Powell's Direction Set Method Research Articles

Experimental and modeling study of the ignition kinetics of dimethyl carbonate

In this work, the ignition delay times (IDTs) of dimethyl carbonate (DMC) were measured by using a rapid compression machine (RCM) over a wide range of temperatures (778–1102 K), pressures (20 and 40 bar), equivalence ratios (φ= 0.5, 1.0, and 2.0) and fuel concentrations (1% and 2%), yielding results which are in substantial variance with those calculated with detailed kinetics in the literature over the entire range of conditions investigated. By further identifying the key reactions controlling ignition under different conditions by using sensitivity and path analyses, and taking the experimental data of typical working conditions as the target variable, the Arrhenius parameters of the main sensitive reactions are optimized through the global optimization using the genetic algorithm and the local optimization using the Powell's Direction Set method. Results show that the overall performance of the optimized kinetics model is in good agreement with the experimental data, and the IDTs of DMC can be predicted over the wide range of conditions.

Robust 2-D-3-D Registration Optimization for Motion Compensation During 3-D TRUS-Guided Biopsy Using Learned Prostate Motion Data.

In magnetic resonance (MR)-targeted, 3-D transrectal ultrasound (TRUS)-guided biopsy, prostate motion during the procedure increases the needle targeting error and limits the ability to accurately sample MR-suspicious tumor volumes. The robustness of the 2-D-3-D registration methods for prostate motion compensation is impacted by local optima in the search space. In this paper, we analyzed the prostate motion characteristics and investigated methods to incorporate such knowledge into the registration optimization framework to improve robustness against local optima. Rigid motion of the prostate was analyzed adopting a mixture-of-Gaussian (MoG) model using 3-D TRUS images acquired at bilateral sextant probe positions with a mechanically assisted biopsy system. The learned motion characteristics were incorporated into Powell's direction set method by devising multiple initial search positions and initial search directions. Experiments were performed on data sets acquired during clinical biopsy procedures, and registration error was evaluated using target registration error (TRE) and converged image similarity metric values after optimization. After incorporating the learned initialization positions and directions in Powell's method, 2-D-3-D registration to compensate for motion during prostate biopsy was performed with rms ± std TRE of 2.33 ± 1.09 mm with ~3 s mean execution time per registration. This was an improvement over 3.12 ± 1.70 mm observed in Powell's standard approach. For the data acquired under clinical protocols, the converged image similarity metric value improved in ≥8% of the registrations whereas it degraded only ≤1% of the registrations. The reported improvements in optimization indicate useful advancements in robustness to ensure smooth clinical integration of a registration solution for motion compensation that facilitates accurate sampling of the smallest clinically significant tumors.

Targeted 2D/3D registration using ray normalization and a hybrid optimizer

X-ray images are often used to guide minimally invasive procedures in interventional radiology. The use of a preoperatively obtained 3D volume can enhance the visualization needed for guiding catheters and other surgical devices. However, for intraoperative usefulness, the 3D dataset needs to be registered to the 2D x-ray images of the patient. We investigated the effect of targeting subvolumes of interest in the 3D datasets and registering the projections with C-arm x-ray images. We developed an intensity-based 2D/3D rigid-body registration using a Monte Carlo-based hybrid algorithm as the optimizer, using a single view for registration. Pattern intensity (PI) and mutual information (MI) were two metrics tested. We used normalization of the rays to address the problems due to truncation in 3D necessary for targeting. We tested the algorithm on a C-arm x-ray image of a pig's head and a 3D dataset reconstructed from multiple views of the C-arm. PI and MI were comparable in performance. For two subvolumes starting with a set of initial poses from +/-15 mm in x, from +/-3 mm (random), in y and z and +/-4 deg in the three angles, the robustness was 94% for PI and 91% for MI, with accuracy of 2.4 mm (PI) and 2.6 mm (MI), using the hybrid algorithm. The hybrid optimizer, when compared with a standard Powell's direction set method, increased the robustness from 59% (Powell) to 94% (hybrid). Another set of 50 random initial conditions from [+/-20] mm in x,y,z and [+/-10] deg in the three angles, yielded robustness of 84% (hybrid) versus 38% (Powell) using PI as metric, with accuracies 2.1 mm (hybrid) versus 2.0 mm (Powell).

Estimation of the number of frequencies and bandwidth for the surface measurement of soil moisture as a function of depth

The feasibility of obtaining estimates in situ of volumetric soil moisture as a function of depth using measurements of radio wave reflection at the soil surface at several discrete frequencies was demonstrated through computer simulation. By deriving empirical relationships between the number of frequencies, the frequency range, and the number of soil layers for which the soil moisture is estimated, the number of frequencies and measurement bandwidth have been determined. The soil moisture profile was obtained to a depth of 1.5 m by inverting, through function optimization, a simulation of the reflection coefficient from layered dielectric materials. The dielectric properties of soil-water mixtures mere obtained from the models of (1962) and (1980) and the function optimization was done with Powell's direction set method (1992). The number of soil layers in which soil moisture could be resolved was found to be twice the number of frequencies used. The required bandwidth increased with the number of soil layers from 20 MHz for six layers to 140 MHz for 16 layers. Within some assumptions about the nature of the radio wave propagation, the theoretical accuracy of the estimate depended only on the quantization error introduced by having to consider discrete layers of uniform soil with finite thicknesses.

Active, optimal control of a model industrial, natural gas-fired burner

Optimal, active control of a model industrial, swirl-stabilized, natural gas-fired burner is considered as a strategy to attain and maintain low flue-gas NO x concentration ([NO x ]) and high combustion efficiency (itη c ), simultaneously. A performance index, J , has been defined such that the maximization of J correlates to optimal burner performance, with respect to [NO x ] and η c . Two parameters, swirl intensity ( S ′) and excess air ( EA ), known to affect the value of J , are made amenable to control and incorporated as variable burner inputs. The two measurable burner outputs, [NO x ] and η c , are continuously monitored via a bank of extractive probe emission analyzers, similar to those proposed for industry as continuous emission monitoring systems (CEMS). The settings of EA and S ′ are automatically adjusted by a specialized search algorithm in order to maximize the performance index, thereby optimizing η c and [NO x ]. Two fundamentally differing search algorithms are explored. The first is a variation of Powell's direction-set method and incorporates a simple hill-climbing, line-maximization technique. The second, technique uses the genetic algorithm analogy, which works in parallel from a population (set) of burner inputs and associated fitness (performance index) values in order to generate more highly fit (better performing) populations. The control scheme is shown, in both cases, to increase overall burner performance. Advantages and disadvantages to each of these algorithms are identified and discussed. While promising, a robust practical application of optimal, active control will benefit from a refined and more mature search technique, possibly including a hybridized combination of one or more methods.