Nelder-Mead Simplex Optimization Method Research Articles

Optimized Load-Independent Hyperelastic Microcharacterization of Human Brain White Matter

Abstract A micromechanical methodology combined with genetic algorithm (GA) as a global optimization method is used to find the material properties of axons and extracellular matrix (ECM) in corpus callosum which is a part of human brain white matter. Studies have shown that axons are highly oriented in the ECM which enables us to approximate brain white matter as a unidirectional fibrous composite model. Using the one-term Ogden hyperelastic constitutive equations for the constituents and knowing the mechanical response of corpus callosum, GA optimization procedure is used in conjunction with finite element (FE) micromechanical analysis to find optimal material parameters for axon and ECM in three uniaxial loading scenarios of tension, compression, and simple shear. Moreover, by simultaneous fitting to the three loading modes' responses and applying Nelder–Mead simplex optimization method, best-fit parameters are found. The best-fit parameters can be used to approximate the behavior of axons and ECM in different uniaxial loading conditions with the minimum error and hence, can be interpreted as load-independent parameters. Micromechanical simulations by best-fit parameters show maximum stress increase of 2% and 29% for tension and shear and less than 1% reduction for compression mode compared to the case where optimal parameters are used. The findings and the methodology of this study can be employed for constitutive modeling of axonal fibers and its implementation in human head FE model where load-independent parameters are needed for simulating different loading scenarios.

Finite element modeling of horizontal load-displacement hysteresis loops in unbonded elastomeric isolators

Finite element simulation of the dynamic response of elastomeric isolators is challenging due to the rate and amplitude dependency of elastomer material within the isolator. Current design codes mandate the use of experimental cyclic tests on prototype isolators to evaluate their dynamic response characteristics for the final design. This paper presents a step-by-step systematic procedure to construct a novel FEM for simulating the cyclic load-displacement hysteresis loops of unbonded fiber-reinforced elastomeric isolators (FREIs). The FEM employs a visco-hyperelastic model together with a piecewise calibration technique and the Nelder-Mead simplex optimization method to simulate both the nonlinear stress-strain relationship and the strain-history dependency of the rubber material within the isolator. Results of the uniaxial tensile test on the rubber specimen and preliminary cyclic shear tests on a prototype isolator are employed to calibrate the model. The proposed FEM leads to an effective response simulation of the unbonded FREIs. Thus, it may serve as a valuable tool to finalize the preliminary design and curb the expensive costs of test repetitions required to achieve the optimized isolator design.

Identifying bedrest using waist-worn triaxial accelerometers in preschool children.

To adapt and validate a previously developed decision tree for youth to identify bedrest for use in preschool children. Parents of healthy preschool (3-6-year-old) children (n = 610; 294 males) were asked to help them to wear an accelerometer for 7 to 10 days and 24 hours/day on their waist. Children with ≥3 nights of valid recordings were randomly allocated to the development (n = 200) and validation (n = 200) groups. Wear periods from accelerometer recordings were identified minute-by-minute as bedrest or wake using visual identification by two independent raters. To automate visual identification, chosen decision tree (DT) parameters (block length, threshold, bedrest-start trigger, and bedrest-end trigger) were optimized in the development group using a Nelder-Mead simplex optimization method, which maximized the accuracy of DT-identified bedrest in 1-min epochs against synchronized visually identified bedrest (n = 4,730,734). DT's performance with optimized parameters was compared with the visual identification, commonly used Sadeh's sleep detection algorithm, DT for youth (10-18-years-old), and parental survey of sleep duration in the validation group. On average, children wore an accelerometer for 8.3 days and 20.8 hours/day. Comparing the DT-identified bedrest with visual identification in the validation group yielded sensitivity = 0.941, specificity = 0.974, and accuracy = 0.956. The optimal block length was 36 min, the threshold 230 counts/min, the bedrest-start trigger 305 counts/min, and the bedrest-end trigger 1,129 counts/min. In the validation group, DT identified bedrest with greater accuracy than Sadeh's algorithm (0.956 and 0.902) and DT for youth (0.956 and 0.861) (both P<0.001). Both DT (564±77 min/day) and Sadeh's algorithm (604±80 min/day) identified significantly less bedrest/sleep than parental survey (650±81 min/day) (both P<0.001). The DT-based algorithm initially developed for youth was adapted for preschool children to identify time spent in bedrest with high accuracy. The DT is available as a package for the R open-source software environment ("PhysActBedRest").

