Levenberg-Marguardt Research Articles

Parameter Estimation of Cellular Communication Systems Models in Computational MATLAB Environment: A Systematic Solver-based Numerical Optimization Approaches

Model-based parameter estimation, identification, and optimisation play a dominant role in many aspects of physical and operational processes in applied sciences, engineering, and other related disciplines. The intricate task involves engaging and fitting the most appropriate parametric model with nonlinear or linear features to experimental field datasets priori to selecting the best optimisation algorithm with the best configuration. Thus, the task is usually geared towards solving a clear optimsation problem. In this paper, a systematic-stepwise approach has been employed to review and benchmark six numerical-based optimization algorithms in MATLAB computational Environment. The algorithms include the Gradient Descent (GRA), Levenberg-Marguardt (LEM), Quasi-Newton (QAN), Gauss-Newton (GUN), Nelda-Meald (NEM), and Trust-Region-Dogleg (TRD). This has been accomplished by engaging them to solve an intricate radio frequency propagation modelling and parametric estimation in connection with practical spatial signal data. The spatial signal data were obtained via real-time field drive test conducted around six eNodeBs transmitters, with case studies taken from different terrains where 4G LTE transmitters are operational. Accordingly, three criteria in connection with rate of convergence Results show that the approximate hessian-based QAN algorithm, followed by the LEM algorithm yielded the best results in optimizing and estimating the RF propagation models parameters. The resultant approach and output of this paper will be of countless assets in assisting the end-users to select the most preferable optimization algorithm to handle their respective intricate problems.

Optimal Radio Propagation Modeling and Parametric Tuning Using Optimization Algorithms

Benchmarking different optimization algorithms is tasky, particularly for network-based cellular communication systems. The design and management process of these systems involves many stochastic variables and complex design parameters that demand an unbiased estimation and analysis. Though several optimization algorithms exist for different parametric modeling and tuning, an in-depth evaluation of their functional performance has not been adequately addressed, especially for cellular communication systems. Firstly, in this paper, nine key numerical and global optimization algorithms, comprising Gauss–Newton (GN), gradient descent (GD), Genetic Algorithm (GA), Levenberg–Marguardt (LM), Quasi-Newton (QN), Trust-Region–Dog-Leg (TR), pattern search (PAS), Simulated Annealing (SA), and particle swam (PS), have been benchmarked against measured data. The experimental data were taken from different radio signal propagation terrains around four eNodeB cells. In order to assist the radio frequency (RF) engineer in selecting the most suitable optimization method for the parametric model tuning, three-fold benchmarking criteria comprising the Accuracy Profile Benchmark (APB), Function Evaluation Benchmark (FEB), and Execution Speed Benchmark (ESB) were employed. The APB and FEB were quantitatively compared against the measured data for fair benchmarking. By leveraging the APB performance criteria, the QN achieved the best results with the preferred values of 98.34, 97.31, 97.44, and 96.65% in locations 1–4. The GD attained the worst performance with the lowest APE values of 98.25, 95.45, 96.10, and 95.70 in the tested locations. In terms of objective function values and their evaluation count, the QN algorithm shows the fewest function counts of 44, 44, 56, and 44, and the lowest objective values of 80.85, 37.77, 54.69, and 41.24, thus attaining the best optimization algorithm results across the study locations. The worst performance was attained by the GD with objective values of 86.45, 39.58, 76.66, and 54.27, respectively. Though the objective values achieved with global optimization methods, PAS, GA, PS, and SA, are relatively small compared to the QN, their function evaluation counts are high. The PAS, GA, PS, and SA recorded 1367, 2550, 3450, and 2818 function evaluation counts, which are relatively high. Overall, the QN algorithm achieves the best optimization, and it can serve as a reference for RF engineers in selecting suitable optimization methods for propagation modeling and parametric tuning.

