Mead Method Research Articles

An explainable hybrid framework for estimating daily reference evapotranspiration: Combining extreme gradient boosting with Nelder-Mead method

Accurate estimation of reference evapotranspiration (ETo) is essential for effective water resources management, irrigation system design, and various hydrological and agricultural applications. This study employed extreme gradient boosting (XGBoost) model, signal decomposition techniques, and XGBoost coupled with Nelder–Mead (NM) method to enhance ETo prediction across two meteorological stations in Iran. This study proposed a novel framework which lies in its comprehensive integration of advanced techniques to create a model that is both interpretable and highly accurate for ETo estimation. For this aim, sixty meteorological variables were categorized into solar and cloud-based, temperature-based, wind and humidity-based, and pressure-based groups to analyze their effect on ETo estimation. Feature selection methods, including the Gradient Boosting Machine, Kendall’s Tau, and Relief Algorithm, were employed to identify the most influential predictors. Variables with normalized weights equal to or greater than 0.9 were selected for model input, resulting in the top 10% of variables being utilized. The XGBoost models were then developed using these selected inputs (level 1), a wavelet-based hybrid was developed according to the most effective features (level 2), and the XGBoost model was coupled by NM algorithm (level 3) for ETo estimation. Results of estimated ETo by levels 1 to 3 were compared with four common empirical approaches. The results indicated that Kendall’s Tau-based feature selection provided the most accurate predictions in Shiraz, achieving an RMSE of 0.721 (mm/day) for solar and cloud-based variables during the test phase. Additionally, the application of wavelet analysis further refined the model inputs, which enhanced ETo estimation in most variable groups. Integrating the NM algorithm with XGBoost demonstrated significant improvements in ETo estimation, where it could improve RMSE to 0.091 and 0.155 (mm/day) for testing section in Fasa and Shiraz, respectively.

Characterization and modelling of the damping properties of composite structures based on flax fibers

In this paper, an experimental-numerical modelling is proposed to determine the damping properties of composite structures based on flax fibers. Assuming that these properties are due to a viscoelastic behavior of each layer and each direction of these structures, three viscoelastic models were considered : the Maxwell-type Zener (ZM) model, the generalized Maxwell (GM) model, and the fractional derivative Zener (ZF) model. As well known, the viscoelastic models involve complex modulus and frequency dependence. So, the free vibration problem of these composite structures is complex and non-linear one. This nonlinear problem is solved by an high order Newton method (HON method) which permits to determine damping properties (damped frequency and the structural loss factor). Using experimental tests, an identification method, based on the HON and the Nelder–Mead methods, is applied to identify the rheological parameters of the proposed viscoelastic models. The comparison between experimental and numerical results demonstrates the efficiency of the proposed experimental–numerical method : all parameters for the three models are successfully identified. From, the results, only the GM or ZF models seem to be suitable for representing the viscoelastic behavior of flax/epoxy composite structures.

Parameter Extraction for a SPICE-like Delphi4LED Multi-Domain Chip-Level LED Model with an Improved Nelder–Mead Method

Parameter Extraction for a SPICE-like Delphi4LED Multi-Domain Chip-Level LED Model with an Improved Nelder–Mead Method

A hybrid The Dwarf Mongoose Optimization Algorithm with Nelder- Mead method and its application for allocation reliability

The Dwarf Mongoose Optimization Algorithm (DMO) is inspired by the behaviour of Dwarf Mongoose which can strike the ideal balance throughout research between exploration and exploitation. In this article, we combine algorithms of the Dwarf Mongoose Optimization Algorithm and the Nelder-Mead Algorithm (DMONM). In addition, the statistically evaluated functions is utilized by calculating the average and the standard deviation values that are used to validate the suggested algorithm's performance. The experimental results are on high-efficiency optimization functions with various dimensions. The hybrid algorithm produces good, encouraging, and better outcomes than the original algorithms. The results show that the proposed algorithm could enhance the effects of DMO when it used to solve the optimization issues of the multi-objective reliability system

