Nelder-Mead Simplex Algorithm Research Articles

Combining optimal SASS (Sparsity Assisted Signal Smoothing) and notch filters for transient measurement signals denoising of large power generating unit

Denoising and harmonic interference removal from the measurement signal is crucial for accurate parameters calculation of a generating unit model. Determining the actual parameters values requires various unit transient signals data recorded during a well-defined testing procedure. However, the recorded signals usually contain noise and harmonic interferences which are difficult to remove due to a presence of different kinds of discontinuities.The paper presents a proposal of optimal denoising and harmonic interference removal method from transient measurement signals of 200 MW power generating unit. The method combines notch filters for harmonic rejection followed by SASS (Sparsity Assisted Signal Smoothing) algorithm for wideband noise rejection. Parameters of the notch filters as well as the SASS are determined using popular optimization algorithms (simulated annealing, Nelder-Mead simplex and gradient algorithm).Performance of the proposed method is compared to its direct Linear Time-Invariant (LTI) competitors such as low-pass and notch filters alone, notch and low-pass filters combined and to the optimal SASS method alone. The performance evaluation is based on a set of specially generated test signals which are using the developed mathematical model of the signals (to set the level of noise and interferences) as well as the mathematical model of the power generating unit (to provide the reference clean signals). The obtained results confirm that the optimal notch-SASS method might be a valuable noise removal tool for considered class of signals and leads to superior results than the LTI filters or the SASS method alone.

Fuzzy analytic hierarchy process based generation management for interconnected power system

Decision makers consistently face the challenge of simultaneously assessing numerous attributes, determining their respective importance, and selecting an appropriate method for calculating their weights. This article addresses the problem of automatic generation control (AGC) in a two area power system (2-APS) by proposing fuzzy analytic hierarchy process (FAHP), an multi-attribute decision-making (MADM) technique, to determine weights for sub-objective functions. The integral-time-absolute-errors (ITAE) of tie-line power fluctuation, frequency deviations and area control errors, are defined as the sub-objectives. Each of these is given a weight by the FAHP method, which then combines them into an single final objective function. This objective function is then used to design a PID controller. To improve the optimization of the objective function, the Jaya optimization algorithm (JOA) is used in conjunction with other optimization techniques such as sine cosine algorithm (SCA), Luus–Jaakola algorithm (LJA), Nelder–Mead simplex algorithm (NMSA), symbiotic organism search algorithm (SOSA) and elephant herding optimization algorithm (EHOA). Six distinct experimental cases are conducted to evaluate the controller’s performance under various load conditions, with data plotted to show responses corresponding to fluctuations in frequency and tie-line exchange. Furthermore, statistical analysis is performed to gain a better understanding of the effectiveness of the JOA-based PID controller. For non-parametric evaluation, Friedman rank test is also used to validate the performance of the proposed JOA-based controller.

Investigation of rank order centroid method for optimal generation control.

Multi-criteria decision-making (MCDM) presents a significant challenge in decision-making processes, aiming to ascertain optimal choice by considering multiple criteria. This paper proposes rank order centroid (ROC) method, MCDM technique, to determine weights for sub-objective functions, specifically, addressing issue of automatic generation control (AGC) within two area interconnected power system (TAIPS). The sub-objective functions include integral time absolute errors (ITAE) for frequency deviations and control errors in both areas, along with ITAE of fluctuation in tie-line power. These are integrated into an overall objective function, with ROC method systematically assigning weights to each sub-objective. Subsequently, a PID controller is designed based on this objective function. To further optimize objective function, Jaya optimization algorithm (JOA) is implemented, alongside other optimization algorithms such as teacher-learner based optimization algorithm (TLBOA), Luus-Jaakola algorithm (LJA), Nelder-Mead simplex algorithm (NMSA), elephant herding optimization algorithm (EHOA), and differential evolution algorithm (DEA). Six distinct case analyses are conducted to evaluate controller's performance under various load conditions, plotting data to illustrate responses to frequency and tie-line exchange fluctuations. Additionally, statistical analysis is performed to provide further insights into efficacy of JOA-based PID controller. Furthermore, to prove the efficacy of JOA-based proposed controller through non-parametric test, Friedman rank test is utilized.

