Number Of Decomposition Levels Research Articles

Preliminary study of radio frequency waves in hypervelocity impact plasma

Orbital debris and meteoroids can cause mechanical and electrical anomalies by impacting spacecraft. Although mechanical damage tends to occur only from particles with masses >10−3g, electrical damage can be a result of hypervelocity (> 10 km/s) impacts (HVI) even with smaller particles. In HVI, the projectile speed exceeds the speed of sound in the material and has enough energy to create plasma by ionizing the material near the surface, which can then emit radio frequency (RF) waves.In this paper, we conduct a preliminary study on the characteristics of impact-generated RF emission with the ultimate goal of building an RF predictive model for risk assessment of HVI electrical effects that can damage spacecraft. First, we introduce wavelet analysis as a method for denoising and quantifying the total RF signal energy. An appropriate mother wavelet and the number of decomposition levels are selected using a synthetic signal. Second, the total energy of the RF emission is calculated using Parseval's theorem. Results suggest that the total RF signal energy is proportional to the energy flux of the impactor. Finally, spectrograms of the RF emission are analyzed to characterize features that can be used in the future to predict impacts that can cause electrical damage to satellites.

Data Compression and Noise Reduction in Smart Grid Using Discrete Wavelet Transform

This paper proposed wavelet-based design using Discrete Wavelet Transform to compress smart grid electrical signals and to reduce noise. For the Smart Grid’s smooth functioning, the power signal must be monitored, and proper actions must be taken quickly for any abnormality. The compressed data takes less time to communicate the disturbances. The proposed design is tested for the phasor measurement unit, which monitors and records the status of the smart grid hence circulating extensive data to utilities, control centers, etc. It is also tested for load voltage data. Effective data compression can reduce the cost of data storage and transmission. Noise dramatically affects the effectiveness of the techniques detecting the disturbances. Hence data compression and denoising the data with minimum distortion is essential. The proposed design is simpler as it uses fewer filters and less number of decomposition level as compared to the existing design. Simulation results show that compression ratio and signal-to-noise ratios are increased as compared to existing design.

INVESTIGATION OF DISCRETE WAVELET TRANSFORM DOMAIN OPTIMAL PARAMETRIC APPROACH FOR DENOISING OF PHONOCARDIOGRAM SIGNAL

Phonocardiogram (PCG) signals are contaminated with various noise signals, which hinders the accurate diagnostic interpretation of the signal. Discrete wavelet transform (DWT) is a well-known technique used to remove noise from PCG signals and improve signal quality. The performance of DWT-based denoising depends upon several parameters involved in the process, such as mother wavelets used for decomposition, the number of decomposition levels (DLs), thresholding technique used and the threshold estimation rule followed. In this work, an investigative study is carried out to select the optimal parameter values which give the best denoising performance. The metrics such as mean-square error (MSE), normalized-mean-square error (NMSE), root-mean-square error (RMSE), percentage root-mean-square difference (PRD) and signal-to-noise ratio (SNR) are used to evaluate the performance of the denoising in this study. The results obtained show that the fifth-order Coiflet wavelet is best suited for denoising PCG signals when applied with the soft thresholding (ST) function and rigrsure threshold selection rule. Also, the optimum number of DLs resulting in better performance is level 6. SNR value obtained from the studies shows the efficacy of the parameters selected for denoising. The denoised PCG signals provide accurate information to determine various kinds of heart valve-related disorders (HVDs).

A Pansharpening Based on the Non-Subsampled Contourlet Transform and Convolutional Autoencoder: Application to QuickBird Imagery

This paper presents a pansharpening technique based on the non-subsampled contourlet transform (NSCT) and convolutional autoencoder (CAE). NSCT is exceptionally proficient at presenting orientation information and capturing the internal geometry of objects. First, it’s used to decompose the multispectral (MS) and panchromatic (PAN) images into high-frequency and low-frequency components using the same number of decomposition levels. Second, a CAE network is trained to generate original low-frequency PAN images from their spatially degraded versions. Low-resolution multispectral images are then fed into the trained convolutional autoencoder network to generate estimated high-resolution multispectral images. Third, another CAE network is trained to generate original high-frequency PAN images from their spatially degraded versions. The result of low-pass CAE is fed to the trained high-pass CAE to generate estimated high-resolution multispectral images. The final pan-sharpened image is accomplished by injecting the detailed map of the spectral bands into the corresponding estimated high-resolution multispectral bands. The proposed method is tested on QuickBird datasets and compared with some existing pan-sharpening techniques. Objective and subjective results demonstrate the efficiency of the proposed method.

