Worst-Case Identification of Uncertain Nonlinear Systems Using Neural Network Models

This paper presents an application of the neural network (NN) model for forecasting and filtering problems. Instead of using the gradient descent method as used by the standard back-propagation network, the present study adopted the Levenberg-Marquardt algorithm. It was shown that the Levenberg-Marquardt algorithm tends to reach termination criteria more quickly making the searches employing the full model less time consuming. In the first part of forecasting problem, multilayer feedforward (MLFF) network was constructed by trials to forecast the tidal-level variations at the Chao Phraya river mouth in Thailand. Unlike the well-known conventional harmonic analysis, the neural network model uses a set of previous data for learning and then forecasting directly the time series of tidal levels. It was found that lead time of 1 to 24 hourly tidal levels can be successfully predicted using only a short-time hourly learning data.In the second part of filtering problem, the MLFF network was also used to establish a stage-discharge relationship for tidal river. Comparisons were made among conventional methods, i.e. by using multivariate functions (Linear and power models) and the NN model. The NN model was found to be able to model the transfer function too much higher accuracy than multiple regression analysis. The root mean square errors (RMSE) and the mean relative error (MRE) for the NN model are about 8 cm and 6.4% whereas the same errors for multiple regression analysis are 16 cm and 12%, respectively. The efficiency index for the linear, power, and NN models is 0.4, 0.7, and 0.9, respectively. In addition, the obtained stage-discharge relationship by the NN model can indicate reasonably important behavior of the tidal influences, i.e. there are stronger influences of tide during the dry period than the flood period.

This paper compares two methods of blind equalization for non-minimum phase systems. Higher order statistics is used to estimate the unknown channel and neural networks are used as equalizers to recover the transmitted signal. Two kinds of neural network equalizers are realized; one is the multilayer feedforward network (MFN) based on the backpropagation algorithm, the other is the minimal resource allocation network (MRAN) which is a radial basis function network. It is shown that the MRAN equalizer performs better and converges faster than MFN equalizer.

Accurate three-dimensional acoustic impedance modeling in offshore clastic reservoirs remains a significant challenge due to sparse well control and the highly nonlinear relationship between seismic attributes and subsurface elastic properties. This study introduces an integrated, physics-guided machine learning (ML) workflow that combines rock-physics-driven pseudo-well generation with neural networks to directly map seismic attributes to acoustic impedance under data-limited conditions. A soft-sand rock physics workflow was applied, in which grain moduli were determined using the Voigt-Reuss-Hill average. The dry rock frame was modeled at critical porosity by Hertz-Mindlin contact theory and then interpolated toward zero porosity using the Modified Hashin-Shtrikman lower bound. Gassmann fluid substitution was subsequently performed. Using this approach, 45 pseudo-wells were generated and conditioned through lithofacies classification and spatial statistics, mitigating the risk of overfitting associated with the three available real wells. Six seismic attributes-envelope, RMS amplitude, instantaneous phase, instantaneous frequency, quadrature trace, and sweetness-were selected as predictors. Two neural architectures, a multi-layer feedforward network (MLFN) and a radial basis function network (RBFN), were trained and benchmarked using a leave-one-well-out cross-validation scheme. The MLFN achieved higher predictive accuracy (CC = 0.87, NRMSE = 0.493) compared to the RBFN (CC = 0.79, NRMSE = 0.613), which may reflect its greater capacity to model broader hierarchical relationships between seismic attributes and acoustic impedance. The resulting impedance volume delineates laterally coherent high-impedance sandstone units and low-impedance porous intervals consistent with geological interpretation. These results suggest that integrating physics-guided pseudo-well augmentation with feed-forward neural networks offers a practical and computationally efficient approach for acoustic impedance inversion in data-limited offshore settings. Future work may explore validation across diverse geological settings to assess the robustness and transferability of the proposed methodology. This study provides a basis for hybrid and uncertainty-aware inversion frameworks that may help address complexities in heterogeneous reservoir systems, highlighting the importance of reproducible and widely applicable data-driven seismic inversion methods under sparse well control.

