Robust Optimization Procedure Research Articles

Some studies on optimization of process parameters for wire ARC additive manufacturing of Hastelloy C276 using GRA-GWO hybrid techniques

Wire arc additive manufacturing (WAAM) has become an inevitable manufacturing technology in the present decade. This article discusses optimizing process variables for fabricating Hastelloy C276 alloy via WAAM. The controlling parameters are gas flow rate (GFR), deposition speed, and welding current, while the depth of penetration, top reinforcement, and bead width are the output parameters considered for optimization. The magnitude of interaction effects between control parameters is equal to that of individual impact on the weld bead characteristics evident from analysis of variance results. Grey relational analysis revealed the optimal parameters (trial 1 with I = 120 A, S = 200 mm/min, GFR = 15 L/min) chosen through its robust optimization procedure. S/N ratio analysis revealed the most influencing parameters at the factor level (current level 1, speed level 1). The Grey Wolf optimizer (GWO) algorithm was used as a precision and confirmation experiment. The GWO optimization results further confirmed that the GFR of 15 L/min, speed of 200 mm/min, and current of 120 A were the optimized parameters used in this design space. Further, normal probability plots with minimal error of around 1% reinforce that the parameters chosen in this design space are well within the optimal limits. The surface plots reported the relationship and variation between control and resulting factors.

X-ray production cross sections for Ir and Bi M-subshells induced by electron impact

M-subshell X-ray production cross sections were indirectly measured for Ir and Bi targets irradiated with monoenergetic electron beams. The projectile energy range ran from 2.2 to 28 keV, impinging on Ir and Bi pure bulk targets in a scanning electron microscope. The resulting X-ray emission spectra were acquired with an energy dispersive spectrometer, and processed afterwards by means of a robust parameter optimization procedure developed previously. X-ray production cross sections were finally obtained through an approach involving an analytical prediction for the emission spectra, which relies on the ionization depth distribution function. The values obtained by this approach were compared with empirical and theoretical predictions, appealing to different relaxation data taken from the literature.

Convex Programming-Based Robust Optimization Procedure for Blast-Excited Structures with Bounded Uncertainty

Application of the robust optimization (RO) technique to ensure the least possible deviation of structural performance is gaining increasing attention in recent years. However, most RO studies have been conducted in the probabilistic domain, where sufficient uncertainty information is available to construct probability distribution functions of response parameters. But, in many cases, such as for structures under underground blast excitation, hazard parameters like charge weight and charge center distance do not have any definite probability density function. Only their ranges of variations are known to an engineer. Hence, it is more logical to model these parameters as uncertain-but-bounded (UBB) type, which requires only bounds of variations to characterize the uncertainty. The available RO studies in the UBB-domain mainly deal with static loads. Studies on time-variant dynamic loads, such as blast load, are scarce in the existing literature. Also, blast load time-histories show record-to-record variations in their signatures, even with the same setup of hazard parameters. This aspect cannot be considered by the conventional convex programming approaches of RO in the UBB domain. To address all these issues, a new RO procedure is proposed in the present study, which is based on the dual response surface method. The proposed RO procedure can transform the complex simulation-based RO procedure under dynamic blast load to an equivalent deterministic problem with explicit constraints. Thereby, the RO can be easily solved by a gradient-based optimizer. The effectiveness of the proposed approach is elucidated by the complex real-world problems of a multistory building and an underground reinforced concrete bunker. The results are compared with conventional RO approaches. The results show that the proposed approach consistently yields more economic as well as robust solutions in a computationally efficient way.

Semi-intrusive approach for stiffness and strength topology optimization under uncertainty

A semi-intrusive approach for robust design optimization is presented. The stochastic moments of the objective function and constraints are estimated using a Taylor series-based approach, which requires derivatives with respect to design variables, random variables as well as mixed derivatives. The required derivatives with respect to design variables are determined using the intrusive adjoint method available in commercial software. The partial derivatives with respect to random parameters as well as the mixed second derivatives are approximated non-intrusively using finite differences. The presented approach provides a semi-intrusive procedure for robust design optimization at reasonable computational cost while allowing an arbitrary choice of random parameters. The approach is implemented as an add-on for commercial software. The method and its limitations are demonstrated by academic test cases and industrial applications.

