Multivariate Optimization Method Research Articles

Effects of the Chemical Structure and Composition of Surrogate Gasoline Fuels on Homogeneous Charge Compression Ignition Combustion in a Single-Cylinder Engine

This paper presents the results from the studies of the combustion performance of surrogate gasoline fuels in a Ricardo Hydra single-cylinder engine under homogeneous charge compression ignition (HCCI) conditions. The studies at fixed engine speed, intake air temperature, and intake manifold pressure (900 rpm, 200 °C, and 1.8 bar, respectively) demonstrated that fuel chemistry, i.e., the chemical nature of the components and their concentration in the mixture, was strongly correlated to selected parameters of HCCI performance, such as thermal efficiency (ηf), combustion phasing (CA50), and maximum pressure rise rate (MPRR). Using a multivariate optimization method based on desirability functions, it was determined that optimal HCCI combustion performance would be obtained with mixtures rich in isooctane, methylcyclohexane, and toluene (about 30 vol % each), with minimal content of n-heptane and 1-hexene (<10%).

A Design Method of Multi-variable Economic Optimization Objective Function Based on Interval Predictive Control

For that there is still a lack of effective methods improving economic performance of the complex process systems in Model Predictive Control (MPC), a design method of multi-variable economic optimization objective function based on interval predictive control is proposed in this paper. The objective function consists of constraint item, control item and economic item, which are separately used to handle the constraint targets, coordinate the operational control and improve the economic indicators. In the process of solving the objective function, the multi-variable economic control optimization strategy is used. Fist, a multi-variable coordination optimization method is used preferentially to satisfy the target set point and constraint interval control of the Controlled Variables (CV s), then the weights of the economic item are adjusted according to the variable priority to achieve optimization of the Manipulated Variables (MV s). The simulation results show that the application of this objective function in MPC is not only able to achieve requirements of the product quality target, but also can significantly increase the economic benefits.

A novel laser intensity function and its fitting method

A novel transcendental function is presented to describe laser intensity distribution instead of Gaussian functions, and its fitting method is given in this paper. The transcendental function based on the Gaussian functions is fitted with multivariate optimization method, which is carried out with direction search method and least square method in practice. Four kinds of distribution laser intensity are fitted with the transcendental function in this article, validity and effectiveness of the fitting method are verified by these numerical simulations.

Multivariate Optimization of the Cutting Parameters when Turning Slender Components

The geometric features of the work piece and the cutting parameters considerably affect the quality of a finished part subjected to any machining operation owing to the imposed elastic and plastic deformations, especially when slender components are produced. This work is focused on the influence of the work piece slenderness ratio and cutting parameters on the quality of the machined part, assessed in terms of surface roughness and both geometric (run-out) and dimensional (diameter) deviations. Turning tests with coated tungsten carbide tools were performed using AISI 1045 medium carbon steel as work material. Differently from the published literature, a statistical analysis based on the multivariate one-way analysis of variance (MANOVA) was applied to the data obtained using a Box-Behnken experimental design. In order to identify the combination of parameters (slenderness ratio, cutting speed, feed rate and depth of cut) levels which simultaneously optimize the responses of interest (surface roughness, run-out and diameter deviation), a multivariate optimization method based on principal component analysis (PCA) and generalized reduced gradient (GRG) was employed.

Comparing reaction orders of anthracite chars with bituminous coal chars at high temperature oxidation conditions

The influence of concentration of oxygen on the oxidation rates of 5 anthracite chars is investigated at gas temperatures ranging from 1223K to 1673K. Reaction orders and kinetic parameters are determined with a multivariable optimization method in which modeled burnout profiles are fitted to experimental burnout profiles from a 4m isothermal plug flow reactor operating at industrially realistic heating rates, i.e., 104–105K/s. The determined reaction orders are compared to reaction orders of 10 bituminous coal chars investigated at similar conditions in a previous study. The results show that the optimized reaction order of the anthracite chars is zero, while the reaction order of the bituminous coal char is one. The difference in the reaction orders cannot be explained by using the two semi-global oxidation reactions: C(O)+O2→CO/CO2 and C(O)→CO. However, by also considering 2C(O)→CO2+C as a possible reaction step, the reaction order difference between the anthracite chars and the bituminous coal chars can be explained. In addition, a first attempt to apply the same multivariable optimization method to determine the reaction order for a biomass char is presented.