Trust region framework-based design of sub-6 GHz m-MIMO antenna and evaluation of SAR

PurposeCurrently, massive multiple-input multiple-output (m-MIMO) antennas are typically designed using complex trial-and-error methods. The purpose of this study is to determine an effective optimization method to achieve more efficient antenna design processes.Design/methodology/approachThis paper presents the design stages of a m-MIMO antenna array compatible with 5G smartphones operating in long term evolution (LTE) bands 42, 43 and 46, based on a specific algorithm. Each antenna element in the designed 10-port m-MIMO antenna array is intended to perfectly cover the three specified LTE bands. The optimization methods used for this purpose include the Nelder–Mead simplex algorithm, covariance matrix adaptation evolution strategy, particle swarm optimization and trust region framework (TRF).FindingsAmong the primary optimization algorithms, the TRF algorithm met the defined objectives most effectively. The achieved antenna efficiency values exceeded 60.81% in the low band and 68.39% in the high band, along with perfect coverage of the desired bands, demonstrating the success of the design with the TRF algorithm. In addition, the potential electromagnetic field exposure caused by the designed m-MIMO antenna array is elaborated upon in detail using computational human models through specific absorption rate analysis.Originality/valueThe comparison of four different algorithms (two local and two global) for use in the design of a 10-element m-MIMO antenna array with a complex structural configuration and the success of the design implemented with the selected algorithm distinguish this study from others.

Detecting self-organising patterns in crowd motion: effect of optimisation algorithms

The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study employs computational methods to analyze real-world crowd behaviors, emphasizing self-organizing patterns. Notably, the intersection of two streams of individuals triggers the spontaneous emergence of striped patterns, validated through both simulations and live human experiments. Addressing a gap in computational methods for studying these patterns, previous research utilized the pattern-matching technique, employing the Nelder-Mead Simplex algorithm for fitting a two-dimensional sinusoidal function to pedestrian coordinates. This paper advances the pattern-matching procedure by introducing Simulated Annealing as the optimization algorithm and employing a two-dimensional square wave for data fitting. The amalgamation of Simulated Annealing and the square wave significantly enhances pattern fitting quality, validated through statistical hypothesis tests. The study concludes by outlining potential applications of this method across diverse scenarios.

Simulation-based process parameter optimization for wire arc additive manufacturing

AbstractDuring manufacturing of components using wire arc additive manufacturing, specific cooling times are required to prevent overheating of the structure and geometrical distortions. Currently, these cooling times are inserted based on experience at certain interlayer temperatures — which reduces the reproducibility, leads to unwanted component properties, and increases the process time. In this contribution, instationary thermal finite element simulations are applied to compute the temperature evolution of additively manufactured components using the inactive element method. This allows to optimize the process parameters, which are — in our considerations here — the welding velocity and the cooling time of each layer, to reduce the total process time while achieving sufficient component properties. The optimization is carried out with the gradient-free Nelder–Mead simplex algorithm, where certain constraints of the process parameters are considered via penalty functions. To obtain reasonable simulation results, the temperature-dependent heat transfer of the experimental setup is modeled and calibrated with experimental data beforehand. It becomes apparent that thermal finite element simulations combined with a gradient-free optimization procedure are a suitable numerical tool to perform the optimization of process parameters for wire arc additive manufacturing. The optimized process parameters fulfill certain requirements regarding the cooling of the manufactured component. Moreover, the optimized parameters can significantly reduce the process time compared to manually chosen parameters. In our example, this is around 48 %.

Optimal Parameter Estimation Techniques for Complex Nonlinear Systems

AbstractAccurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This paper fills a critical gap in previous research by investigating tailored optimization methods for parameter estimation in nonlinear system modeling, with a particular emphasis on chaotic dynamical systems. We introduce and compare three optimization methods: a gradient-based iterative algorithm, the Levenberg-Marquardt algorithm, and the Nelder-Mead simplex method. These methods are strategically employed to simplify complex nonlinear optimization problems, rendering them more manageable. Through a comprehensive exploration of the performance of these methods in determining parameters across diverse systems, including the van der Pol oscillator, the Rössler system, and pharmacokinetic modeling, our study revealed that the accuracy and reliability of the Nelder-Mead simplex method were consistent. The Nelder-Mead simplex algorithm emerged as a powerful tool, that consistently outperforms alternative methods in terms of root mean squared error (RMSE) and convergence reliability. Visualizations of trajectory comparisons and parameter convergence under various noise levels further emphasize the algorithm’s robustness. These studies suggest that the Nelder-Mead simplex method has potential as a valuable tool for parameter estimation in chaotic dynamical systems. Our study’s implications extend beyond theoretical considerations, offering promising insights for parameter estimation techniques in diverse scientific fields reliant on nonlinear system modeling.

