Use Of Numerical Optimization Research Articles

A Multidisciplinary Possibilistic Approach to Size the Empennage of Multi-Engine Propeller-Driven Light Aircraft

In considering aircraft design, it is very important to effectively size the tail configuration for stability and control. Multidisciplinary design optimization (MDO) focuses on the use of numerical optimization in the design of systems with multiple subsystems or disciplines of consideration. However, MDO uses deterministic calculations, and does not consider the uncertainties that arise from the employed analyses, including errors due to linearization and simplification. For problems with inadequate input data, the possibility-based design optimization (PBDO) scheme can be implemented in its stead to achieve reliable designs using membership functions for epistemic uncertainties. A multidisciplinary, possibilistic approach is presented to define the sizing of the empennage configuration of a twin-engine propeller-driven aircraft by changing shape parameters while satisfying the design requirements given the tailless aircraft configuration, the flight conditions, and various uncertainties. The corresponding disciplines are aerodynamics, stability and control, propulsion and weight and balance. Herein, different design requirements are considered including longitudinal/lateral/directional trim and stability characteristics, manufacturing and controllability criteria, handling qualities, operational requirements, airworthiness and survivability. The resulting aerodynamic characteristics and flight dynamic stability outcomes show that the optimized tail configuration for the proposed aircraft fully complied with airworthiness requirements and predefined constraints while considering several uncertainties due to the use of early-stage statistical estimations. The proposed approach can be used to enhance the preliminary design of multi-engine propeller-driven light aircraft where only low-fidelity, statistical estimations are available. The resulting output is not only an optimized aircraft configuration, but one where the stability of the design has been ensured. In this work, the aerodynamic characteristics have been determined using a validated semi-empirical program called MAPLA, developed for light aircraft designs and development in the preliminary design phase. Furthermore, the optimization framework consists of a deterministic optimizer that runs sequentially with a possibility assessment algorithm.

Analytical solution for one-dimensional three-phase incompressible flow in porous media for concave relative permeability curves

Three-phase flow in porous media may appear in different scenarios during the production life of a hydrocarbon reservoir. The simultaneous flow of different phases is modeled by relative permeability curves which are fundamental to petroleum production analysis and forecast. Laboratory experiments are the main source of data for relative permeability curves. Mathematical solutions for multiphase flow in porous medium are key for determining relative permeability curves from laboratory data, to check numerical reservoir simulation results and for screening an enhanced oil recovery technique. The complexity of reservoir modeling and the use of numerical optimization to history match the laboratory data have shown the importance of concave relative permeability curves. In this paper we present the analytical solution for one-dimensional incompressible immiscible three-phase flow in porous media, where the relative permeability functions are described by concave curves. The hyperbolic system of equations that results from mass conservation is solved by the method of characteristics. The results show close agreement to numerical solutions.

Topologically optimized magnetic lens for magnetic resonance applications.

Improvements to the signal-to-noise ratio of magnetic resonance detection lead to a strong reduction in measurement time, yet as a sole optimization goal for resonator design, it would be an oversimplification of the problem at hand. Multiple constraints, for example for field homogeneity and sample shape, suggest the use of numerical optimization to obtain resonator designs that deliver the intended improvement. Here we consider the 2D Lenz lens to be a sufficiently broadband flux transforming interposer between the sample and a radiofrequency (RF) circuit and to be a flexible and easily manufacturable device family with which to mediate different design requirements. We report on a method to apply topology optimization to determine the optimal layout of a Lenz lens and demonstrate realizations for both low- (45 MHz) and high-frequency (500 MHz) nuclear magnetic resonance.

Accelerated design of Fe-based soft magnetic materials using machine learning and stochastic optimization

Machine learning was utilized to efficiently boost the development of soft magnetic materials. The design process includes building a database composed of published experimental results, applying machine learning methods on the database, identifying the trends of magnetic properties in soft magnetic materials, and accelerating the design of next-generation soft magnetic nanocrystalline materials through the use of numerical optimization. Machine learning regression models were trained to predict magnetic saturation (BS), coercivity (HC) and magnetostriction (λ), with a stochastic optimization framework being used to further optimize the corresponding magnetic properties. To verify the feasibility of the machine learning model, several optimized soft magnetic materials – specified in terms of compositions and thermomechanical treatments – have been predicted and then prepared and tested, showing good agreement between predictions and experiments, proving the reliability of the designed model. Two rounds of optimization-testing iterations were conducted to search for better properties.

