage samples, but the spectral continuous wavelet coefficients could reflect these subtle changes with varying degrees of sensitivity. The continuous wavelet coefficients corresponding to these stresses may have high potential for infection detection. Meanwhile, the highest overall accuracy of the model based on chlorophyll content, fresh weight moisture content and dry weight moisture content were 90.48%, 85.71% and 90.48% respectively, and the Kappa coefficients were 0.85, 0.79 and 0.86 respectively.

A Wavelet-Based Diagnostic Framework for CRD Engine Injection Systems under Emulsified Fuel Conditions

The impact of the constituent oxides of nitrogen, carbon, sulphur, and other particulate matter which make up the gas emissions from diesel engines has motivated several control techniques for these pollutants. Water-in-diesel emulsions provide a reliable solution, but the wear effects on the fuel injection system (FIS) still pose remarkable concerns. Because pressure signals from the common rail (CR) reflect the dynamics associated with varying emulsion compositions and at varying engine RPMs, an investigative (and diagnostic) study was conducted on a KIA Sorento 2004 four-cylinder line engine at various water-in-diesel emulsion compositions and engine speeds. Alongside visual/microscopic inspections and spectral analyses, the diagnostic framework proposed herein functions on the use of standardized first-order differentials of the CR pressure signals to generate reliable continuous wavelet coefficients (CWCs) which capture discriminative spectral and transient information for accurate diagnosis. The results show that by extracting the CWCs from the first-order CR pressure differentials up to the 512th scale on a Mexican hat wavelet, adequate fault parameters can be extracted for use by a deep neural network (DNN) whose hyperparameters were globally optimized following a grid search. With a test accuracy of 92.3% against other widely-used ML-based diagnostic tools, the proposed DNN-based diagnostics tool was empirically assessed using several performance evaluation metrics.

Adaptive observer design for time-varying nonlinear systems with unknown polynomial parameters

The paper considers the construction of optoelectronic systems for monitoring near-Earth space, the choice of algorithms for identifying and obtaining the most reliable coordinate and non-coordinate information about space objects of natural and man-made origin. Experimental mock-up studies using the developed installation were performed. The plant allows the calibration of the optoelectronic system and the study of algorithms for obtaining coordinate and detailed data about the observed objects. The authors apply the method of image registration by a telescopic system in the astrograph with a digital camera mode and a digital camera with a microlens array mode. The work uses the methods for analyzing two-dimensional images by algorithms for measuring binary clusters in an image structure, investigating the brightness structure of an image with a circular boundary in a given area, determining the centers and radii of the circles inscribed in clusters, calculating and estimating the maxima for the curves of the coefficients of continuous wavelet transformation in the image profile lines with real wavelets. The composition and structure of a complex of algorithms and a methodology for their application have been developed. The methodology makes it possible to increase the accuracy and reliability of information obtained about the observed objects in a wide range of changes in the characteristics of the background target environment. The results substantiate the possibility of increasing the accuracy and reliability of coordinate information about the observed objects by analyzing the curves of the coefficients of continuous wavelet transform or analyzing the brightness gradient, provided that the algorithm for analyzing clusters of binarized images is used. The algorithm makes it possible to determine the areas of localization of objects of interest in the observed space. The developed methodology can be applied to assess the accuracy and reliability of the results of determining the coordinates and detailed features of objects. At the same time, it is possible to scale the algorithms to the means of observation and the tasks being solved, which makes it possible to use them in automated monitoring systems for near-earth space and increases the efficiency of detection and identification of objects.