State of charge estimation for Li-ion batteries based on iterative Kalman filter with adaptive maximum correntropy criterion

Nonlinear filter methods are commonly employed for model-driven based battery state of charge (SOC) estimation because of their ability to suppress Gaussian noise. Due to the uncertainty of complicated operational conditions, the minimum mean square error (MMSE) criterion based Kalman filter (KF) methods may not guarantee sufficient SOC estimation accuracy in the presence of non-Gaussian noise. To enhance the anti-interference performance of the KFs based SOC estimation method, a novel methodology that combines the adaptive kernel width based maximum correntropy criterion (AMCC) with the Levenberg-Marguardt (L-M) principle based adaptive iterative extended KF (AIEKF) is proposed. Firstly, the MMSE criterion of the EKF is replaced by the MCC criterion and an adaptive kernel width strategy is designed to weaken the effect of anomalous data. Then, the AMCC-corrected covariance matrix and state are updated using an L-M optimized multi-step iterative filter during the measurement update phase. Finally, the combination of AMCC and AIEKF is devised to execute SOC estimation. Several sets of data from different temperatures and operational conditions are used to verify the validity of the proposed AMCC-AIEKF method. Compared with the adaptive EKF (AEKF) and the adaptive iterative EKF (AIEKF) method, the AMCC-AIEKF method has the advantage in terms of SOC estimation accuracy and robustness under different operational conditions with noiseless, Gaussian noise and non-Gaussian noise.

Modeling of Heat Transfer Around a Square and a Circle: A Novel ANN-Based Approch

Artificial neural network (ANN) is a modelling of the human brain. The aim of this study is to estimate the heat distribution with ANN around different cylinders. Within the scope of the study, square and circular cylinders were discussed. In this study, the temperature analysis of the cylinders was carried out with a program written in Fortran, not using a package program whose exact background is unknown. The results obtained from a writing code are more reliable. The study is discussed in two dimensions. The 3 most commonly used algorithms (Levenberg – Marguardt (LM), Pola-Ribiere Conjugate Gradient (CGP) and Scaled Conjugate Gradient (SCG)) were used to train with ANN. Cylinder type, x-coordinate and y-coordinate were the input variables; and temperature was the output variable. The most suitable algorithm was found to be LM-18 algorithm. The proximity of artificial neural networks and real values was evaluated statistically. These were R2, CoV and RMSE. R2, CoV and RMSE values in the training phase of Levenberg – Marguardt -18 neuron were determined to be 0.9939, 0.0044, 0.0107 while their values in the test phase were 0.9850, 0.0043 and 0.0190 respectively. The fact that the R2 value is so close to 1 is an indication that ANN is working very well.

New algorithm for optimised fitting of DIC data to crack tip plastic zone using the CJP model

The work presented in this paper provides guidance in optimally determining the appropriate fitting region used in digital image correlation (DIC) when fitting a crack tip field model to DIC data. In this work, the technique is applied to the CJP crack tip field model and uses the Levenberg-Marguardt (L-M) iterative method to solve for the crack tip position. This is combined with an error analysis of the main term of the Williams series expansion for crack tip stresses and the extrapolation of Saint-Venant’s principle to determine the optimum fitting region for use in DIC fit with the multi-parameter solution for the CJP crack tip field model. A comparison is then made between the size and shape of the crack tip plastic zone obtained using the Williams and the CJP models. This demonstrated that as the plastic zone size increased, there was a deterioration in accuracy of the description of the crack tip plastic zone using the Williams series expansion, while the CJP description remains more accurate. In addition, KF, the stress-intensity factor that drives crack growth in the CJP model has a strong linear relationship with the plastic zone area, which indicates that KF is a direct driving force for crack growth and there is a clear relationship between ΔKCJP and ΔKI.

An innovative design approach of hot water storage tank for solar water heating system using artificial neural network

Overall Conductance is considered to be the most important parameter to design hot water storage tank. This is computed in terms of equivalent thermal resistance considering the total heat loss from hot water storage tank. Computed results attained have been confirmed with an Artificial Neural Network (ANN) with three design input data. The back-propagation learning algorithm with the Levenberg–Marguardt (LM) was used in the artificial neural network with 608 known values. Thus, the network was prepared to provide various possible designs of hot water storage tank quickly and accurately. A maximum error of 2.62% was obtained with an ANN. Therefore, proposed innovative design approach can successfully be used for the designing of Overall Conductance of hot water storage tank in solar water heating system. In present work total 612 design combinations used which includes the diameter of the tank, thickness of insulation and conductivity of insulating material.