A NEURAL NETWORK MODEL AND AN UPDATED CORRELATION FOR ESTIMATION OF DEAD CRUDE OIL VISCOSITY

Viscosity is one of the most important physical properties in reservoir simulation, formation evaluation, in designing surface facilities and in the calculation of original hydrocarbon in-place. Mostly, oil viscosity is measured in PVT laboratories only at reservoir temperature. Hence, it is of great importance to use an accurate correlation for prediction of oil viscosity at different operating conditions and various temperatures. Although, different correlations have been proposed for various regions, the applicability of the existing correlations for Iranian oil reservoirs is limited due to the nature of the Iranian crude oil. In this study, based on Iranian oil reservoir data, a new correlation for the estimation of dead oil viscosity was provided using non-linear multivariable regression and non-linear optimization methods simultaneously with the optimization of the other existing correlations. This new correlation uses API Gravity and temperature as an input parameter. In addition, a neural-network-based model for prediction of dead oil viscosity is presented. Detailed comparisons show that validity and accuracy of the new correlation and the neural-network model are in good agreement with large data set of Iranian oil reservoir when compared with other correlations.

One-Parameter Model for the Oxidation of Pulverized Bituminous Coal Chars

In this study, the oxidation of 22 bituminous coal chars is modeled with (i) an individual activation energy for each char and (ii) constant activation energy for all the chars. Modeled burnout profiles, from 0 to 75% of burnout, are compared to experimental measurements from a 4 m isothermal plug flow reactor operating at temperatures and heating rates typical of pulverized fuel industrial combustion. The fuel and the gas rates are chosen such that temperature gradients in the radial direction and along the centerline of the reactor are minimized. In this study, the objective is to predict the burnout profiles with a model suitable for the comprehensive computational fluid dynamics (CFD) modeling of pulverized fuel boilers. Therefore, a power law model that takes into account external diffusion and apparent kinetics is used. The kinetic parameters that are used in the model are determined with a suggested multivariable optimization method. The results show that the experimental burnout profiles of the 22 individual chars are not predicted with a significantly higher accuracy using separately determined activation energy for each char than they were using a constant activation energy for all the chars. Thus, only one fuel specific parameter (i.e. the pre-exponential factor) is needed to model the burnout profiles. These findings are in agreement with some previous studies but are important considering the significant amount of experimental data and the large number of coal chars investigated using a systematic approach.

Multivariate optimization of the Kharasch–Sosnovsky allylic oxidation of olefins

The multivariate optimization method known as simplex is applied to the Kharasch–Sosnovsky allylic oxidation of double bonds. By applying this method, the amounts of three variables (copper source, oxidant, and additive) are optimized at the same time. Under the conditions thus obtained the reaction takes place in a considerable shorter time, being the alkene the limiting reagent. These conditions are applied to some monoterpenes and sesquiterpenes leading regioselectively to the corresponding benzoate esters, opening a route to the employment of this reaction in the synthesis of more complex molecules.

The Research of the Four-Bar Bionic Active Knee

The robot joints are usually rotational axis by two link joints, bionic features is not strong. The shortcomings of intelligent MR damper control multi-axis bionic knee can only provide resistance and certain sizes to regain momentum, cannot provide larger power, therefore this paper gives by the multi-axis four-bar structure, ball screw transmission multiaxial bionic active knee institutions. And analysis the human leg institutions and commonly used two-bar structure, through multi-variable optimization method to solve the design parameters of knee joint structure, the motor angular velocity and torque. And established in a bionic active the knee's virtual prototype.

