Simplex Search Method Research Articles

Iterative integral parameter identification of a respiratory mechanics model.

BackgroundPatient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual’s model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions.MethodsAn iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients.ResultsThe iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested.ConclusionThese investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

A Modified NM‐PSO Method for Parameter Estimation Problems of Models

Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder‐Mead simplex search and particle swarm optimization (M‐NM‐PSO) method for solving parameter estimation problems. The M‐NM‐PSO method improves the efficiency of the PSO method and the conventional NM‐PSO method by rapid convergence and better objective function value. Studies are made for three well‐known cases, and the solutions of the M‐NM‐PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M‐NM‐PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real‐coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM‐PSO method.

A New Hybrid Nelder‐Mead Particle Swarm Optimization for Coordination Optimization of Directional Overcurrent Relays

Coordination optimization of directional overcurrent relays (DOCRs) is an important part of an efficient distribution system. This optimization problem involves obtaining the time dial setting (TDS) and pickup current (Ip) values of each DOCR. The optimal results should have the shortest primary relay operating time for all fault lines. Recently, the particle swarm optimization (PSO) algorithm has been considered an effective tool for linear/nonlinear optimization problems with application in the protection and coordination of power systems. With a limited runtime period, the conventional PSO considers the optimal solution as the final solution, and an early convergence of PSO results in decreased overall performance and an increase in the risk of mistaking local optima for global optima. Therefore, this study proposes a new hybrid Nelder‐Mead simplex search method and particle swarm optimization (proposed NM‐PSO) algorithm to solve the DOCR coordination optimization problem. PSO is the main optimizer, and the Nelder‐Mead simplex search method is used to improve the efficiency of PSO due to its potential for rapid convergence. To validate the proposal, this study compared the performance of the proposed algorithm with that of PSO and original NM‐PSO. The findings demonstrate the outstanding performance of the proposed NM‐PSO in terms of computation speed, rate of convergence, and feasibility.

An improved chaos optimization algorithm-based parameter identification of synchronous generator

This paper proposes an improved chaos optimization algorithm (ICOA)-based parameter identification approach of synchronous generator. The proposed ICOA is the combination of mutative-scale parallel chaos optimization algorithm and simplex search method. The parameter identification of synchronous generator is considered as an optimization process with a fitness function minimizing the errors between the estimated values and measured values, and the proposed ICOA will search the optimal parameters values of the plant. Simulation results have show the effective performance of the proposed parameter identification approach.

A new hybrid evolutionary algorithm based on new fuzzy adaptive PSO and NM algorithms for Distribution Feeder Reconfiguration

Network reconfiguration for loss reduction in distribution system is a very important way to save the electrical energy. This paper proposes a new hybrid evolutionary algorithm to solve the Distribution Feeder Reconfiguration problem (DFR). The algorithm is based on combination of a New Fuzzy Adaptive Particle Swarm Optimization (NFAPSO) and Nelder–Mead simplex search method (NM) called NFAPSO–NM. In the proposed algorithm, a new fuzzy adaptive particle swarm optimization includes two parts. The first part is Fuzzy Adaptive Binary Particle Swarm Optimization (FABPSO) that determines the status of tie switches (open or close) and second part is Fuzzy Adaptive Discrete Particle Swarm Optimization (FADPSO) that determines the sectionalizing switch number. In other side, due to the results of binary PSO(BPSO) and discrete PSO(DPSO) algorithms highly depends on the values of their parameters such as the inertia weight and learning factors, a fuzzy system is employed to adaptively adjust the parameters during the search process. Moreover, the Nelder–Mead simplex search method is combined with the NFAPSO algorithm to improve its performance. Finally, the proposed algorithm is tested on two distribution test feeders. The results of simulation show that the proposed method is very powerful and guarantees to obtain the global optimization.