A Case Study of Nelder Mead Simplex Optimization Algorithm: Trade-Offs of Sprienski Fractal Bowtie Antenna Parameters

In this study, tri-band antenna design adapted for wireless communication, Internet of Things (IoT) and RFID systems is examined. The simulation results indicate that the proposed antenna has three distinct frequency bands. Band 1 (lower band) covers the frequency range of 1.64-1.78 GHz with a resonance frequency of 1.7 GHz. Band 2 covers the range of 3.06-3.9 GHz with a resonance frequency of 3.4 GHz with a high gain of 10 dBi and a radiation efficiency of 92% for long-range communication. Band 3 radiates from 6.25 to 7.6 GHz with a resonance frequency of 6.62 GHz, which is suitable for higher-frequency applications. The antenna design is simulated and analyzed regarding S11, VSWR, gain, radiation efficiency, and bandwidth. Especially, Band 2 (mid-band) provides notable performance, with its 10 dBi gain and 92% efficiency, which makes the proposed antenna an ideal structure for high-data-rate, long-distance communication systems, and 5G (midband) applications. This study also employs the Nelder-Mead Simplex algorithm to observe the optimization of the physical parameters of the proposed antenna via multiple objective functions. The optimization results outlines that longer the arm length of the proposed antenna causes to decrease the resonance frequency of Band 3. Addition to this, the gain is higher with the lower arm length except for the arm length of 90.467 mm and flare angle of 64.77o. That’s, the trade-off condition occurs between minimum return loss and gain. At this point, it can be concluded from this optimization algorithm results that each objective function should be evaluated separately due to this trade-off condition.

Weighted Centroids in Adaptive Nelder–Mead Simplex: With heat source locator and multiple myeloma predictor applications

This paper introduces a novel approach for enhancing the Nelder–Mead Simplex method by utilizing the weighted mean of simplex vertices to efficiently determine the search direction towards optima. The Nelder–Mead algorithm is commonly used for solving unconstrained optimization problems through iterative direct search. While the Nelder–Mead algorithm excels in low-dimensional scenarios, its challenges in higher dimensions are addressed in our study.We reveal that the Nelder–Mead Simplex algorithm’s operations rely not only on the problem dimension but also on adaptive descending parameters for calculating the weighted centroid of vertices. The adaptive weights are determined based on the concept that generating a descending sequence depends on the fitness values of vertices. Consequently, the search direction tends to prioritize vertices with superior fitness values over others.Through extensive testing on renowned high-dimensional benchmark functions, the proposed algorithm outperforms both the standard and adaptive Nelder–Mead simplex algorithms in terms of performance demonstrating superior consistency and reliability. Furthermore, it is applied to an inverse heat source location problem formulated as a linear elliptic partial differential equation, serving as a large-scale real-world application. Additionally, the algorithm successfully addresses a neural network model solving a classification problem concerning the prediction of multiple myeloma, a type of bone marrow cancer, in patients, achieving an average accuracy of 92.3% with a minimal standard deviation of 0.13%. When the results obtained from eight different methods used in the study are compared in terms of performance in general, the proposed method is among the top three optimization algorithms. These real-world applications showcase the method’s versatility.

Parameter identification of hysteretic model of UHPC-connected precast segmental columns under cyclic loading

Due to their numerous advantages, precast segmental columns have emerged as an important development direction in bridge engineering. Understanding and researching their hysteretic characteristics holds great significance. Precast columns connected with UHPC achieve performance similar to cast-in-place (CIP) monolithic columns, making them suitable for use in constructing bridges located in high seismic regions. In this study, the Bouc-Wen-Baber-Noori (BWBN) model was employed to characterize the hysteretic behaviors of UHPC-connected precast segmental columns, considering strength degradation, stiffness degradation, and pinching effects. The Nelder-Mead simplex (NMS) algorithm was utilized to identify the parameters of the BWBN model, demonstrating its computational efficiency. The proposed parameter identification method was validated using experimental data derived from cyclic loading tests performed on five UHPC-connected precast segmental columns of three structural types. Comparative analyses encompassing force-displacement relationship, residual drift and energy consumption convincingly affirmed the applicability and precision of the proposed method for UHPC-connected precast segmental columns.

