Levenberg-Marquart Research Articles

Intelligent adaptive nonlinear autoregressive eXogeneous neuro‐structure for ferromagnetic Powell‐Eyring fluidic involving cubic autocatalysis chemical reaction

AbstractThe scope of artificial intelligence in the field of fluid mechanics has been expanded with the development sophisticated technology to enhance the efficiency, reliability, solve complexities, introduced alternate transformation and enabling more dependable solutions with their analysis. The goal of this study is to investigate the ferromagnetic Powell‐Eyring fluids (FMPEFs) model with non‐Fourier heat flux by using artificial intelligence‐based scheme by exploiting the adaptive nonlinear autoregressive eXogenous (NARX) neuro‐architecture with backpropagation of Levenberg Marquart (LM), that is, NARX‐LM. The developed NARX‐LM methodology applied on synthetic datasets acquired with the help of Adams numerical method for FMPEF system by prudently changing physical quantities that is, material parameters of Eyring Powell, homogeneous reaction, heterogeneous reaction, dimensionless thermal relaxation time, Prandtl number, Schmidt number with fixed values parameter of ferrohydrodynamic interaction, rate of diffusion coefficient. Outcomes of NARX‐LM are regularly overlapping with the numerical results for the FMPEFs system having reasonable small error magnitude for each variant. The proficiency of intelligent computing anticipated on FMPEFs is depicted exhaustively with iterative mean squared error based iconvergence curves, analysis of adaptive controlling factors, error frequency distribution on the histograms, auto‐correlation, and correlation measures.

A new relation for nuclear masses based on the nuclide chain with the same number of neutrons

There are many studies in Odd–Even staggering (OES) of nuclear masses, but the research on nuclear masses by using the systematicness of OES is indeed very few. In this work, we analyze the relationship among the four neighboring nuclei based on the OES of nuclide chain with the same number of neutrons in atomic mass evaluation database (AME2016 database). Our purpose in this paper is to describe an empirical formula with one constant for OES of nuclear masses that can be useful in describing and predicting nuclear masses with mass number [Formula: see text]. With the empirical formula and AME2016 database, the root-mean-square deviation (RMSD) of the nuclei that we have successfully obtained 172[Formula: see text]keV for [Formula: see text] (the RMSD is 140[Formula: see text]keV for [Formula: see text]). This paper also uses Levenberg–Marquart (L-M) neural network approach to study the OES of nuclear masses ([Formula: see text], RMSD [Formula: see text][Formula: see text]keV; [Formula: see text], RMSD [Formula: see text][Formula: see text]keV). The results show that the RMSD of nuclear masses for [Formula: see text] based on neural network approach 30[Formula: see text]keV decreases than that based on empirical formula (the accuracy is increased by about 17%). In addition, the predicted values based on the empirical formula and L-M neural network approach are consistent with the values in AME2020 database, and the difference between our predicted values based on AME2016 database and experimental values measured in recent years is small. These results show that the new relation for nuclear masses has good simplicity, accuracy and reliability. Accurate nuclear mass is helpful to the research of nuclear physics, nuclear technology and astrophysics.

Terrain-based adaption of propagation model loss parameters using non-linear square regression

Reliable and real-time propagation loss modeling play a significant role in the efficient planning, development, and optimization of macrocellular communication networks in a given terrain. Thus, the need to adapt or tune an existing model to enhance its signal prediction accuracy in a specified terrain becomes imperative. In this paper, we proposed and applied a non-linear square regression method based on the Levenberg-Marquart (LM) algorithm to adapt and improve the empirical propagation loss estimation accuracy of the Egli model for two major cities in Nigeria. A comprehensive propagation loss measurement acquired over Long Term Evolution (LTE) mobile broadband networks operating at 2630 MHz for four different cities was collected using TEMS investigation tools to achieve the Egli model adaption. Results indicate that the adapted Egli model displays a high estimation accuracy over the Gauss-Newton (GN) algorithm leveraging the non-linear regression method employed to benchmark the propagation loss estimation. Using six standard statistical indicators, the adapted Egli model displayed lower estimation errors than the classical Egli model across the tested locations in the two cities investigated. Finally, the LM-adapted Egli model was compared with extensive measurements from another eNodeB in Port Harcourt different from the initial four eNodeBs investigated. The results indicate that the adapted model is suitable for deployment in related macrocellular environments.