In this study, barley yield has been estimated via radial basis function network (RBF) and feed-forward neural networks (GFF) models of artificial neural network (ANNs) in Torbat-Heydarieh of Iran. For this purpose, a dataset consists of 200 data at three levels of irrigation with well water, industrial wastewater (sugar factory wastewater), a combination of well water and wastewater in two levels (complete irrigation and irrigation with 75 % water stress) and soil characteristics of area were used as input parameters. To achieve this goal, based on the number of data and inputs, 200 barley field experiments data set were used, of which 80 % (160 data) was used for the training and 20 % (40 data) for the testing the network. The results showed that RBF model has high potential in estimating barley yield with Levenberg Marquardt training and 4 hidden layers. Also the values of statistical parameters R2 and RMSE were 0.81 and the 33.12, respectively. In general, the results showed that ANNs model is able to better estimate the barley yield when irrigation water level parameter with well water is selected as input.

Fatigue crack growth and deformation in weldments of aluminium alloys Hermann, R. Mater. Sci. Eng. A (15 Oct. 1994) 186 (1–2), 45–53

The equalization of digital communication channel is an important task in high speed data transmission techniques. The multipath channels cause the transmitted symbols to spread and overlap over successive time intervals. The distortion caused by this problem is called inter-symbol interference (ISI) and is required to be removed for reliable communication of data over communication channels. In this task of ISI removal, the signals are complex-valued and processing has to be done in a complex multidimensional space. The growing interest in complex-valued neural networks has spurred the development of many new algorithms for equalization of communication channels in the recent past. This chapter illustrates the application of various types of complex-valued neural networks such as radial basis function networks (RBFN), multilayer feedforward networks and recurrent neural networks for training sequence-based as well as blind equalization of communication channels. The structures and algorithms for these equalizers are presented and performances based on simulation studies are analyzed highlighting their advantages and the important issues involved.

In order to forecast missile storage reliability better, the paper researched a forecasting method based on neural network which is with the ability of actualizing multi-nonlinear mapping from input to output, and discussed steps of forecasting based on back propagation (BP) network and radial basis function (RBF) network respectively. At last, the storage reliability of one type ship-to-ship missile is forecasted based on BP network and RBF network respectively. The results show that both of the BP and RBF are suitable for Missile storage reliability forecasting, and the precision of the train goal is better by using RBF network. RBF network is more suitable for dealing with this problem.

This article explores the use of single trial EEG signals to predict the voluntary movements of single hand and two hands. During single-hand movements, three kinds of task, grasping, releasing, and holding were considered. The tasks considered during two-hand movements are left and right grasping, left and right releasing, and holding. The subject performs the tasks spontaneously without waiting for and responding to any external cues. In addition, a neural adaptive noise canceller is developed that accomplishes eye blinks suppression. The neural adaptive filter is here implemented by means of a three-layer feed-forward neural network. The feature vectors are formed from the three channels (Fz, C3, and F3). We employ the multilayer perceptron (MLP) with back-propagation learning algorithm and Radial Basis Function (RBF) network with stochastic gradient learning rule for discriminating different patterns of the EEG signals. In the classical approach to RBF and MLP network implementation, the number of hidden units is predetermined. It, usually, results in too many hidden units. To overcome this drawback, we develop an enhanced resource-allocating network (RAN) for discriminating the EEG patterns. These networks start with no hidden units and grow by allocating new hidden units based on the novelty in the EEG signals, which arrive sequentially. The results of this analysis show that the neural networks would be able to detect the movements of a single hand and two hands with an average classification accuracy of 98.82% and 96.40%, respectively. Moreover, the RAN provides a reduction in the training epochs as compared to the MLP and RBF networks. This work represents a promising approach to control prosthesis device.

The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.

This paper investigates the potential application of artificial neural networks in permanent deformation parameter identification for rockfill dams. Two kinds of neural network models, multilayer feedforward network (BP) and radial basis function (RBF) networks, are adopted to identify the parameters of seismic permanent deformation for Zipingpu Dam in China. The dynamic analysis is carried out by three‐dimensional finite element method, and earthquake‐induced permanent deformation is calculated by an equivalent nodal force method. Based on the sensitivity analysis of permanent deformation parameters, an objective function for network training is established by considering parameter sensitivity, which can improve the accuracy of parameter identification. By comparison, it is found that RBF outperforms the BP network in this problem. The proposed inverse analysis model for earth‐rockfill dams can identify the seismic deformation parameters with just a small amount of sample designs, and much calculation time can be saved by this method.

