Nelder-Mead Optimization Method Research Articles

Radicals ([rad]OH, Cl[rad], ClO[rad] and Cl2[rad]−) concentration profiles in the intensified degradation of reactive green 12 by UV/chlorine process: Chemical kinetic analysis using a validated model

Understanding the production of reactive species in chlorine photolysis is critical for applying advanced oxidation processes (AOPs) in future. This paper developed a chemical kinetic model consisting of 66 chemical reactions, including many radicals and non-radical intermediates/products, to elucidate the intensified removal of reactive green 12 (RG12) dye by UV/chlorine AOP. The generated kinetic model fits our experimental data satisfactorily across a broad range of solution pH and initial chlorine concentration. The simulation process was accomplished by COPASI® software coupled with the deterministic Nelder-Mead optimization method for determining some unavailable rate constants, including the reaction of RG12 with OH (k = 1.2 × 1010 M−1 s−1), Cl (k = 2.1 × 109 M−1 s−1), Cl2− (k = 1.26 × 107 M−1 s−1) and ClO (k = 6.12 × 104 M−1 s−1). As well, the first-order rate constants of chlorine photolysis, HOCl + hv → OH + Cl and OCl− + hv → O− + Cl, were respectively (0.81–6.90) × 10−3 s−1 and (0.87–8.29) × 10−3 s−1, depending on the solution pH and chlorine dosage. The radicals concentration (and RG12 degradation rate) increased with the increase of initial chlorine dosage, whereas a solution pH of 5 is recorded for the best process efficiency (i.e., radicals’ yield and dye destruction rate). Even though the steady-state concentration of ClO (∼10−8 M) and Cl2− (∼10−11 M) are highest compared to OH (∼10−12 M) and Cl (∼10−12 M), the selectivity analysis results showed that OH radicals contributed majorly in the degradation (∼85 %) for the different investigated scenarios of pH and initial chlorine concentration. The remaining portion (∼15 %) is ensured by Cl and ClO nearly equitably. These findings were attributed to the high reactivity of RG12 toward OH rather than reactive chlorine radicals, as reflected by the initial rates of the different RG12-degradation by-products.

A new data-driven framework for prediction of molten pool evolution and lack of fusion defects in multi-track multi-layer laser powder bed fusion processes

This study proposes a new data-driven approach to predict the area fraction of lack of fusion and morphology of 3D-printed parts produced using the laser powder bed fusion process. Different processing parameters were considered to develop this methodology, such as laser power, laser speed, hatch spacing, and layer thickness. Melt pool geometrical parameters were numerically predicted using a mathematical model optimized using the Nelder-Mead optimization method and a machine learning model. The Gaussian process was later employed to further modify the layerwise deposition. The accuracy of the proposed methodology was then extended to predictions of the area fraction of lack of fusion and the morphological aspects of the melt pools in 3D-printed parts by comparing them with the experimental observations. The results revealed that this data-driven approach, which is independent of the thermophysical properties of the material, is capable of reasonably predicting the area fraction of lack-of-fusion formed during material deposition using the laser powder bed fusion process.

Design and fused filament fabrication of multilayered microchannels for subwavelength and broadband sound absorption

A comprehensive procedure to design and manufacture multilayered microchannels presenting competitive mechanical properties, effective subwavelength and near perfect broadband sound absorption in targeted frequency ranges is presented. The acoustic properties of microchannels are predicted with the Johnson-Champoux-Allard-Lafarge (JCAL) model. The JCAL parameters are calculated with the Two-scale Asymptotic Method (TAM) and the sound absorption coefficient of multilayered microchannels is simulated with the transfer matrix method (TMM). The simplex Nelder-Mead optimization method is used to find the size of the channels and the stacking sequence leading to effective acoustic absorption for three different frequency ranges (500–2400 Hz, 2400–6500 Hz and 500–6500 Hz). 30 mm-thick samples with up to 30-layers of unobstructed and non interconnected channels and microchannels were successfully produced via fused filament fabrication (FFF). The minimum channel size is ~ 100 µm which is very appropriate to produce micro-perforated panels or acoustic liners with optimal absorption and different degrees of freedom. Multilayered microchannels with absorption average up to 0.87 and noise reduction coefficient (NRC) up to 0.49 were produced. The multilayered microchannels offer a good compromise between effective acoustic properties and useful mechanical properties compared to other 3D printed acoustic structures and can be considered as viable candidates for applications where structural resistance is required. • Multilayered microchannels with high broadband sound absorption at three frequency ranges are presented. • Innovative FFF manufacturing technique allows production of 100 μm perforations and structure with up to 30-layer. • 30mm-thick multilayered microchannels present sound absorption average up to 0.87. • PLA 3D printed multilayered microchannels exhibit up to 468MPa compressive modulus and 9MPa compressive yield strength.