A comparison on design of multi-channel sampled fiber Bragg gratings with phase-shifts

Multi-channel sampled fiber Bragg gratings with purely phase shifts can be designed in three different ways using an appropriate phase shift pattern. In this paper, three syntheses methods, two of them associated with Fourier transform of phase shift pattern and one associated with Fourier transform of index variable of grating are proposed. The first synthesis method uses non-equally separated π-phase shifts, the second and the third syntheses use equally separated but variable phase shifts in the sampling period of fiber grating. In all methods, the phase shift patterns are optimized to match their Fourier transforms to a target reflection spectrum. It is demonstrated that a reflection spectrum with desired number of channels can be easily synthesised using a general multi-variable optimization method. Finally, the reflection spectra of the designed multi-channel sampled fiber Bragg gratings are analyzed and the comparisons between these three methods are given.

Multiple Layer Superconducting Magnet Design for Magnetic Resonance Imaging

A design method of multiple layers superconducting magnet for MRI is introduced. Considering the actual coils layout, the candidate domain is divided into several layers. The current density curves of each layer are solved by Quadratic Programming optimization with Minimum Stored Energy. The seed coils are arranged at the peak positions of current curves. Based on the regularization solution, the current of the seed coils can be solved. According to the coil's current, selecting the current density of the superconducting wires, the original sections for the coils can be obtained. Then a further optimization about the homogeneity based on constrained nonlinear multivariable optimization method is employed to determine the final coils' geometries. The method is especially suitable for short superconducting MRI magnet design.

A constitutive model for dynamic plasticity of FCC metals

This paper proposes a new constitutive model to describe the dynamic plasticity of FCC metals using the thermal activation mechanism of dislocation motion. In the model development, the constitutive parameters were directly linked with the characteristics of microstructures of materials. As an example of its application, the model was used to describe the behavior of OFHC copper. To determine the globally optimized parameters of the constitutive model for OFHC copper, an improved multi-variable optimization method of constrained nonlinear programming was used based on the flow stress of the material measured experimentally. A comparison with some models and experimental data in the literature shows that the new model is simple to apply and is much better in terms of its prediction accuracy. It was shown that compared with the MTS model the new constitutive equation is explicit and can be easily embedded into a computational code of material dynamics; while compared with the Zerilli–Armstrong and Johnson–Cook models the new one reflects more precisely experimental observations. It was concluded that the new model is applicable to a wide range of problems with temperature variation from 77 K to 1096 K, strain rates ranging from 10 −3 s −1 to 10 4 s −1, and strain as high as 1.

Updating of a lumped model for an experimental web tension control system using a multivariable optimization method

The modelling and the control of web handling systems have been studied for a long time; correct modelling is necessary in order to design a better control system or to identify the plant parameters experimentally. On the web dynamics itself, lumped parameters expressions may be used to designate a web section between two adjacent drive rolls, and there is the necessity of incorporating the property of viscoelasticity to the web. In this paper the lumped model of a new web tension experimental system is updated; the model is based on the conservation mass, torque balance and viscoelasticity (Voigt approach). The experimental system consists of four sections each of which is driven by a servomotor; the speed and tension feedback, by using encoders and tension sensors, drives simultaneously the four servomotors through a real time C programmed D/A board. Usually, as described in the literature, these kinds of models are developed in the Laplace domain and the block scheme gives a graphical interpretation of the interaction between different sections. The transformation of the block scheme in a differential equation system in the time domain is fully described in this paper; it is not a simple step and it requires the introduction of not null initial condition for the derivative of physical variables. Moreover, the problem of validation has been dealt with in detail in this paper, considering simultaneously 2 different combinations of input data in open loop and a multivariable optimization method in order to estimate a certain number of unknown parameters. The results will show the accuracy of this kind of lumped parameters model for the complex experimental systems and useful information for successively designing an efficient control strategy.