Quasi-maximum likelihood-based estimator of the hyperbolic frequency modulated signals

The quasi-maximum likelihood (QML) algorithm has been extended to estimate the phase parameters and the instantaneous frequency (IF) of the hyperbolic frequency modulated (HFM) signals. The Nelder-Mead simplex algorithm (NMSA) is adopted for a fine estimation. The obtained accuracy is excellent with the estimates achieving the Cramer-Rao lower bound (CRLB) above the signal-to-noise (SNR) threshold of 0 dB. The proposed technique is capable of functioning with signals that are sampled below the requirements of the sampling theorem, which is particularly important for HFM signals. Additionally, there are no limitations for signals with monotonic IF and/or group delay (GD) functions.

Waste corn husk fibers for sound absorption and thermal insulation applications: A step towards sustainable buildings

In the last decade, noise pollution and global warming and their effects on human health and the environment have received much attention. Building sectors are one of the most important areas for potential improvements. To this end, sound-absorbing and thermal insulation construction materials are being used effectively. Recently, a great deal of interest has arisen in using various natural fibers as sound-absorbing and/or thermal insulation materials. In line with these studies, this work investigates the acoustic absorption and thermal insulation characteristics of corn husk fiber (CHF). The results showed that the samples enjoy excellent noise reduction coefficients of 0.36–60 and effective thermal conductivities of 0.038–0.042 W/mK. It was found that the thermal insulation properties of CHFs are not significantly influenced by the moisture content. The Dunn and Davern (DD) model and a modified model of DD based on the Nelder-Mead simplex algorithm were also used to predict the acoustic behavior of the samples. It was found that the proposed model provides very excellent prediction accuracy.

Optimization of Parameters Related to Grain Growth of Spring Wheat in Dryland Based on the Next-Generation APSIM

To improve the applicability of crop models, this study compared two algorithms for optimizing the single objective parameters of the spring wheat in the dryland grain growth sub-model to identify the more efficient algorithm for application in future model parameter optimization. Based on field experiments from 2015 to 2021 in Gansu Province, this study combined weather data and yearbook yield data from 1984 to 2021 to optimize parameters related to grain growth of spring wheat in dryland based on the next-generation APSIM using two algorithms: the Nelder–Mead simplex algorithm and the DREAM-zs algorithm. The results were as follows: the optimization results of both algorithms were the same, but the DREAM-zs algorithm converged faster; the optimized parameters for the grain growth stage of Dingxi35 spring wheat were: a grain number per gram stem of 25 grains, an initial grain proportion of 0.05, and a maximum grain size of 0.049 g; after optimization, the root mean square error (RMSE) of observed and simulated yield values decreased from 186.84 kg/hm2 to 115.71 kg/hm2, and the normalized root mean square error (NRMSE) decreased from 10.33% to 6.40%. The optimized results were consistent with the growth and development process of wheat and had high applicability.

Forecast for peak infections in the second wave of the Omicron after the adjustment of zero-COVID policy in the mainland of China.

On December 7, 2022, the Chinese government optimized the current epidemic prevention and control policy, and no longer adopted the zero-COVID policy and mandatory quarantine measures. Based on the above policy changes, this paper establishes a compartment dynamics model considering age distribution, home isolation and vaccinations. Parameter estimation was performed using improved least squares and Nelder-Mead simplex algorithms combined with modified case data. Then, using the estimated parameter values to predict a second wave of the outbreak, the peak of severe cases will reach on 8 May 2023, the number of severe cases will reach 206,000. Next, it is proposed that with the extension of the effective time of antibodies obtained after infection, the peak of severe cases in the second wave of the epidemic will be delayed, and the final scale of the disease will be reduced. When the effectiveness of antibodies is 6 months, the severe cases of the second wave will peak on July 5, 2023, the number of severe cases is 194,000. Finally, the importance of vaccination rates is demonstrated, when the vaccination rate of susceptible people under 60 years old reaches 98%, and the vaccination rate of susceptible people over 60 years old reaches 96%, the peak of severe cases in the second wave of the epidemic will be reached on 13 July 2023, when the number of severe cases is 166,000.