Estimation of groundwater recharge using simulation-optimization model and cascade forward ANN at East Nile Delta aquifer, Egypt

Study regionThe Quaternary Aquifer at the Eastern Nile Delta (QAEND), Egypt. Study focusA novel model is studied to build relationships between the available geomorphological and hydrogeological data, and the unknown time-dependent recharge rates. This is useful in performing inexpensive sustainable simulation and management of the proposed aquifer. Recharge rates in the year 2005 are calibrated using the observed hydraulic heads. The unstructured grid version of MODFLOW (MFUSG) coupled with the Particle Swarm Optimization (PSO) algorithm is used to solve the calibration problem. Then, a multilayer Cascade Forward Artificial Neural Network (CFNN) is trained using the calibrated recharge rates to conclude the required relationships between available data and unknown recharge rates, for any subsequent year. Four different training methods are adopted for CFNN: 1) PSO, 2) Levenberg Marquart (LM), 3) LM in combination with the Bayesian Regularization (BR), and 4) hybrid algorithm between LM - BR and PSO, which is used for the first time in training the CFNN to predict the net recharge rates and is found to be the best one. New hydrological insights for the regionThe trained CFNN is used to provide the groundwater flow model, MFUSG, with necessary recharge rates during the transient simulation of the groundwater between 2005 and 2015. Good matching between simulated and observed hydraulic heads is validating the model in forcasting future recgharge rates.

Non-unit Traveling Wave Protection of HVDC Grids Using Levenberg–Marquart Optimal Approximation

The fast and selective protection using fast dc circuit breaker to break the fault current and isolate faulty lines satisfies the requirement of fault clearance in HVDC grids. However, traditional derivative-based traveling wave protection suffers from low-sensitivity problem when high-impedance faults occur. Based on the analysis of the fault initial traveling wave, it is concluded that the distortion degree of the fault initial traveling wave is related to the location of the fault, and the amplitude of the fault initial traveling wave is related to the fault impedance. Then a Levenberg–Marquart (LM) optimal approximation method is proposed to extract the fault distance information from zero-sequence fault current initial traveling wave. The optimal approximation parameters respectively reflecting the fault distance and fault impedance can be obtained. A non-unit traveling wave protection scheme is proposed based on the parameters. A ±400 kV modular multilevel converter (MMC) HVDC grid test system is built in PSCAD/EMTDC to verify the proposed method. The simulation results show that the parameters can directly correspond to the fault distance and fault impedance, and the proposed method can fast and reliably identify dc line faults. Finally, the sensitivity of the proposed method is studied by comparing with three different methods.

Application of intelligent models and spectrophotometry method for simultaneous determination of Dorzolamide and Timolol in ophthalmic dosage form

In this study, intelligent techniques including artificial neural network (ANN) with Levenberg Marquart (LM) algorithm, fuzzy inference system (FIS), and adaptive Neuro-fuzzy inference system (ANFIS) with the spectrophotometry method were used for simultaneous measurement of Dorzolamide (DOR) and Timolol (TIM) in the Zilomole eye drop. Among different layers and neurons that were investigated in the ANN model, layer = 5 with neuron = 4 and layer = 2 with neuron = 6 were selected as the best layers and neurons for DOR and TIM, respectively. Mean square error (MSE) of these layers was 1.09 × 10−29 and 6.77 × 10-30for DOR and TIM, respectively. On the other hand, the root mean square error (RMSE) of the FIS and ANFIS methods was obtained 0.632, 0.568 and 0.200, 0.094 for DOR and TIM, respectively. Comparison of the results of eye drops analysis with proposed methods and high-performance liquid chromatography (HPLC) as a reference method was performed by one-way analysis of variance (ANOVA) test at 95% confidence level. Statistical data showed no significant difference between them.