Wavelets and digital filters designed and synthesized in the time and frequency domains.

The relevance of the problem under study is due to the fact that the comparison is made for wavelets constructed in the time and frequency domains. The wavelets constructed in the time domain include all discrete wavelets, as well as continuous wavelets based on derivatives of the Gaussian function. This article discusses the possibility of implementing algorithms for multiscale analysis of one-dimensional and two-dimensional signals with the above-mentioned wavelets and wavelets constructed in the frequency domain. In contrast to the discrete wavelet transform (Mallat algorithm), the authors propose a multiscale analysis of images with a multiplicity of less than two in the frequency domain, that is, the scale change factor is less than 2. Despite the fact that the multiplicity of the analysis is less than 2, the signal can be represented as successive approximations, as with the use of discrete wavelet transform. Reducing the multiplicity allows you to increase the depth of decomposition, thereby increasing the accuracy of signal analysis and synthesis. At the same time, the number of decomposition levels is an order of magnitude higher compared to traditional multi-scale analysis, which is achieved by progressive scanning of the image, that is, the image is processed not by rows and columns, but by progressive scanning as a whole. The use of the fast Fourier transform reduces the conversion time by four orders of magnitude compared to direct numerical integration, and due to this, the decomposition and reconstruction time does not increase compared to the time of multiscale analysis using discrete wavelets.

Detection of heart valve disorders from PCG signals using TQWT, FA-MVEMD, Shannon energy envelope and deterministic learning

Heart valve disorders (HVDs) are the major causes of cardiovascular diseases (CVD), which may be detected at the early stage using routine auscultation examination. The phonocardiogram (PCG) is a graphical representation of the physiological condition of the heart, which differs with respect to heart diseases. It is closely related to valve functionality which provides vital information for the diagnosis of CVD. However, visual inspection of PCG is tedious and error-prone, which makes it necessary and urgent to develop an automated system for the detection of HVDs with PCG recordings. In the present study we propose a novel method for the identification and classification of normal and abnormal non-segmented PCG recordings based on hybrid signal processing tools and deterministic learning theory. First, PCG signal and its first derivative are decomposed into a set of frequency subbands with a number of decomposition levels by using the tunable Q-factor wavelet transform method. Second, fast and adaptive multivariate empirical mode decomposition decomposes the subbands of the PCG signal and its derivative into scale-aligned intrinsic mode components (IMFs). The first two IMFs are extracted, which contain most of the energy of the PCG signal and its derivative and are considered to be the predominant IMFs. Third, Shannon energy is used to extract the characteristic envelope of predominant IMFs. The properties associated with the nonlinear PCG system dynamics are preserved. They are utilized to derive features, which demonstrate significant difference in PCG system dynamics between normal versus abnormal individual heartbeats. Fourth, neural networks are then used to model, identify and classify PCG system dynamics between normal and abnormal PCG signals based on deterministic learning theory. Finally, experiments have been carried out on a publicly available PCG database to verify the effectiveness of the proposed method, which include two types of classification, one for binary classification (normal vs. abnormal) and the other for multi-class classification (normal vs. aortic stenosis vs. mitral regurgitation vs. mitral stenosis vs. mitral valve prolapse). The overall average accuracy for binary, four-class and five-class classification are reported to be 97.75, 98.69 and 98.48%, respectively. The proposed method has obtained the highest overall accuracy in comparison to other state-of-the-art approaches using the same database, which can serve as an assistant diagnostic tool for the automated detection of HVDs in clinical applications.

