Bayesian Regularization Training Algorithm Research Articles

Application of Feed Forward Neural Network for Prediction of Optimum Coagulant Dose in Water Treatment Plant

Coagulation is anecessary process used mainly to reduce turbidity and natural organic matter in water treatment. The dosage of coagulant required is conventionally determined by carrying out jar tests which consume time and chemicals.In India, coagulant dose in a WTP remains constant during certain periods due to delay in jar testing, which may lead to under-dosing or over-dosing of coagulant. This research work is focused on applying artificial neural network (ANN) approach to predict coagulant dose in a WTP. Forty-eight months daily water testing data concerning inlet & outlet water turbidity and coagulant dose were obtained from the plant laboratory for ANN modelling. The appropriate architecture of feed forward neural network (FFNN) coagulant models were established with several steps of training and testing by applying various training algorithms vizLevenberg-Marquardt (LM) and Bayesian regularization (BR), resilient back propagation (RBP), one step secant(OSS),variants of conjugate gradient(CG) and modifications of gradient descent (GD) with evaluating coefficient of correlation (R) & mean square error (MSE). Further, best performed LM and BR training algorithm were used for development of four ANN models of FFNN for prediction of coagulant dose at WTP. FFNN coagulant model with BR training algorithm provided excellent estimates with network architecture (2-50-1) for coagulant dose with maximum value of R= 0.943 (training) and R = 0.945 (testing). Thus, ANN provided an effective diagnosing tool to understand the non-linear behavior of the coagulation process, and can be used as a valuable performance assessment tool for plant operators and decision makers.

Hysteresis nonlinear modeling and inverse compensation of piezoelectric actuators

The tilt mirrors and deformable mirrors in adaptive optics system are usually using piezoelectric ceramic actuators for precise displacement, however, piezoelectric ceramic actuators own obviously nonlinear hysteresis effect which affects the positioning performance of the system. In order to compensate the hysteresis, there is a need to model hysteresis effects. In this paper, hysteresis operator is introduced and using Bayesian regularization training algorithm to train BP neural network to construct hysteresis model of piezoelectric ceramic actuator, an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. The final experimental results show that the hysteresis model of piezoelectric ceramic actuators constructed by BP neural network has more accurate identification capability. The relative error of the positive model is 0.0127 and the relative error of the inverse model is 0.014. The nonlinearity of the piezoelectric actuators has been reduced from 14.6% to 1.43%.

Thermal and Thermomechanical Responses Prediction of a Steel Ladle Using a Back‐Propagation Artificial Neural Network Combining Multiple Orthogonal Arrays

To facilitate industrial vessel lining design for various material properties and lining configurations, a method, being composed of the back‐propagation artificial neural network (BP‐ANN) with multiple orthogonal arrays, is developed, and a steel ladle from secondary steel metallurgy is chosen for a case study. Ten geometrical and material property variations of this steel ladle lining are selected as inputs for the BP‐ANN model. A total of 160 lining configurations nearly evenly distributed within the ten variations space are designed for finite element (FE) simulations in terms of five orthogonal arrays. Leave‐One‐Out cross validation within various combinations of orthogonal arrays determines 7 nodes in the hidden layer, a minimum ratio of 16 between dataset size and number of input nodes, and a Bayesian regularization training algorithm as the optimal definitions for the BP‐ANN model. The thermal and thermomechanical responses of two optimal lining concepts from a previous study using the Taguchi method are predicted with acceptable accuracy.

Probabilistic Fatigue Life Prediction of Dissimilar Material Weld Using Accelerated Life Method and Neural Network Approach

Welding alloy 617 with other metals and alloys has been receiving significant attention in the last few years. It is considered to be the benchmark for the development of economical hybrid structures to be used in different engineering applications. The differences in the physical and metallurgical properties of dissimilar materials to be welded usually result in weaker structures. Fatigue failure is one of the most common failure modes of dissimilar material welded structures. In this study, fatigue life prediction of dissimilar material weld was evaluated by the accelerated life method and artificial neural network approach (ANN). The accelerated life testing approach was evaluated for different distributions. Weibull distribution was the most appropriate distribution that fits the fatigue data very well. Acceleration of fatigue life test data was attained with 95% reliability for Weibull distribution. The probability plot verified that accelerating variables at each level were appropriate. Experimental test data and predicted fatigue life were in good agreement with each other. Two training algorithms, Bayesian regularization (BR) and Levenberg–Marquardt (LM), were employed for training ANN. The Bayesian regularization training algorithm exhibited a better performance than the Levenberg–Marquardt algorithm. The results confirmed that the assessment methods are effective for lifetime prediction of dissimilar material welded joints.