Efficient Parameters Estimation Method for the Separable Nonlinear Least Squares Problem

In this work, we combine the special structure of the separable nonlinear least squares problem with a variable projection algorithm based on singular value decomposition to separate linear and nonlinear parameters. Then, we propose finding the nonlinear parameters using the Levenberg–Marquart (LM) algorithm and either solve the linear parameters using the least squares method directly or by using an iteration method that corrects the characteristic values based on the L-curve, according to whether or not the nonlinear function coefficient matrix is ill posed. To prove the feasibility of the proposed method, we compared its performance on three examples with that of the LM method without parameter separation. The results show that (1) the parameter separation method reduces the number of iterations and improves computational efficiency by reducing the parameter dimensions and (2) when the coefficient matrix of the linear parameters is well-posed, using the least squares method to solve the fitting problem provides the highest fitting accuracy. When the coefficient matrix is ill posed, the method of correcting characteristic values based on the L-curve provides the most accurate solution to the fitting problem.

Comparison between UV/Vis spectrophotometry based on intelligent systems and HPLC methods for simultaneous determination of anti-diabetic drugs in binary mixture

In this study, the spectrophotometric method and intelligent chemometrics approaches, including artificial neural network (ANN) and least squares support vector machine (LS-SVM) were developed to determine metformin (MET) and sitagliptin (STG) in the pharmaceutical dosage form. Feed-forward backpropagation neural network (FFBP-NN) with Levenberg Marquart (LM) and conjugate gradient (SCG) algorithms was used. The results of ANN indicated that the LM algorithm with 3 layers and 6 neurons, as well as 5 layers and 8 neurons, had better performance with mean square error (MSE) of 9.12 × 10−29 and 3.56 × 10−29 for MET and STG, respectively. Also, layers 2 and 5 with the 8 neurons showed the least error for MET and STG in the scaled conjugate gradient (SCG) algorithm, respectively. Next, the least support vector machine method was used to estimate the mentioned components simultaneously. The regularization (γ) and width (σ) parameters of the LS-SVM method were optimized based on the leave-one-out (LOO) cross-validation method and the root mean square error (RMSE) of MET and STG were 0.4884 and 0.9336, respectively. Real pharmaceutical sample analysis was performed using the proposed methods and high-performance liquid chromatography (HPLC). One-way analysis of variance (ANOVA) test with a 95 % confidence level was applied to the results. Obtained statistical data from the comparison of the proposed methods with the reference technique showed no significant differences.

Parameter Self-Tuning PID Control for Greenhouse Climate Control Problem

The difficulty of the greenhouse climate control is the great uncertainties of the weather and greenhouse climate. Although many control approaches have been proposed to solve this problem, the structures of the controllers are usually complex, and the reliability of the controllers is usually not good in practice. Therefore, to improve the reliability of the controllers, this article proposes a parameter self-tuning PID control approach (STPID). In this PID control scheme, three environmental outputs including the inside temperature, humidity and CO2 concentration are firstly transformed into four equivalent unit outputs, and the equivalent outputs are controlled by four PID controllers respectively. Thus, each PID controller and the corresponding equivalent output construct a single closed-loop system, and the original system can be decoupled. To ensure the desired control performance, the Levenberg-Marquart (LM) algorithm is introduced to tune the PID parameters. Based on the real weather data, a simulation was performed to illustrate the effectiveness of the proposed method, and a comparison study was done to observe the performance of the proposed method. The results indicate that control performance is good.

Biosorption of chromium (VI) from aqueous solutions and ANN modelling.