Quality Assurance of Thin-Walled Nickel Tubes by Eddy Current (EC) Testing Using the Discrete Wavelet Transform (DWT) Processing Methodology

ABSTRACT In this study, the discrete wavelet transform (DWT)-based signal processing methodology is applied for eliminating noise due to permeability variations in saturation eddy current (EC) testing signals from nickel tubes. The nickel tubes are of 0.3 mm thickness and 6.6 mm outer diameter. Systematic studies have been carried out to optimize the wavelet functions, number of decomposition levels, and thresholding algorithm for DWT processing based on the signal-to-noise ratio (SNR). The DWT processing has enabled reliable detection of a 0.1 mm deep notch located on the inner surface of the tubes meeting its stringent quality requirements. Application of signal processing-based methodology has resulted in an improvement in SNR of 11.4 dB as against 5.1 dB for the raw signals.

A new approach for the detection of abnormal heart sound signals using TQWT, VMD and neural networks

Phonocardiogram (PCG) plays an important role in evaluating many cardiac abnormalities, such as the valvular heart disease, congestive heart failure and anatomical defects of the heart. However, effective cardiac auscultation requires trained physicians whose work is tough, laborious and subjective. The objective of this study is to develop an automatic classification method for anomaly (normal vs. abnormal) detection of PCG recordings without any segmentation of heart sound signals. Hybrid signal processing and artificial intelligence tools, including tunable Q-factor wavelet transform (TQWT), variational mode decomposition (VMD), phase space reconstruction (PSR) and neural networks, are utilized to extract representative features in order to model, identify and detect abnormal patterns in the dynamics of PCG system caused by heart disease. First, heart sound signal is decomposed into a set of frequency subbands with a number of decomposition levels by using the TQWT method. Second, VMD is employed to decompose the subband of the heart sound signal into different intrinsic modes, in which the first four intrinsic modes contain the majority of the heart sound signal’s energy and are considered to be the predominant intrinsic modes. They are selected to construct the reference variable for analysis. Third, phase space of the reference variable is reconstructed, in which the properties associated with the nonlinear PCG system dynamics are preserved. Three-dimensional PSR together with Euclidean distance has been utilized to derive features, which demonstrate significant difference in PCG system dynamics between normal and abnormal heart sound signals. Finally, PhysioNet/CinC Challenge heart sound database is used for evaluation and the synthetic minority over-sampling technique method is applied to balance the datasets. By using the 10-fold cross-validation style, experimental results demonstrate that the proposed features with dynamical neural networks based classifier yield classification performance with sensitivity, specificity, overall score and accuracy values of 97.73 $$\%$$ , 98.05 $$\%$$ , 97.89 $$\%$$ , and 97.89 $$\%$$ , respectively. The results verify the effectiveness of the proposed method which can serve as a potential candidate for the automatic anomaly detection in the clinical application.

Classification of myocardial infarction based on hybrid feature extraction and artificial intelligence tools by adopting tunable-Q wavelet transform (TQWT), variational mode decomposition (VMD) and neural networks.