Inverse analysis of Navier–Stokes equations using simplex search method

The 2-D Navier–Stokes (N–S) equation is solved for the simultaneous estimation of three parameters such as the Reynold's number (Re), the length of the enclosure (lx) and the width of the enclosure (ly). The simplex search method (SSM) based on Nelder–Mead algorithm is used for minimizing the square of the error between a guessed centreline velocity field and an available one. For known values of the parameters such as Re, lx and ly, the reference field is first obtained by solving a forward problem using the finite difference method (FDM). To test the estimation accuracy corresponding to the reference field, next, an inverse problem is solved in which the above three parameters are taken as unknown variables. The estimation accuracy and the objective function are studied for the effects of initial guess, random and biased errors and CPU time. An excellent estimation of the unknowns is obtained using the SSM–FDM combination. The investigated errors have not found to contribute significantly to the estimation accuracy. Streamline patterns confirm that the centreline velocity field is sufficient to estimate the unknowns with an excellent accuracy.

A simplex search method for a conductive–convective fin with variable conductivity

An inverse problem is solved for simultaneously estimating the convection–conduction parameter and the variable thermal conductivity parameter in a conductive–convective fin with temperature dependent thermal conductivity. Initially, the temperature field is obtained from a direct method using an analytical approach based on decomposition scheme and then using a simplex search minimization algorithm an inverse problem is solved for estimating the unknowns. The objective function to be minimized is represented by the sum of square of the error between the measured temperature field and an initially guessed value which is updated in an iterative manner. The estimation accuracy is studied for the effect of measurement errors, initial guess and number of measurement points. It is observed that although very good estimation accuracy is possible with more number of measurement points, reasonably well estimation is obtained even with fewer number of measurement points without measurement error. Subject to selection of a proper initial guess, it is seen that the number of iterations could be significantly reduced. The relative sensitiveness of the estimated parameters is studied and is observed from the present work that the estimated convection–conduction parameter contributes more to the temperature distribution than the variable conductivity parameter.

A Modified Differential Evolution Optimization Algorithm with Random Localization for Generation of Best-Guess Properties in History Matching

Computer aided history matching techniques are increasingly playing a role in reservoir characterization. This article describes the implementation of a differential evolution optimization algorithm to carry out reservoir characterization by conditioning the reservoir simulation model to production data (history matching). We enhanced the differential evolution algorithm and developed the modified differential evolution optimization method with random localization. The proposed technique is simple-structured, robust, and computationally efficient. We also investigated the convergence characteristics of the algorithm in some synthetic oil reservoirs. In addition, the proposed method is compared with the Nelder-Mead simplex search method and a standard Genetic algorithm.

Optimal four-impulse rendezvous between coplanar elliptical orbits

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden’s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital rendezvous in a near circular orbit and achieved great success. Extending Prussing’s work, this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large eccentricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden’s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution. If the initial values are taken randomly, it is difficult to converge to the optimal solution.

Semi-analytical formulation for the guided waves-based reconstruction of elastic moduli

In this study an inverse procedure based on the propagation of guided ultrasonic waves is proposed for the characterization of the elastic material constants of plates. The procedure consists of an optimization problem in which the discrepancy between the dispersion curves obtained through a semi analytical finite element (SAFE) formulation and numerical or experimental dispersion curves is minimized. The numerical dispersion curves were obtained from the application of the commercial finite element analysis software ANSYS. Finally experimental data were obtained by adopting a hybrid broadband laser/PZT ultrasonic set-up in a pitch-catch configuration. For both numerical and experimental data, the joint time–frequency analysis of the continuous wavelet transform was used. The optimization scheme proposed in this study is based on an improved version of the simplex search method. The scheme inputs an initial guess of the material parameters in the SAFE formulation. The values of these parameters are iteratively updated until the discrepancy between the SAFE-based group velocity dispersion curves and the numerical or experimental curves is minimized. The scheme is designed to minimize the discrepancy associated with the lowest symmetric and anti-symmetric order mode simultaneously. The validity of the SAFE method coupled to the inverse procedure scheme is tested to characterize the elastic material properties of a 2.54 mm thick aluminum plate. As the SAFE formulation is valid for waveguides of arbitrary cross-section the paper represents the first step toward the integration of an inversion scheme applicable into the SAFE algorithm to characterize the material properties of waveguides of complex geometries and various boundary conditions.