The use of sustainable, green and biodegradable natural wastes for Cr(VI) detoxification from the contaminated wastewater is considered as a challenging issue. The present research is aimed to assess the effectiveness of seven different natural biomaterials, such as jackfruit leaf, mango leaf, onion peel, garlic peel, bamboo leaf, acid treated rubber leaf and coconut shell powder, for Cr(VI) eradication from aqueous solution by biosorption process. Characterizations were conducted using SEM, BET and FTIR spectroscopy. The effects of operating parameters, viz., pH, initial Cr(VI) ion concentration, adsorbent dosages, contact time and temperature on metal removal efficiency, were studied. The biosorption mechanism was described by the pseudo-second-order model and Langmuir isotherm model. The biosorption process was exothermic, spontaneous and chemical (except garlic peel) in nature. The sequence of adsorption capacity was mango leaf > jackfruit leaf > acid treated rubber leaf > onion peel > bamboo leaf > garlic peel > coconut shell with maximum Langmuir adsorption capacity of 35.7mgg-1 for mango leaf. The treated effluent can be reused. Desorption study suggested effective reuse of the adsorbents up to three cycles, and safe disposal method of the used adsorbents suggested biodegradability and sustainability of the process by reapplication of the spent adsorbent and ultimately leading towards zero wastages. The performances of the adsorbents were verified with wastewater from electroplating industry. The scale-up study reported for industrial applications. ANN modelling using multilayer perception with gradient descent (GD) and Levenberg-Marquart (LM) algorithm had been successfully used for prediction of Cr(VI) removal efficiency. The study explores the undiscovered potential of the natural waste materials for sustainable existence of small and medium sector industries, especially in the third world countries by protecting the environment by eco-innovation.

Prediction of Parameters of Soil Stratums and Earthen Dams from Free Field Acceleration Records

This paper is dedicated to the identification of parameters of soil stratums and earthen dams from accelerometer records by inverse analysis using three kinds of optimization algorithms. The first one is the Levenberg-Marquart (L-M) gradient-based method, the second one is based on a genetic algorithm (G-A) optimization process, and the third one combines the two search algorithms to complete the identification task more efficiently. The efficiency of the two first algorithms is studied by identifying the unknown parameters of a multilayer soil profile. Then, the global -local hybrid scheme is applied to identify the soil profile characteristics and determine some information gaps using experimental data recorded within the Adapazari city during the Kocaeli earthquake of August 17, 1999. Finally, the applicability of the proposed identification procedure is verified through comparison of the parameter identification results and experimental ones at Bradbury dam by using ground motions records during the 1978 Santa Barbara earthquake (in USA).

Fault and sensor error diagnostic strategies for a vapor compression refrigeration system by using fuzzy inference systems and artificial neural network

A fuzzy inference system (FIS) and an artificial neural network (ANN) were used for diagnosis of the faults of a vapor compression refrigeration experimental setup. A separate FIS was developed for detection of sensor errors. The fault estimation error of the FIS and ANN were evaluated by using the experimentally obtained sensor data. Separate FIS estimated the system faults and detected defective sensors in all test cases without any error. Levenberg Marquart (LM) type ANN algorithm was implemented to diagnose the system faults. Scaled conjugate gradient (SCG) and resilient backpropagation (RB) network type were also used to compare performances with the estimation of the LM algorithm. The LM type ANN estimated all fault conditions accurately in the test cases never observed before. The study demonstrated that the FIS and ANN could be used effectively to estimate the faulty conditions of the vapor compression refrigeration system.

Face Recognition Based on Improved Fuzzy RBF Neural Network for Smar t Device

Face recognition is a science of automatically identifying individuals based their unique facial features. In order to avoid overfitting and reduce the computational reduce the computational burden, a new face recognition algorithm using PCA-fisher linear discriminant (PCA-FLD) and fuzzy radial basis function neural network (RBFNN) is proposed in this paper. First, face features are extracted by the principal component analysis (PCA) method. Then, the extracted features are further processed by the Fisher's linear discriminant technique to acquire lower-dimensional discriminant patterns, the processed features will be considered as the input of the fuzzy RBFNN. As a widely applied algorithm in fuzzy RBF neural network, BP learning algorithm has the low rate of convergence, therefore, an improved learning algorithm based on Levenberg-Marquart (L-M) for fuzzy RBF neural network is introduced in this paper, which combined the Gradient Descent algorithm with the Gauss-Newton algorithm. Experimental results on the ORL face database demonstrate that the proposed algorithm has satisfactory performance and high recognition rate.