Synthesis of waste heat recovery using solar organic Rankine cycle in the separation of benzene/toluene/p-xylene process

Current energy intensification measures of dividing wall columns are mainly based on vapor recompression and organic Rankine cycle technologies. Vapor recompression can achieve self-heat recovery of the dividing wall column to use a large part of the waste heat. And the organic Rankine cycle recovers the surplus low-temperature waste heat. However, the efficiency of such low-temperature waste heat recovery by organic Rankine cycle is always low. Additionally, the current design of such energy systems is based on conventional fossil fuels, which are not conducive to long-term development. This paper proposes using solar energy to improve the efficiency of low-temperature waste heat recovery. Based on this concept, a novel waste heat recovery combined solar organic Rankine cycle is established, which is integrated into a vapor recompression assisted dividing wall column system to simultaneously recover waste heat and produce electric power. In addition, the organic Rankine cycle and solar organic Rankine cycle assisted systems were compared. Furthermore, a robust solar-energy design and optimization procedure was used to optimize the three proposed schemes by considering the actual solar fluctuations in Islamabad. Performance analysis and techno-economic evaluation were executed under nominal and actual conditions. The results show that solar radiation can increase the waste heat recovery efficiency and reduce the actual total annual cost.

An application of adaptive normalization evolutionary optimization ANMOGA for missile fin design based on trajectory parameters

System design is a complicated and iterative process. Accordingly, a robust optimization procedure should be involved during the design process to minimize complications and time consumed for the whole process. The present research proposes a new methodology to design missile fins that can lessen the gap between the conceptual and final phases during the missile design process. The proposed methodology is based on a new dynamic adaptive multi-objective optimization algorithm accompanied by a selection scheme to choose a single optimum design amongst a Pareto set of solutions. The adaptive normalization multi-objective evolutionary algorithm can be used in any system design. This algorithm is capable of predicting Pareto fronts for multi-objective optimization problems at very good dispersion. In addition, a selection scheme is provided to help decision-makers choose a single optimum amongst Pareto front points. The proposed algorithm is tested against several multi-objective test functions as well as the application of a selection scheme to the obtained Pareto fronts. The results showed the robustness of the proposed algorithm in the prediction of convex fronts. However, it still needs more improvement to deal with non-convex ones. An application for the considered algorithm is also provided as a case study to design tail fins for a conventional missile configuration. The output configuration of the designed fins has very reasonable dimensions when compared to similar configurations.

An interval-based multi-objective robust design optimization for vehicle dynamics

This study presents an Interval-based Multi-objective Robust Design Optimization (IB-MORDO) algorithm applied to a vehicle dynamic problem. The proposed algorithm optimizes a full 15 degrees-of-freedom (15-DOF) vehicle model, subjected to a double-lane change (DLC) maneuver under random road profiles, to attain driver comfort and safety. This study does not make assumptions about uncertain parameter statistics; instead, the uncertainties are quantified using a non-probabilistic α-cut level interval analysis. These uncertainties are applied to the system parameters and design variables to ensure robust results. After the optimization process, the root mean square (RMS) vertical acceleration at the driver’s seat resulted in a robust solution of 1.041 m/s2 and a parameter interval radius (IR) equals to 0.631 m/s2, whereas the RMS lateral acceleration at the driver’s seat resulted in a solution of 1.908 m/s2 with an interval radius of 0.168 m/s2. Unlike the Robust Optimization, the algorithm proposed herein considers uncertainties at system parameters and design variables without assuming any statistical data. HIGHLIGHTS An Interval-based Robust Multi-objective Optimization procedure is proposed and tested on a 15-DOF vehicle model. Αn α-cut level methodology is used to deal with the uncertainty propagation. Resulted optimal suspension parameters minimize center and interval radius of driver’s vertical and lateral accelerations.