Prediction of variation of oxides of nitrogen in plasma-based diesel exhaust treatment using artificial neural network

Diesel exhaust treatment in plasma environment is a complex phenomenon mainly involving oxidation of several gaseous pollutants. With the help of artificial neural network, an attempt has been made in this paper to predict the variation of nitric oxide/nitrogen dioxide when the exhaust is subjected to discharge plasma. Electrical (power and frequency) and physical (engine load and flow rate) parameters have been considered as inputs of a three-layered artificial neural network model to track the performance of the treatment. Two different backpropagation algorithms named Bayesian regularization and Levenberg–Marquardt have been applied to compare the prediction performance. Bayesian regularization training algorithm shows better agreement with the experimental data than Levenberg–Marquardt in terms of root-mean-square error and correlation coefficient. Further, sensitivity analysis has been carried out to obtain an insight about the relative importance of input parameters on output parameters. This investigation shows that the applied input power is the most influential among the four input parameters from the point of variation of nitric oxide/nitrogen dioxide.

Non-linear system identification of a latent heat thermal energy storage system

Latent heat storage systems utilising phase change materials have potential to offer several advantages over sensible heat storage, including higher energy storage densities and thermal modulation. Despite these advantages, only a few commercialised products incorporating this technology exist due to several engineering challenges. One problem is how to model this technology in a computationally efficient manner which allows simulating this technology with variable heat sources such as solar thermal and heat pump systems and assess their long-term system performance. In this study, the application of a dynamic neural network for this purpose is investigated, where a Layered Digital Dynamic Neural (LDDN) type network is trained using experimental data to approximate the outlet fluid temperature of a latent heat storage system given inlet fluid temperature and mass flow rate.To acquire the training data necessary for the neural network, an experimental apparatus was designed, built and operated under laboratory conditions. Twenty experiments were conducted to obtain training data where the latent heat storage system was charged to different operating temperatures ranging from 25 to 70 °C. The mass flow rate of the heat exchanger fluid flowing through the heat exchanger was also varied: 0.045 and 0.05 kg/s such that the flow of heat exchanger fluid remained turbulent. These data were then presented to the network for training and optimisation of the network architecture using the Bayesian Regularization training algorithm. It was found, that the LDDN type architecture was suitable to characterise the thermal operational behaviour of a latent heat storage system with good accuracy and with little computational effort once trained. Based on an energy analysis, the neural network response predicted the quantity of energy stored and discharged with approximately 5% and 7% accuracy respectively when presented with data not used during the training process. These results indicate that a dynamic neural network may be a computationally efficient method to model the non-linear operational characteristics of a latent heat storage system. It may therefore be implemented within a simulation environment such as TRNSYS or Simulink.

DendroTools: R package for studying linear and nonlinear responses between tree-rings and daily environmental data

We introduce in this paper the dendroTools R package for studying the statistical relationships between tree-ring parameters and daily environmental data. The core function of the package is daily_response(), which works by sliding a moving window through daily environmental data and calculating statistical metrics with one or more tree ring proxies. Possible metrics are correlation coefficient, coefficient of determination and adjusted coefficient of determination. In addition to linear regression, it is possible to use a nonlinear artificial neural network with the Bayesian regularization training algorithm (brnn). dendroTools provides the opportunity to use daily climate data and robust nonlinear functions for the analysis of climate-growth relationships. Models should thus be better adapted to the real (continuous) growth of trees and should gain in predictive capabilities. The dendroTools R package is freely available in the CRAN repository. The functionality of the package is demonstrated on two examples, one using a mean vessel area (MVA) chronology and one a traditional tree-ring width (TRW).

Modeling of process indices of Aloe vera gel extraction machine using artificial neural network

AbstractThe performance evaluation of Aloe vera gel extraction machine in terms of extraction efficiency, gel recovery, and extraction loss were evaluated at three level of roller speeds (11.40, 15.10, and 18.80 rpm) and roller clearance (4, 5, and 6 mm). The data obtained were used for development of artificial neural network (ANN) model. The roller speed, roller clearance, extraction efficiency, gel recovery, and extraction loss were used as the inputs and the gel extraction efficiency, gel recovery, and extraction loss were the output from the model. New feed forward neural network was used for the model building and trained using Bayesian regularization training algorithm. Optimum ANN architecture was obtained by trial and error method. The results showed that the correlation coefficient for calibration and validation was .9751 and .9982, respectively, the root mean square error for calibration and validations was .4746 and .1258, respectively, and the ANN efficiency for calibration and validation was .9507 and .9964, respectively, were recorded for ANN model 5‐10‐3. Results indicated that ANN can be used efficiently for the modeling of the process indices of the Aloe vera gel extraction machine.Practical applicationsUsing a set of experimental data from Aloe vera gel extraction machine artificial neural network (ANN) model was developed to evaluate and predict the performance of Aloe vera gel extraction machine in terms of extraction efficiency, gel recovery, and extraction loss. The evaluation of ANN model with test data proved that model has very good accuracy. Using this model one can search for optimum operation conditions of Aloe vera gel extraction machine to maximize the efficiency and gel recovery and minimize the extraction loss.