Form Errors Evaluation Based on a Hybrid Optimization Algorithm

In order to realize precision measurement of parts, based on the analysis of existent evaluation methods for form errors, a hybrid evaluation method is provided in this paper. The hybrid global optimization algorithm based on ant colony optimization and simplex search method is proposed. The optimum model and the calculation process are introduced, where the planar straightness error is discussed as an example. The hybrid optimization algorithm can improve the efficiency and accuracy of searching in the whole field by gradually shrinking the area of optimization variable. Finally, a control experiment is carried out, and the calculation results by using different method such as the least square, simplex search, Powell optimum methods and GA, show that the hybrid evaluation method is feasible and satisfactory in the evaluation of form errors.

Kinematics Design of a Planar Parallel Controllable Mechanism Based on Particle Swarm Optimization Algorithm

Planar parallel controllable mechanism, which is a combination of two types of motor and mechanism, has better flexible transmission behavior. In this paper, the kinematics analysis for a planar parallel controllable five-bar mechanism is introduced. In order to improve kinematic performance of the controllable mechanism, an optimization design for the mechanism is performed with reference to kinematics objective function. A hybrid optimization algorithm which combines Particle Swarm Optimization (PSO) with MATLAB Optimization Toolbox is proposed to solve the optimal design problem with constraint condition. Compared with conventional optimum evaluation methods such as Simplex search and Powell method, PSO algorithm can improve the efficiency of searching in the whole field by gradually shrinking the area of optimization variable. Compared to GA, PSO is easy to implement and there are few parameters to adjust. Finally, a numerical example and discuss are carried out, the simulation and analysis results show that the optimization method is feasible and satisfactory in the design of the controllable mechanism.

Probabilistic Damage Characterisation in Beams using Guided Waves

This paper presents a model-based probabilistic damage characterisation methodology for beams using guided waves. Damage location, length, depth and Young's modulus of the material are treats as unknown parameters and are determined using optimisation approach to maximise the probability density function of the damage scenario conditional on the measured guided wave signals. A two-stage optimisation strategy is proposed using simulated annealing to first guarantee the solution is close to the global optimum, a standard simplex search method is then employed to precisely determine the global optimum. In addition to damage characterisation, the proposed methodology is developed based on the Bayesian statistical framework, hence, it allows quantification of the uncertainties associated with damage characterisation results. The accuracy and robustness of the proposed methodology are investigated through a series of numerical case studies in which the spectral element method is employed to model the wave propagation and scattering at the damage.

Conditional Nonlinear Optimal Perturbations: Adjoint-Free Calculation Method and Preliminary Test

Abstract An ensemble-based approach is proposed to obtain conditional nonlinear optimal perturbation (CNOP), which is a natural extension of linear singular vector to a nonlinear regime. The new approach avoids the use of adjoint technique during maximization and is thus more attractive. Comparisons among CNOPs of a simple theoretical model generated by the ensemble-based, adjoint-based, and simplex-search methods, respectively, not only show potential equivalence of the first two approaches in application according to their very similar spatial structures and time evolutions of the CNOPs, but also reveal the limited performance of the third measure, an existing adjoint-free algorithm, due to its inconsistent spatial distribution and weak net growth ratio of norm square of CNOP comparing with the results of the first two methods. Because of its attractive features, the new approach is likely to make it easier to apply CNOP in predictability or sensitivity studies using operational prediction models.

A multistage system of microbial fed-batch fermentation and its parameter identification

In fed-batch fermentation of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, glycerol and alkali are fed into the reactor to provide nutrient and maintain a suitable environment for cells growth. Taking the feeding process as a time-continuous process, we present a nonlinear multistage dynamical system to formulate the fed-batch fermentation. In view of the big errors between experimental data and computational values, a parameter identification model is established. Finally, an improved Nelder-Mead simplex search method is developed to seek the unknown parameters in the model. Numerical simulations show that the multistage dynamical system can describe the fed-batch process better, compared with the previous results.