Evolution of COVID-19 Disease Using a One Prey-Two Predator Mode

Mathematical modeling is used to understand the dynamics of transmission of infectious diseases such as COVID-19, SARS, Ebola, and Dengue among populations. In this work, a one prey-two predator model has been developed to understand the underlying dynamics of COVID-19 disease transmission. We considered the infected, recovered, and death populations with the fact that an infected person can be transformed into the recovered or death group assuming that the infected ones are the prey, and the other two populations are the two predators in the one prey-two predator model. It was found that the proposed model has four equilibrium points; the vanishing equilibrium point ( ), recovered and death-free equilibrium point ( ), recovered population-free equilibrium point ( ), and the death-free equilibrium point ( ). Stability analysis of the equilibrium points shows that except all the other equilibrium points are locally asymptotically stable. Global asymptotic stability of the recovered population-free equilibrium point and death-free equilibrium point are also analyzed. Moreover, the existence and uniqueness of the solution were proved. The parameters for the model are estimated from a data set that consists of the total number of infected, recovered, and dead populations worldwide in the year 2020 using the Nelder-Mead optimization method. When the time approaches infinity, the infected population converges to a constant value, the recovered population declines and reaches zero, and the death population attains a constant value. However, some modifications to the system are needed. In future work, measures such as health precautions, vaccinations are needed to be considered for the formulation of the mathematical model.

MANAGING THE CAPACITY OF INTERMEDIATE POINTS IN AN EXTENSIVE TRANSPORT NETWORK

Relevance. A special case of a transport problem with intermediate points, when the throughput capacity of these points is not specified, is considered, which is important for practice. Purpose. The problem of finding an unknown distribution of the throughput capacity in intermediate points, which minimizes the total transport costs, is formulated. Method. Two methods for solving the problem are proposed. The first one implements an iterative procedure for improving the initial plan for dual model of original problem. The computational scheme at each iteration is a two-step one. At the first step of iteration, a coordinating problem is solved, the solution of which sets the next set of values for throughput of intermediate points. In the second step, this set is used to solve the original transport problem. The resulting solution is tested for optimality. If it is not optimal, then transition to the next iteration is performed. To implement proposed computational scheme, the Nelder-Mead zero-order optimization method was used. Tasks. Statement of problem for controlling the throughput capacities of intermediate points in triaxial transport problem. The developed method has high performance due to the use of the structural decomposition of problem. The method has low computational complexity, which is a significant advantage for practical application. Results. The constructive possibility use of this method has been proved, taking into account a large number of transport-type restrictions. In order to simplify the technology for solving transport problems at each iteration of the algorithm, their dual models are introduced. Due to the fact that computational complexity of proposed method grows rapidly with an increase in the number of intermediate points, a simple alternative approximate method for solving the problem is proposed. Conclusions. The proposed method solves problem of calculating the throughput of intermediate points in "production - delivery - consumption" system.

Reconstruction of strains with a non-smooth distribution using optical fiber Bragg grating

The paper presents a reconstruction of strains with a non-smooth distribution affecting the optical fiber Bragg grating based on its reflection intensity spectrum. The reconstruction was performed for a grating strained along 0.25, 0.5 and 0.75 of its length. The transition matrix method and the Nelder-Mead nonlinear optimization method were used for this purpose. The results of simulations and reconstruction of the strain profile indicate good consistency with the original strain profiles. Reconstruction errors of these profiles are within the single digit percentage range. For a grating strained along 0.5 or 0.75 of its length, the error does not exceed 0.34% when the reconstruction is based on a simulated reflection spectrum; the use of a measured spectrum results in an error of up to 2.2%.