Investigation of the accuracy of measuring the parameters of remote objects observed by the optical-electronic system with a light field recorder

The paper considers the construction of optoelectronic systems for monitoring near-Earth space, the choice of algorithms for identifying and obtaining the most reliable coordinate and non-coordinate information about space objects of natural and man-made origin. Experimental mock-up studies using the developed installation were performed. The plant allows the calibration of the optoelectronic system and the study of algorithms for obtaining coordinate and detailed data about the observed objects. The authors apply the method of image registration by a telescopic system in the astrograph with a digital camera mode and a digital camera with a microlens array mode. The work uses the methods for analyzing two-dimensional images by algorithms for measuring binary clusters in an image structure, investigating the brightness structure of an image with a circular boundary in a given area, determining the centers and radii of the circles inscribed in clusters, calculating and estimating the maxima for the curves of the coefficients of continuous wavelet transformation in the image profile lines with real wavelets. The composition and structure of a complex of algorithms and a methodology for their application have been developed. The methodology makes it possible to increase the accuracy and reliability of information obtained about the observed objects in a wide range of changes in the characteristics of the background target environment. The results substantiate the possibility of increasing the accuracy and reliability of coordinate information about the observed objects by analyzing the curves of the coefficients of continuous wavelet transform or analyzing the brightness gradient, provided that the algorithm for analyzing clusters of binarized images is used. The algorithm makes it possible to determine the areas of localization of objects of interest in the observed space. The developed methodology can be applied to assess the accuracy and reliability of the results of determining the coordinates and detailed features of objects. At the same time, it is possible to scale the algorithms to the means of observation and the tasks being solved, which makes it possible to use them in automated monitoring systems for near-earth space and increases the efficiency of detection and identification of objects.

Spectroscopic detection of rice leaf blast infection from asymptomatic to mild stages with integrated machine learning and feature selection

Rice blast is considered as the most destructive disease that threatens global rice production and causes severe economic losses worldwide. A detection of rice blast infection in an early manner is vital to limit its expansion and proliferation. However, little research has been devoted to spectral detection of rice leaf blast (RLB) infection, especially at the asymptomatic or early stages. To fill the gap, this study aimed to examine the feasibility of detecting RLB infection from leaf reflectance spectra at asymptomatic, early and mild stages of disease development. Greenhouse experiments were conducted over two consecutive years to collect hyperspectral data (350–2500 nm) on various days after inoculation (DAIs) for the three infection stages. These hyperspectral data were processed to select disease specific spectral features (DSSFs). Such DSSFs were then used to feed the machine learning based sequential floating forward selection (ML-SFFS) methodology for determining the optimal feature combination (OFC) and overall accuracy (OA) in the detection of RLB at various infection stages.The results demonstrated that the rice plants displayed considerable biochemical and spectral variations and this pattern of variations existed consistently during plant-pathogen interactions. A multivariate pool of DSSFs comprising two reflectance bands, fourteen SIs, and five continuous wavelet coefficients, were determined for revealing the dynamic response of RLB infection across two years. The combination of 2 to 4 spectral features selected by the ML-SFFS algorithm was sufficient to identify infected leaves with classification accuracies over 65% and 80% for the asymptomatic and early infection stages, respectively. The OA could rise up to 95% for the mild stage. Compared to the use of all DSSFs with a support vector machine (SVM) classifier, the SVM-based SFFS (SVM-SFFS) algorithm prevailed in the classification accuracy up to 10% over the sampling period. Our results demonstrated the feasibility of accurate classification of RLB infected samples by ML-SFFS. This study suggests that reflectance spectroscopy has great potential in the pre-visual detection of RLB infection and airborne or spaceborne imaging spectroscopy is promising for the mapping of early occurrence and severity levels of RLB infection at large scales.

AE signature analysis using continuous and discrete wavelet transforms to predict grinding wheel conditions

In this study, experiments were conducted in a surface grinding operation to acquire and analyze the AE signature to establish a statistical correlation between Acoustic Emission features extracted in wavelet domain with grinding wheel conditions. Grinding wear plot was established to identify the grinding wheel conditions by monitoring the wear in the abrasive grinding wheel and workpiece. Continuous and Discrete Wavelet transforms were carried out to extract the wavelet coefficients. Decision Tree based statistical models were built using discrete and continuous wavelet coefficients. The performance of J48 Decision tree and Classification and Regression Decision Tree (CART) are compared using the classification accuracy and kappa statistics measures. In discrete wavelet transforms, wavelet coefficients are extracted using four mother wavelets namely Haar, Daubechies, Symlet, and Coiflet. In Continuous Wavelet Transforms, the Morlet wavelet is used to extract the 1D wavelet coefficients using 2D scalograms.