Robust Optimization for Stability of I-Walls and Levee System Resting on Sandy Foundation

During Hurricane Katrina in 2005 and the events thereafter, failures of levees with I-walls caused extensive flooding and damage. The geological background in the New Orleans area and associated uncertainties contributed significantly to the failures. To increase the robustness of the I-walls and levee system and reduce the associated risk of failure, the uncertainties of the system must be incorporated into the design procedures, especially in a geological environment mainly composed of sand deposits. This paper presents a robust optimization procedure to identify optimal designs for the stability of an I-walls and levee system supported on sandy foundation soil in the face of flood hazards. The uncertainties associated with the I-walls and levee system, including the strength parameters of levee and foundation soils and the height of the floodwater behind the I-walls, were considered in a systematic manner. The wall embedded depth, levee crown width, and slope ratio of the levee in the landside were considered as the design parameters. For the robust optimization, the construction cost of the I-walls and levee system and the standard deviation of the failure probability were considered as the design objectives. Finally, the multi-objective optimization resulted in a set of acceptable designs that were presented in a graphical form called Pareto front, which is combined with the knee point concept to provide useful decision aids for selecting the most preferred design that meets both the economics and performance requirements.

Special Section on Degradation Prediction and Recycling of Renewable Energy and Energy Storage Systems: Scenarios of 2020–2025

Abstract Given the degrading environment, countries across the globe have strongly emphasized the development and deployment of renewable energy and energy storage systems across various sectors such as residential, commercial, industry, rural households, charging stations, etc. Given with this pace of deployment, there will be unforeseen problems in next decade on how to diagnose, perform online monitoring and regular maintenance and recycle these millions of these renewable energy and energy storage systems whose life span is over (spent systems). Main challenges that exist includes the heterogeneity of the systems (different standards, size and shape) adding complexity to recycling procedures, laboratory based models having assumptions for online prediction and monitoring, non-uniform reusability and recycling procedures. Due to this, the process adopted for recycling and reusability of the spent systems is mainly manual. There is a strong need for designing and developing the automation, Artificial intelligence (AI) and robust optimization procedures for making these recycling and reusability procedures smart and efficient

Methodology for the Implementation of Internal Standard to Laser-Induced Breakdown Spectroscopy Analysis of Soft Tissues.

The improving performance of the laser-induced breakdown spectroscopy (LIBS) triggered its utilization in the challenging topic of soft tissue analysis. Alterations of elemental content within soft tissues are commonly assessed and provide further insights in biological research. However, the laser ablation of soft tissues is a complex issue and demands a priori optimization, which is not straightforward in respect to a typical LIBS experiment. Here, we focus on implementing an internal standard into the LIBS elemental analysis of soft tissue samples. We achieve this by extending routine methodology for optimization of soft tissues analysis with a standard spiking method. This step enables a robust optimization procedure of LIBS experimental settings. Considering the implementation of LIBS analysis to the histological routine, we avoid further alterations of the tissue structure. Therefore, we propose a unique methodology of sample preparation, analysis, and subsequent data treatment, which enables the comparison of signal response from heterogenous matrix for different LIBS parameters. Additionally, a brief step-by-step process of optimization to achieve the highest signal-to-noise ratio (SNR) is described. The quality of laser–tissue interaction is investigated on the basis of the zinc signal response, while selected experimental parameters (e.g., defocus, gate delay, laser energy, and ambient atmosphere) are systematically modified.

Design and Optimization of a Radial Turbine to Be Used in a Rankine Cycle Operating with an OTEC System