Autonomous hybrid optimization of a SiO2 plasma etching mechanism

Computational modeling of plasma etching processes at the feature scale relevant to the fabrication of nanometer semiconductor devices is critically dependent on the reaction mechanism representing the physical processes occurring between plasma produced reactant fluxes and the surface, reaction probabilities, yields, rate coefficients, and threshold energies that characterize these processes. The increasing complexity of the structures being fabricated, new materials, and novel gas mixtures increase the complexity of the reaction mechanism used in feature scale models and increase the difficulty in developing the fundamental data required for the mechanism. This challenge is further exacerbated by the fact that acquiring these fundamental data through more complex computational models or experiments is often limited by cost, technical complexity, or inadequate models. In this paper, we discuss a method to automate the selection of fundamental data in a reduced reaction mechanism for feature scale plasma etching of SiO2 using a fluorocarbon gas mixture by matching predictions of etch profiles to experimental data using a gradient descent (GD)/Nelder–Mead (NM) method hybrid optimization scheme. These methods produce a reaction mechanism that replicates the experimental training data as well as experimental data using related but different etch processes.

Example of Using Particle Swarm Optimization Algorithm with Nelder–Mead Method for Flow Improvement in Axial Last Stage of Gas–Steam Turbine

Example of Using Particle Swarm Optimization Algorithm with Nelder–Mead Method for Flow Improvement in Axial Last Stage of Gas–Steam Turbine

Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection

Jeffrey fluid flow past an inclined stretchable sheet affected by magnetic dipole and suction/injection was investigated. The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. Considering the prescribed surface temperature (PST) and prescribed heat flux (PHF) heat processes, the effect of inclination angle, the Grashof number, and other parameters on the velocity and temperature of the fluid were documented by graphs and tables. Without the angle of inclination, the solutions from this paper were found to agree with those of the Generic algorithm and Nelder Mead method. The fluid is slower when the plate is inclined at a larger angle and this tends to allow for higher fluid temperature. The ferromagnetic interaction parameter and the ratio of relaxation to retardation time have the same effect on fluid velocity and temperature as the angle of inclination. The suction parameter and Prandtl number amplify the Nusselt number, while, as the suction increases, the skin friction increases for all inclination angles. With these results, engineers in chemical/polymer industries can make appropriate changes that can lead to more quality production.

Automatic peak annotation and area estimation of glycan map peaks directly from chromatograms

AbstractThe present bottleneck in biosimilar bioprocess development has become evaluation of analytical results, due to recent advances in analytics, such as automated sample preparation and development of high‐throughput methods. Currently automated chromatogram integration and annotation is only efficient for simple chromatograms. In an ever more competitive field of biosimilars, this represents a serious drawback because chromatographic analytical methods that provide some of the most valuable physicochemical quality attributes of the product also require careful chromatogram integration and annotation. This work focuses on the glycan mapping analytical method as utilized in development of monoclonal antibody biosimilars, evaluating more than 2000 chromatograms spanning the life cycle of multiple biosimilar development projects. It proposes a modified workflow by implementing automatic machine learning algorithms to determine the proportion of specific relevant glycan species in a sample directly from the chromatogram. Data preparation and analysis is performed using a pipeline approach. Pipeline is a modular design of data processing where signal “travels” through various active modules in a series. Each module performs a specific function or transformation on the signal and propagates the transformed signal to the next module. The pipeline is designed in a way that modules can be independently improved and exchanged. Module functions currently implemented are chromatogram resampling by spline interpolation, baseline removal by asymmetric least squares, peak alignment using parametric time warping, and quantification of the relative proportion of a glycan species using partial least squares regression. Hyper‐parameters of the pipeline are then optimized using the Nelder–Mead method. The approach stands out for its ability to accommodate a broad landscape of samples, covering multiple different proteins in different stages of biosimilar development, analyzed using different adaptations of the glycan map analytical method. The pipeline presents an intuitive, flexible, and creatively simple method design capable of providing reliable results for a wide range of glycan species essential for biosimilar development. It enables transparent, faster, and less subjective evaluation of analytic raw data (from sample to result). Furthermore, our automated approach maintained an accuracy comparable with manual integration thus demonstrating its readiness for implementation in the conservative and highly regulated environment. The presented methodology reduces the cost and time of biosimilar development and should be applicable for any chromatogram‐based analytical method.