Detection of geochemical anomalies using a fractal-wavelet model in Ipack area, Central Iran

The purpose of this study is to detect geochemical anomalies utilizing a Wavelet-Number (W-N) fractal model based on combination of a two-dimensional Discrete Wavelet Transformation (DWT) signal analysis and a Concentration-Area (C-A) fractal modeling. The DWT was carried by Sym8 as a selected wavelet pattern (by energy matching method) for Zn and Pb based on rock samples collected from the Ipack area, Central Iran. In addition, the DWT was decomposed by continuous wavelet coefficients at five levels and a final image was synthesized. Furthermore, the DWT data were classified using a fractal-wavelet model for delineation of both Zn and Pb anomalies from background levels in this area. Moreover, a Spectrum-Area (S-A) fractal modeling and classical statistics analysis were carried out and their results were compared with the wavelet-fractal modeling. As a result, the main Zn and Pb anomalies are located in the central and southern parts of the Ipack area. The results obtained by the proposed fractal-wavelet modeling are in connection with drilling for Zn and Pb exploration.

A Multi-Domain Diagnostics Approach for Solenoid Pumps Based on Discriminative Features

Accurate condition monitoring of industrial cyber-physical systems/components demands the use of reliable fault detection and isolation (FD&I) methodologies. Meta-heuristic algorithms for feature selection have good exploration capability for optimal discriminative feature selection for fault isolation/classification of which the Binary Particle swarm optimization (BPSO) is superior to its counterparts. This study presents a robust approach for vibration-based failure diagnostics of electromagnetic/solenoid pumps which employ a multi-domain feature extraction procedure (statistical time-domain and frequency-domain features, Mel frequency cepstral coefficients, and continuous wavelet coefficients) for capturing linear and nonlinear properties from the signals. Compared with other filter and wrapper methods for supervised feature selection, a hybrid filter-wrapper (Pearson’s correlation-BPSO ( $\rho $ -BPSO)) feature selection procedure is proposed for global search of optimal discriminative (uncorrelated) features for fault diagnosis with an RBF-kernel support vector machine (SVM*). Subsequently, a practical case study involving five VSC63A5 solenoid pumps at various operating/fault conditions is presented for validating the performance of the proposed approach. Results show the superior performance of the proposed hybrid filter-wrapper approach against filter-based and wrapper-based techniques for discriminative feature selection. Also, the proposed $\rho $ -BPSO-SVM* diagnostics model performance was compared with other standard fault isolation/classification methods.

Time–frequency analysis for bearing fault diagnosis using multiple Q-factor Gabor wavelets

Rolling element bearings are key and also vulnerable machine elements in rotating machinery. Fault diagnosis of rolling element bearings is significant for guaranteeing machinery safety and functionality. To accurately extract bearing diagnostic information, a time–frequency analysis method based on continuous wavelet transform (CWT) and multiple Q-factor Gabor wavelets (MQGWs) (termed CMQGWT) is introduced in this paper. In the CMQGWT method, Gabor wavelets with multiple Q-factors are adopted and sets of the continuous wavelet coefficients for each Q-factor are combined to generate time–frequency map. By this way, the resolution of the CWT time–frequency map can be greatly increased and the diagnostic information can be accurately identified. Numerical simulation is carried out and verified the effectiveness of the proposed method. Case studies and comparisons with the continuous Morlet wavelet transform (CMWT) and the tunable Q-factor wavelet transform (TQWT) demonstrate the effectiveness and superiority of the CMQGWT for bearing diagnostic information extraction and fault identification.

