Nelder-Mead Research Articles

Exponential stability for uncertain nonlinear time-delay system via memory-based saturated controller

This paper establishes an exponential H ∞ stabilisation method for uncertain nonlinear system with time-varying delay and external disturbance via non-fragile memory-based saturated controller. Based on the construction of an augmented Lyapunov–Krasovskii functional (LKF) and distributed-delay polytopic method, some delay-dependent and delay-derivation-dependent criteria to ensure the exponential H ∞ stabilisation of the nonlinear system are derived in terms of linear matrix inequalities (LMIs). Then, the optimisation problems with reduced conservatism concerning the admissible initial condition set are specifically formulated. Subsequently, simulation results are presented to demonstrate the validity and practicality of the suggested method.

Fast magnetic field compensation algorithm based on the Nelder–Mead simplex method for dual-beam optically pumped magnetometers

Fast magnetic field compensation algorithm based on the Nelder–Mead simplex method for dual-beam optically pumped magnetometers

Deep Eutectic Solvent-Assisted Synthesis of Ni-Graphene Composite Supported on Screen-Printed Electrodes for Biogenic Amine Detection.

Deep eutectic solvents (DES) have emerged as versatile, sustainable media for the synthesis of nanomaterials due to their low toxicity, tunability, and biocompatibility. This study develops a one-step method to modify commercially available screen-printed electrodes (SPE) using laser-induced pyrolysis of DES, consisting of choline chloride and tartaric acid with dissolved nickel acetate and dispersed graphene. The electrodes were patterned using a 532 nm continuous-wave laser for the in situ formation of Ni nanoparticles decorated on graphene sheets directly on the SPE surface (Ni-G/SPE). The synthesis parameters, specifically laser power and graphene concentration, were optimized using the Nelder-Mead method to produce modified Ni-G/SPEs with maximized electrochemical response to dopamine. Electrochemical characterization of the developed sensor by differential pulse voltammetry revealed its broad linear detection range from 0.25 to 100 μM and high sensitivity with a low detection limit of 0.095 μM. These results highlight the potential of laser-assisted DES synthesis to advance electrochemical sensing technologies, particularly for the detection of biogenic amines.

Python-Based Algorithm for Estimating NRTL Model Parameters with UNIFAC Model Simulation Results.

A major challenge in bioprocess simulation is the lack of physical and chemical property databases for biochemicals. A Python-based algorithm was developed for estimating the nonrandom two-liquid (NRTL) model parameters of aqueous binary systems in a straightforward manner from simplified molecular-input line-entry specification (SMILES) strings of substances in a system. This algorithm conducts a series of procedures: (1) fragmentation of the molecules into functional groups from SMILES, (2) calculation of activity coefficients under predetermined temperature and mole fraction conditions by employing universal quasi-chemical functional group activity coefficient (UNIFAC) model, and (3) regression of NRTL model parameters by employing UNIFAC model simulation results in the differential evolution algorithm (DEA) and Nelder-Mead method (NMM). The algorithm was applied to aqueous, binary mixture systems composed of 37 common biochemical substances such as amino acids, organic acids, and sugars. The obtained NRTL parameters were compared with those from Aspen Plus, a commercial software, which has an equivalent function for estimating the NRTL parameters. The percentage mean absolute residuals of the activity coefficients obtained using DEA, NMM, and the parameter estimation tool in Aspen Plus were in the ranges of 0.05-16.69, 0.05-16.69, and 0.09-326.77%, respectively. This in-house algorithm will be helpful for obtaining more accurate NRTL parameters in a timely manner and will facilitate the simulation of biochemical processes for process optimization, energy consumption estimation, and life cycle assessment.

MSBKA: A Multi-Strategy Improved Black-Winged Kite Algorithm for Feature Selection of Natural Disaster Tweets Classification.