Lipase-catalysed synthesis of a novel galanthamine derivative: Process optimization by artificial neural networks

Artificial neural networks (ANNs) analysis was carried out to optimize the esterification of galanthamine and acetic acid in a solvent system. To predict performance parameters of the enzymatic reaction conditions, several parameters were studied which were reaction temperature (50–90 °C), enzyme amount (2–5 wt%), reaction time (6–18 h), and substrate molar ratio of galanthamine to acetic acid (2–5:1). The algoritms used in the network were batch back propagation (BBP), incremental back propagation (IBP), genetic algorithm (GA), Levenberg–Marguardt (LM) and quick propagation (QP) algorithms. The configuration of 4 inputs, one hidden layer with 7 nodes, and 1 output using the batch back propagation (BBP) was determined as the optimum algorithm. The predicted and experimental percentage yield value were 60.24% and 60.36%, respectively. These results prove the validity of ANN model.

Feasibility design and techno-economic analysis of hybrid renewable energy system for rural electrification

This paper validates the optimal design and techno-economic feasibility of hybrid renewable energy system (HRES) for rural area electrifying applications. Plan to a design of improved performance electrification system through village owned renewable resources, such as solar irradiations, wind speed and bio mass etc. The selected HRE system has to meet out electrical needs in optimum performance manner. Hear conducted a case study on remote village Korkadu is located in Union Territory of Pondicherry, India. The expected village demand of 179.32 Kwh/day and peak of 19.56 Kw was met with proposed HRE structure, which is consists of solar PV array, wind turbine, Bio mass power generator and Battery backup system in effectively. Load growth of the village was predicted through artificial neural network (ANN-BP) feed-back propagation and Levenberg-Marguardt (LM) data training optimum technique. Encounter the optimum performance of different HRE configuration was evaluated over by HOMER software. System’s economic dispatch was analysed through various dispatch strategy and come across the proposing companied dispatch strategy has more economical and performance benefits as total NPC of system as INR 1.21 million, one unit energy generation cost as INR 13.71 and annual battery throughput as 36.648 KWh/yr. This study also expresses the comparison analysis between proposed HRES structure performance with basic utility grid extension. The consequence of the proposed work shows the HRES in remote location can be a cost effective solution for sustainable development of rural regions.

Review on Feature Extraction and Classification of WBC in Bone Marrow for Disease Diagnosis

In this paper, we make a review on different features and classification methods for white blood cells in bone marrow for disease diagnosis. A new set of features based on the wavelet and Radon transform to bone marrow blood cell differential classification solution. The transform based novel features are the coefficient values of decomposition for horizontal, vertical & diagonal factors with two levels. the factors where the coefficient values are of six in numbers the first and second level coefficient method to the classifiers by the desired output using a previous information of the number of coefficients as a samples in each class. Artificial neural networks Levenberg-Marguardt (LM) back propagation algorithm for validation is applied in the experiments. The results are used in various disease diagnoses.

Performance prediction of a solar thermal energy system using artificial neural networks

This paper describes in details an application of artificial neural networks (ANNs) to predict the performance of a solar thermal energy system (STES) used for domestic hot water and space heating application. Experiments were conducted on the STES under a broad range of operating conditions during different seasons and Canadian weather conditions in Ottawa, over the period of March 2011 through December 2012 to assess the system performance. These experimental data were utilised for training, validating and testing the proposed ANN model. The model was applied to predict various performance parameters of the system, namely the preheat tank stratification temperatures, the heat input from the solar collectors to the heat exchanger, the heat input to the auxiliary propane-fired tank, and the derived solar fractions. The back-propagation learning algorithm with two different variants, the Levenberg–Marguardt (LM) and scaled conjugate gradient (SCG) algorithms were used in the network. It was found that the optimal algorithm and topology were the LM and the configuration with 10 inputs, 20 hidden and 8 output neurons/outputs, respectively.The preheat tank temperature and solar fraction predictions agreed very well with the experimental values using the testing data sets. The ANNs predicted the preheat water tank stratification temperatures and the solar fractions of the STES within less that ±3% and ±10% errors, respectively.The results confirmed the effectiveness of this method and provided very good accuracy even when the input data are distorted with different levels of noise. Moreover, the results of this study demonstrate that the ANN approach can provide high accuracy and reliability for predicting the performance of complex energy systems such as the one under investigation. Finally, this method can also be exploited as an effective tool to develop applications for predictive performance monitoring system, condition monitoring, fault detection and diagnosis of STES.