Cardiovascular diseases (CVD) is the leading cause of human mortality and morbidity around the world, in which myocardial infarction (MI) is a silent condition that irreversibly damages the heart muscles. Currently, electrocardiogram (ECG) is widely used by the clinicians to diagnose MI patients due to its inexpensiveness and non-invasive nature. Pathological alterations provoked by MI cause slow conduction by increasing axial resistance on coupling between cells. This issue may cause abnormal patterns in the dynamics of the tip of the cardiac vector in the ECG signals. However, manual interpretation of the pathological alternations induced by MI is a time-consuming, tedious and subjective task. To overcome such disadvantages, computer-aided diagnosis techniques including signal processing and artificial intelligence tools have been developed. In this study we propose a novel technique for automatic detection of MI based on hybrid feature extraction and artificial intelligence tools. Tunable quality factor (Q-factor) wavelet transform (TQWT), variational mode decomposition (VMD) and phase space reconstruction (PSR) are utilized to extract representative features to form cardiac vectors with synthesis of the standard 12-lead and Frank XYZ leads. They are combined with neural networks to model, identify and detect abnormal patterns in the dynamics of cardiac system caused by MI. First, 12-lead ECG signals are reduced to 3-dimensional VCG signals, which are synthesized with Frank XYZ leads to build a hybrid 4-dimensional cardiac vector. Second, this vector is decomposed into a set of frequency subbands with a number of decomposition levels by using the TQWT method. Third, VMD is employed to decompose the subband of the 4-dimensional cardiac vector into different intrinsic modes, in which the first intrinsic mode contains the majority of the cardiac vector's energy and is considered to be the predominant intrinsic mode. It is selected to construct the reference variable for analysis. Fourth, phase space of the reference variable is reconstructed, in which the properties associated with the nonlinear cardiac system dynamics are preserved. Three-dimensional (3D) PSR together with Euclidean distance (ED) has been utilized to derive features, which demonstrate significant difference in cardiac system dynamics between normal (healthy) and MI cardiac vector signals. Fifth, cardiac system dynamics can be modeled and identified using neural networks, which employ the ED of 3D PSR of the reference variable as the input features. The difference of cardiac system dynamics between healthy control and MI cardiac vector is computed and used for the detection of MI based on a bank of estimators. Finally, data sets, which include conventional 12-lead and Frank XYZ leads ECG signal fragments from 148 patients with MI and 52 healthy controls from PTB diagnostic ECG database, are used for evaluation. By using the 10-fold cross-validation style, the achieved average classification accuracy is reported to be 97.98%. Currently, ST segment evaluation is one of the major and traditional ways for the MI detection. However, there exist weak or even undetectable ST segments in many ECG signals. Since the proposed method does not rely on the information of ST waves, it can serve as a complementary MI detection algorithm in the intensive care unit (ICU) of hospitals to assist the clinicians in confirming their diagnosis. Overall, our results verify that the proposed features may satisfactorily reflect cardiac system dynamics, and are complementary to the existing ECG features for automatic cardiac function analysis.

Decision tree‐based method for optimum decomposition level determination in wavelet transform for noise reduction of partial discharge signals

Partial discharge (PD) monitoring in high-voltage equipment is one of the effective methods for assessment of its insulation strength. To do this, noise reduction is one of the essential processes on measured PD signals. One of the most popular tools employed for PD de-noising is wavelet transform. To exploit this transformation, three main parameters, including ‘mother wavelet’, ‘number of decomposition level’, and ‘thresholding procedure’, should be assigned. In this study, a novel and also more accurate method for the determination of required decomposition level is suggested. The proposed method employs a decision tree which takes the pattern of energy spectral density of PD signals in the frequency domain and delivers the optimum decomposition level for de-noising by wavelet transform. The results, as compared with others, show the superiority of the proposed method in noise reduction of PD signals, both for simulations and field measured signals.

Machine‐learning approach for fault detection in brushless synchronous generator using vibration signals

In order to maintain continuous production and to avoid the maintenance cost increment in power plants, it is important to monitor the condition of equipment, especially the generator. Regarding the impossibility of direct access to rotating diodes in brushless synchronous generators, the condition monitoring of these elements is very important. Here, a novel fault detection method is proposed for the diode rectifier of brushless synchronous generator. At the first stage of this method, the vibration signals are recorded and feature extraction is performed by calculating the relative energy of discrete wavelet transform components. Multiclass support vector machine (MSVM) is used for classification, and the best mother wavelet and number of decomposition level are chosen based on classification performance. To enhance the performance of the classification, a modified sequential forward subset selection approach is included by which the best statistical features are selected. In this approach, besides selecting the best subset of statistical features, the classification parameter is tuned according to the selected subset to achieve the best performance. The result of the proposed method is eventually compared with those results of classification performance using conventional subset selection. Experimental results show that the proposed method can detect rectifier faults effectively.

Early fault detection model for rolling bearing based on an iterative tunable Q-factor wavelet transform

To reduce the adverse effect of incorrect parameters for the traditional iterative tunable Q-factor wavelet transform, this paper proposes an iterative tunable Q-factor wavelet transform method for fault feature extraction. Firstly, before decomposing the bearing vibration signal by an iterative tunable Q-factor wavelet transform, the initial values of 3 basic factors should be set: the quality factor Q, redundancy r and the number of decomposition level J. Secondly, the kurtosis of a high resonance component, which is the result of an iterative tunable Q-factor wavelet transform, is calculated through multistep iteration until it meets the iteration stop condition. Finally, the envelope spectrum of the final low resonance component is calculated, and the type of bearing fault can be recognized according to the frequency of extreme points. The results show that this method can effectively suppress noise and in-band interference and avoid fault identification inaccuracies caused by improper parameters and can also identify the fault feature frequency more clearly.