A general kinematic approach to the seismic stability assessment of slopes

Most of the current studies concerning slope stability assume a toe failure mechanism, which fails to capture the full complexity of slope collapse. In this study, a more comprehensive approach is developed for analyzing seismic slope stability by defining an instability behavior coefficient that considers different failure patterns, including toe, face, and base failure. The proposed coefficient is integrated with a kinematic method of limit analysis to establish a three-dimensional (3D) collapse mechanism that can describe all possible instability behaviors. The impact of earthquake forces on instability behaviors and slope stability is assessed in a modified pseudodynamic manner, which is capable of accounting for the spatiotemporal feature of seismic acceleration. A horizontal slice method is executed for calculating earthquake-induced work rates, as well as a double integral technique to compute dissipation rates due to soil resistance along the sliding surface and work rates generated by soil weight. By applying the principle of energy conservation, the lower-bound solutions of stability numbers are derived, and a further critical solution can be obtained by the combination of the Marine Predators Algorithm and the Nelder-Mead Simplex Algorithm. The proposed method is confirmed to be accurate and effective through comparisons with previous solutions. In addition, a parametric study reveals the effect of the dynamic characteristics of seismic waves on slope stability and instability behaviors. The general approach developed in this study offers a more comprehensive and accurate way to assess seismic slope stability.

AN ALGORITHM FOR DETECTING PRECIPITATION IN COMPUTER PROCESSING OF VIDEO IMAGES

The importance of detecting and reducing the visibility of precipitation in video images obtained by fixed cameras is shown. A statistical analysis of the geometric (area, shape factor, and orientation deviation from the frame average), and color–brightness (intensity and color saturation) characteristics of rain and snow particles is performed in order to substantiate decision rules for detecting pixels corresponding to precipitation particles. This analysis consists in obtaining distributions of the particle parameters and approximating them by known distribution laws using the family of Pearson’s curves, the Kolmogorov criterion, and the Nelder–Mead simplex algorithm. An algorithm for detecting raindrops and snowflakes in video sequences is developed, which is supposed to be used as part of an algorithm for reducing the visibility of precipitation. The proposed approach is presented in the form of a multistage classification of frame pixels into zones with moving objects and regions of a stationary background distorted and undistorted by precipitation particles in accumulated frames. Depending on the region to which the processed pixel belongs, the final decision to assign it to the class of precipitation is made using the proposed decision rules or the developed thresholding procedure with automatic determination of local threshold values. The proposed algorithm is experimentally investigated and, using a two-criteria approach, the optimal values for the number of accumulated frames for the correct operation of the algorithm are determined—100 frames for video images with rain and 140 frames for video with snow. The gain of the developed approach in comparison with the known estimates of the probabilities of false positives and false negatives is up to 1.7% and 9.1%, respectively.

Performance analysis of ICI self-cancellation schemes in OFDM systems

Abstract Orthogonal frequency division multiplexing (OFDM) is a promising technique in modern high data rate wireless communication system. However, the serious problem in OFDM system is the inter-carrier-interference (ICI) that is produced by the carrier frequency offset (CFO). CFO destroys the orthogonal properties among the sub-carriers and introduces ICI. ICI is a major impairment in OFDM system as it can degrade the bit error rate (BER) performance of the system. In this paper we have proposed an optimal ICI self-cancellation scheme that can maximize the carrier-to-interference-ratio (CIR) of the system. This scheme is based on optimizing the data allocation and combining parameters where, for estimated CFO, the optimized values of these parameters are calculated using Nelder Mead simplex algorithm. An approach to calculate the sub-optimized values of data allocation and combining parameters is also proposed, where the knowledge of CFO estimation can be avoided. In this paper, we have carried out the complete performance analysis of ICI self-cancellation schemes. We have also derived the mathematical expressions for ICI coefficients and presented a comparative analysis of standard OFDM system with different ICI cancellation schemes. The mathematical expressions for CIR and BER performance are further derived. To confirm the validity of the results Monte Carlo simulations using Matlab are also performed. We have also done the comparison of peak-to-average power ratio (PAPR) of conventional ICI self-cancellation scheme and proposed scheme.