Minimum entropy production in a distillation column for air separation described by a continuous non-equilibrium model

In this work, we apply the rate-based model of Taylor and Krishna to describe the separation of air in a low-pressure, packed distillation column. By use of numerical optimization, we identify the temperature profile for heat exchange with the column and its surroundings that minimizes the total entropy production. Optimal operation of the column reduces the entropy production by nearly 50%, and the total heating- and cooling duties by 30% and 50%, respectively. We find that the local entropy production is more uniform for the optimal solution than in the adiabatic column, a property that may be helpful for new designs. Using the equilibrium stage model, the state of minimum entropy production has higher cooling/heating duties than in the rate-based model case. This shows that more sophisticated models can be beneficial for the development of reliable strategies to improve the energy efficiency of distillation columns.

Suppressing unsteady flow in arterio-venous fistulae

Arterio-Venous Fistulae (AVF) are regarded as the “gold standard” method of vascular access for patients with end-stage renal disease who require haemodialysis. However, a large proportion of AVF do not mature, and hence fail, as a result of various pathologies such as Intimal Hyperplasia (IH). Unphysiological flow patterns, including high-frequency flow unsteadiness, associated with the unnatural and often complex geometries of AVF are believed to be implicated in the development of IH. In the present study, we employ a Mesh Adaptive Direct Search optimisation framework, computational fluid dynamics simulations, and a new cost function to design a novel non-planar AVF configuration that can suppress high-frequency unsteady flow. A prototype device for holding an AVF in the optimal configuration is then fabricated, and proof-of-concept is demonstrated in a porcine model. Results constitute the first use of numerical optimisation to design a device for suppressing potentially pathological high-frequency flow unsteadiness in AVF.

Optimization methods for petroleum fields development and production systems: a review

In this review, we survey the widespread use of numerical optimization or mathematical programming approaches to develop and produce petroleum fields for design and operations; lift gas and rate allocation; and reservoir development, planning, and management. Early applications adopted linear programming alongside heuristics. With continuous advancements in computing speed and algorithms, we have been able to formulate more complex and meaningful models including nonlinear programs and mixed-integer linear and nonlinear programs. Various formulations and solution strategies have been used including continuous and discrete optimization, stochastic programming to handle uncertainty, and metaheuristics such as genetic algorithms to increase solution quality while reducing computational load.

Optimal static strain sensor placement for truss bridges

A method to identify optimal strain sensor placement for examining structural static responses is presented. The method is based on the use of numerical optimization. Based on an assumed set of applied static forces, the optimal sensor placement can be obtained, and the measured strains can be used to provide the information needed to describe the structural stiffness. For example, the cross-sectional area can be determined by minimizing the difference between the analytical and measured strains. This approach is used to identify the optimized sensor placement. The objective of this study is to identify the minimum number of static strain sensors and the optimal sensor layout needed to evaluate a bridge’s structural condition. This study includes an automatic model parameter identification method, optimal static strain sensor placement, damage detection, and application to an actual bridge.

A novel approach for the assessment of robustness of vehicle structures under crash

ABSTRACTThe use of numerical optimisation in vehicle development aiming at designing increasingly lighter vehicle structures may lead to a highly sensitive behaviour in terms of crashworthiness. Methods for the analysis of robustness have been introduced to account for the impact of varying input parameters, possibly detecting undesired deformation modes due to bifurcations. The objective of this paper is to introduce an index for the quantitative assessment of robustness of vehicle structures under crash. The novel approach is applied to axially impacted extrusion profiles as well as to an assembly of extrusion profiles under varying input parameters. It was found that the new Robustness Index accurately reflects the findings from state-of-the-art methods of robustness analysis, enabling an objective and transparent overall assessment of robustness prior to a potential in-depth analysis.

