Numerical Optimization Approach Research Articles

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

The aim of this paper is to determine the optimal open loop solution and a nonlinear delay‐dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

Optimal control of diffuser shapes for non-uniform flow

A simplified model is used to identify the diffuser shape that maximises pressure recovery for several classes of non-uniform inflow. We find that optimal diffuser shapes strike a balance between not widening too soon, as this accentuates the non-uniform flow, and not staying narrow for too long, which is detrimental for wall drag. Three classes of non-uniform inflow are considered, with the axial velocity varying across the width of the diffuser entrance. The first case has inner and outer streams of different speeds, with a velocity jump between them that evolves into a shear layer downstream. The second case is a limiting case when these streams are of similar speed. The third case is a pure shear profile with linear velocity variation between the centre and outer edge of the diffuser. We describe the evolution of the time-averaged flow profile using a reduced mathematical model that has been previously tested against experiments and computational fluid dynamics models. The model consists of integrated mass and momentum equations, where wall drag is treated with a friction factor parameterisation. The governing equations of this model form the dynamics of an optimal control problem where the control is the diffuser channel shape. A numerical optimisation approach is used to solve the optimal control problem and Pontryagin’s maximum principle is used to find analytical solutions in the second and third cases. We show that some of the optimal diffuser shapes can be well approximated by piecewise linear sections. This suggests a low-dimensional parameterisation of the shapes, providing a structure in which more detailed and computationally expensive turbulence models can be used to find optimal shapes for more realistic flow behaviour.

Benchmarking the HRP-2 Humanoid Robot During Locomotion.

In this paper we report results on benchmarking a HRP-2 humanoid robot. The humanoid robots of this serie are known to be very robust. They have been successfully used by several research groups for the design of new motion generation algorithms. As such it is a reference in the category of electrically driven humanoid robot. As new humanoid robots are continuously built it is interesting to compare the performances of these new prototypes to those of HRP-2. This benchmarking study was realized through a campaign of measurements in an advanced equipped testing laboratory that provides a well adapted controlled environment. We have investigated the effect of temperatures variation on the robot walking capabilities. In order to benchmark various environmental conditions and algorithms we computed a set of performance indicators for bipedal locomotion. The scope of the algorithms for motion generation evaluated here ranges from analytical solution to numerical optimization approach, enabling real-time walking or multi-contacts motions.

Influence of altered geometry and material properties on tissue stress distribution under load in tendinopathic Achilles tendons – A subject-specific finite element analysis

Achilles tendon material properties and geometry are altered in Achilles tendinopathy. The purpose of this study was to determine the relative contributions of altered material properties and geometry to free Achilles tendon stress distribution during a sub-maximal contraction in tendinopathic relative to healthy tendons. Tendinopathic (n = 8) and healthy tendons (n = 8) were imaged at rest and during a sub-maximal voluntary isometric contraction using three-dimensional freehand ultrasound. Images were manually segmented and used to create subject-specific finite element models. The resting cross-sectional area of the free tendon was on average 31% greater for the tendinopathic compared to healthy tendons. Material properties for each tendon were determined using a numerical parameter optimisation approach that minimised the difference in experimentally measured longitudinal strain and the strain predicted by the finite element model under submaximal loading conditions for each tendon. The mean Young’s modulus for tendinopathic tendons was 53% lower than the corresponding control value. Finite element analyses revealed that tendinopathic tendons experience 24% less stress under the same submaximal external loading conditions compared to healthy tendons. The lower tendon stress in tendinopathy was due to a greater influence of tendon cross-sectional area, which alone reduced tendon stress by 30%, compared to a lower Young’s modulus, which alone increased tendon stress by 8%. These findings suggest that the greater tendon cross-sectional area observed in tendinopathy compensates for the substantially lower Young’s modulus, thereby protecting pathological tendon against excessive stress.

Topology Optimization of Segmented Thermoelectric Generators

The thermoelectric (TE) power output, $$f_P$$ , and conversion efficiency, $$f_{\eta }$$ , for segmented thermoelectric generators (TEGs) have been optimized by spatially distributing two TE materials (BiSbTe and Skutterudite) using a numerical gradient-based topology optimization approach. The material properties are temperature-dependent, and the segmented TEGs are designed for various heat transfer rates at the hot and cold reservoirs. The topology-optimized design solutions are characterized by spike-shaped features which enable the designs to operate in an intermediate state between the material phases. Important design parameters, such as the device dimensions, objective functions and heat transfer rates, are identified, investigated and discussed. Comparing the topology optimization approach with the classical segmentation approach, the performance improvements of $$f_P$$ and $$f_{\eta }$$ design problems depend on the heat transfer rates at the hot and the cold reservoirs, the objective function and the device dimensions. The largest performance improvements for the problems investigated are $$\approx $$ 6%.