Instantaneous learning is a desirable feature in neural networks. This type of learning enables the network to be trained very quickly, typically in just one or two passes of the training set as opposed to hundreds or even thousands of passes for networks trained by an iterative process, such as the error backpropagation (BP) algorithm. This dissertation first reviews several existing types of neural networks with instantaneous learning capability. It then proposes a new network called the Fuzzy Classification (FC) Neural Network that can be trained with two passes of the training samples. The first pass assigns the synaptic weights for the input and output layers. The second pass determines the radius of generalization r for each training sample. The network exhibits fuzziness in two regards: (1) by fuzzification of the location of each training vector in the input space; and (2) by assigning fuzzy memberships of output classes to new input vectors. The operation of the FC network is analyzed from different perspectives, namely, separability of patterns, curve fitting and kernel regression. It is shown that one mode of operation of the FC network can be made to behave like a Radial Basis Function (RBF) network by proper choice of membership function and network parameter. The performance of the FC network as a pattern classifier is also discussed in a statistical framework. The generalization performance of the FC network is compared against that of the CC4 Comer Classification Neural Network, the RBF network, and the Multilayer Perceptron network trained by the BP algorithm. Experiments involving a Henon map time series, a Mackey-Glass time series, and a spiral pattern are used in the comparison. The performance of the FC network is found to be comparable to that of RBF and BP networks, and better than that of the CC4 network. Its performance is also more scalable than those of CC4 and RBF networks. Further, the time taken to design an FC network for any given problem is much shorter compared to the other three networks.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.

To improve the network performance of radial basis function (RBF) and back-propagation (BP) networks on complex nonlinear problems, an integrated neural network model with pre-RBF kernels is proposed. The proposed method is based on the framework of a single optimized BP network and an RBF network. By integrating and connecting the RBF kernel mapping layer and BP neural network, the local features of a sample set can be effectively extracted to improve separability; subsequently, the connected BP network can be used to perform learning and classification in the kernel space. Experiments on an artificial dataset and three benchmark datasets show that the proposed model combines the advantages of RBF and BP networks, as well as improves the performances of the two networks. Finally, the effectiveness of the proposed method is verified.

This paper presents a method for analog circuit fault diagnosis by using neural networks. This method exploits a DC approach for constructing a dictionary in fault diagnosis using the neural network's classification capability. Also, Radial Basis Function (RBF) and backward error propagation (BEP) networks are considered and compared for analog fault diagnosis. The primary focus of the paper is to provide robust diagnosis using a mechanism to deal with the problem of component tolerance and reduce testing time. Simulation results show that the radial basis function network with reasonable dimension has double precision in fault classification but its classification is local, while the backward error propagation network with reasonable dimension has single precision in fault classification but its classification is global.

A new approach is presented to enhance fuzzy modeling using multidimensional fuzzy sets directly in the fuzzy model in place of decomposed fuzzy sets by projection. The antecedent fuzzy sets in the form of multivariable functions are represented in continuous form. This is accomplished by using a multi input and multi output neural network, which is in particular radial basis functions (RBF) network providing the required multivariable function approximation properties in a fuzzy model. The inputs of the network are fuzzy model inputs, outputs are the membership function values as to the multivariable fuzzy sets involved in the model. Thus, each output is restricted to one multivariable fuzzy set. The RBF network is trained according to the multidimensional fuzzy sets which are identified after fuzzy clustering of the data. Based on this, the linear model parameters are determined by the method of least squares in a straightforward manner. The transparency issues can be handled by means of projection process to have information about the shape and locations of the membership functions pertinent to each variable at the input. The accurate fuzzy modeling having been thus guaranteed the information on the linear model parameters are used to establish the multivariable fuzzy rules with their respective validity regions. The redundancy of the number of fuzzy sets can be circumvented by classical cluster merging algorithms available. In this approach, the fuzzy rules are determined from the local linear models, however in contrast with the conventional fuzzy modeling, the model outputs are determined by the multivariable fuzzy sets. To obtain regular sets, RBF network is trained by means of orthogonal least squares (OLS) method so that at the same time the convergence issues of general neural network training is eliminated.