With the advancement of the Internet, social media platforms have gradually become powerful in spreading crisis-related content. Identifying informative tweets associated with natural disasters is beneficial for the rescue operation. When faced with massive text data, choosing the pivotal features, reducing the calculation expense, and increasing the model classification performance is a significant challenge. Therefore, this study proposes a multi-strategy improved black-winged kite algorithm (MSBKA) for feature selection of natural disaster tweets classification based on the wrapper method's principle. Firstly, BKA is improved by utilizing the enhanced Circle mapping, integrating the hierarchical reverse learning, and introducing the Nelder-Mead method. Then, MSBKA is combined with the excellent classifier SVM (RBF kernel function) to construct a hybrid model. Finally, the MSBKA-SVM model performs feature selection and tweet classification tasks. The empirical analysis of the data from four natural disasters shows that the proposed model has achieved an accuracy of 0.8822. Compared with GA, PSO, SSA, and BKA, the accuracy is increased by 4.34%, 2.13%, 2.94%, and 6.35%, respectively. This research proves that the MSBKA-SVM model can play a supporting role in reducing disaster risk.

Modern Free-Derivative Numerical Optimization of Approximate Algorithms Convergence and Neutrosophic Convergence

The aim of this study is to compare common and previously used numerical algorithms for nonlinear problems under different conditions. This study proposes a parallel implementation of two free derivative optimization methods, Powell's method and Nelder-Mead's method, combined with two restart strategies to achieve a global search. In terms of total time, the Powell method converges faster than the Nelder-Mead method. The final function value obtained by the Powell method is slightly lower. Both are optimization techniques used to find the minimum of an objective function in multidimensional space, without requiring derivatives. Also, we extend our results to apply to some neutrosophic non-linear problems under different neutrosophic-based conditions with many examples that explain the validity of our approach.

A Direct Search Nelder Mead MPPT Based Induction Motor Drive for Solar PV Water Pumping System

A Direct Search Nelder Mead MPPT Based Induction Motor Drive for Solar PV Water Pumping System

Boosting Performance of SVM in Koi Classification Using Direct Methods-Based Optimization

Many koi fish enthusiasts keep or buy them just for their attractive colors without knowing what type of koi fish they are. The manual classification of koi fish species is still frequently incorrect. As a result, it is critical to apply a machine learning technique to identify various koi fish species. This research implemented a computer vision algorithm to classify koi fish species using the Support Vector Machine (SVM) as the classifier. However, the maximum accuracy SVM can achieve in our koi fish classification system is 79%. To achieve better performance, the SVM was optimized by applying various optimization methods from the Direct Method group, i.e., the Generalized Pattern Search (GPS), the Powell method, and the Nelder-Mead method. Three optimization methods from the Direct Method group have successfully improved the performance of SVM in this task. Experimental results demonstrated that using the Generalized Pattern Search (GPS) in our classification system can increase the accuracy to 98%. Also, implementing the Powell and the Nelder-Mead method can make the koi classification system obtain a better accuracy of 99%. These results indicate that the proposed approach is a viable solution to overcome the limitations of the SVM algorithm.

Time-Varying Autoregressive Models for Economic Forecasting

This research introduces a time-varying autoregressive (TVAR) model, developed to improve the precision of forecasting in economic time series data. The model advances the conventional TVAR framework by incorporating potential mean adjustments and utilizing the Kalman Filter within a Maximum Likelihood Estimation (MLE) framework, with further optimization through the NelderMead method. Applied to the real gross national product (GNP) data of the United States (U.S.), the model effectively captures dynamic patterns and structural changes that traditional models often overlook. The model’s performance is rigorously compared with the widely used Markov switching autoregressive (MSAR) model, demonstrating superior results in both training and testing forecasts. The TVAR model consistently achieves lower error metrics, underscoring its robustness and flexibility in capturing dynamic economic trends and providing reliable forecasts. This research emphasizes the TVAR models potential for broader applications in economic policy analysis, strategic planning, and decision-making processes, particularly in understanding and predicting economic growth. The models adaptability and precision make it a valuable tool for economists and policymakers aiming to navigate complex economic fluctuations with greater confidence as well as accuracy.