Incoherent Shallow-Water Seabed Logging Using Numerical-Model-Based Optimization for the Prediction of Unperturbed UEP Signatures

Underwater electric potential (UEP) ship signatures are evaluated at a test site that provides only incoherent data from electric field sensors placed on the seabed. This paper shows how these data sets can be used to extract significant seabed parameters, which are evaluated by a numerical model combined with an optimization process in the frequency range from 1 Hz up to 100 kHz. This is in contrast to the controlled electromagnetic source technology used by geophysicists, which has to track both phase and amplitude, and, therefore, cannot simply be applied to data from per se stationary systems. Using the aforementioned frequency range within COMSOL Multiphysics (v6.0), the finite-element-based simulation software, a sensitivity analysis of seabed parameter behavior within a seabed depth range from 1 m to 20 m is evaluated for the highest sensitivity for each of the measurable field amplitudes of the locally available sensors. From this, the electrical conductivities of two seabed layers and the depth of the first layer can be extracted using a combination of a genetic algorithm and the Nelder–Mead method. In summary, phase information is not required to characterize the stratified seabed, providing a cost-effective approach to obtaining effective environmental conditions for free-water signature calculations.

A battery capacity estimation method based on the equivalent circuit model and quantile regression using vehicle real-world operation data

Battery capacity estimation is critical for evaluating the battery performance and safety. Currently, the sampling interval of battery operation data on the cloud is 10–30 s, and relatively poor data quality poses difficulties in battery capacity estimation. In this study, a battery capacity estimation method is proposed based on the battery equivalent circuit model and a quantile regression method using real-world vehicle operation data on the cloud. The battery parameters were identified based on the Thevenin battery model, and the state of charge (SOC) was estimated using a joint Kalman filter. Then, the discharge electric quantity–SOC data was fitted using quantile regression to obtain the preliminary capacity estimation results. To describe the battery capacity degradation along with driving mileage, this estimation result was further fitted using the Arrhenius empirical aging model and another quantile regression. The Nelder–Mead method was used to estimate the coefficients in quantile regression-related algorithms. Because quantile regression is not sensitive to the outliers of data points, it can reduce the impact of poor data quality on battery capacity estimation results. The proposed battery capacity estimation method was verified using real-world vehicle operation data, and the capacity estimation errors were within 3.2%.

Enhancing Optimization of Mixed Variables on a Robotic Flow Platform: Integrating Statistical Filtering with Nelder–Mead and Bayesian Methods

Enhancing Optimization of Mixed Variables on a Robotic Flow Platform: Integrating Statistical Filtering with Nelder–Mead and Bayesian Methods

Performance of a pilot-scale BDD reactor by numerical analysis of reaction rate parameters and additional numbers for mass transfers

The performance of a pilot-scale boron-doped diamond (BDD) reactor through a numerical analysis of reaction rate parameters and enhanced mass transfer has been investigated. The main objective of this research is to evaluate the efficiency of the reactor in mineralizing and degrading caffeine as an emerging contaminant. Based on the kinetic mechanisms and mass transport correlations reported in the literature, two reaction rate kinetic models for caffeine degradation are proposed and analyzed. The models consider different electrolytes (NaCl and Na2SO4) and applied current densities. The kinetic fitting process utilizes the gradient-maximal electrochemical approach, together with orthogonal placement methods, fourth-order Runge-Kutta (RK4) methods, and Nelder & Mead methods for optimization of kinetic parameters and spatial discretization of the material balance. Experimental data obtained from a factorial design with four factors and two levels (24) validate the proposed kinetic models. Caffeine degradation is achieved with NaCl and Na2SO4 electrolytes at concentrations of 60 ppm and 100 ppm, respectively. The corresponding applied loads are 1.5 AhL−1 and 3 AhL−1. Na2SO4 exhibits superior performance with a total organic carbon (TOC) removal efficiency of 99.13%, while NaCl achieves 31.47% mineralization. The behavior of caffeine degradation under the operational and scale conditions demonstrates that NaCl, as a support electrolyte, enables controlled charge transfer (current density) during the degradation process. In contrast, Na2SO4 as a support electrolyte introduces a mixed control of charge and mass transfer. The pilot-scale kinetic parameters obtained in this study provide valuable insights into the support electrolyte dynamics and current density dynamics in BDD-based Electrooxidation (EO) systems, particularly in complex matrix applications. Furthermore, the observed electrical consumption supports the potential application of EO as a viable technology for industrial-scale tertiary wastewater treatment, specifically for caffeine removal.