Polarization-Independent Circulator Based on Composite Rod of Ferrite and Plasma in Photonic Crystal Structure.

We propose a type of polarization-independent circulator based on a composite rod of ferrite and plasma materials in a two-dimensional photonic crystal (PhC) slab. Only one composite rod was set at the center of the structure to provide circulation for both TE- and TM-polarized waves. Additionally, to improve the performance of the circulator, three additional rods were inserted to improve the coupling condition between the center magneto-optical microcavity and the corresponding waveguides. Finite element method was used to calculate the characteristics of the structure and the Nelder–Mead optimization method was employed to obtain the optimum parameters. The results show that a low insertion loss (~0.22 dB) and high isolation (~14 dB) can be achieved in our structure for waves of both TE and TM polarizations. The idea presented here may be useful for designing compact polarization devices in large-scale integrated photonic circuits.

Modeling Grounding Systems Response to Current Impulses Considering Nonlinear Effects

Modeling grounding systems is necessary for the calculation of ground potential rise (GPR), power system simulations and insulation coordination studies. In this work, a methodology for estimating equivalent circuit parameters through the optimization of the time-domain impulse response was developed. It allows to obtain equivalent circuits with positive parameters that accurately represent grounding systems considering both effects related to frequency and soil ionization. Additionally, linear and nonlinear equivalent circuits for calculating the impulse response of typical grounding systems were proposed. The Nelder-Mead optimization method was applied to adjust the circuit parameters. For evaluating the methodology developed and the proposed models, data from impulse current tests was used. It was found that the use of nonlinear circuits increases the accuracy of the simulated response, resulting in errors of less than 4% in the estimation of GPR. The proposed methodology allows obtaining representative circuits of typical grounding systems used in the electrical system. The circuits can be used for systemic studies and calculation of GPR considering short-circuit or lightning currents.

Determination of single-phase transformer saturation characteristic by using Nelder–Mead optimization method

Correctly modelling the nonlinear saturation characteristics of the transformer iron core is of great importance in steady-state calculations (harmonics and power quality) and calculations of the electromagnetic transients (inrush current, ferroresonance, temporary overvoltages). Thus, this paper presents an original estimation algorithm for determining the transformer nonlinear saturation characteristic from the measured inrush and steady-state current waveforms in entire windows of occurrences. The proposed algorithm is based on the minimization of a specifically defined cost function by applying the Nelder–Mead method, which was used to create a balance between the transformer steady-state current and the inrush current at zero residual flux. The algorithm uses the BDF numerical method in the background to solve the stiff differential equation system. By applying the appropriate indexes of quality estimation, it was demonstrated that, out of a total of twelve proposed analytical functions, the best optimization results were achieved with three proposed functions (the Frolich extended, three-term polynomial and special hyperbolic function). Detailed performances and accuracy suggested that the estimation algorithm has been verified by a very close agreement between the simulation results and measured transformer current waveforms in the steady-state and different inrush current scenarios.

Method for hyperparameter tuning in machine learning tasks for stochastic objects classification

Subject of Research. The paper presents a simple and practically effective solution for hyperparameter tuning in classification problem by machine learning methods. The proposed method is applicable for any hyperparameters of the real type with the values which lie within the known real parametric compact. Method. A random sample (trial network) of small power is generated within the parametric compact, and the efficiency of hyperparameter tuning is calculated for each element according to a special criterion. The efficiency is estimated by the value of a real scalar, which does not depend on the classification threshold. Thus, a regression sample is formed, the regressors of which are the random sets of hyperparameters from the parametric compact, and regression values are classification efficiency indicator values corresponding to these sets. The nonparametric approximation of this regression is constructed on the basis of the formed data set. At the next stage the minimum value of the constructed approximation is determined for the regression function on the parametric compact by the Nelder-Mead optimization method. The arguments of the minimum regression value appear to be an approximate solution to the problem. Main Results. Unlike traditional approaches, the proposed approach is based on non-parametric approximation of the regression function: a set of hyperparameters – classification efficiency index value. Particular attention is paid to the choice of the classification quality criterion. Due to the use of the mentioned type approximation, it is possible to study the performance indicator behavior out of the trial grid values (“between” its nodes). As it follows from the experiments carried out on various databases, the proposed approach provides a significant increase in the efficiency of hyperparameter tuning in comparison with the basic variants and at the same time maintains almost acceptable performance even for small values of the trial grid power. The novelty of the approach lies in the simultaneous use of non-parametric approximation for the regression function, which links the hyperparameter values with the corresponding values of the quality criterion, selection of the classification quality criterion, and search method for the global extremum of this function. Practical Relevance. The proposed algorithm for hyperparameters tuning can be used in any systems built on the principles of machine learning, for example, in process control systems, biometric systems and machine vision systems.