A novel probabilistic wind speed prediction approach using real time refined variational model decomposition and conditional kernel density estimation

Short-term wind speed prediction is an important task for the wind energy development. However, due to intermittency and uncertainty of wind resources, it is difficult to be achieved only by the deterministic prediction. Hence, there is a motivation to develop a novel method to further consider the uncertainty. The originality is to develop an innovative hybrid wind speed forecasting model based on empirical mode decomposition, variational mode decomposition, sample entropy and conditional kernel density estimation. More specifically, the original data are decomposed in real time by the refined variational mode decomposition, where the number of decomposition levels is adaptively determined by empirical mode decomposition and sample entropy. Then, conditional kernel density estimation with the bandwidth optimized by normal reference criterion is used to obtain the predictive probability density function for each subseries, by which the expectations and variances are derived. Finally, the deterministic prediction is produced by summarizing these expectations and the probabilistic prediction interval is obtained by the covariance and the Gaussian distribution assumption on target wind speed. It should be emphasized that some hypotheses are adopted in the proposed method: the correlations among different subseries can be characterized by the covariance and the target wind speed follows Gaussian distribution. Two case studies based on the measured data are used to evaluate the performance of the proposed method. The results show the improvement by the proposed method is up to 20% compared with empirical mode decomposition-based method. The main conclusion is that the proposed method may provide the better prediction over other models for the wind speed data with nonstationarity.

Gearbox Composite Fault Diagnosis Method Based on Minimum Entropy Deconvolution and Improved Dual-Tree Complex Wavelet Transform.

Dual-tree complex wavelet transform has been successfully applied to the composite diagnosis of a gearbox and has achieved good results. However, it has some fatal weaknesses, so this paper proposes an improved dual-tree complex wavelet transform (IDTCWT), and combines minimum entropy deconvolution (MED) to diagnose the composite fault of a gearbox. Firstly, the number of decomposition levels and the effective sub-bands of the DTCWT are adaptively determined according to the correlation coefficient matrix. Secondly, frequency mixing is removed by notch filter. Thirdly, each of the obtained sub-bands further reduces the noise by minimum entropy deconvolution. Then, the proposed method and the existing adaptive noise reduction methods, such as empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and variational mode decomposition (VMD), are used to decompose the two sets of simulation signals in comparison, and the feasibility of the proposed method has been verified. Finally, the proposed method is applied to the compound fault vibration signal of a gearbox. The results show the proposed method successfully extracts the outer ring fault at a frequency of 160 Hz, the gearbox fault with a characteristic frequency of 360 Hz and its double frequency of 720 Hz, and that there is no mode mixing. The method proposed in this paper provides a new idea for the feature extraction of a gearbox compound fault.

Texture description using multi-scale morphological GLCM

Texture is the collective repetitive pattern that characterizes the surface of real world objects. The main challenge in the texture description is its application specific definition. The present work aims at bringing the definition of textures under a generalized framework and propose some texture descriptors. In order to accomplish this, authors have extensively studied the properties of texture, drawn four observations and used some of them to devise two texture descriptors under the framework of multi-scale mathematical morphology and co-occurrence matrices. Thereafter, the descriptors are used for texture classification and tested on three benchmark datasets. Before applying the descriptors to texture classification, a dependence between number of decomposition levels (scales) and classification percentage is established using hypothesis testing. Once the dependence is established, the corresponding scale and distance parameter is chosen for each dataset. The classification results are compared with a number of existing methods. The efficacy of results prove the supremacy of the proposed methods over the existing ones.

Heart Sound Extraction From Sternal Seismocardiographic Signal

The phonocardiogram (PCG) signal indicates closing instants of atrio-ventricular and semilunar valves, and this information can also be extracted from two major profiles of a seismocardiographic (SCG) cycle. This letter presents a method to extract fundamental heart sounds (HSs) from a SCG signal. The proposed method employs discrete wavelet transform for signal decomposition, and subsequently, center of gravity (CoG) of power spectrum for each of the subbands is computed. Our method can optimally select wavelet subbands for any combination of sampling frequencies of the signal and number of decomposition levels. Based on proposed CoG criterion, the signal is reconstructed from a number of selected subbands, and instantaneous Hilbert envelope is constructed for localizing peaks of the signal. Finally, a simple decision rule is applied to annotate S1 and S2 sounds of the PCG signal. Experimental results show that the HS waves S1 and S2 can be well localized with the help of one SCG cycle without using a reference ECG cycle.

