Training wavelet networks for nonlinear dynamic input–output modeling

Demodulation of EM Telemetry Data Using Fuzzy Wavelet Neural Network with Logistic Response

Data telemetry is a critical element of successful unconventional well drilling operations, involving the transmission of information about the well-surrounding geology to the surface in real-time to serve as the basis for geosteering and well planning. However, the data extraction and code recovery (demodulation) process can be a complicated system due to the non-linear and time-varying characteristics of high amplitude surface noise. In this work, a novel model fuzzy wavelet neural network (FWNN) that combines the advantages of the sigmoidal logistic function, fuzzy logic, a neural network, and wavelet transform was established for the prediction of the transmitted signal code from borehole to surface with effluent quality. Moreover, the complete workflow involved the pre-processing of the dataset via an adaptive processing technique before training the network and a logistic response algorithm for acquiring the optimal parameters for the prediction of signal codes. A data reduction and subtractive scheme are employed as a pre-processing technique to better characterize the signals as eight attributes and, ultimately, reduce the computation cost. Furthermore, the frequency-time characteristics of the predicted signal are controlled by selecting an appropriate number of wavelet bases “N” and the pre-selected range for pij3 to be used prior to the training of the FWNN system. The results, leading to the prediction of the BPSK characteristics, indicate that the pre-selection of the N value and pij3 range provides a significantly accurate prediction. We validate its prediction on both synthetic and pseudo-synthetic datasets. The results indicated that the fuzzy wavelet neural network with logistic response had a high operation speed and good quality prediction, and the correspondingly trained model was more advantageous than the traditional backward propagation network in prediction accuracy. The proposed model can be used for analyzing signals with a signal-to-noise ratio lower than 1 dB effectively, which plays an important role in the electromagnetic telemetry system.

Joint angle estimation with wavelet neural networks

This paper presents a wavelet neural network (WNN) based method to reduce reliance on wearable kinematic sensors in gait analysis. Wearable kinematic sensors hinder real-time outdoor gait monitoring applications due to drawbacks caused by multiple sensor placements and sensor offset errors. The proposed WNN method uses vertical Ground Reaction Forces (vGRFs) measured from foot kinetic sensors as inputs to estimate ankle, knee, and hip joint angles. Salient vGRF inputs are extracted from primary gait event intervals. These selected gait inputs facilitate future integration with smart insoles for real-time outdoor gait studies. The proposed concept potentially reduces the number of body-mounted kinematics sensors used in gait analysis applications, hence leading to a simplified sensor placement and control circuitry without deteriorating the overall performance.

Satellite-Based Bathymetric Modeling Using a Wavelet Network Model

Accurate bathymetric modeling is required for safe maritime navigation in shallow waters as well as for other marine operations. Traditionally, bathymetric modeling is commonly carried out using linear models, such as the Stumpf method. Linear methods are developed to derive bathymetry using the strong linear correlation between the grey values of satellite imagery visible bands and the water depth where the energy of these visible bands, received at the satellite sensor, is inversely proportional to the depth of water. However, without satisfying homogeneity of the seafloor topography, this linear method fails. The current state-of-the-art is represented by artificial neural network (ANN) models, which were developed using a non-linear, static modeling function. However, more accurate modeling can be achieved using a highly non-linear, dynamic modeling function. This paper investigates a highly non-linear wavelet network model for accurate satellite-based bathymetric modeling with dynamic non-linear wavelet activation function that has been proven to be a valuable modeling method for many applications. Freely available Level-1C satellite imagery from the Sentinel-2A satellite was employed to develop and justify the proposed wavelet network model. The top-of-atmosphere spectral reflectance values for the multispectral bands were employed to establish the wavelet network model. It is shown that the root-mean-squared (RMS) error of the developed wavelet network model was about 1.82 m, and the correlation between the wavelet network model depth estimate and “truth” nautical chart depths was about 95%, on average. To further justify the proposed model, a comparison was made among the developed, highly non-linear wavelet network method, the Stumpf log-ratio method, and the ANN method. It is concluded that the developed, highly non-linear wavelet network model is superior to the Stumpf log-ratio method by about 37% and outperforms the ANN model by about 21%, on average, on the basis of the RMS errors. Also, the accuracy of the bathymetry-derived wavelet network model was evaluated on the basis of the International Hydrographic Organization (IHO)’s standards for all survey orders. It is shown that the accuracy of the bathymetry derived from the wavelet network model does not meet the IHO’s standards for all survey orders; however, the wavelet network model can still be employed as an accurate and powerful tool for survey planning when conducting hydrographic surveys for new, shallow water areas.