Integrated-reservoir-model-based critical oil rate correlation for vertical wells in thin oil rim reservoirs in the Niger Delta

Thin oil rim reservoirs are mostly characterized by development and production challenges; one of which is early water coning tendency. In the Niger Delta, most developed critical oil rate correlations to avert coning focused on conventional bottom-water drive reservoirs, while thin oil rim reservoirs received limited attention. Available correlations to estimate critical oil rate of thin oil rim reservoirs in Niger Delta are based on generic reservoir models, which does not consider the reservoir heterogeneity. Hence, it leaves these available correlations’ predictions in doubt, considering the sensitive nature of developing thin oil rim reservoirs. Thus, a correlation for critical oil rate (qc) based on integrated reservoir model in the Niger Delta was develop for thin oil rim reservoirs using multivariable numerical optimization approach. The obtained result indicated that the developed correlation predicted 226.05 bbl/day compared to the actual Oilfield critical oil rate of 226.11 bbl/day. Furthermore, sensitivity study indicated that the developed correlation and the integrated reservoir model predictions of fractional well penetration (hp/h) and height below perforation - oil column (hbp/h) on critical oil rate (qc) were close and resulted in coefficient of determination (R2) of 0.9266 and 0.9525, Chi square (X2) of 0.539 and 0.655, and RMSE of 4.336 and 4.357. Additionally, the results depict that critical oil rate depends indirectly on fractional well penetration and directly on height above perforation for vertical wells. Therefore, to delay water-coning tendency in thin oil rim reservoirs these completion parameters are consideration in vertical wells to establish optimum critical oil rate during hydrocarbons production. Also, the developed correlation can be used as a quick tool to estimate critical oil rate of thin oil rim reservoirs in the Niger Delta.

Enhancement of wear resistance of Ti—6Al—4V alloy by picosecond laser surface micro texturing process

A pulsed, picosecond Nd:YAG laser with a wavelength of 532 nm is used to texture the surface of grade 5 titanium alloy (Ti—6Al—4V) for minimizing its wear rate. The wear properties of the base samples and laser surface textured samples are analyzed by conducting wear tests under a sliding condition using pin-on-disk equipment. The wear tests are conducted based on the Box—Benhken design, and the interaction of the process parameters is analyzed using response surface methodology. The wear analysis is conducted by varying the load, rotating speed of the disc, and track diameter at room temperature with a sliding distance of 1500 m. The results demonstrate that the laser textured surfaces exhibited a lower coefficient of friction and good anti-wear properties as compared with the non-textured surfaces. A regression model is developed for the wear analysis of titanium alloy using the analysis of variance technique. It is also observed from the analysis that the applied load and sliding distance are the parameters that have the greatest effect on the wear behavior followed by the wear track diameter. The optimum operating conditions have been suggested based on the results obtained from the numerical optimization approach.

Empirical values of branching ratios in the three-body recombination reaction for O(1S) and O2(0,0) airglow chemistry

The branching ratios ε and α in the three-body recombination reaction for O(1S) greenline and O2(0,0) atmospheric band airglow chemistry represent the fraction of O2 that branch into the b1∑g+ and c1∑u- electronic states, respectively. In the present work, the empirical values of these branching ratios have been deduced using a numerical optimization approach. They were obtained using the optimization scheme known as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with our MACD-00 model and simultaneous volume emission rate (VER) measurements of the O(1S) greenline and O2(0,0) atmospheric band emissions. The CMA-ES was employed as the optimization algorithm that would match the O(1S) and O2(0,0) VER profiles simulated by the MACD-00 model to observations made by OXYGEN/S35, S310.10, NASA Flight 4.339, ETON flights P229H and P230H, OASIS, SOAP/WINE, MULTIFOT, and WINDII. We found that most of the values deduced for ε were in the [0.1, 0.3] range, while most of the values of α were in the [0.01, 0.03] range. Excluding the outliers, the average branching ratio values involving the production of O2(b1∑g+) and O2(c1∑u-) were determined to be ε = 0.15 ± 0.02 and α = 0.018 ± 0.004, respectively. Overall, the simulations showed good agreement with the observations albeit with some discrepancies in the peak altitudes and shape of the profiles, possibly due to small perturbations in the observed VER profiles that are not considered in our simulations.

Closed-Form Expressions for Channel Shortening Receivers Using $A\ Priori$ Information

Channel shortening has been studied in the context of intersymbol interference and multi-in multi-out channels as a means to compute a posteriori probabilities with a BCJR algorithm at a reduced computational complexity. This is done by considering an approximate channel response of reduced length. In a turbo receiver, soft a priori information can be linearly combined with the received sequence to form a new input to the BCJR trellis-based processing. In this letter, we provide closed-form expressions for the channel shortening filters using a generalized mutual information objective function. The proposed receiver allows a complexity reduction with respect to numerical optimization approaches which may also present stability, precision, and convergence issues.