Impact of multi-resolution analysis of artificial intelligence models inputs on multi-step ahead river flow forecasting

Summary In this paper an attempt is made to show that the performance of daily river flow forecasting is improved when data-preprocessing techniques are used with computational intelligence methods. Especially for forecasting longer lead-times, one of the inherent problems in all forecasting methods is that the reliability of forecasting decreases with increasing the lead-time. Therefore wavelet multi-resolution analysis is coupled with artificial neural networks (ANN) and adaptive neuro-fuzzy interface system (ANFIS) which are two promising methods for forecasting nonlinear and non-stationary time series. Different models with a combination of the different input data sets are developed for 1, 2, 3, 4 and 5 days ahead forecasting in Harvey River, Western Australia. Daubechies and Symlet wavelets are used to decompose river flow time series to different levels. Hybrid wavelet neural networks (WNN) models are trained using Levenberg–Marquart (LM) algorithm and the wavelet neuro-fuzzy (WNF) models with subtractive clustering method to find the optimum number of fuzzy rules. Comparing the results with those of the original ANN and ANFIS models indicates that the hybrid models produce significantly better results, especially for the peak values and longer lead-times.

Simultaneous determination of iron and manganese in water using artificial neural network catalytic spectrophotometric method

A new analytical method using Back-Propagation (BP) artificial neural network and kinetic spectrophotometry for simultaneous determination of iron and magnesium in tap water, the Yellow River water and seawater is established. By conditional experiments, the optimum analytical conditions and parameters are obtained. Levenberg-Marquart (L-M) algorithm is used for calculation in BP neural network. The topological structure of three-layer BP ANN network architecture is chosen as 15-16-2 (nodes). The initial value of gradient coefficient µ is fixed at 0.001 and the increase factor and reduction factor of µ take the default values of the system. The data are processed by computers with our own programs written in MATLAB 7.0. The relative standard deviation of the calculated results for iron and manganese is 2.30% and 2.67% respectively. The results of standard addition method show that for the tap water, the recoveries of iron and manganese are in the ranges of 98.0%–104.3% and 96.5%–104.5%, and the RSD is in the range of 0.23%–0.98%; for the Yellow River water (Lijin district of Shandong Province), the recoveries of iron and manganese are in the ranges of 96.0%–101.0% and 98.7%–104.2%, and the RSD is in the range of 0.13%–2.52%; for the seawater in Qingdao offshore, the recoveries of iron and manganese are in the ranges of 95.3%–104.8% and 95.3%–104.7%, and the RSD is in the range of 0.14%–2.66%. It is found that 21 common cations and anions do not interfere with the determination of iron and manganese under the optimum experimental conditions. This method exhibits good reproducibility and high accuracy in the determination of iron and manganese and can be used for the simultaneous determination of iron and manganese in tap water and natural water. By using the established ANN-catalytic spectrophotometric method, the iron and manganese concentrations of the surface seawater at 11 sites in Qingdao offshore are determined and the level distribution maps of iron and manganese are drawn.

ANN model of RF MEMS Lateral SPDT switches for millimeter wave applications

This paper presents Artificial Neural Network (ANN) implementation for the Radio Frequency (RF) and Mechanical modeling of lateral RF Micro Electro Mechanical System (MEMS) series micro machined Single pole double through (SPDT) switch. We propose an efficient approach based on ANN for analyzing the losses in ON and OFF state of lateral RF MEMS series switch by calculating the S-parameters. The double beam structure has been analyzed in terms of its return, isolation and insertion losses with the variation of its passive circuit component values. The effect of design parameters has been analyzed and the lateral switch was realized with low insertion loss, high return and isolation losses. ANN model were trained with five different training algorithms namely Levenberg-Marquart (LM), Bayesian Regularization (BR), Quasi - Newton (QN), Scaled Conjugate Gradient (SCG) and Conjugate Gradient of Fletcher - Powell (CGF) to obtain better performance and fast convergence. The results from the neural model trained by Levenberg-Marquardt back propagation algorithm are highly agreed with the theoretical results available in the literature. The neural networks shows the better results with the highest correlation coefficient which measures the strength and direction of linear relation between two variables (actual and predicted values) (0.9998) along with lowest root mean square error (MSE) of (0.0039).