A MODIFIED NUMERICAL METHOD OF DETERMINING HYDRAULIC SYSTEM PARAMETERS FOR THE DEVELOPMENT OF MATHEMATICAL MODELS AND INFORMATION COMPLEXES OF COMPUTER SIMULATION MODELS FOR INDUSTRIAL CHEMICAL PRODUCTION

The paper introduces a modified numerical method for determining the parameters of hydraulic systems used in mathematical modeling and simulation-based computer systems for industrial chemical production. It explores the dynamics of fluids, gases, and their mixtures as they traverse pipelines equipped with valves, compressors, and other complex components. Traditional methods for solving nonlinear equation systems often face limitations, including sensitivity to initial approximations and the need for relaxation coefficient adjustments, which complicate simulation processes. The proposed method converts nonlinear equations into an optimization problem, us- ing the Nelder-Mead algorithm to minimize deviations between initial estimates and comput- ed parameters. This derivative-free approach employs a simplex geometric transformation, overcoming issues associated with iterative methods and delivering high accuracy, stable convergence, and computational efficiency. Its adaptability makes it suitable for handling in- tricate hydraulic systems. To validate the method, a practical example involving a pipeline system with multiple restricting devices is analyzed. The mathematical model includes equations for pressures and flow rates, supplemented by material balance constraints at branching points. Numerical ex- periments evaluate how input pressure influences system parameters, demonstrating the mod- el's robustness and precision. The results confirm that the method accurately simulates system parameters under steady-state conditions and identifies critical optimization points. This innovative approach offers significant advantages for designing and managing industrial chemical facilities. By simplifying model construction, enhancing reliability, and accelerating simulation processes, the method provides a powerful tool for optimizing the op- eration and control of complex technological systems.

OPTIMIZATION METHODS FOR PARAMETER IDENTIFICATION MODEL OF TEST ELECTRORETINOSIGNAL TO ASSESS NEUROTOXICITY RISKS

Introduction. The development of advanced optimization methods plays a crucial role in the enhancement of diagnostic tools in the biomedical field, particularly in the analysis of complex physiological signals. Electroretinography (ERG) is a widely used diagnostic technique that records electrical responses generated by the retina in response to light stimuli, providing valuable insights into the functional health of retinal cells. ERG is instrumental in diagnosing conditions such as retinitis pigmentosa, diabetic retinopathy, and neurotoxicity. However, the analysis of low-intensity electroretinograms (ERG) presents numerous challenges, particularly due to noise and signal distortion, which complicate accurate signal interpretation. Main purpose of this study.This paper is dedicated to developing an expert system for real-time analysis of electroretinographic signals (ERS), focusing on optimizing the parameters of a mathematical model for ERS analysis in conditions where noise and other distortions are present. The primary aim is to improve the accuracy and efficiency of ERG data processing, enabling early detection of neurotoxicity and other retinal conditions. To achieve this, we applied advanced optimization techniques, such as the Nelder-Mead method, known for its effectiveness in handling non-smooth, noisy functions. Conclusions. 1. The application of the Nelder-Mead algorithm for optimizing the complex and noisy ERS model significantly improved the performance of ERG data analysis. The algorithm's adaptability to varying optimization conditions allowed for more accurate model parameter determination, particularly in the context of real-time neurotoxicity detection. Reduction in Processing Time: The time complexity analysis revealed that the Nelder-Mead method reduced the time required to compute the model coefficients by approximately 15%. This improvement was achieved while maintaining the necessary precision for reproducing the test electroretinosignal, making it suitable for real-time applications. Computational Efficiency: One of the key findings of this study is that the use of the Nelder-Mead algorithm reduced the computational load by up to 30%. This makes the method feasible for use in expert systems designed for real-time ERS analysis, allowing for the monitoring of functional changes in the retina during the early stages of neurotoxicity detection.

Nelder–Mead Optimization of Dual-Wave EMAT for Defect Recognition With Grey Relational Analysis

Nelder–Mead Optimization of Dual-Wave EMAT for Defect Recognition With Grey Relational Analysis

Optimization of Maize Irrigation Strategies in the Middle Reaches Irrigation Area of the Heihe River Using a Differential Evolution Algorithm

Optimizing maize irrigation strategies is essential for improving water use efficiency and crop yields in arid regions. However, limited quantitative research exists on these optimizations. This study focuses on the Heihe River Basin in China, aiming to (1) optimize maize irrigation strategies using a differential evolution (DE) algorithm integrated with the AquaCrop model and remote sensing data; (2) compare the DE algorithm’s performance with the traditional Nelder–Mead (fmin) algorithm regarding yield improvement and irrigation water use; and (3) assess the benefits of different irrigation strategies under limited water availability. Covering 22 irrigation management zones in Zhangye City, Gansu Province, the study utilized soil, weather, and crop data from Google Earth Engine to drive the AquaCrop model. Results indicate that the DE algorithm achieved higher simulated maize yields, increasing by 0.5 to 1 t/ha on average compared to the fmin algorithm, albeit with a 30% rise in irrigation water usage. The integration of both the DE and fmin algorithms with the AquaCrop model facilitates the development of tailored irrigation strategies, providing a scientific foundation for sustainable agricultural water management. These findings can guide efficient irrigation management plans in the region and similar arid systems.