Three-dimensional seismic stability of locally loaded slopes under a rotational velocity field

In practical engineering, slopes subjected to local loads, like footings of buildings, are common. This paper aims to give an insight into the effect of seismic force on the stability of locally loaded slopes. Numerical methods can be used to study this problem, but they require much computational time. Contrarily, limit analysis method is an approach to perform slope stability analysis with high computational efficiency. Thus, an accurate approach in mechanical points is proposed for this problem based on limit analysis method herein. In the framework of limit analysis, existing research about this problem used a kinematically translational velocity field. However, the velocity field of the locally loaded slope at failure is proved to be rotational possibly. Thus, to fill this gap, a 3D rotational velocity field is employed herein to obtain limit loads on the slope top, which improves the existing upper-bound solutions obtained by using the translational velocity field. The particle swarm optimization algorithm and the Nelder-Mead simplex algorithm are employed to search the global minimum of the upper-bound estimation of the limit load. Parametric analysis is performed and it shows that the limit load increases with the increase of a/H or the internal friction angle φ but decreases as the slope angle β or the length-to-width ratio (L/t) of the local load increases. Furthermore, the limit load is found to decrease with the increase of the seismic coefficient kh and it is proportional to the seismic coefficient.

Implementation of various-fidelity methods for viscous effects modeling on the design of a waverider

In the present study, the implementation of three viscous effects modeling methods at hypersonic flow conditions is investigated. The design of a hypersonic passenger transport waverider configuration is employed as a case study. The methods, each of which has a different fidelity level, are evaluated in terms of their capability to predict aerodynamic performance, as well as their effect on the final geometric design of the waverider. More specifically, for the same mission profile and design constraints, three different waverider configurations (Cases A, B and C) are designed with the osculating cone methodology, and each employing a different viscous effect modeling method. These three configurations are designed (a) assuming a purely inviscid flowfield, (b) using Eckert's Reference Temperature and (c) Van Driest's viscous effects modeling semi-empirical methods respectively, each subsequent one of higher complexity and fidelity than the previous. An optimization loop, employing the Nelder-Mead simplex algorithm, is also incorporated into the overall design process. Each configuration is evaluated with all three viscous effects modeling methods and the analytical results are compared against those of CFD modeling. The CFD analyses are performed by solving the steady-state three-dimensional Euler and Reynolds Averaged Navier Stokes (RANS) equations. Overall, the three configurations are evaluated in terms of aerodynamic performance, design/optimization computational cost, and accuracy between the analytical and CFD results. All inviscid analytical calculations demonstrate very good agreement with the Euler CFD results. Indicatively, the lift-to-drag predictions deviate by as much as 2% between the two approached. The Van Driest's method predictions result to 5%-6.5% lower lift-to-drag ratios compared to the RANS CFD, and to higher wall shear stress values. Contrarily, the Ref. Temperature method predictions are in a much closer agreement to the RANS CFD results, leading to a slight overprediction (0%-2.4%) of lift-to-drag ratios. The incorporation of viscous effects in the design process reduces the waverider's aerodynamic efficiency by about 8.5%-11% and results in a 46%-98% increase in computational time, compared to the inviscid analysis.

Purification of Ionic Liquid Solvents in a Self-Optimizing, Continuous Microfluidic Process via Extraction of Metal Ions and Phase Separation

Industrial applications of ionic liquids (ILs)─solvents that can serve as green alternatives to volatile organic compounds─are often hampered by their high cost. Solvent recycling provides a feasible pathway to recover IL solvents to reduce lifecycle costs. Herein, we demonstrate a continuous microfluidic process to purify metal-ion-loaded IL solvents, wherein Fe(III) ions are extracted from a prototypical IL, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIM-NTf2), to deionized (DI) water with subsequent membrane separation of the IL and aqueous phases. Inline analytical tools, design of experiment statistical optimization, and a self-optimizing, modified Nelder-Mead simplex algorithm facilitate locating the best parametric operating conditions to optimize both ion extraction and physical phase separation. This process was then adapted to a more challenging purification application: recovery of the IL trihexyl(tetradecyl)phosphonium bis(2,4,4-trimethyl-pentyl)phosphinate (Cyphos 104) from the rare-earth metal Nd(III). This application demonstrated that optimized conditions obtained from a single stage could be applied across a multistage process. Together, these results demonstrate that statistical and inline optimization tools can be used to identify working parameters for different flow systems with a variety of governing fluid properties, for example, viscosity and interfacial tension.