Identification of relevant wavelet functions for multiscale characterization of manufactured surfaces using a genetically optimized neural network

Multiscale surface characterization is a powerful tool that is used for process monitoring, surface quality control, and manufacturing optimization by establishing a link between process variables and functional performances. The multiscale decomposition approach using continuous and discrete wavelets is widely applied to take into account scales dependency. However, the optimal choice of the analysis wavelet function and the number of decomposition level is still a big issue. In this article, the artificial neural network theory was combined with the wavelet concept and was optimized based on the genetic algorithm to identify the relevant wavelet function for multiscale characterization of abraded surface topographies. Then, an extensive wavelet function library was developed and the proposed algorithm was applied to topographic data obtained from various abrasive finishing processes. The results show the pertinence of this approach to select the relevant wavelet, and a universal relevant wavelet function for abraded surface characterization was determined.

The use of Haar and OB wavelets in the signals analysis

In this paper, two mathematical methods of wavelet transform are presented: Haar’s wavelet transform and wavelet transform at oriented basis (OB). Unlike traditional wavelet transforms (like classical Haar’s wavelet) this mathematical approach allows getting more information about the details and behavior of original signal due to more amount of discrete filters that are used for its decomposition. In Haar’s and other wavelet methods there are only two discrete filters are used to decompose initial signal – one low-frequency filter and one high-frequency filter. Low-frequency wavelet coefficients (marked as s-coefficients) give the compressed and approximated version of the initial signal (called trend), and high-frequency wavelet coefficients (marked as d-coefficients) give the high-frequency oscillations around the trend. Such decomposition and calculation of wavelet coefficients is realized at each level of wavelet analysis. While using wavelet transform at oriented basis, there are more than one type of high-frequency wavelet coefficients (marked as d(1)-, d(2)-,…, d(m)-coefficients) where m is defined by the type of spectral transform at oriented basis (dimension of the matrix of basic function). Number of decomposition levels is defined by the length of initial signal’s interval. In the case of Haar’s wavelet transform this length is determined as N=2n, and in the case of wavelet transform at oriented basis this length is determined as N=mn. The main principle of wavelet transform lies in the use of scaled and shifted basic functions. The structure and algorithm of multiscale analysis is considered for the cases of Haar’s wavelet where the interval of initial signal is defined as N=2n, and for OB wavelet with the interval N=mn. The feature of OB wavelet transform is the possibility to operate with more than one high-pass filters that gives more details about the initial signal. In partial case for m=3 basic functions of OB wavelet contains only integer numbers. Moreover, approximately 1/3 of them are zero. Thus, it simplify the calculation significantly. Matrix form of wavelet decomposition is considered for Haar and OB wavelets. Use of matrices generalizes calculation process by combining all decomposition levels in one formula. The matrix method of the calculation of wavelet coefficients simplify the decomposition procedure for initial signal. Thus, it has the advantage against the direct calculation of wavelet coefficients by recurrent formulas. The coefficients of approximation and detailing for the above methods were calculated. It has been proved that wavelet transform at oriented basis has an advantage because it allows to achieve more information about the investigated signal for less amount of decomposition steps and with less calculation losses. As an interesting example, time dependence of discrete function that describes electrical energy consumption in MicroGrid system could be considered as an object for compressing and removing of casual high-frequency oscillations with the help of wavelet analysis.Ref. 5, fig. 7