Optimizing the Design of an Interior Permanent Magnet Synchronous Motor for Electric Vehicles with a Hybrid ABC-SVM Algorithm

This paper presents a comprehensive investigation of the optimal design of an interior permanent magnet synchronous motor (IPMSM) for electric vehicles (EVs), utilizing the hybrid artificial bee colony algorithm–support vector machine (HAS) algorithm. The performance of the drive motor is a crucial determinant of the overall vehicle performance, particularly in EVs that rely solely on a motor for propulsion. In this context, interior permanent magnet synchronous motors (IPMSMs) offer a compelling choice due to their high torque density, wide speed range, superior efficiency, and robustness. However, accurate analysis of the nonlinear characteristics of IPMSMs necessitates finite element analysis, which can be time-consuming. Therefore, research into methods for deriving an optimal model with minimal computation is of significant importance. The HAS is a powerful multimodal optimization technique that is capable of exploring several optimal solutions. It enhances the navigation capability by combining the artificial bee colony algorithm (ABC) with the kernel support vector machine (KSVM). Specifically, the algorithm improves the search ability by optimizing the movement of bees in each region generated by the KSVM. Furthermore, hybridization with the Nelder–Mead method ensures accurate and quick convergence at pointers discovered in the ABC. To demonstrate the effectiveness of the proposed algorithm, this study compared its performance with a conventional algorithm in two mathematical test functions, verifying its remarkable performance. Finally, the HAS algorithm was applied to the optimal design of the IPMSM for EVs. Overall, this paper provides a thorough investigation of the application of the HAS algorithm to the design of IPMSMs for electric vehicles, and its application is expected to benefit from the combination of machine-learning techniques with various other optimization algorithms.

A Stochastic Convergence Result for the Nelder–Mead Simplex Method

We prove that the Nelder–Mead simplex method converges in the sense that the simplex vertices converge to a common limit point with a probability of one. The result may explain the practical usefulness of the Nelder–Mead method.

Multiobjective Optimal Dispatch of Mobile Energy Storage Vehicles in Active Distribution Networks

In active distribution networks (ADNs), mobile energy storage vehicles (MESVs) can not only reduce power losses, shave peak loads, and accommodate renewable energy but also connect to any mobile energy storage station bus for operation, making them more flexible than energy storage stations. In this article, a multiobjective optimal MESV dispatch model is established to minimize the power loss, renewable energy source curtailment, and total operating cost of ADNs. Additionally, a method to directly obtain the compromise optimal solution (COS) of the Pareto optimal solutions (POSs) of a three-objective optimization problem is proposed. Based on the normalized normal constraint (NNC) method for solving the POSs of a three-objective optimization problem, a bilevel optimization model is established to directly obtain the COS. The innerlayer model uses the NNC method to calculate the POS corresponding to a point on the Utopia plane, and the outerlayer model uses the improved Nelder–Mead (INM) method to directly search the POS with the minimum distance to the Utopia point as the COS. Compared with the traditional method, which first solves the POSs of the three-objective optimization problem and then selects the COS, the proposed INM method has higher computational efficiency and obtains a better COS. Finally, case studies on the modified IEEE-33 bus distribution network and an actual 180 bus distribution network demonstrate the effectiveness of the proposed method.

