Dynamic Wavelet Research Articles

Dynamic Wavelet Synopses Management over Sliding Windows in Sensor Networks

Due to the dynamic nature of data streams, a sliding window is used to generate synopses that approximate the most recent data within the retrospective horizon to answer queries or discover patterns. In this paper, we propose a dynamic scheme for wavelet synopses management in sensor networks. We define a data structure sliding dual tree, abbreviated as SDT, to generate dynamic synopses that adapts to the insertions and deletions in the most recent sliding window. By exploiting the properties of Haar wavelet transform, we develop several operations to incrementally maintain SDT over consecutive time windows in a time- and space-efficient manner. These operations directly operate on the transformed time-frequency domain without the need of storing/reconstructing the original data. As shown in our thorough analysis, our SDT-based approach greatly reduces the required resources for synopses generation and maximizes the storage utilization of wavelet synopses in terms of the window length and quality measures. We also show that the approximation error of the dynamic wavelet synopses, i.e., L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -norm error, can be incrementally updated. We also derive the bound of the overestimation of the approximation error due to the incremental thresholding scheme. Furthermore, the synopses can be used to answer various kinds of numerical queries such as point and distance queries. In addition, we show that our SDT can adapt to resource allocation to further enhance the overall storage utilization over time. As demonstrated by our experimental results, our proposed framework can outperform current techniques in both real and synthetic data.

Lamb wave characterization of corrosion-thinning in aircraft stringers: Experiment and three-dimensional simulation

The development of automatic guided wave interpretation for detecting corrosion in aluminum aircraft structural stringers is described. The dynamic wavelet fingerprint technique (DWFT) is used to render the guided wave mode information in two-dimensional binary images. Automatic algorithms then extract DWFT features that correspond to the distorted arrival times of the guided wave modes of interest, which give insight into changes of the structure in the propagation path. To better understand how the guided wave modes propagate through real structures, parallel-processing elastic wave simulations using the finite integration technique (EFIT) has been performed. Three-dimensional (3D) simulations are used to examine models too complex for analytical solutions. They produce informative visualizations of the guided wave modes in the structures and mimic the output from sensors placed in the simulation space. Using the previously developed mode extraction algorithms, the 3D EFIT results are compared directly to their experimental counterparts.

Lamb wave detection of limpet mines on ship hulls

This paper describes the use of ultrasonic guided waves for identifying the mass loading due to underwater limpet mines on ship hulls. The Dynamic Wavelet Fingerprint Technique (DFWT) is used to render the guided wave mode information in two-dimensional binary images because the waveform features of interest are too subtle to identify in time domain. The use of wavelets allows both time and scale features from the original signals to be retained, and image processing can be used to automatically extract features that correspond to the arrival times of the guided wave modes. For further understanding of how the guided wave modes propagate through the real structures, a parallel processing, 3D elastic wave simulation is developed using the finite integration technique (EFIT). This full field, technique models situations that are too complex for analytical solutions, such as built up 3D structures. The simulations have produced informative visualizations of the guided wave modes in the structures as well as mimicking directly the output from sensors placed in the simulation space for direct comparison to experiments. Results from both drydock and in-water experiments with dummy mines are also shown.

Power signal classification using dynamic wavelet network

A new approach to classification of non-stationary power signals based on dynamic wavelet has been considered. This paper proposes a model for non-stationary power signal disturbance classification using dynamic wavelet networks (DWN). A DWN is a combination of two sub-networks consisting of a wavelet layer and adaptive probabilistic network. The DWN has the capability of automatic adjustment of learning cycles for different classes of signals, for minimizing error. DWN models are specifically suitable for application in dynamic environments with time varying non-stationary power signals. The test results showed accurate classification, fast and adaptive learning mechanism, fast processing time and overall model effectiveness in classifying various non-stationary power signals. The classification result of the DWN has been compared with that of the probabilistic neural network (PNN).

Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings

AbstractA non‐parametric system identification‐based model is presented for damage detection of highrise building structures subjected to seismic excitations using the dynamic fuzzy wavelet neural network (WNN) model developed by the authors. The model does not require complete measurements of the dynamic responses of the whole structure. A large structure is divided into a series of sub‐structures around a few pre‐selected floors where sensors are placed and measurements are made. The new model balances the global and local influences of the training data and incorporates the imprecision existing in the sensor data effectively, thus resulting in fast training convergence and high accuracy. A new damage evaluation method is proposed based on a power density spectrum method, called pseudospectrum. The multiple signal classification (MUSIC) method is employed to compute the pseudospectrum from the structural response time series. The methodology is validated using the data obtained for a 38‐storey concrete test model. The results demonstrate the effectiveness of the WNN model together with the pseudospectrum method for damage detection of highrise buildings based on a small amount of sensed data. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Dynamic recurrent wavelet network controllers for nonlinear system control

