Wavelet Packet Transform Algorithm Research Articles

Conditional simulation of spatially correlated earthquake accelerograms based on wavelet packet coefficients

Herein, a method is developed, within the framework of the multivariate linear prediction (MLP), for conditionally simulating spatially correlated nonstationary ground motions at unobserved points measured in this local region. Given the limitation of recognizing the characteristics of the original signal, this scheme is based on the extension of the MLP to the wavelet packet transform (WPT). In this process, the WPT algorithm is used to estimate the corresponding wavelet packet coefficients from the decomposed orthogonal component time-histories corresponding to nonoverlapping frequency bands, which can accurately describe the time-varying nonstationary characteristics of the original signals. The original signal used in the MLP is replaced; instead, the wavelet packet coefficients are regarded as signals and are decomposed into different nonoverlapping subfrequency bands. Subsequently, this simulating process is transformed into a solution of the wavelet packet coefficients at the target points. Finally, an inverse WPT is added to obtain the corresponding ground motions. In addition to matching the specified coherency values, the earthquake time-histories generated by the proposed scheme inherit the physical properties of the predefined recordings well, including the waveform, cumulative energy, response spectrum, and nonstationary characteristics. Two numerical examples and blind tests are employed to simulate an ensemble of spatially correlated ground motions using data from the SMART-1 array. The proposed method will have a significant influence on engineering applications and regional hazard analyses.

Classification and Inspection of Debonding Defects in Solid Rocket Motor Shells Using Machine Learning Algorithms

Debonding problems along the propellant/liner/insulation interface are a critical factor affecting the integrity of solid rocket motors and one of the major causes of their structural failure. Due to the complexity of interface debonding detection and its low accuracy, a method of wavelet packet transform (WPT) combined with machine learning is proposed. In this research, multi-layer structure specimens were prepared to simulate the structure of a solid rocket motor. First, ultrasonic non-destructive testing technology was used to obtain defect data. Then, WPT algorithm was employed to extract characteristic signals of the defect data. Moreover, k-nearest neighbor model, Random Forest model and support vector machine model were applied to the classification. The results showed that the accuracies of the three models were 84.67%, 90.66% and 95.33%, respectively. Positive results indicate that WPT with machine learning model exhibited excellent classification performance. Therefore, WPT combined with machine learning can achieve a precise classification of debonding defects and has the potential to assist or even automate the debonding inspection process of solid rocket motors.

Surface quality monitoring in abrasive water jet machining of Ti6Al4V–CFRP stacks through wavelet packet analysis of acoustic emission signals

Machining such as trimming and drilling of aerospace composite structures is often required to meet the intended geometric tolerances and functional requirements. Abrasive water jet (AWJ) is a primary candidate for high speed machining of difficult-to-cut materials. The AWJ process performance is sensitive to the online faults and non-optimal process parameters, necessitating efficient techniques for online process control. In this study, acoustic emission (AE) signals are used to monitor AWJ machining of stacked titanium-CFRP. Owing to the non-stationary nature of the AE signals, this work is focused on the precision-driven predictive approach in simultaneous time-frequency domain. The AE signals were analyzed using wavelet packet transform (WPT), and an algorithm was proposed to identify and characterize these signals. Thirty-five different mother wavelets and decomposition levels up to 10 were used. The wavelet parameters (mother wavelet and decomposition) were deemed optimal when the identified signal characteristics could strongly correlate with the process parameters and kerf wall quality (surface roughness). Coiflets and Symlets were identified as the optimal wavelets with energy-entropy coefficient as the qualifying characteristic of the wavelet packet resulting in R2 > 90%. A comparative study was conducted to qualify the proposed algorithm against standard time domain analysis measures. The maximum R2 and CV (RMSD)—coefficient of variation of root mean square deviation for time domain was observed as 88.6% and 12.5% respectively as opposed to R2 = 97.12% and CV (RMSD)= 6% for the proposed WPT algorithm. Overall, an efficient algorithm was proposed in monitoring the process quality and controlling the process parameters based on the identified signal signatures.