Application of a novel chemometric approach to the determination of aqueous photolysis rates of organic compounds in natural waters

The utility of multivariate optimization methods in the determination of aqueous photolysis rates of organic compounds is examined in this study. A basic pursue was to designate the appropriate experimental design plan that extend the analytical utility of multivariate methods from qualitative data interpretation approaches, as applied thus far, to quantitative estimation methods. A three-level second-order central composite design with parameter concentrations (factor levels) beyond the environmental realistic concentrations was employed for that purpose enabling statistically significant effects to be determined. Method application is demonstrated in the first photodegradation study of two UV absorbing chemicals in natural waters. The results suggest that the proposed approach of enables a good approximation of the real behavior in terms of both qualitative and quantitative data interpretation with minimal loss of information.

Concentration of alpha-lactalbumin from cow milk whey through expanded bed adsorption using a hydrophobic resin

The design of novel applications for the use of new high-density adsorbents in the direct recovery of proteins requires analysis of the fluid dynamics and mass transfer characteristics of the column used with the solid-liquid system. In this article we describe the operating parameters related to the use of a high-density, hydrophobic resin (Streamline® Phenyl) for the recovery of alpha-lactalbumin from cow milk whey in an expanded-bed adsorption mode of operation. The adsorption isotherm, kinetic curves and chromatographic curves for adsorption and elution were determined for alpha-lactalbumin recovered from whole whey. The experiments were used to confirm the theoretical model that involves the combination of resistance to the mass transfer in the liquid phase and diffusivity in the adsorbent resin pores. The model solution was obtained through the orthogonal collocation method. A nonlinear multivariable optimization method was used to fit the model to experimental results. A purity of 79% was obtained with the adsorption/elution protocol prior to any polishing procedure.

Crop yield estimation model for Iowa using remote sensing and surface parameters

Numerous efforts have been made to develop various indices using remote sensing data such as normalized difference vegetation index (NDVI), vegetation condition index (VCI) and temperature condition index (TCI) for mapping and monitoring of drought and assessment of vegetation health and productivity. NDVI, soil moisture, surface temperature and rainfall are valuable sources of information for the estimation and prediction of crop conditions. In the present paper, we have considered NDVI, soil moisture, surface temperature and rainfall data of Iowa state, US, for 19 years for crop yield assessment and prediction using piecewise linear regression method with breakpoint. Crop production environment consists of inherent sources of heterogeneity and their non-linear behavior. A non-linear Quasi-Newton multi-variate optimization method is utilized, which reasonably minimizes inconsistency and errors in yield prediction.Minimization of least square loss function has been carried out through iterative convergence using pre-defined empirical equation that provided acceptable lower residual values with predicted values very close to observed ones (R2=0.78) for Corn and Soybean crop (R2=0.86) for Iowa state. The crop yield prediction model discussed in the present paper will further improve in future with the use of long period dataset. Similar model can be developed for different crops of other locations.

Deformation and creep modeling in polycrystalline Ti–6Al alloys

This paper develops an experimentally validated computational model for titanium alloys accounting for plastic anisotropy and time-dependent plasticity for analyzing creep and dwell phenomena. A time-dependent crystal plasticity formulation is developed for hcp crystalline structure, with the inclusion of microstructural crystallographic orientation distribution. A multi-variable optimization method is developed to calibrate crystal plasticity parameters from experimental results of single crystals of α-Ti–6Al. Statistically equivalent orientation distributions of orientation imaging microscopy data are used in constructing the polycrystalline aggregate model. The model is used to study global and local response of the polycrystalline model for constant strain rate, creep, dwell and cyclic tests. Effects of stress localization and load shedding with orientation mismatch are also studied for potential crack initiation.