Employing numerical techniques in the analysis and design of musical instruments

In the simplest of terms, a musical instrument consists of a source of oscillation coupled to a resonating body. The exception to this is an idiophone such as a triangle or gong, where the vibrating source is able to be its own radiator of sound. Whatever the configuration, the radiating structure is generally not a simple shape easily represented by a mathematical formulation, and analytical solutions to the governing equations of even a simplified model are often not obtainable. Working with Neville Fletcher in the 1980’s a personal computer was employed to undertake a time-stepping routine through the equations of a simplified model of a kinked metal bar, to depict nonlinear coupling of its modes of vibration. Similar analysis of a gong modelled by a spherical shell with a kinked edge was well beyond the available computing power. In this paper we illustrate how the development of computers and numerical techniques over the intervening thirty years means that we are now able to describe and analyse complex shapes and are encroaching on the domain of the instrument maker through the use of numerical optimisation for instrument design.

EMG-based estimation of muscular efforts exerted during human movements

The quantification of muscle efforts can be very helpful in achieving important goals in clinical or sports biomechanics. However, the estimation of muscle moments and force requires to solve the problem of redundancy inherent in the musculoskeletal system. This paper covers the steps involved in developing an original EMG-based optimization methodology for estimating opposing muscle group moments and individual muscle force during static contractions or dynamic movements, even in the presence of fatigue. The combined use of numerical optimization and EMG data greatly improved our confidence in the estimates of agonist and antagonist moments, as well as muscle force. The generalization of the proposed method might be of particular interest in biomechanics of sport and exercise.

A robust and flexible optimization technique for efficient shrinking of MEMS accelerometers

We report on the automated determination of the minimal required area of a MEMS accelerometer conforming to given specifications. For a realistic nonlinear sensor model this process is only possible by the use of numerical optimization, which typically has the difficulty of finding the global minimum or is time consuming. A miniaturized sensor’s chip size reduces manufacturing cost and leads to more competitive package sizes and new, unforeseen applications. Size reduction is especially important for consumer applications like mobile phones and navigation devices, where an increasing demand for accelerometers is expected in the near future. With further miniaturization of a sensor it is increasingly important to find the optimal design in order to use chip area as efficiently as possible. To achieve a robust and flexible automated area reduction without loss of functionality we uniquely combine available genetic and gradient-based optimization algorithms. Furthermore, we reduce the model complexity, apply different scaling techniques and adapt optimization algorithm settings. The application to a capacitive and a piezoresistive MEMS accelerometer shows significant improvement of efficiency when compared with the use of currently available optimization algorithms.

Use of numerical optimization to determine the effect of the roll stiffness distribution on race car performance

The use of active systems for controlling suspensions has been used before in Formula One and other open wheel racing series but at present this form of active control is not allowed by Formula One regulations. The roll stiffness distribution is a key element of suspension design and it has an influence on the dynamic weight transfer of the vehicle. In this paper, the roll stiffness distribution has been optimized during a calculation process to simulate and quantify the possible benefits of controlling the distribution of roll stiffness between the front and rear axles of an open wheel race car. The roll axis concept has been used to provide the roll component to the lateral load transfer evaluation. The benefits shown by the optimization of the roll stiffness distribution have created a mean handling performance improvement over the base vehicle of over 10 per cent, which on the lap of the Barcelona Grand Prix circuit yielded a lap time improvement of 2.71 s, using a quasi-steady-state calculation method. Additionally, it has been shown how this improvement has been realized in terms of the change in vehicle dynamics. This research also shows that circuit dependent analysis is possible to exploit the value of the static setting of the roll stiffness distribution. Further work and validation are required to explore this avenue of vehicle set-up optimization, but it does appear that the optimized calculation approach offers a way of helping to make an objective choice of a static roll stiffness distribution setting for particular circuits.