Application of Improved BP Neural Networks Based on LM Algorithm in Characteristic Curve Fitting of Fiber-Optic Micro-Bend Sensor

As a key factor in a testing system, sensor nonlinearity has always been the study focus in the field of engineering and techniques. In order to accurately reflect the practical characteristics of a fiber-optic micro-bend sensor, Levenberg-Marguardt (LM) algorithm is used to optimize the correction of the weight values of standard back propagation neural network (BPNN). The learning process of improved BPNN based on LM algorithm (LM-BPNN) is also illustrated mathematically, and LM-BPNN is applied in fitting the input and output characteristic curve of a fiber-optic micro-bend sensor. The simulation results show that LM-BPNN is superior both in its convergence rate and fitting precision over standard BPNN.

An Investigation of Drying Process of Shelled Pistachios in a Newly Designed Fixed Bed Dryer System by Using Artificial Neural Network

In this paper, the drying of Siirt pistachios (SSPs) in a newly designed fixed bed dryer system and the prediction of drying characteristics using artificial neural network (ANN) are presented. Drying characteristics of SSPs with initial moisture content (MC) of 42.3% dry basis (db) were studied at different air temperatures (60, 80, and 100 °C) and air velocities (0.065, 0.1, and 0.13 m/s) in a newly designed fixed bed dryer system. Obtained results of experiments were used for ANN modeling and compared with experimental data. Falling rate period was observed during all the drying experiments; constant rate period was not observed. Furthermore, in the presented study, the application of ANN for predicting the drying time (DT) for a good quality product (output parameter for ANN modeling) was investigated. In order to train the ANN, experimental measurements were used as training data and test data. The back propagation learning algorithm with two different variants, so-called Levenberg–Marguardt (LM) and scaled conjugate gradient (SCG), and tangent sigmoid transfer function were used in the network so that the best approach can be determined. The most suitable algorithm and neuron number in the hidden layer are found out as LM with 15 neurons. For this number level, after the training, it is found that Root-mean squared (RMS) value is 0.3692, and absolute fraction of variance (R2) value is 99.99%. It is concluded that ANNs can be used for prediction of drying SSPs as an accurate method in similar systems.

Application of Artificial Neural Networks (ANNs) for Weight Predictions of Blue Crabs (Callinectes sapidus RATHBUN, 1896) Using Predictor Variables

An evaluation of the performance of artificial networks (ANNs) to estimate the weights of blue crab (Callinectes sapidus) catches in Yumurtalık Cove (Iskenderun Bay) that uses measured predictor variables is presented, including carapace width (CW), sex (male, female and female with eggs), and sampling month. Blue crabs (n=410) were collected each month between 15 September 1996 and 15 May 1998. Sex, CW, and sampling month were used and specified in the input layer of the network. The weights of the blue crabs were utilized in the output layer of the network. A multi-layer perception architecture model was used and was calibrated with the Levenberg Marguardt (LM) algorithm. Finally, the values were determined by the ANN model using the actual data. The mean square error (MSE) was measured as 3.3, and the best results had a correlation coefficient (R) of 0.93. We compared the predictive capacity of the general linear model (GLM) versus the Artificial Neural Network model (ANN) for the estimation of the weights of blue crabs from independent field data. The results indicated the higher performance capacity of the ANN to predict weights compared to the GLM (R=0.97 vs. R=0.95, raw variable) when evaluated against independent field data.

ANN based optimization of supercritical ORC-Binary geothermal power plant: Simav case study

Abstract Artificial neural network is a new tool, which works rapidly for decision making and modeling of the processes within the expertise. Therefore, ANN can be a solution for the design and optimization of complex power cycles, such as ORC-Binary. In the present study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola-Ribiere Conjugate Gradient (CGP), and Scaled Conjugate Gradient (SCG) were used in the network to find the best approach. The most suitable algorithms found were LM 16 for s1 type cycle and LM 14 for s2 type cycle. The Organic Rankine Cycle (ORC) uses organic fluids as a working fluids and this process allows the use of low temperature heat sources and offers an advantageous efficiency in small-scale concepts. The most profitable cycle is obtained with a benefit of 124.88 million US$ from s1 type supercritical ORC-Binary plant with an installed capacity of 64.2 MW when the working fluid is R744 and the design parameters of T 1b , T 2a and P 2a are set to 80 °C, 130 °C and 12 MPa, respectively.