To solve nonlinear system control problems, a Recurrent Wavelet Network Controller (RWNC) is proposed in this paper. The proposed RWNC model has four‐layer structure. Temporal relations embedded in the network by adding some feedback connections representing the memory units in the second layer. A self‐organizing learning algorithm, which consists of structure learning and parameter learning, is proposed and is able to construct the recurrent wavelet network dynamically. The structure learning is based on the input partitions to determine the number of wavelet bases, and the parameter learning is based on the supervised gradient descent method to adjust the shape of wavelet functions, feedback weights, and the connection weights. Computer simulations were conducted to illustrate the performance and applicability of the proposed model.

Dynamic Wavelet Neural Network Model for Traffic Flow Forecasting

Accurate and timely forecasting of traffic flow is of paramount importance for effective management of traffic congestion in intelligent transportation systems. In this paper, a novel nonparametric dynamic time-delay recurrent wavelet neural network model is presented for forecasting traffic flow. The model incorporates the self-similar, singular, and fractal properties discovered in the traffic flow. The concept of wavelet frame is introduced and exploited in the model to provide flexibility in the design of wavelets and to add extra features such as adaptable translation parameters desirable in traffic flow forecasting. The statistical autocorrelation function is used for selection of the optimum input dimension of traffic flow time series. The model incorporates both the time of the day and the day of the week of the prediction time. As such, it can be used for long-term traffic flow forecasting in addition to short-term forecasting. The model has been validated using actual freeway traffic flow data. The model can assist traffic engineers and highway agencies to create effective traffic management plans for alleviating freeway congestions.

Dynamic Wavelet Neural Network for Nonlinear Identification of Highrise Buildings

Abstract: Recently, the authors presented a multiparadigm dynamic time-delay fuzzy wavelet neural network (WNN) model for nonparametric identification of structures using the nonlinear autoregressive moving average with exogenous inputs. Compared with conventional neural networks, training of a dynamic neural network for system identification of large-scale structures is substantially more complicated and time consuming because both input and output of the network are not single valued but involve thousands of time steps. In this article, an adaptive Levenberg–Marquardt least-squares algorithm with a backtracking inexact linear search scheme is presented for training of the dynamic fuzzy WNN model. The approach avoids the second-order differentiation required in the Gauss–Newton algorithm and overcomes the numerical instabilities encountered in the steepest descent algorithm with improved learning convergence rate and high computational efficiency. The model is applied to two highrise moment-resisting building structures, taking into account their geometric nonlinearities. Validation results demonstrate that the new methodology provides an efficient and accurate tool for nonlinear system identification of high-rising buildings.

The implementation of nonlinear dynamical systems with wavelet network

A dynamic wavelet network circuit implementation for modelling the nonlinear dynamical networks has been proposed in this study. The dynamical wavelet network includes static wavelet network with Mexican hat wavelet function, the voltage-controlled switches and capacitors. The circuit simulations have been done in Spice for the period-1 limit cycle, the spiral and double scroll attractors of the Chua's circuit.

Ultrasonic Periodontal Probing Based on the Dynamic Wavelet Fingerprint

Manual pocket depth probing has been widely used as a retrospective diagnosis method in periodontics. However, numerous studies have questioned its ability to accurately measure the anatomic pocket depth. In this paper, an ultrasonic periodontal probing method is described, which involves using a hollow water-filled probe to focus a narrow beam of ultrasound energy into and out of the periodontal pocket, followed by automatic processing of pulse-echo signals to obtain the periodontal pocket depth. The signal processing algorithm consists of three steps: peak detection/characterization, peak classification, and peak identification. A dynamic wavelet fingerprint (DWFP) technique is first applied to detect suspected scatterers in the A-scan signal and generate a two-dimensional black and white pattern to characterize the local transient signal corresponding to each scatterer. These DWFP patterns are then classified by a two-dimensional FFT procedure and mapped to an inclination index curve. The location of the pocket bottom was identified as the third broad peak in the inclination index curve. The algorithm is tested on full-mouth probing data from two sequential visits of 14 patients. Its performance is evaluated by comparing ultrasonic probing results with that of full-mouth manual probing at the same sites, which is taken as the "gold standard."