Multiscale analysis of discrete functions with a given number of filters

The method of discrete wavelet transforms at oriented basis that is constructed by use discrete spectral transform of the functions with modular argument is considered and generalized. Unlike traditional wavelet transforms (like classical Haar’s wavelet) this mathematical approach allows getting more information about the details and behavior of original signal due to more amount of discrete filters that are used for its decomposition. In Haar’s and other wavelet methods there are only two discrete filters are used to decompose initial signal – one low-frequency filter and one high-frequency filter. Low-frequency wavelet coefficients (marked as s-coefficients) give the compressed and approximated version of the initial signal (called trend), and high-frequency wavelet coefficients (marked as d-coefficients) give the high-frequency oscillations around the trend. Such decomposition and calculation of wavelet coefficients is realized at each level of wavelet analysis. While using wavelet transform at oriented basis, there are more than one type of high-frequency wavelet coefficients (marked as d(1)-, d(2)-,…, d(m)-coefficients) where m is defined by the type of spectral transform at oriented basis (dimension of the matrix of basic function). Number of decomposition levels is defined by the length of initial signal’s interval. In the case of Haar’s wavelet transform this length is determined as N=2n, and in the case of wavelet transform at oriented basis this length is determined as N=mn. While selecting the value m equal to three it gives some advantages in calculation volume and consequently, in the speed of wavelet analysis that could be very useful for the processing of the signals with large interval of definition and non-stationery signals. As an interesting example, time dependence of discrete function that describes electrical energy consumption in MicroGrid system could be considered as an object for compressing and removing of casual high-frequency oscillations with the help of wavelet analysis. The use of wavelet transforms with more than two high-frequency filters makes it possible to increase the quantity of data about signal fluctuations and to better localize its characteristic intervals compared with traditional discrete wavelets that operates with one low-frequency and one high-frequency filters. The principle of wavelet transform is based on a multiscale analysis. Basic functions are scaled and shifted along the time axis and by amplitude. A feature of the represented wavelet transform is the using of basic functions of new spectral transforms. These are functions of a symmetric transform on finite intervals and transform at oriented basis. The system of these functions is orthogonal and contains Np discrete functions of different shapes. One of these functions is a low-pass filter, and all the others are high-pass filters. Sphere of application of wavelet transforms with N basic functions is diagnostics of semiconductor converters, predictive energy-efficient control of energy consumption, analysis of bio-telemetric signals, processing and transmission of images and video signals.Ref. 7, fig. 1, tabl. 3.

THE DATA EXCHANGE IN THE PROCESS OF AUTOMATED SYNTHESIS OF THE FINITE-ELEMENT MODEL OF WING BOX OF THE TRANSPORT CATEGORY AIRCRAFT

For the solving of task of optimization of power structure of wing box of transport aircraft the analysis of significant volume of random variants of wing box element composition is needed. The most effective method for modeling the elastic properties of random structures and analyzing their stress-strain state under the action of random loads is the finite element method. In this case, the complexity of the structure of the finite element model (the number of elements and the number of links between elements) is comparable to the complexity of the model being modeled. In modern CAD-systems this problem is solved with the help of the decomposition method. In accordance with this method, the process of creating a common structure model is transformed into relatively independent processes for creating models of structure elements. At that there is a problem of coordination the parameters of local models, without the solution of which the synthesis of the common model is impossible.Unlike 3D models, the process of combining local finite element models include the change in their internal data. That is, the data exchange between local models is also performed in the process of synthesis of the common finite element model. The article investigates the schemes of data exchange between the local finite element models of structure elements of transport aircraft at the synthesis of common finite element model wing box.It is shown that when using the method of automatic building of finite elements on the basis of geometric models of structure elements on which all modern CAE systems are based, the number of decomposition levels is limited to two. The use of the substructures (superelements) method significantly expands the capabilities of CAE-systems in the modeling of complex structures, since the division of the general geometric model into several parts increases the number of levels of its decomposition to three. Increase the number of levels of decomposition makes it possible to divide the process of building of local geometric by transferring each part of the common model to separate specialist. As a result, the time of building of local finite-element models is reduced. At that, the synthesis of finite element models of fragments of the common geometric model is first performed, which are then combined into a common model. Unlike CAD-systems, CAE-systems do not have an interface with database management systems and do not support the required functions of data management. This significantly complicates the process of coordination models of substructures.It is shown that to solve the problem of data exchange in the process of synthesis of the finite-element model of the wing box, it is necessary to use individual algorithms for models of each class of structural elements. At that the data exchange must take place in an automatic mode. Implementation of these conditions is possible only with the use of object-oriented information technologies and, in particular, object-oriented systems for project data management.