Optimized Design and Simulation of Optical Section in Electro-Reflective Modulators Based on Photonic Crystals Integrated with Multi-Quantum-Well Structures

In the design of photonic integrated circuits (PICs), the optical connections of the PIC surface, along with the electronic components of the chips, are significant issues. One of the optoelectronics components that utilizes these surface connections are electro-reflective modulators, consisting of an optical section and an electronic section. In this paper, a novel scheme of two-dimensional photonic crystals (PhCs) is presented for the optical and reflective sections of this device. This design is two-dimensional; thus, it has less volume than the current bulky structures. The finite element method is utilized to simulate and optimize the scheme of PhCs and gold layer parameters. Furthermore, optimization of design parameters is accomplished through the Nelder–Mead method. Moreover, the modeling and simulation of the proposed hybrid PhCs has been investigated according to the structural parameters with tolerance. These tolerances, related to the nanorods’ radius and lattice constants, are considered to justify and vindicate the fabrication technology limitations and conditions. In the “on” state of the modulator, the light transmission ratio is 98% for a 903 nm wavelength with a 45° angle of deflection and incident light, nd the bandwidth is 20 nm. For an 897 nm wavelength with a 41° angle, the transmission ratio is 95%, and the bandwidth is 7 nm.

Orthogonal Msplit Estimation for Consequence Disaster Analysis

Nowadays, the data processing used for analyzing multifaceted disasters is based on technologies of mass observation acquisition. Terrestrial laser scanning is one of those technologies and enables the quick, non-invasive acquisition of information about an object after a disaster. This manuscript presents an improvement in the approach to the reconstruction and modeling of objects, based on data obtained by terrestrial laser scanning presented by the authors in previous work, as a method for the detection and dimensioning of the displacement of adjacent planes. The original Msplit estimation implemented in previous research papers has a specific limitation: the functional model must be selected very carefully in terms of the mathematical description of the estimated model and its data structure. As a result, using Msplit estimation on data from laser scanners is not a universal approach. The solution to this problem is the orthogonal Msplit estimation method proposed by the authors. The authors propose a new solution: the orthogonal Msplit estimation (OMsplit). The authors propose a modification of the existing method using orthogonal regression and the Nelder–Mead function as the minimization function. The implementation of orthogonal regression facilitates the avoidance of misfitting in cases of unfavorable data acquisition because the corrections are calculated perpendicularly to the estimated plane. The Nelder–Mead method was introduced to the orthogonal Msplit estimation due to it being more robust to the local minimum of the objective function than the LS method. To present the results, the authors simulated the data measurement of a retaining wall that was damaged after a disaster (violent storm) using a terrestrial laser scanner and their own software. The conducted research confirmed that the OMsplit estimation can be successfully used in the two-plane detection of terrestrial laser scanning data. It allows one to conduct the correct separation of the data set into two sets and to match the planes to the appropriate data set.

The Mechanical Characteristics Range Spread Determined by the Nelder–Mead Method for a Production Elastic Element Made of Polymer Composite Materials

The Mechanical Characteristics Range Spread Determined by the Nelder–Mead Method for a Production Elastic Element Made of Polymer Composite Materials

Practical initialization of the Nelder–Mead method for computationally expensive optimization problems

Black-box optimization (BBO) algorithms are widely employed by practitioners to address computationally expensive real-world problems such as automatic tuning of machine learning models and evacuation route planning. The Nelder–Mead (NM) method is a well-known local search heuristic for BBO that has been applied to solve many real-world problems from way back because of its promising performance. However, this method has a strong dependence on initialization due to its local search tendency. Nevertheless, a discussion on the proper initialization of the NM method is limited to the recent study by Wessing (Optim Lett 13(4):847–856, 2019), which is solely based on an analysis using the simple sphere function. In this study, we take a further step to improve Wessing’s result by massively investigating how the initialization affects the search performance in views of the initial simplex size and shape and a constraint handling method that is employed on 24 BBO benchmarking problems. Based on the numerical results, we present the empirical best practice for the initialization of the NM method for cases involving a limited evaluation budget.

Application of the Nelder–Mead Method to Optimize the Way for Selection of the Likhachev–Volkov Model Constants

Application of the Nelder–Mead Method to Optimize the Way for Selection of the Likhachev–Volkov Model Constants