Power generation from medium temperature geothermal resources: ANN-based optimization of Kalina cycle system-34

Recent technical developments have made it possible to generate electricity from geothermal resources of low and medium enthalpy. One of these technologies is the Kalina Cycle System. In this study, electricity generation from Simav geothermal field was investigated using the Kalina cycle system-34 (KCS-34). However, the design of these technologies requires more proficiency and longer times within complex calculations. An artificial neural network (ANN) is a new tool used to make a decision for the optimum working conditions of the processes within the expertise. In this study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola–Ribiere Conjugate Gradient (CGP), and Scaled Conjugate Gradient (SCG), were used in the network so that the best approach could be found. The most suitable algorithm found was LM with 7 neurons in a single hidden layer. The obtained weights were used in optimization process by coupling the life-cycle-cost concepts.

Modelling of a vertical ground coupled heat pump system by using artificial neural networks

This paper describes the applicability of artificial neural networks (ANNs) to estimate of performance of a vertical ground coupled heat pump (VGCHP) system used for cooling and heating purposes experimentally. The system involved three heat exchangers in the different depths at 30 (VB1), 60 (VB2) and 90 (VB3) m. The experimental results were obtained in cooling and heating seasons of 2006–2007. ANNs have been used in varied applications and they have been shown to be particularly useful in system modeling and system identification. In this study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola–Ribiere conjugate gradient (CGP), and scaled conjugate gradient (SCG), and tangent sigmoid transfer function were used in the network so that the best approach could be found. The most suitable algorithm and neuron number in the hidden layer were found as LM with 8 neurons for both cooling and heating modes.

Performance prediction of a ground-coupled heat pump system using artificial neural networks

This paper describes the applicability of artificial neural networks (ANNs) to predict performance of a horizontal ground-coupled heat pump (GCHP) system. Performance forecasting is the precondition for the optimal control and energy saving operation of heat pump systems. ANNs have been used in varied applications and they have been shown to be particularly useful in system modelling and system identification. In order to train the ANN, limited experimental measurements were used as training data and test data. In this study, in input layer, there are air temperature entering condenser unit and air temperature leaving condenser unit, and ground temperatures (1 and 2m); coefficient of performance of system (COPS) is in output layer. The back propagation learning algorithm with three different variants, namely Levenberg-Marguardt (LM), Pola-Ribiere conjugate gradient (CGP), and scaled conjugate gradient (SCG), and tangent sigmoid transfer function were used in the network so that the best approach can find. The most suitable algorithm and neuron number in the hidden layer are found as LM with seven neurons. For this number level, after the training, it is found that Root-mean squared (RMS) value is 1%, and absolute fraction of variance (R^2) value is 99.999% and coefficient of variation in percent (COV) value is 28.62%. It is concluded that, ANNs can be used for prediction of COPS as an accurate method in the systems.

Model-based shape from shading for microelectronics applications

Model-based shape from shading (SFS) is a promising paradigm introduced by Atick et al. [Neural Comput 8 (1996), 1321–1340] in 1996 for solving inverse problems when we happen to have a lot of prior information on the depth profiles to be recovered. In the present work we adopt this approach to address the problem of recovering wafer profiles from images taken using a scanning electron microscope (SEM). This problem arises naturally in the microelectronics inspection industry. A low-dimensional model, based on our prior knowledge on the types of depth profiles of wafer surfaces, has been developed, and based on it the SFS problem becomes an optimal parameter estimation. Wavelet techniques were then employed to calculate a good initial guess to be used in a minimization process that yields the desired profile parametrization. A Levenberg–Marguardt (LM) optimization procedure has been adopted to address ill-posedness of the SFS problem and to ensure stable numerical convergence. The proposed algorithm has been tested on synthetic images, using both Lambertian and SEM imaging models. © 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 65–76, 2006

05/01089 A study on luminous efficacy of global radiation under clear sky conditions in Athens, Greece

Recent technical developments have made it possible to generate electricity from geothermal resources of low and medium enthalpy. One of these technologies is the Kalina Cycle System. In this study, electricity generation from Simav geothermal field was investigated using the Kalina cycle system-34 (KCS-34). However, the design of these technologies requires more proficiency and longer times within complex calculations. An artificial neural network (ANN) is a new tool used to make a decision for the optimum working conditions of the processes within the expertise. In this study, the back-propagation learning algorithm with three different variants, namely Levenberg–Marguardt (LM), Pola–Ribiere Conjugate Gradient (CGP), and Scaled Conjugate Gradient (SCG), were used in the network so that the best approach could be found. The most suitable algorithm found was LM with 7 neurons in a single hidden layer. The obtained weights were used in optimization process by coupling the life-cycle-cost concepts.