Adaptive impedance control of uncertain robot manipulators with saturation effect based on dynamic surface technique and self-recurrent wavelet neural networks

Saturation nonlinearities, among the known challenges in control engineering, are ubiquitous in robotic systems and can lead to stability and performance degradation. In this paper, an adaptive dynamic surface impedance (ADSI) control approach is developed for an n-link robotic manipulator by employing self-recurrent wavelet neural networks (SRWNNs) in order to overcome the saturation effect. The proposed control approach is inspired by the theory of dynamic surface control (DSC) and SRWNNs. As a novel application of the dynamic surface method to obtain a simple structure, the target impedance is formulated in the state–space, and effective dynamic surfaces are defined to track the desired impedance behavior. In fact, DSC is used to force the robot manipulator to track the desired impedance, while the robot interacts with an environment. In addition, SRWNNs are applied to approximate the parametric uncertainties and external disturbances in the robot dynamical model. Self-feedback neurons are embedded as memory units in SRWNNs to model the sudden dynamic jumps of the environment. Using Lyapunov's method, an ADSI controller is designed, and adaptation laws are induced to guarantee the stability of the closed-loop system. Finally, simulations are conducted to verify the proper performance of the proposed approach for removing the saturation effect and tracking the target impedance. It is worth noting that the simulation results indicate the robustness of the controller against uncertainties and external disturbances.

Adaptive Formation Control of Electrically Driven Nonholonomic Mobile Robots With Limited Information

We present a leader-follower-based adaptive formation control method for electrically driven nonholonomic mobile robots with limited information. First, an adaptive observer is developed under the condition that the velocity measurement is not available. With the proposed adaptive observer, the formation control part is designed to achieve the desired formation and guarantee the collision avoidance. In addition, neural network is employed to compensate the actuator saturation, and the projection algorithm is used to estimate the velocity information of the leader. It is shown, by using the Lyapunov theory, that all errors of the closed-loop system are uniformly ultimately bounded. Simulation results are presented to illustrate the performance of the proposed control system.

An adaptive wavelet neural network for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks (AWNN) is introduced for spatio-temporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework.

Dynamic Modeling of Nonlinear Systems Using Wavelet Networks

The purpose of this paper is to present wavelet networks as a new scheme to model nonlinear systems. The capabilities of wavelet networks in function approximation make them appealing for system modeling. The wavelet networks presented are utilized in the dynamic modeling of a nonlinear servomechanism. A new wavelet network scheme is proposed for the identification of the nonlinearity in the servomechanism. Simulation results show the modeling performance of both schemes.

Robust control for nonlinear motor-mechanism coupling system using wavelet neural network

A robust controlled toggle mechanism, which is driven by a permanent magnet (PM) synchronous servo motor is studied in this paper. First, based on the principle of computed torque control, a position controller is developed for the motor-mechanism coupling system. Moreover, to relax the requirement of the lumped uncertainty in the design of a computed torque controller, a wavelet neural network (WNN) uncertainty observer is utilized to adapt the lumped uncertainty online. Furthermore, based on the Lyapunov stability a robust control system, which combines the computed torque controller, the WNN uncertainty observer and a compensated controller is proposed to control the position of the motor-mechanism coupling system. The computed torque controller with WNN uncertainty observer is the main tracking controller, and the compensated controller is designed to compensate the minimum approximation error of the uncertainty observer. Finally, simulated and experimental results due to a periodic sinusoidal command show that the dynamic behaviors of the proposed robust control system are robust with regard to parametric variations and external disturbances.