Research on Recognition Algorithm of Offshore Oil Pipeline Defect Inspection Based on Magnetic Flux Leakage Method

Pipeline safety evaluation is an important issue in the industry. Based on magnetic flux leakage (MFL) method, this paper presents an automated inspection device to inspect pipeline defects, analyzes the MFL inspection theory and some defect feature parameters, and gives a recognizing algorithm based on the dynamic wavelet basis function (WBF) neural network. The dynamic network utilizes multiscale and multiresolution orthogonal wavelet, through signals backwards propagation (BP), has more significant advantages than BP or other neural networks used in MFL inspection. It can also control the accuracy of the predicted defect profiles, possessing high-speed convergence and good approaching features. The performance applying the algorithm based on the network to predict defect profile from experimental MFL signals is also presented.

Automatic multi-mode Lamb wave arrival time extraction for improved tomographic reconstruction

An ultrasonic signal processing technique is applied to multi-mode arrival time estimation from Lamb waveforms. The basic tool is a simplified timescale projection called a dynamic wavelet fingerprint (DWFP) which enables direct observation of the variation of features of interest in non-stationary ultrasonic signals. The DWFP technique was used to automatically detect and evaluate each candidate through-transmitted Lamb mode. The area of the DWFP was then used as a feature to distinguish false modes caused by noise and other interference from the true modes of interest. The set of estimated arrival times were then used as inputs for tomographic reconstruction. The Lamb wave tomography images generated with these estimated arrival times were able to indicate different defects in aluminium plates.

A dynamic wavelet network based adaptive load frequency control in power systems

This paper proposes a new adaptive load frequency controller based on a ‘dynamic wavelet network (DWN)’ that has lag dynamics, non-orthogonal mother wavelets as activation function and interconnection weights. A DWN is connected between the two area power systems. The input signals of the DWN are the ACEs and their changes. The outputs of the DWN are the control signals for the two-area load frequency control. Adaptation is based on adjusting parameters of DWN for load frequency control. This is done by minimizing the cost functional of load frequency errors. The cost gradients with respect to the network parameters are calculated by adjoint sensitivity analysis. It is illustrated in simulations that this control approach is more successful than conventional integral controller for load frequency control in two area systems.

A dynamic wavelet network based adaptive load frequency control in power systems

This paper proposes a new adaptive load frequency controller based on a ‘dynamic wavelet network (DWN)’ that has lag dynamics, non-orthogonal mother wavelets as activation function and interconnection weights. A DWN is connected between the two area power systems. The input signals of the DWN are the ACEs and their changes. The outputs of the DWN are the control signals for the two-area load frequency control. Adaptation is based on adjusting parameters of DWN for load frequency control. This is done by minimizing the cost functional of load frequency errors. The cost gradients with respect to the network parameters are calculated by adjoint sensitivity analysis. It is illustrated in simulations that this control approach is more successful than conventional integral controller for load frequency control in two area systems.

On three intelligent systems: dynamic neural, fuzzy, and wavelet networks for training trajectory

Intelligent systems cover a wide range of technologies related to hard sciences, such as modeling and control theory, and soft sciences, such as the artificial intelligence (AI). Intelligent systems, including neural networks (NNs), fuzzy logic (FL), and wavelet techniques, utilize the concepts of biological systems and human cognitive capabilities. These three systems have been recognized as a robust and attractive alternative to the some of the classical modeling and control methods. The application of classical NNs, FL, and wavelet technology to dynamic system modeling and control has been constrained by the non-dynamic nature of their popular architectures. The major drawbacks of these architectures are the curse of dimensionality, such as the requirement of too many parameters in NNs, the use of large rule bases in FL, the large number of wavelets, and the long training times, etc. These problems can be overcome with dynamic network structures, referred to as dynamic neural networks (DNNs), dynamic fuzzy networks (DFNs), and dynamic wavelet networks (DWNs), which have unconstrained connectivity and dynamic neural, fuzzy, and wavelet processing units, called “neurons”, “feurons”, and “wavelons”, respectively. The structure of dynamic networks are based on Hopfield networks. Here, we present a comparative study of DNNs, DFNs, and DWNs for non-linear dynamical system modeling. All three dynamic networks have a lag dynamic, an activation function, and interconnection weights. The network weights are adjusted using fast training (optimization) algorithms (quasi-Newton methods). Also, it has been shown that all dynamic networks can be effectively used in non-linear system modeling, and that DWNs result in the best capacity. But all networks have non-linearity properties in non-linear systems. In this study, all dynamic networks are considered as a non-linear optimization with dynamic equality constraints for non-linear system modeling. They encapsulate and generalize the target trajectories. The adjoint theory, whose computational complexity is significantly less than the direct method, has been used in the training of the networks. The updating of weights (identification of network parameters) is based on Broyden–Fletcher–Goldfarb–Shanno method. First, phase portrait examples are given. From this, it has been shown that they have oscillatory and chaotic properties. A dynamical system with discrete events is modeled using the above network structure. There is a localization property at discrete event instants for time and frequency in this example.