Predictive Abilities of Bayesian Regularization and Levenberg–Marquardt Algorithms in Artificial Neural Networks: A Comparative Empirical Study on Social Data

The objective of this study is to compare the predictive ability of Bayesian regularization with Levenberg–Marquardt Artificial Neural Networks. To examine the best architecture of neural networks, the model was tested with one-, two-, three-, four-, and five-neuron architectures, respectively. MATLAB (2011a) was used for analyzing the Bayesian regularization and Levenberg–Marquardt learning algorithms. It is concluded that the Bayesian regularization training algorithm shows better performance than the Levenberg–Marquardt algorithm. The advantage of a Bayesian regularization artificial neural network is its ability to reveal potentially complex relationships, meaning it can be used in quantitative studies to provide a robust model.

Mathematical and neural network modelling of terebinth fruit under fluidized bed drying

The paper presents an application which uses Feed Forward Neural Networks (FFNNs) to model the non-linear behaviour of the terebinth fruit drying. Mathematical models and Artificial Neural Networks (ANNs) were used for prediction of effective moisture diffusivity, specific energy consumption, shrinkage, drying rate and moisture ratio in terebinth fruit. Feed Forward Neural Network (FFBP) and Cascade Forward Neural Network (CFNN) as well as training algorithms of Levenberg-Marquardt (LM) and Bayesian regularization (BR) were used. Air temperature and velocity limits were 40–80°C and 0.81–4.35 m/s, respectively. The best outcome for the use of ANN for the effective moisture diffusivity appertained to CFNN network with BR training algorithm, topology of 2-3-1 and threshold function of TANSIG. Similarly, the best outcome for the use of ANN for drying rate and moisture ratio also appertained to CFNN network with LM training algorithm, topology of 3-2-4-2 and threshold function of TANSIG.

Bayesian Regularization Neural Networks for Prediction of Austenite Formation Temperatures (Ac1 and Ac3)

A neural network with a feed forward topology and Bayesian regularization training algorithm is used to predict the austenite formation temperatures (Ac1 and Ac3) by considering the percentage of alloying elements in chemical composition of steel. The data base used here involves a large variety of different steel types such as structural steels, stainless steels, rail steels, spring steels, high temperature creep resisting steels and tool steels. Scatter diagrams and mean relative error (MRE) statistical criteria are used to compare the performance of developed neural network with the results of Andrew's empirical equations and a feed forward neural network with “gradient descent with momentum” training algorithm. The results showed that Bayesian regularization neural network has the best performance. Also, due to the satisfactory results of the developed neural network, it was used to investigate the effect of the chemical composition on Ac1 and Ac3 temperatures. Results are in accordance with materials science theories.

Artificial neural network modeling of dissolved oxygen in the Heihe River, Northwestern China

Identification and quantification of dissolved oxygen (DO) profiles of river is one of the primary concerns for water resources managers. In this research, an artificial neural network (ANN) was developed to simulate the DO concentrations in the Heihe River, Northwestern China. A three-layer back-propagation ANN was used with the Bayesian regularization training algorithm. The input variables of the neural network were pH, electrical conductivity, chloride (Cl(-)), calcium (Ca(2+)), total alkalinity, total hardness, nitrate nitrogen (NO3-N), and ammonical nitrogen (NH4-N). The ANN structure with 14 hidden neurons obtained the best selection. By making comparison between the results of the ANN model and the measured data on the basis of correlation coefficient (r) and root mean square error (RMSE), a good model-fitting DO values indicated the effectiveness of neural network model. It is found that the coefficient of correlation (r) values for the training, validation, and test sets were 0.9654, 0.9841, and 0.9680, respectively, and the respective values of RMSE for the training, validation, and test sets were 0.4272, 0.3667, and 0.4570, respectively. Sensitivity analysis was used to determine the influence of input variables on the dependent variable. The most effective inputs were determined as pH, NO3-N, NH4-N, and Ca(2+). Cl(-) was found to be least effective variables on the proposed model. The identified ANN model can be used to simulate the water quality parameters.