Novel Time Method of Identification of Fractional Model Parameters of Supercapacitor

Accurate dynamic models of supercapacitors (SCs) are a basis for the design, control and exploitation of the hybrid energy storage systems for electric vehicles. This paper concerns a fractional model of SC impedance, based on the Cole–Cole equation describing relaxation in electric double layer. This article provides a new method of identifying the parameters of fractional order model of SC impedance, performed without disconnecting the SC module from the energy storage system. The test drive for this purpose needs only the respect a few simple recommendations. The article presents the conditions of the mentioned test drive that will ensure the frequency spectra of the recorded signals lying in the bandwidth necessary for the correct identification of the model parameters. These parameters are determined by means of the Nelder–Mead simplex optimization method. The results of the identification described by the time method coincide with those obtained in the frequency domain. It has been shown in the last part of the article that the real energy losses in these systems significantly exceed the losses determined only on the basis of the nominal capacity and series equivalent resistance (ESR), to which the SC catalogue data are usually limited. This paper also provides an auxiliary frequency criterion for the selection of SCs intended for energy storage systems of electric vehicles.

Power density optimization of PEMFC cathode with non-uniform catalyst layer by Simplex method and numerical simulation

One of the factors that has hindered the commercialization of Polymer Electrolyte Membrane Fuel Cells (PEMFCs) has been the high cost per kW from the high cost of platinum catalyst. Hence it is important to optimize the use of the platinum catalyst. In many previous PEMFC models, the catalyst distribution in Cathode Catalyst Layer (CCL) was assumed to be uniform, and there are very few models in which the variation of catalyst loading across the CCL is taken into account. This paper aims to enhance PEMFC power density by optimally distributing the catalyst used in CCL employing a computational fluid dynamic (CFD) simulation in conjunction with agglomerate model of the CCL. First, a numerical approach is presented to evaluate the effect of variant catalyst loading in the CCL of a PEMFC. A two-dimensional, steady state, isothermal implicit model for PEMFC has been developed. A spherical flooded agglomerate model is considered for CCL in which transport of both chemical species and charges are also taken into account. The numerical domain includes channel, land, Gas Diffusion Layer (GDL), and CCL. The developed model is used to determine the optimum catalyst loading distribution along CCL using a novel algorithm based on combining the numerical model and Nelder-Mead Simplex optimization method. In this novel algorithm, the optimum catalyst distribution function is assumed as different order polynomial functions with unknown coefficients. Unknown coefficients are calculated by considering the numerical model as a set of constraints for the optimization method. Nelder-Mead optimization method which is an unconstraint minimization heuristic method is employed to find the unknown coefficients. It is seen that in the optimum case, the maximum PEMFC density is increased about 7 percent. This improvement is a huge leap toward the commercialization of PEMFC.

A Monte Carlo simulation based inverse propagation method for stochastic model updating

This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder–Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.

A Simulation Optimization Approach to Epidemic Forecasting.

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.

A Collaborative Multilateral Localization Algorithm for Wireless Sensor Networks

Localization technology is one of the key supporting technologies in wireless sensor networks. In this paper, a collaborative multilateral localization algorithm is proposed to localization issues for wireless sensor networks. The algorithm applies anchor nodes within two hops to localize unknown nodes, and uses Nelder-Mead simplex optimization method to compute coordinates of the unknown nodes. If an unknown node can not be localized through two-hop anchor nodes, it is localized by anchor nodes and localized nodes within two hops through auxiliary iterative localization method. Simulation results show that the localization accuracy of this algorithm is very good, even in larger range errors.

Modeling of the adsorption breakthrough behaviors of oil from salty waters in a fixed bed of commercial organoclay/sand mixture

A commercial powdered organoclay in a mixture with inert sand particles was used to study its capability for removal of a crude oil from salty water in a fixed bed adsorption column. For this purpose, after obtaining adsorption isotherm, the fixed bed breakthrough experiments were accomplished. In addition a dispersed plug flow model with an overall mass transfer resistance through column was proposed and solved numerically. The axial dispersion coefficient (DL) and the overall mass transfer coefficient (KF) were estimated using the experimental data and Nelder–Mead simplex optimization method. The results of modeling and optimization showed that the presence of inert particles and agglomeration of powdered organoclay decrease the mass transfer coefficient extremely. This parameter is also decreased by increasing of bed height and organoclay percentage in the mixture. In addition, the obtained results showed that breakthrough curve becomes steeper with decreasing bed height, increasing flow rate and increasing feed concentration. Furthermore break point time is decreased with decreasing bed height, increasing flow rate and increasing inlet oil content.

Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method

This paper is devoted to the description of a newly developed methodology for the determination of the parameters of the Prony series in rubber compounds. Four hyperelastic constitutive equations were selected and combined with the Prony equation to describe the hyper-viscoelastic behaviour of a rubber compound. An in-house simple uniaxial tension test was designed and performed on the three rubber strips with the same length and different widths of 1, 2 and 3cm. The corresponding finite element meshes of these samples were developed using an adaptive meshing technique. The numerical result of the first sample was compared with experimental results of the associated experiment in conjunction with a Nelder–Mead Simplex optimization method to determine the parameters of the Prony equation. These parameters were further used for the simulation of the other two samples to show applicability and repeatability of the developed method. The comparison of the associated force–extension curves with the experimentally measured data of the two samples confirmed the accuracy and reliability of the predicted parameters by this technique.

Optimization of operating conditions for compressor performance by means of neural network inverse

A way to optimize the parameters (i.e. operating conditions), related to compressor performance, based on artificial neural network and the Nelder–Mead simplex optimization method is proposed. It inverts the neural network to find the optimum parameter value under given conditions (artificial neural network inverse, ANNi). In order to do so, first an artificial neural network (ANN) was developed to predict: compressor pressure ratio, isentropic compressor efficiency, corrected speed, and finally corrected air mass flow rate. Input variables for this ANN include: ambient pressure, ambient temperature, wet bulb temperature, cooler temperature drop, filter pressure drop, outlet compressor temperature, outlet compressor pressure, gas turbine net power, exhaust gas temperature, and finally fuel flow mass rate. For the network, a feed-forward with one hidden layer, a Levenberg–Marquardt learning algorithm, a hyperbolic tangent sigmoid transfer-function and a linear transfer-function were used. The best fitting with the training database was obtained with 12 neurons in the hidden layer. For the validation of present database, simulation and experimental database were in good agreement ( R 2 > 0.99 ) . Thus, the obtained ANN model can be used to predict the operating conditions when input parameters are well-known. Second, results from the ANNi that was developed also show good agreement with experimental and target data (error <0.1%), in this case, cooler temperature was found for a required efficiency. Therefore, the proposed methodology of ANNi can be applied to optimize the performance of the compressor with an elapsed time minor to 0.5 s.

A Novel Algorithm for Fiber-Optic Alignment Automation

An efficient and robust fiber-optic active alignment algorithm for locating the optimal fiber-optic coupling position is critical to the fiber-optic packaging automation, and thus to the cost effective manufacturing of fiber optic components and modules. A robust and speedy fiber-optic alignment algorithm must be capable of avoiding local power peak trapping and simultaneous multidegree of freedom alignment. The currently most widely employed fiber-optic alignment algorithms are based on the so-called hill-climbing method. Because the hill-climbing method is a "one-dimensional-at-a-time" gradient searching method, it can only deal with the alignment on one direction at one time, so it is usually time-consuming and often the real peak cannot be detected because of local peak trapping. Another disadvantage of the hill-climbing method is that it is especially difficult when dealing with angular alignment and arrayed device alignment. Our novel approach is based on the application of the Nelder-Mead Simplex optimization method. The performance of the algorithm is investigated for the first time for three different fiber-optic alignment conditions, i.e., 1) two-dimensional (X and Y) alignment in the presence of side-modes for a single channel fiber-optic device; 2) simultaneous six-dimensional (i.e., three linear, two angular, and one rotational) alignment for a wedged fiber to a laser diode; 3) three-dimensional (X, Y, and rotation) alignment of eight-channel fiber-arrayed devices. We have found that this method has the advantage of fast convergence and easy-implementation. Simulation results indicates that the algorithm converges five times faster than the conventional hill-climbing method; it works well in the presence of side-modes; and it converges to the maximum coupling efficiency within 15 Simplex iterations for the six-DOF alignment; for the arrayed devices, it also only requires less than 15 iterations to reach a balanced optimal coupling position for each channel.