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization.

In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach. The model represents the words using circles, the time-varying area of which displays the importance of the words in each time period. Word location in the visualization region is guided by three criteria, namely, the accurate representation of semantic relatedness, the spread of the words in the visualization region to improve the quality of the visualization, and the visual stability over the time horizon. Our approach is flexible, allowing the user to interact with the display, as well as incremental and scalable. We show results for three case studies using data from Danish news sources.

Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy Data: A Review on Retrieval Methods.

An unprecedented spectroscopic data stream will soon become available with forthcoming Earth-observing satellite missions equipped with imaging spectroradiometers. This data stream will open up a vast array of opportunities to quantify a diversity of biochemical and structural vegetation properties. The processing requirements for such large data streams require reliable retrieval techniques enabling the spatiotemporally explicit quantification of biophysical variables. With the aim of preparing for this new era of Earth observation, this review summarizes the state-of-the-art retrieval methods that have been applied in experimental imaging spectroscopy studies inferring all kinds of vegetation biophysical variables. Identified retrieval methods are categorized into: (1) parametric regression, including vegetation indices, shape indices and spectral transformations; (2) nonparametric regression, including linear and nonlinear machine learning regression algorithms; (3) physically based, including inversion of radiative transfer models (RTMs) using numerical optimization and look-up table approaches; and (4) hybrid regression methods, which combine RTM simulations with machine learning regression methods. For each of these categories, an overview of widely applied methods with application to mapping vegetation properties is given. In view of processing imaging spectroscopy data, a critical aspect involves the challenge of dealing with spectral multicollinearity. The ability to provide robust estimates, retrieval uncertainties and acceptable retrieval processing speed are other important aspects in view of operational processing. Recommendations towards new-generation spectroscopy-based processing chains for operational production of biophysical variables are given.

Topology optimization of conductive heat transfer devices: An experimental investigation

For optimal tree-like heat conductive structures obtained numerically by topology optimization (TO), few experimental investigations exist in the literature to author’s knowledge. In this context, the present study deals with an experimental investigation of tree-like structures obtained by topology optimization (known also by bi-material volume-to-point problems). For a volume (of lower conductivity material) that is continuously generating heat, TO predicts tree-like structures (of higher conductivity material) to evacuate efficiently the amount of heat being generated. Experimental measurements were carried out on two tree-like structures using infrared thermography in order to test the validity of the developed numerical topology optimization approach. It is found that the experimental thermal measurements are in good agreement with numerical data obtained by TO, which was developed in this work by coupling the method of moving asymptotes (MMA) as optimization algorithm to the solid isotropic material with penalization (SIMP) as a bi-material distribution technique.

Numerical optimization of gourd-shaped surface texture and experiment of tribological performance

A numerical optimization approach based on the finite element (FE) simulation was used to design the optimum irregular gourd-shaped pattern parameters for generating the highest hydrodynamic pressure. Then the optimum parameters of the gourd-shaped surface texture were determined and the textures were processed on the stainless steel surface by the laser technology. The tribological performance of gourd-shaped surface texture was analyzed using the type of UMT2 tester, and compared with that of the regular circle surface texture and none-texture surface by considering the effect of sliding speeds and applied loads on the tribological performance. The results show that the compound factor n, the diameter ratio Dr and the texture depth Hd are more significant parameters and the optimum values are 0.618, 2.0 and 4 μm, respectively. In addition, irregular gourd-shaped surface texture with optimum parameters is the most effective in the friction reduction among the patterns investigated under different speeds and applied loads in this work. Moreover, better coordination and combination effect can be obtained by gourd-shaped surface texture. The main reason responsible for the results is the irregular symmetric nature of the gourd-shaped texture along the direction of lubricants flowing which can generate the higher fluid dynamic pressure.

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

Optimization Settings in the Fuzzy Combined Mamdani PID Controller

In the present work the actual problem of determining the optimal settings of fuzzy parallel proportional-integral-derivative (PID) controller is considered to control nonlinear plants that is not always possible to perform with classical linear PID controllers. In contrast to the linear fuzzy PID controllers there are no analytical methods of settings calculation. In this paper, we develop a numerical optimization approach to determining the coefficients of a fuzzy PID controller.Decomposition method of optimization is proposed, the essence of which was as follows. All homogeneous coefficients were distributed to the relevant groups, for example, three error coefficients, the three coefficients of the changes of errors and the three coefficients of the outputs P, I and D components. Consistently in each of such groups the search algorithm was selected that has determined the coefficients under which we receive the schedule of the transition process satisfying all the applicable constraints. Thus, with the help of Matlab and Simulink in a reasonable time were found the factors of a fuzzy PID controller, which meet the accepted limitations on the transition process.