Adaptive Dynamic Surface Control of Flexible-Joint Robots Using Self-Recurrent Wavelet Neural Networks

A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.

Classification of EMG signals using wavelet neural network

An accurate and computationally efficient means of classifying electromyographic (EMG) signal patterns has been the subject of considerable research effort in recent years. Quantitative analysis of EMG signals provides an important source of information for the diagnosis of neuromuscular disorders. Following the recent development of computer-aided EMG equipment, different methodologies in the time domain and frequency domain have been followed for quantitative analysis. In this study, feedforward error backpropagation artificial neural networks (FEBANN) and wavelet neural networks (WNN) based classifiers were developed and compared in relation to their accuracy in classification of EMG signals. In these methods, we used an autoregressive (AR) model of EMG signals as an input to classification system. A total of 1200 MUPs obtained from 7 normal subjects, 7 subjects suffering from myopathy and 13 subjects suffering from neurogenic disease were analyzed. The success rate for the WNN technique was 90.7% and for the FEBANN technique 88%. The comparisons between the developed classifiers were primarily based on a number of scalar performance measures pertaining to the classification. The WNN-based classifier outperformed the FEBANN counterpart. The proposed WNN classification may support expert decisions and add weight to EMG differential diagnosis.

Adaptive Wavelet Neural Network Control With Hysteresis Estimation for Piezo-Positioning Mechanism

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.

Backstepping Wavelet Neural Network Control for Indirect Field-Oriented Induction Motor Drive

This study address a newly designed decoupling system and a backstepping wavelet neural network (WNN) control system for achieving high-precision position-tracking performance of an indirect field-oriented induction motor (IM) drive. First, a decoupling mechanism with an online inverse time-constant estimation algorithm is derived on the basis of model reference adaptive system theory to preserve the decoupling control characteristic of an indirect field-oriented IM drive. Moreover, based on the backstepping design methodology, a desired feedback control law is developed for ensuring the favorable control performance. However, the uncertainties, such as mechanical parameter uncertainty, external load disturbance, unstructured uncertainty due to nonideal field orientation in transient state, and unmodeled dynamics in practical applications, are difficult to know in advance. Thus, the stability of the desired feedback control may be destroyed. Due to the powerful approximation ability of WNN, a backstepping WNN control scheme is designed in this study to control the rotor position of an indirect field-oriented IM drive for periodic motion. This control scheme contains two parts: one is a WNN control that is utilized to mimic the desired feedback control law, and the other is a robust control that is designed to recover the residual part of approximation for ensuring the stable control characteristic. In addition, numerical simulation and experimental results due to periodic commands are provided to verify the effectiveness of the proposed control strategy.

Wavelet neural network control for linear ultrasonic motor drive via adaptive sliding-mode technique

A wavelet neural network (WNN) control system is proposed to control the moving table of a linear ultrasonic motor (LUSM) drive system to track periodic reference trajectories in this study. The design of the WNN control system is based on an adaptive sliding-mode control technique. The structure and operating principle of the LUSM are introduced, and the driving circuit of the LUSM, which is a voltage source inverter using two-inductance two capacitance (LLCC) resonant technique, is introduced. Because the dynamic characteristics and motor parameters of the LUSM are nonlinear and time varying, a WNN control system is designed based on adaptive sliding-mode control technique to achieve precision position control. In the WNN control system, a WNN is used to learn the ideal equivalent control law, and a robust controller is designed to meet the sliding condition. Moreover, the adaptive learning algorithms of the WNN and the bound estimation algorithm of the robust controller are derived from the sense of Lyapunov stability analysis. The effectiveness of the proposed WNN control system is verified by some experimental results in the presence of uncertainties.