Magnetorheological elastomer peristaltic pump capable of flow and viscosity control

In this article, a magnetorheological elastomer peristaltic pump capable of bidirectionally conveying Newtonian and non-Newtonian fluids with precise net pumped volume and required viscosity patterns of fluids is presented and numerically investigated. The basic element is very succinct, which is composed of only a magnetorheological elastomer tube and an electromagnet. Two basic elements in series constitute a magnetorheological elastomer peristaltic pump. The maximum pumped volume can be achieved using maximum lag between voltage parameters gap1 and gap2. The Nelder–Mead optimization method is applied to realize the precise control of the net pumped volume during a steady working cycle. For a certain net pumped volume, the viscosity of fluids can also be adjusted through the modulation of the driving voltage parameters obtained from the Nelder–Mead optimization method.

Improved models for the prediction of asphalt binder dynamic shear modulus and phase angle

In this paper, new set of models for predicting the dynamic shear modulus and phase angle of asphalt binders from conventional viscosity are developed and presented. Based on theoretical considerations, suitable forms of general logistic functions are introduced to develop new models for binder dynamic shear modulus and phase angle over a wide range of temperature and loading conditions. A nonlinear optimization technique based on the Nelder-Mead optimization method is used to obtain the coefficients for the new binder dynamic shear modulus and phase angle models. The experimental binder testing database consisting of dynamic shear modulus, phase angle, frequency, viscosity measurements of thirty-two (32) unmodified and nine (9) modified binders from different sources is used in the study. A total of 7, 120 binder data points are used for the model development, evaluation and validation. The new models deliver very accurate prediction of the binder dynamic shear modulus and phase angle from the conventional steady-state viscosity indicated by very high goodness of fit using 7,120 binder data points. A new parameter termed the “reduced viscosity” is identified which produces a smooth continuous function of the binder phase angle for both modified and unmodified binders using a single viscosity shift factor. The reduced viscosity is considered as the independent variable in the new dynamic shear modulus and phase angle predictive models.

Optimization of TIG Welding Parameters Using a Hybrid Nelder Mead-Evolutionary Algorithms Method

A number of evolutionary algorithms such as genetic algorithms, simulated annealing, particle swarm optimization, etc., have been used by researchers in order to optimize different manufacturing processes. In many cases these algorithms are either incapable of reaching global minimum or the time and computational effort (function evaluations) required makes the application of these algorithms impractical. However, if the Nelder Mead optimization method is applied to approximate solutions cheaply obtained from these algorithms, the solution can be further refined to obtain near global minimum of a given error function within only a few additional function evaluations. The initial solutions (vertices) required for the application of Nelder-Mead optimization can be obtained through multiple evolutionary algorithms. The results obtained using this hybrid method are better than that obtained from individual algorithms and also show a significant reduction in the computation effort.

Optimization of catenary risers with hydrodynamic dampers

This study presents an optimization process on the design of an improved steel catenary riser configuration with hydrodynamic dampers that seek to minimize the effects caused by compression waves along the risers. The dimensions and positioning of these dampers are obtained using the Globalized Bounded Nelder–Mead optimization method (GBNM). This method requires no gradient and is proved to be capable of identifying the best feasible riser configurations according to a specific performance criteria. A case study addresses the operational viability of the catenary riser with hydrodynamic dampers (CRHD) in an effort to reduce its material cost and improve its structural behavior. A nonlinear dynamic finite element analysis is necessary to evaluate the mechanical behavior of each candidate configuration, which makes the optimization process computationally expensive. As such, we discuss ways of improving the overall efficiency of the method by reducing the number of analyzed configurations.