Gearbox fault diagnosis using acoustic signals, continuous wavelet transform and adaptive neuro-fuzzy inference system

This paper proposes a method of diagnosing faults in a single stage spur gearbox based on an analysis of acoustic signals acquired under various fault conditions. The time domain acoustic signals acquired from the gearbox are converted into a number of angular domain signals, each representing one revolution of the gearbox drive shaft. The resultant angular domain signals are averaged in order to improve the signal to noise ratio. The angular domain averaged signals thus obtained are decomposed using continuous wavelet transform. A range of optimal scales is then identified based on the energy-Shannon’s entropy ratio of continuous wavelet coefficients. The wavelet amplitude maps pertaining to the various gear health conditions are segmented into 6 parts and continuous wavelet coefficients from optimal scales fed directly to the ANFIS in the form of data samples. The results demonstrate that acoustic signals and ANFIS can effectively be utilized to diagnose the condition of the gearbox.

Gearbox fault diagnosis under non-stationary conditions with independent angular re-sampling technique applied to vibration and sound emission signals

An analysis of gearbox vibration signals is almost always the default choice when diagnosing the condition of a gearbox because of the rich information contained in the vibration signals and their ease of measurement. At times, however, the gearbox vibration signal may not be available and the sound emission signal may serve as an alternative to diagnose the condition of the gearbox. Gearbox vibration and sound emission signals are mostly non-stationary owing to uncertainties associated with the drive and load mechanisms. The signals acquired from the gearbox are then required to be converted into stationary signals for further analysis. In the present work, the independent angular re-sampling (IAR) technique is employed to convert non-stationary vibration signals (measured in two mutually perpendicular directions) and sound emission signals into quasi-stationary signals in the angular domain. The resulting angular domain averaged (ADA) signals for each gear health condition are then decomposed with continuous wavelet transform and continuous wavelet coefficients (CWCs) fed directly to a back propagation neural network with the objective of diagnosing the condition of the gearbox. Promising results are obtained when the sound emission signals are analyzed to diagnose the condition of the gearbox.

Gearbox fault diagnosis under fluctuating load conditions with independent angular re‐sampling technique, continuous wavelet transform and multilayer perceptron neural network

Most research efforts in gearbox fault diagnosis thus far have focused on diagnosing gearbox faults under stationary conditions. Efforts in diagnosing gearbox faults under non-stationary conditions have mostly involved an analysis of gearbox vibration signals under the speed-up or run-down processes. This paper attempts to diagnose faults in a single stage spur gearbox under non stationary conditions arising from fluctuating loads at the output of gearbox. The vibration signal corresponding to each independent revolution is synchronized from the revolution point of view by converting into the angular domain. This is accomplished experimentally by a simple process referred to as the independent angular re-sampling (IAR) technique. The IAR technique is accomplished by employing a multiple pulse tachometer arrangement. Through the IAR process, non-stationary signals in the time domain are converted into quasi-stationary signals in the angular domain. The angular domain signals, each representing one revolution of the gearbox drive shaft, are then decomposed with continuous wavelet transform. Optimal scales are identified based on superior energy-Shannon's entropy ratio of continuous wavelet coefficients (CWCs). The classification accuracy of a multilayer perceptron neural network is compared when CWCs from all scales and when CWCs from the optimal scales are fed to the neural network.

Detection on Structural Sudden Damage Using Continuous Wavelet Transform and Lipschitz Exponent

The degradation of civil engineering structures may lead to a sudden stiffness reduction in a structure and such a sudden damage will cause a discontinuity in the dynamic responses. The detection on structural sudden damage has been actively carried out in this study. The signal singularity of the acceleration responses with sudden stiffness reduction is characterized by the coefficients of continuous wavelet transform with fine scales. A detection approach based on the CWT is proposed in terms of the decomposed detail coefficients of continuous wavelet transform to detect the damage time instant and location. The Lipschitz exponent is mathematically used to estimate the local properties of certain function and is applied to reflect the damage severity. Numerical simulation using a five-story shear building under different types of excitation is carried out to assess the validity of the proposed detection approach for the building at different damage levels. The sensitivity of the damage index to the intensity and frequency range of measurement noise is also investigated. The effects of both measurement noise intensity and frequency range on the damage detection are numerically investigated.