Design and optimization of flexible DGS-based microstrip antenna for wearable devices in the Sub-6 GHz range using the nelder-mead simplex algorithm

This study introduces a Nelder-Mead Simplex Algorithm based low-profile, flexible, and wearable defected ground structure (DGS)-loaded deformed microstrip antenna for Sub-6 GHz 5 G applications. It is fabricated on a low-loss 20 mil Rogers RT/Duroid 5880 substrate and the antenna demonstrates robust performance with reflection coefficient magnitude (|S11|) of –22.34 dB with peak gain of about 5.57 dBi at resonant frequency (fr) of 2.185 GHz. Comprehensive key performance metrics such as |S11|, far-field gain patterns, and specific absorption rate (SAR) of the proposed antenna is demonstrated. The SAR for 1 g and 10 g tissues at various separation distances are analyzed and presented by utilizing human multilayer phantom model with antenna. Additionally, the lowest SAR is measured to be 0.0959 W/kg for 1 g of tissue and 0.0755 W/kg for 10 g of tissue when the antenna is placed 0.291λ0 away from the model. The study also explores the proposed antenna performance under various bending conditions for the conformability analysis and in different on-body scenarios, with placement on the hand, leg, and chest. The measured |S11| values, particularly strong on the chest, underscore the antenna effectiveness for wearable technology.

Highly sensitive photonic crystal fiber sensor for detection of hemoglobin and sucrose concentration

Abstract In this research, a flower-shape photonic crystal fiber sensor is proposed and designed. In this sensor, the most electromagnetic field is concentrated in the core part of the flower causing a surprising increase in the sensitivity of the sensor. Gold is used as a plasmonic material for stability in the environment. The analyte is placed outside the sensor and it makes the possibility of fabrication simple. The geometrical parameters of the sensor are optimized with the Nelder Mead algorithm. The detection power of the sensor is in the bio range and in this research, it is proposed to determine the concentration of sucrose and the concentration of hemoglobin. Taking advantage of the amazing geometry of nested circles to confine the electromagnetic field in the center of the fiber and increase the sensitivity of the sensor is a significant achievement. Using the optimal algorithm for design leads to the adaptation of the optimal geometry and the efficient construction of the sensor. The results show an excellent amplitude sensitivity of 5285 (RIU−1) and a suitable wavelength sensitivity of 11000 (nm RIU−1).

Application of Real-Time Palm Imaging with Nelder-Mead Particle Swarm Optimization/Regression Algorithms for Non-Contact Blood Pressure Detection.

In response to the rising prevalence of hypertension due to lifestyle changes, this study introduces a novel approach for non-contact blood pressure (BP) monitoring. Recognizing the "silent killer" nature of hypertension, this research focuses on developing accessible, non-invasive BP measurement methods. This study compares two distinct non-contact BP measurement approaches: one combining the Nelder-Mead simplex method with particle swarm optimization (NM-PSO) and the other using machine learning regression analysis. In the NM-PSO method, a standard webcam captures continuous images of the palm, extracting physiological data through light wave reflection and employing independent component analysis (ICA) to remove noise artifacts. The NM-PSO achieves a verified root mean square error (RMSE) of 2.71 mmHg for systolic blood pressure (SBP) and 3.42 mmHg for diastolic blood pressure (DBP). Alternatively, the regression method derives BP values through machine learning-based regression formulas, resulting in an RMSE of 2.88 mmHg for SBP and 2.60 mmHg for DBP. Both methods enable fast, accurate, and convenient BP measurement within 10 s, suitable for home use. This study demonstrates a cost-effective solution for non-contact BP monitoring and highlights each method's advantages. The NM-PSO approach emphasizes optimization in noise handling, while the regression method leverages formulaic efficiency in BP estimation. These results offer a biomimetic approach that could replace traditional contact-based BP measurement devices, contributing to enhanced accessibility in hypertension management.