Improved Nelder-Mead Optimization Method in Learning Phase of Artificial Neural Network

It is difficult to find the optimum weight values of artificial neural networks for optimization problem. In this study, Nelder-Mead optimization method [17] has been improved and used for determining the optimal values of weights. The results of the proposed improved Nelder-Mead method are compared with results of the standard Nelder-Mead method which is used in ANNs learning algorithm. The most common data sets are taken from UCI machine learning repository. According to the experimental results, in this study better results are achieved in terms of speed and performance.

Spring Inserts for the Intensification of the Heat Exchange Process during Boiling in Vertical Tubes—Optimization of Geometric Parameters

The paper presents new criteria for calculation of heat transfer coefficients and flow resistance during boiling inside vertical tubes with spring inserts, developed on the basis of own experimental research. Calculations of the geometric parameters of the spring insert were carried out using the Nelder-Mead optimization method for various optimization criteria (maximizing the increase ratios for heat transfer coefficient and flow resistance, minimizing entropy, own optimization criterion). The results of optimization calculations were verified by the optimization procedures available in Statistica.

Polarization-independent circulator based on ferrite and plasma materials in two-dimensional photonic crystal

We propose a type of polarization-independent circulator based on ferrite and plasma materials in a two-dimensional photonic crystal (PhC) slab. First, on the basis of analyzing the wave equations in ferrite and plasma materials, TE and TM circulators are realized with ferrite and plasma in PhCs, respectively. Then, by properly combining these two types of circulators together, a polarization-independent circulator is achieved and investigated. The results show that, for both polarizations, the insertion loss and isolation for the polarization-independent circulator are less than 0.15 dB and more than 20 dB, respectively. Finite-element method is used to calculate the characteristics of the circulators and Nelder-Mead optimization method is employed to obtain the optimized parameters. The idea presented here may have potential applications in integrated photonic circuits and devices.

Optimization of PI Coeffecients of Permanent Magnet Synchronous Motor Drive

Background/Objective: This paper enhances the responses of Permanent Magnet Synchronous Motor (PMSM) drive system with design of PI controller based on Nelder-Mead optimization Method implemented in Matlab environment and Optimization Toolbox. Methods/Statistical Analysis: The minimization requirements on control quality such as overshoot, settling time and steady-state error have been realized by choosing objective function based on ITAE criterion. The speed error for control of the speed of PMSM based on field oriented control is considered for implementation of ITAE criterion. Findings: The standard AC6 model (Field oriented control of PMSM drive) of MATLAB Simpower system is analyzed for optimal design of the coefficients of the PI controller. Improvements: The effectiveness of responses of torque, current and speed tracking are verified with random PI and optimized PI coefficients.

Nonlinear model predictive control based on Nelder Mead optimization method

In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm.

Compact, low-loss and broadband photonic crystal circulator based on a star-type ferrite rod

Abstract We propose and investigate a compact, low-loss and broadband circulator based on a star-type ferrite rod in two-dimensional square-lattice photonic crystals. Only one ferrite rod is required to be inserted in our structure. Firstly, the performances of circulator based on the star-type, circle, and square ferrite rod are compared, showing that the circulator with the star-type ferrite rod performs better than the other two ones. And then, based on the star-type ferrite rod circulator, four cases of improvement, in which the background rods around the center ferrite rod are replaced respectively by the backward-triangle, forward-triangle, backward-semicircle, and forward-semicircle rods, are investigated to modulate the coupling between the center magneto-optical micro-cavity and the corresponding waveguides. The results show that, with proper parameters, all the four cases can greatly improve the output properties of the circulator, and different cases have its own advantages. The mechanism behind these improvements is also discussed. Finite-element method is used to calculate the characteristics of the circulator and Nelder-Mead optimization method is employed to obtain the optimized parameters. The ideas presented here are useful for designing broadband, low insertion loss, and high-isolation circulators which have potential application in integrated photonic crystal devices.