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 design of thin-walled functionally graded beams for buckling problems

This paper presents a modeling as well as a numerical approach for geometric and material optimization of thin-walled functionally graded I-shaped cross-section beam focusing on lateral and flexural–torsional buckling problems. Material properties are assumed to be varied through the shell thickness by a non-monotonic function in which volume fractions of constituent phases have been estimated according to a piecewise cubic interpolation. Governing buckling equations, also a finite element method based on Vlasov’s thin-walled theory are developed. Genetic algorithm (GA) is utilized as an optimal tool that preserving the computational efficiency of the overall analysis. N-point volume fraction through-the-thickness direction, as well as width-to-thickness, span-to-height ratios are simultaneously considered as design variables. The obtained critical buckling parameters are verified via several benchmark problems. Optimum results are found to be beneficial for a specific design of thin-walled functionally graded beams.

Portfolio selection in a multi-moment setting: A simple Monte-Carlo-FDH algorithm

This paper proposes a non-parametric efficiency measurement approach for the static portfolio selection problem in a general inputs–outputs space, where inputs can include variance and kurtosis and outputs can include mean and skewness. Our work is in the vein of Briec, Kerstens, and Jokung (2007) and Jurzenko, Maillet, and Merlin (2006) who develop a directional distance (shortage function) approach to evaluate the performance of portfolios in Mean–Variance–Skewness and in Mean–Variance–Skewness–Kurtosis spaces. Our approach use the Free Disposal Hull (FDH) estimator to derive an algorithm avoiding the heavy and non-robust numerical optimization approaches suggested so far. This new approach is much faster, more robust to reach the optimum and more flexible since it can be extended to more general situations. We illustrate the algorithm with a data set on the French CAC 40 already used in the literature, to compare our method with the numerical optimization approaches. It appears that our approach is much more performant than the numerical optimization techniques, both in terms of computing time, but also in terms of robustness, avoiding the pitfall of local numerical optima.

Model-based optimal scenario planning in EAST

Ongoing work in the fusion community focuses on developing advanced plasma scenarios characterized by high plasma confinement, magnetohydrodynamic (MHD) stability, and noninductively driven plasma current. The toroidal current density profile, or alternatively the q profile, together with the normalized beta, are often used to characterize these advanced scenarios. The development of these advanced scenarios is experimentally carried out by specifying the devices’ actuator trajectory waveforms, such as the total plasma current, the plasma density, and the auxiliary heating and current-drive (H&CD) sources based on trial-and-error basis. In this work, a model-based numerical optimization approach is followed to complement the experimental effort on actuator trajectory planning in the EAST tokamak. The evolution of the q profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). In this work, the MDE is combined with physics-based correlations obtained from EAST experimental data for the plasma density, temperature, resistivity and non-inductive current drives to develop a control-oriented nonlinear PDE model. The optimization objective is to design feedforward trajectories for the plasma current, plasma density, electron cyclotron heating power, neutral beam injection power and lower hybrid current drive power that steer the plasma to desired q profile and βN such that the achieved state is stationary in time. The optimization is subject to the plasma dynamics (described by the physics-based PDE model) and plasma state and actuator constraints, such as the maximum available amount of H&CD power and MHD stability limits. This defines a nonlinear, constrained optimization problem that is solved by employing sequential quadratic programming. The optimized actuator trajectories are assessed in nonlinear transport simulations in preparation for experimental tests in EAST.

Efficient and multi-objective cavitating propeller optimization: An application to a high-speed craft

The design of a propeller for a high-speed craft is addressed by using a multi-objective numerical optimization approach. By combining a fast and reliable Boundary Elements Method (BEM), a viscous flow solver based on the RANSE approximation, a parametric 3D description of the blade and a genetic algorithm, the new propeller shape is designed to improve the propulsive efficiency, reduce the cavitation extension, increase the cavitation inception speed and maximize, at the same time, the ship speed. Rather than by constraining the propeller delivered thrust, indeed, the proposed procedure works together with an engine-propeller matching algorithm that, each time a new propeller is defined, identifies the achievable maximum ship speed and the resulting engine functioning point that turn in additional goals for the multi-objective optimization. A set of optimal propellers, obtained through the design by optimization based on potential flow calculations (via the Boundary Elements Method), are selected for additional viscous analyses (RANSE calculations) in order to further validate the results of the BEM calculations and provide a deeper insight into the complex flow fields of high speed propellers. Among this subset of optimal configurations, a final geometry is selected to verify the reliability of the design procedure by means of dedicated cavitation tunnel tests and full-scale measurements on a high-speed craft provided by Azimut|Benetti.