Design and optimization of a radial turbine for a Rankine cycle were accomplished ensuring higher thermal efficiency of the system despite the low turbine inlet temperature. A turbine design code (TDC) based on the meanline design methodology was developed to construct the base design of the turbine rotor. Best design practices for the base design were discussed and adopted to initiate a robust optimization procedure. The baseline design was optimized using the response surface methodology and by coupling it with the genetic algorithm. The design variables considered for the study are rotational speed, total to static speed ratio, hub radius ratio, shroud radius ration, and number of blades. Various designs of the turbine were constructed based on the Central Composite Design (CCD) while performance variables were computed using the in-house turbine design code (TDC) in the MATLAB environment. The TDC can access the properties of the working fluid through a subroutine that links NIST’s REFPROP to the design code through a subroutine. The finalization of the geometry was made through an iterative process between 3D-Reynolds-Averaged Navier-Stokes (RANS) simulations and the one-dimensional optimization procedure. 3D RANS simulations were also conducted to analyze the optimized geometry of the turbine rotor for off-design conditions. For computational fluid dynamics (CFD) simulation, a commercial code ANSYS-CFX was employed. 3D geometry was constructed using ASYS Bladegen while structured mesh was generated using ANSYS Turbogrid. Fluid properties were supplied to the CFD solver through a real gas property (RGP) file that was constructed in MATLAB by linking it to REFPROP. Computed results show that an initial good design can reduce the time and computational efforts necessary to reach an optimal design successfully. Furthermore, it can be inferred from the CFD calculation that Response Surface Methodology (RSM) employing CFD as a model evaluation tool can be highly effective for the design and optimization of turbomachinery.

Fuzzy robust control applied to rotor supported by active magnetic bearing

The technology associated with active magnetic bearings has been widely used in the last years and can be considered as being one of the most promising solutions for several applications in rotating machinery. Lubricants are not necessary, and high rotation speeds are reached without any relevant heating. Active magnetic bearings are classified as mechatronic systems because they are composed of mechanical and electronic parts that are controlled by using dedicated software. In this context, the present work is devoted to the design of robust controllers applied to supercritical rotors supported by active magnetic bearings. For this aim, numerical and experimental tests were carried out. Different from previous studies reported in the literature, the present contribution proposes a novel design procedure to robustify the neuro-fuzzy controller of a rotor supported by active magnetic bearings based on optimal robust design. This optimal design procedure tunes the robust neuro-fuzzy controller taking into account the optimal balance between vibration attenuation performance and robustness, that is the increase in vibration attenuation implies the reduction in the robustness. The first stage of the controller synthesis is dedicated to the specification of all design requirements. Then, the adaptative neuro-fuzzy controller was obtained, starting from the determination of the plant dominant poles and finally performing the model-based analysis of the system stability and performance. Finally, the vibration control performance and robustness are optimally balanced by using a robust optimization procedure. The behavior of the controller was evaluated by investigating the unbalance response of the rotating system. The obtained results demonstrated the effectiveness of the conveyed approach.

Robust evolutionary shape optimization for ergonomic excellence based on contact pressure distribution

The aim of this paper is the development of a robust evolutionary shape optimization procedure for ergonomic excellence based on contact pressure distribution. FEM - based numerical analysis is implemented to obtain the resulting contact pressure distribution. An example of person-seat interaction is analysed in this paper since plenty of experimental data set exists on this topic. A simplified geometrical model of the human body and seat is used and partly parameterized using a generic B-spline surface. The impact of the changes in geometry on the pressure distribution is analysed by the optimizer, and the seat geometry is steered into a shape with minimal high contact pressure areas. The procedure is general and can be adapted (with changes in geometry and boundary conditions) to distinct ergonomic problems such as footwear, therapeutic beds, automotive or aeronautical seating. The developed procedure can aid in virtual testing during the seat development phase in cases when the seat is designed for a selected population or for a single person and expected postural variations.

Preference elicitation and robust winner determination for single- and multi-winner social choice

The use of voting schemes based on rankings of alternatives to solve social choice problems can often impose significant burden on voters, both in terms of communication and cognitive requirements. In this paper, we develop techniques for preference elicitation in voting settings (i.e., vote elicitation) that can alleviate this burden by minimizing the amount of preference information needed to find (approximately or exactly) optimal outcomes. We first describe robust optimization techniques for determining winning alternatives given partial preference information (i.e., partial rankings) using the notion of minimax regret. We show that the corresponding computational problem is tractable for some important voting rules, and intractable for others. We then use the solution to the minimax-regret optimization as the basis for vote elicitation schemes that determine appropriate preference queries for voters to quickly reduce potential regret. We apply these techniques to multi-winner social choice problems as well, in which a slate of alternatives must be selected, developing both exact and greedy robust optimization procedures. Empirical results on several data sets validate the effectiveness of our techniques.