Sensorless detection of mechanical faults in electromechanical systems

Practical early fault detection and diagnosis systems must exhibit high level of detection accuracy, while exhibiting acceptably low false alarm rates. Further, it is desirable not to make use of add-on sensors, and require minimal information regarding the specific machine component parameters and design. In this paper the development and experimental demonstration of a sensorless detection and diagnosis system is presented for incipient faults in electromechanical systems, such as electric motors. The developed system uses recent developments in dynamic recurrent neural networks and wavelet signal processing. The signals utilized are only the motor currents and voltages, whereas the transient mechanical speed is estimated from these measurements using a recently developed speed filter. The effectiveness of the fault diagnosis system is demonstrated by detecting a wide range of mechanical faults at varying levels of deterioration. Furthermore, the ability of the diagnosis system to discriminate between false alarms and actual incipient failure conditions is demonstrated. Experimental test results from small machines, 2.2 kW, and large machines, 373 and 597 kW, are presented demonstrating the effectiveness of the proposed approach to scale-up with motor power rating.

Dynamic Multidimensional Wavelet Neural Network and Its Application

We propose an efficient neural network called a dynamic multidimensional wavelet neural network (DMWNN). Since the resulting network based on wavelet theory can provide the efficient representation of a nonlinear function and has the capability to keep some previous information for later use, it can perform effective dynamic mapping with lower input signal dimensions. These features of the DMWNN show one way to compensate for the weakness of the diagonal recurrent neural network (DRNN) and feed-forward wavelet neural network (FWNN). Effectiveness in application of the proposed neural network is also demonstrated through simulation results.

Fuzzy Logic and Intelligence System

These papers are originally published in the proceedings of Korea fuzzy logic and intelligent systems society (KFIS) fall conference in 1999. Eight papers are selected for this special issue. Major topics of them are fuzzy theory, neural network, inference system, intelligent controller, etc. In this issue, Seihwan Park and Hyung Lee-Kwang extend the concept of fuzzy hypergraph to type-2 fuzzy hypergraph using type-2 fuzzy sets. It has not only the same properties of hypergraphs but also the extended properties of them. It is also shown that interval valued fuzzy hypergraph is a special case of type-2 fuzzy hypergraph. Jung-Heum Yon, Yong-Taek Kim, Jae-Yong Seo and Hong-Tae Jeon design an efficient neural network called dynamic multidimensional wavelet neural network. It can perform an effective dynamic mapping with less dimensions of the input signal. These features show one way to compensate the weakness of the diagonal recurrent neural network and feedforward wavelet neural network. Yigon Kim, Yang Hee Jung and Young Chel Bae propose a new method for diagnosis of insulation aging using wavelet. It measures the partial discharge on-line from data acquisition system and analyses it using wavelet to acquire 21) patterns. They design a neuro-fuzzy model that diagnoses an electrical equipment using the data. Byung-Jae Choi, Seong-Woo Kwak and Byung Kook Kim develop an adaptive fuzzy logic controller. A sole input fuzzy variable is used to simplify the design procedure and the switching hyperplane of sliding mode control is used to improve the adaptability. Myung-Geun Chun, Keun-Chang Kwak and Jeong-Woong Ryu show an efficient fuzzy rule generation scheme for adaptive network-based fuzzy inference system using the conditional fuzzy c-means and fuzzy equalization methods. They apply this method to the truck backer-upper control and Box-Jenkins modeling problem. Daijin Kim proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Twostage classification method is used. All data are classified by using the lower approximation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. Min-Soeng Kim, Sun-Gi Hong and Ju-Jang Lee incorporate the Q-learning algorithm into the fuzzy logic controller. Modified fuzzy rule is used for the incorporation. As a result, a fuzzy logic controller is obtained that can learn through experience. Dong Hwa Kim designs a new 2-DOF PID controller and applies it to the operating data based transfer function of Gun-san Gas turbine in Korea. We hope that this issue can be helpful to readers and we appreciate professor Kaoru Hirota for his interest and support for the publication.

Letters to the Editor on the paper ‘Dynamic Wavelet and Equivalent Models’ by O.M. Boaghe and S.A. Billings

Letters to the editor on the paper 'dynamic wavelet and equivalent models' by O.M. Boaghe and S.A. Billings

Dynamic Wavelet and Equivalent Models

The representation of nonlinear dynamic wavelet models in the form of an equivalent global model which is valid over the operating range of the system is investigated. The results are used to analyse and interpret the nonlinear wavelet models using nonlinear frequency response functions.