Surface plasmon resonance spectrometer in the double prism configuration: Fast characterization of the thickness and dielectric constant dispersion of thin films

Surface plasmon resonance (SPR)-based sensors are widely used to measure thin film thickness, material dielectric constants, biomolecular interactions, and more. However, conventional monochromatic setups limit the simultaneous determination of dielectric constant dispersion and film thickness. To address this, we developed a fully automated wavelength-resolved SPR using a double-prism Kretschmann configuration. Combining this setup with a computational approach based on Fresnel equations and the Nelder-Mead optimization method, we introduced a novel technique to simultaneously determine the dispersion (520–1000 nm) of the real and imaginary components of the dielectric constant of thin films directly from SPR curves. As far as we know, this is the first time an SPR spectrometer has accomplished such a remarkable achievement. As a proof of concept for biosensor applications, we determined the thickness and dielectric constant dispersion of gold and bovine serum albumin thin film. These thicknesses were validated through atomic force microscopy, and the dielectric constants aligned closely with literature values obtained by ellipsometry. The developed SPR system enables precise measurements of these parameters within a short time (10 minutes), paving the way for future applications in advanced sensors and biosensors.

Evaluation of Two-Dimensional DBH Estimation Algorithms Using TLS

Terrestrial laser scanning (TLS) has become a vital tool in forestry for accurately measuring tree parameters, such as diameter at breast height (DBH). However, its application in Mexican forests remains underexplored. This study evaluates the performance of five two-dimensional DBH estimation algorithms (Nelder–Mead, least squares, Hough transform, RANSAC, and convex hull) within a temperate Mexican forest and explores their broader applicability across diverse ecosystems, using published point cloud data from various scanning devices. Results indicate that algorithm accuracy is influenced by local factors like point cloud density, occlusion, vegetation, and tree structure. In the Mexican study area, the Nelder–Mead algorithm achieved the highest accuracy (R² = 0.98, RMSE = 1.59 cm, MAPE = 6.12%), closely followed by least squares (R² = 0.98, RMSE = 1.67 cm, MAPE = 6.42%), with different outcomes in other sites. These findings advance DBH estimation methods by highlighting the importance of tailored algorithm selection and environmental considerations, thereby contributing to more accurate and efficient forest management across various landscapes.

Optimal design configuration of grading ring for polymeric insulator under different environmental conditions

Polymeric insulators play a crucial role in power transmission lines. To ensure safe and reliable operation at High Voltage (HV), they are often equipped with single or double grading rings to uniformly distribute the electric field and voltage along the creepage distance. This study investigates the impact of optimal grading ring configurations on electric field distribution using the Finite Element Method (FEM). In addition, an adaptable method for achieving optimal grading ring design is proposed. Numerical results demonstrate that employing the Nelder-Mead (NM) optimization algorithm helps determine the ideal configuration for grading ring material, dimensions, and location to achieve uniform electric field distribution compared to insulators without grading rings or with original designs. This method has also been adapted for different environmental conditions, including pollution, water droplets, and icing conditions.

GPU based discrete element modeling for convex polyhedral shape particles: Development and validation

Particle dynamics simulations face a significant challenge in understanding the intricate behaviors of convex polyhedral particles due to their complex geometries and interactions. DEM emerges as a key method, illuminating the concealed intricacies of these geometric entities. Traditional algorithms often require cumbersome processes to check each type of contact individually. However, Gilbert–Johnson–Keerthi’s (GJK) and the expanding polytope algorithm (EPA) provide efficient numerical solutions for polyhedral contact detection and contact resolution. These Minkowski difference-based methods streamline contact detection and overlap computation, paving the way for deeper exploration of three-dimensional contact theory within DEM simulations. By leveraging GPU computational power, this paper outlines key algorithmic steps and verifies the solver’s accuracy through comparison with simulated and experimental data, with an average deviation of less than 5%. This study explores the impact of particle shape on the dynamics and mechanical behavior of densely packed systems, particularly in hoppers and tumblers. Spherical particles discharge faster but mix more slowly than polyhedral shapes, with icosahedrons achieving quicker full mixing. These results align with experimental findings, further validating the simulation approach.