Rapid Determination of Enantiomeric Excess of Tert-Butoxycarbonyl (BOC-Protected) Amino Acids Based on Infrared Spectra Technique with Optimal Wavelet Packet Transform Decomposition Frequency Band

A method was employed to determine enantiomeric excess (ee) value of chiral tert-butoxycarbonyl (Boc-protected) amino acids in a rapid way by using an infrared spectroscopy technique combined with wavelet packet transform (WPT) and least squares support vector machines (LS-SVM). Infrared spectral data were decomposed by using WPT algorithm. Simulated annealing (SA) algorithm was then used to search the optimal decomposed frequency band that had the greatest contribution to the quantitative analysis of ee values. As a result, the band (7, 34) with 34 variables and the band (5, 1) with 116 variables were determined as the optimal ones for the determination of Boc-protected proline and alanine, respectively. The selected variables in the optimal band were used as the inputs of LS-SVM models. The spectral variables selected by the WPT-SA method had lower predicting errors than full range spectra and the spectral variables selected by some traditional variable selection methods. Reasonable good results with root mean-square error of prediction (RMSEP) of 7.51 and 3.80 were obtained for the determination of ee values of two Boc-protected amino acids, showing that it is possible to rapidly determine ee values of amino acids by using IR spectroscopy rapidly.

Combining direct orthogonal signal correction and wavelet packet transform with partial least squares to analyze overlapping voltammograms of nitroaniline isomers

A novel method named DOSCWPTPLS approach based on partial least squares (PLS) regression with direct orthogonal signal correction (DOSC) and wavelet packet transform (WPT) as pre-processed tools was proposed for the simultaneous differential pulse voltammetric determination of o-nitroaniline, m-nitroaniline and p-nitroaniline with overlapping peaks. The method combines the ideas of DOSC and WPT with PLS regression for enhancing the ability in the extraction of characteristic information and the quality of regression. Data reduction was performed using DOSC, WPT and PLS algorithm. DOSC is used to remove information in the response matrix D by subtracting the structured noise that is orthogonal to the concentration matrix C. Wavelet packet representations of signals provide a local time–frequency description, thus in the wavelet packet domain, the quality of the noise removal, data compression, and relevant information extraction can be improved. PLS was applied for multivariate calibration and reduced noise by eliminating the less important latent variables. In this case, by optimization, the kind of wavelet function, the decomposition level, and the number of DOSC components, tolerance factor and the number of PLS factors for the DOSCWPTPLS method were selected as Coiflet 2, 3, 3, 0.001 and 3, respectively. A program (PDOSCWPTPLS) was designed to perform the simultaneous voltammetric determination of o-nitroaniline, m-nitroaniline and p-nitroaniline. The relative standard errors of prediction (RSEP) obtained for all components using DOSCWPTPLS, DOSCPLS, WPTPLS and PLS were compared. Experimental results demonstrated that the DOSCWPTPLS method had the best result among the four methods and was successful even when there was severe overlap of voltammograms.

Investigation of the harmonic behavior of three phase transformer under nonsinusoidal operation using finite element and wavelet packets

This paper investigates the harmonic behavior of three phase power transformers under nonsinusoidal operations. The terminal behavior of the transformer was obtained by coupling the transformer transient finite-element (FE) model and external electric circuits. Such a technique would allow the physical representation of the nonlinear magnetization behavior of the transformer as well as the strong frequency dependence of the transformer parameters. The harmonic behavior of the transformer currents and the dc load current were analyzed using wavelet packet transform algorithm (WPT). The key findings are, uniform frequency bands resulting from WPT decomposition process of the current waveforms can be used for identification of harmonic components. The flattened input voltage distorted by 3rd harmonic component has the highest impact on the dc load current harmonics (with respect to the sinusoidal case). The peaking input voltage distorted by the 5th harmonic component has the highest impact on the transformer secondary current and the magnetizing current harmonics