An integrated model for multiobjective design optimization of hydraulic fracturing

An integrated novel model for hydraulic fracturing design optimization is presented, which recognizes complex interactions between a hydraulically coupled fracture geometry module, a hydrocarbon production module and an investment-return cash flow module. Free design variables are identified and various design constraints are formulated, which must be satisfied so that an optimum design obtained is executable in the field using the specified surface equipment (pump, tubing, etc.) and that the treatment does not cause any undesirable formation damage by uncontrolled fracture growth and/or multiple secondary fracture initiation. The model is formulated within the framework of a multivariate and multiobjective optimization method, which is based on the combined features of Genetic Algorithm and Evolutionary Operation. A 2D fracture model is used to establish relationships between treatment parameters and fracture growth. The potential for hydraulic fracturing design improvement is demonstrated by application to a tight gas reservoir. Results show that the proposed model is instrumental in improving hydraulic fracturing design and achieving a goal-oriented optimum design in a conflicting environment. About 12% compromise with maximum possible production, or net present value (NPV), over 10 years can save up to 44% of initial hydraulic fracturing treatment cost. Furthermore, the 88% production, or net present value, as a result of an optimum treatment program is significantly higher than any arbitrary design. The issues of real-time design modification, however, are not included in this study.

A Biomathematical Model of Particle Clearance and Retention in the Lungs of Coal Miners: II. Evaluation of Variability and Uncertainty

The objective of this study is to investigate the sources of variability and uncertainty in a previously developed human lung dosimetry model. That three-compartment model describes the retention and clearance kinetics of respirable particles in the gas-exchange region of the lungs. It was calibrated using exposure histories and lung dust burden data in U.S. coal miners. A multivariate parameter estimation and optimization method was developed for fitting the dosimetry model to these human data. Models with various assumptions about overloading of alveolar clearance and interstitialization (sequestration) of particles were evaluated. Variability in the estimated clearance rate coefficients was assessed empirically by fitting the model to groups' and to each miner's data. Distributions of lung and lymph node particle burdens were computed at working lifetime exposures, using the variability in the estimated individual clearance rate coefficients. These findings confirm those of the earlier analysis; i.e., the best-fitting exposure–dose model to these data has substantial interstitialization/sequestration of particles and no dose-dependent decline in alveolar clearance. Among miners with different characteristics for smoking, disease, and race, the group median estimated alveolar clearance rate coefficients varied by a factor of approximately 4. Adjustment for these group differences provided some improvement in the dosimetry model fit to all miners (up to 25% reduction in MSE), although unexplained interindividual differences made up the largest source of variability. The predicted mean lung and lymph node particle burdens at age 75 after exposure to respirable coal mine dust at 2 mg/m2 for a 45-year working lifetime were 12 g (5th and 95th percentiles, 3.0–26 g) and 1.9 g (0.26–5.3), respectively. This study provides quantitative information on variability in particle retention and clearance kinetics in humans. It is useful for risk assessment by providing estimated lung dust burdens associated with occupational exposure to respirable particles.

Identification of Fuzzy Relational Models from Unevenly Distributed Data Using Optimization Methods

A wide range of algorithms for Fuzzy Relational Model (FRM) identification from process data have been developed over the last decade. It has been shown that the use of multi-variable optimization methods to establish the strengths of fuzzy relationships results in accurate models. Accuracy means here, however, the fit between training data and model predictions. If the available training data is unevenly distributed then optimization results in good model fit in regions where training data is clustered, but the regions where training data is sparse are less well modelled. The problem is frequently encountered as little influence is often possible on how training data is acquired. In this paper identification methods are proposed which take into account the distribution of training data. To enhance the model quality over the entire model range the input space is divided into regions in which the model error is considered separately during optimization. It is shown that the division of the input space by fuzzy partitioning is not sufficient. Problems which can occur due to unevenly distributed data are discussed and, based on the fuzzy partitioning, a new division of the input space is derived. These new input regions are described using rectangular or triangular fuzzy sets. It is shown that both shapes of fuzzy regions result in FRM with better predictive capabilities on unseen process data. An example for the application of the FRM in a Model Predictive Controller (MPC) is also given.