A multiscale permutation entropy based approach to select wavelet for fault diagnosis of ball bearings

The detection and diagnosis of bearing health status using vibration signal has been an important subject for extensive research over the past few decades. The objective of this paper is to proposed permutation entropy as a tool to select best wavelet for feature selection for the detection as well as fault classification of ball bearings. The continuous wavelet coefficients of the time domain signal are calculated at real, positive scales using various real and complex wavelets. Best wavelet and corresponding scale is selected based on minimum permutation entropy. Eleven statistical parameters were used for defect classification in outer race, inner race, ball defect and healthy bearing respectively. Proposed methodology for fault classification is compared with two artificial intelligence techniques such as artificial neural network and support vector machine. Results revealed that permutation entropy based feature extraction techniques provide higher classification accuracy even when there is a slight variation in operating condition which is useful for development of online fault diagnosis.

Application of continuous‐time wavelet entropy for detection of cardiac repolarisation alternans

Prognostic utility of microvolt T-wave alternans (TWAs) has been established since its clinical acceptance as markers for malignant ventricular arrhythmias, leading to sudden cardiac death. Accurate detection of TWA from surface electrocardiography is a challenge because of invisible nature of the phenomenon. A novel TWA detection scheme based upon analysis of continuous-time wavelet entropy (CTWE) trend of consecutive ventricular repolarisation complexes is presented. The CTWE is computed using relative wavelet energy coefficients of continuous wavelet transform. Variety of simulated alternan waveforms, wavelet functions, frequency bands and noise levels are used to test the algorithm. The algorithm achieves a sensitivity of 100% at signal-to-noise ratio (SNR) >35 dB for all the selected wavelet functions and sensitivities of 99.5, 97 and 92% for Symlet4, Mexican Hat and truncated Morlet functions, respectively, at 30 dB SNR. A performance improvement of 5 dB is achieved by only computing the wavelet coefficients at the optimal frequency band. This study concludes that CTWE can successfully characterise the heterogeneity of cardiac repolarisation and detect TWA phenomenon.

Random Vibration Analysis for a Building under Evolutionary Random Excitations

For a building under evolutionary random excitations, a new random vibration analysis based on equivalent excitation method is presented, in which, the equivalent excitation is constructed by using continuous wavelet transform. When the input power spectral density of a seismic excitation is modulated by a time varying function, the continuous wavelet coefficients are calculated firstly by using scales and the evolutionary power spectral density, then the equivalent excitation is constructed by inverse continuous wavelet transform, finally the random vibration analysis is carried out following the procedures of the equivalent excitation method. An example is given to show the whole procedure, in which the special ability of the method for dealing with the evolutionary random excitation is discussed in detail.

Research on a Building under Multi-Dimensional Seismic Excitations

For a building under multi-dimensional seismic excitations, a new random vibration analysis based on equivalent excitation method is presented, in which, a new equation of motion of the building is used to depict its dynamics and kinematics features. Since most of the earth shocks are non-stationary random processes, the input power spectral density of the seismic excitations are modulated by a time varying function, and their equivalent excitations are constructed by using continuous wavelet transform, where the continuous wavelet coefficients are calculated by using scales and the evolutionary power spectral density, while the equivalent excitations are constructed by inverse continuous wavelet transform. The random vibration analysis is carried out following the procedures of the equivalent excitation method. A simulation example is given to investigate some affection of the multi-dimensional seismic inputs, especially the rotational one.