A DIFFERENT APPROACH on SPATIAL PERCEPTION

In this study, an experimental study was conducted with 4th grade students at classroom teaching department in Turkey in an attempt to describe the ideal classroom space for primary education students. In the research, photographs (images) of 20 different primary education classrooms were evaluated by 4th grade 100 students. The students evaluated the images by means of surveys in which they were asked questions on four concepts: belonging, like (partiality), learning and safety. Reliability analyses of numeric data obtained from student surveys were made and they were subjected to various statistical analyses. In the second part of the study, the students' preferences for the classroom spaces were evaluated by means of Artificial Neural Networks (ANN) method, by using numerical data obtained from the student about concepts as well as the classroom space photos. Levenberg-Marquart (LM) back-propagation algorithm has been used to train ANN model. Numerical data were treated and test procedures were performed to ensure that ANN makes decisions in the name of 4th grade students at classroom teaching department. It has been seen that ANN has been successful on solving complex problems such as user-perception evaluations thanks to its dynamic structure.

Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials

This paper considers the implementation of Bezier–Bernstein polynomials and the Levenberg–Marquart algorithm for identifying multiple-input single-output (MISO) Hammerstein models consisting of nonlinear static functions followed by a linear dynamical subsystem. The nonlinear static functions are approximated by the means of Bezier curves and Bernstein basis functions. The identification method is based on a hybrid scheme including the inverse de Casteljau algorithm, the least squares method, and the Levenberg–Marquart (LM) algorithm. Furthermore, results based on the proposed scheme are given which demonstrate substantial identification performance.

Simultaneous determination of calcium and magnesium in water using artificial neural network spectro-photometric method

A new analytical method using Back-Propagation (BP) artificial neural networks and spectrophotometry for simultaneous determination of calcium and magnesium in tap water, the Yellow River water and seawater is established. By condition experiment, the optimum analytical conditions for calcium, magnesium and Arsenazo (III) color reactions are obtained. Levenberg-Marquart (L-M) algorithm is used for calculation in BP neural network. The topological structure of three-layer BP ANN network architecture is chosen as 11-10-2 (nodes). The initial value of gradient coefficient μ is fixed at 0.001 and the increase factor and reduction factor of μ take the default values of the system. The data are processed by computers with our own programs written in MATLAB 7.0. The relative standard deviations of the calculated results for calcium and magnesium are 2.31% and 2.14%, respectively. The results of standard addition method show that the recoveries of calcium and magnesium are 103.6% and 100.8% in the tap water, 103.2% and 96.6% in the Yellow River water (Lijin district of Shandong Province), and 98.8%–103.3% and 98.43%–103.4% in seawater from Jiaozhou Bay of Qingdao. It is found that 14 common cations and anions do not interfere with the determination of calcium and magnesium under the optimum experimental conditions. The comparative experiments do not show any obvious difference between the results obtained by this new method and those obtained by the classical complexometric titration method in seawater medium. This method exhibits good reproducibility and high accuracy in the determination of calcium and magnesium and can be used for the simultaneous determination of Ca2+ and Mg2+ in tap water and natural water.

Daily river flow forecasting using wavelet ANN hybrid models

Advance time step stream flow forecasting is of paramount importance in controlling flood damage. During the past few decades, artificial neural network (ANN) techniques have been used extensively in stream flow forecasting and have proven to be a better technique than other forecasting methods such as multiple regression and general transfer function models. This study uses discrete wavelet transformation functions to preprocess the time series of the flow data into wavelet coefficients of different frequency bands. Effective wavelet coefficients are selected from the correlation analysis of the decomposed wavelet coefficients of all frequency bands with the observed flow data. Neural network models are proposed for 1-, 2- and 3-day flow forecasting at a site of Brahmani River, India. The effective wavelet coefficients are used as input to the neural network models. Both the wavelet and ANN techniques are employed to form a loose type of wavelet ANN hybrid model (NW). The hybrid models are trained using Levenberg–Marquart (LM) algorithm and the results are compared with simple ANN models. The results revealed that the predictabilities of NW models are significantly superior to conventional ANN models. The peak flow conditions are predicted with better accuracy using NW models than compared to ANN models.