Parameter identification of electronic throttle using a hybrid optimization algorithm

Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach.

5143 Resource-based data availability for erbB2-driven breast cancer in Asian women: experts' opinion

In this study, simplex search method (SSM) and a differential evolution (DE) based inverse algorithm are applied to estimate fuel flow rate (FFR), boiler pressure (BP) and steam turbine (ST) inlet temperature (STIT) of a ST based power cycle. First a theoretical model simulates the cycle performance in terms of net power, efficiency (energy and exergy) and total irreversibility at various FFRs, BPs and STITs. The forward model based results show that the net power increases linearly with FFR while also producing more irreversible losses at higher FFR. The cycle performance also improves at higher BP and STIT. The inverse analysis shows that the DE based method is more appropriate than the SSM where the searching range of parameters is specified and parameter estimation is done from the range of specified parameter values. In SSM, the estimation depends upon the chosen initial guess values and convergence criterion sometimes is not fulfilled with some guessed values of the parameters. Both the inverse methods, however give multiple combinations of parameters and thus provides sufficient scope at the hands of the designer to select the appropriate combinations of parameters required for meeting a particular power requirement.

Digital redesign of uncertain interval systems based on extremal gain/phase margins via a hybrid particle swarm optimizer

In this paper, a hybrid optimizer incorporating particle swarm optimization (PSO) and an enhanced NM simplex search method is proposed to derive an optimal digital controller for uncertain interval systems based on resemblance of extremal gain/phase margins (GM/PM). By combining the uncertain plant and controller, extremal GM/PM of the redesigned digital system and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimization problem of an aggregated error function in terms of deviation on extremal GM/PM between the redesigned digital system having an interval plant and its continuous counterpart, and subsequently optimized by the proposed optimizer to obtain an optimal set of parameters for the digital controller. Thanks to the performance of the proposed hybrid optimizer, frequency-response performances of the redesigned digital system using the digital controller evolutionarily derived by the proposed approach bare a far better resemblance to its continuous-time counter part in comparison to those obtained using existing open-loop discretization methods.

Guided wave damage characterisation in beams utilising probabilistic optimisation

This paper introduces a probabilistic optimisation approach to the characterisation of damage in beams using guided waves. The proposed methodology not only determines the multivariate damage characteristics, but also quantifies the associated uncertainties of the predicted values, thus providing essential information for making decisions on necessary remedial work. The damage location, length and depth and the Young’s modulus of the material are treated as unknown model parameters. Characterisation is achieved by applying a two-stage optimisation process that uses simulated annealing to guarantee that the solution is close to the global optimum, followed by a standard simplex search method that maximises the probability density function of a damage scenario conditional on the measurement data. The proposed methodology is applied to characterise laminar damage and is verified through a comprehensive series of numerical case studies that use spectral finite element wave propagation modelling with the consideration of both measurement noise and material uncertainty. The methodology is accurate and robust, and successfully detects damage even when the fault is close to the end of the beam and its length and depth are small. The particularly valuable feature of the proposed methodology is its ability to quantify the uncertainties associated with the damage characterisation results. The effects of measurement noise level, damage location, length and depth on the uncertainties in damage detection results are studied and discussed in detail.

Robust optimization for multiple responses using response surface methodology

AbstractTypically in the analysis of industrial data for product/process optimization, there are many response variables that are under investigation at the same time. Robustness is also an important concept in industrial optimization. Here, robustness means that the responses are not sensitive to the small changes of the input variables. However, most of the recent work in industrial optimization has not dealt with robustness, and most practitioners follow up optimization calculations without consideration for robustness. This paper presents a strategy for dealing with robustness and optimization simultaneously for multiple responses. In this paper, we propose a robustness desirability function distinguished from the optimization desirability function and also propose an overall desirability function approach, which makes balance between robustness and optimization for multiple response problems. Simplex search method is used to search for the most robust optimal point in the feasible operating region. Finally, the proposed strategy is illustrated with an example from the literature. Copyright © 2009 John Wiley & Sons, Ltd.