Investigation of Resonantly Enhanced Modulators on<tex>$hboxLiNbO_3$</tex>Using FEM and Numerical Optimization Technique

Highly efficient resonantly enhanced modulators on X-cut LiNbO/sub 3/ are investigated through the use of numerical optimization. We describe the optimization technique and present a new design trend relating the link-gain efficiency of optical radio systems that employ external modulation to the choice of modulator electrode geometric dimensions, especially the electrode gap. Using this optimization technique, resonant-type modulators with link gain enhancement up to 6 dB are achievable while maintaining excellent return loss at a resonant frequency of 1.8 GHz. The characteristics of both the optical waveguide and the coplanar electrode are characterized by finite-element simulation.

Search for high-performance probe-fed stacked patches using optimization

High-performance circular probe-fed stacked patch antenna designs are explored through the use of numerical optimization. New trends are sought to aid understanding and to suggest novel solutions. We describe the optimization technique, present a new design trend relating efficiency and bandwidth to the choice of substrate dielectric, and propose and demonstrate a novel, optimized antenna achieving 33% bandwidth whilst maintaining greater than 80% surface wave efficiency.

Adjustment of Exciting Period for a Stepping Motor by Numerical Optimization.

In this work, the authors suggest the use of numerical optimization for on-line adjustment of the exciting period in electronic damping of a stepping motor. The simplex method, which consists of some simple procedures only, is adopted as the optimization technique. In the process of adjustment, a speed sensor is used instead of a position sensor, because of its cheapness. The suggested method is applied to adjustment of the backphasing damping method, and the effectiveness is confirmed

The Electrical Double Layer Parameters for the Group 4 Metal Oxide/Electrolyte System

The electrical double layer parameters for Group 4 metal oxide/NaCl solution systems are presented. The surface charge density and the adsorption of background electrolyte ions as a function of the pH of the solution and the concentration of the electrolyte for the ZrO2 and HfO2 systems are presented. Through the use of numerical optimization, the apparent reaction constants for the surface hydroxy group were calculated. The characteristic points of the electrical double layer and the ionization and complexation constants of the surface hydroxy groups are compared with those predicted semi-theoretically.

CALCULATING MAXIMUM ENTROPY FLOWS IN MULTI-SOURCE, MULTI-DEMAND NETWORKS

Previous work has shown how maximum entropy flows in a water distribution network can be calculated by maximizing a nodal entropy function. This requires the use of numerical nonlinear optimization. In the case of single-source networks a much simpler path entropy formulation exists which permits solutions to be obtained quickly by manual calculations not requiring numerical optimization. This paper extends the path entropy formulation to general multi-source, multi-demand networks and develops a simple manual calculation method for maximum entropy flows in these general networks. The method is quick, non-iterative and does not directly involve the use of numerical optimization. Examples are presented and discussed.

Preliminary Design of Centrifugal Impellers Using Optimization Techniques

The paper proposes a design method which may be used to evaluate the detailed geometry of an impeller (handling compressible and perfect fluid) from a prescribed mean streamline velocity distribution. The analysis makes use of numerical optimization, firstly in the step by step channel geometry calculation, and secondly in controlling the manner in which the relative velocity components are permitted to vary along the mean streamline for the condition of minimum entropy generation along the flow path. The components distribution of the relative velocity were not allowed to take arbitrary values, the variation of the radial, axial and tangential components was governed in such a way that the prescribed diffusion schedule is satisfied at every calculation point. The general configuration of the example design shows it to be well proportional and should not be difficult to manufacture.

H ∞ Disturbance Rejection of LEB Regulators and l 1 Time-domain Bounds

Most of the standard regulator solutions applicable to linear systems focus exclusively on time-domain or frequency-domain results. The few techniques that do accomodate mixed-domain performance specifications provide solutions through the use of numerical optimization but do not give insight into the conditions under which such solutions exist or how to perform tradeoffs. Here we present a technique that allows one to find a regulator to make a linear system satisfy control and output l 1 -norm bounds and, modifying them, to achieve a desired H ∞ -norm of the disturbance to output transfer function. Also, frequency weightings are added to the input and states of the original plant to allow more flexibility in the frequency domain. The effect of a feedforward term on disturbance rejection is analyzed by means of an example.