Bounded distortion tetrahedral metric interpolation

We present a method for volumetric shape interpolation with unique shape preserving features. The input to our algorithm are two or more 3-manifolds, immersed into R 3 and discretized as tetrahedral meshes with shared connectivity. The output is a continuum of shapes that naturally blends the input shapes, while striving to preserve the geometric character of the input. The basis of our approach relies on the fact that the space of metrics with bounded isometric and angular distortion is convex [Chien et al. 2016b]. We show that for high dimensional manifolds, the bounded distortion metrics form a positive semidefinite cone product space. Our method can be seen as a generalization of the bounded distortion interpolation technique of [Chen et al. 2013] from planar shapes immersed in R 2 to solids in R 3 . The convexity of the space implies that a linear blend of the (squared) edge lengths of the input tetrahedral meshes is a simple yet powerful-and-natural choice. Linearly blending flat metrics results in a new metric which is, in general, not flat, and cannot be immersed into three-dimensional space. Nonetheless, the amount of curvature that is introduced in the process tends to be very low in practical settings. We further design an extremely robust nonconvex optimization procedure that efficiently flattens the metric. The flattening procedure strives to preserve the low distortion exhibited in the blended metric while guaranteeing the validity of the metric, resulting in a locally injective map with bounded distortion. Our method leads to volumetric interpolation with superb quality, demonstrating significant improvement over the state-of-the-art and qualitative properties which were obtained so far only in interpolating manifolds of lower dimensions.

Operational stability of a spark ignition engine fuelled by low H2 content synthesis gas: Thermodynamic analysis of combustion and pollutants formation

The paper focuses on the implementation of a comprehensive and robust optimization procedure for a synthesis gas fired four-cylinder, spark ignited, 2.2 L industrial engine used in combined heat and power applications. Innovatively designed workflow is for the first time incorporating also a thorough operational stability analysis for evaluation of the engine operation durability while using off-design fuels. Design constraints of the engine operational space are set after in depth investigation of knock phenomena, cycle to cycle variations, emission formation phenomena and engine performance parameters. These are derived from experimental data, obtained from the engine, equipped with newly designed components. Throughout the paper, results obtained with synthesis gas are benchmarked to natural gas. With significant emphasis laid on analysis of lean operation conditions, as a measure to reduce environmental footprint of energy generation, a newly proposed optimum operation points reveal a possibility to obtain TA-Luft and EPA emission limits already with stoichiometric mixture. This allows to achieve a remarkably low power de-rating factor of only 16.5% and omission of any aftertreatment system. Therefore, findings of this study represent a significant improvement of current control strategies and enable further increase in specific power and thus economic attractiveness of distributed power generation techniques at enhanced durability while using low-carbon and renewable fuels.

A Pixelated Microwave Near-Field Sensor for Precise Characterization of Dielectric Materials

A highly sensitive microwave near-field sensor based on electrically-small planar resonators is proposed for highly accurate characterization of dielectric materials. The proposed sensor was developed in a robust complete-cycle topology optimization procedure wherein first the sensing area was pixelated. By maximizing the sensitivity as our goal, a binary particle swarm optimization algorithm was applied to determine whether each pixel is metalized or not. The outcome of the optimization is a pixelated pattern of the resonator yielding the maximum possible sensitivity. A curve fitting method was applied to the full-wave simulation results to derive a closed form expression for extracting the dielectric constant of a chemical material from the shift in the resonance frequency of the sensor. As a proof of concept, the sensor was fabricated and used to measure the permittivity of two known liquids (cyclohexane and chloroform) and their mixtures with different volume ratios. The experimentally extracted dielectric constants were in an excellent agreement with the reference data (for pure cyclohexane and chloroform) or those obtained by mixture formulas.

A reduced random sampling strategy for fast robust well placement optimization

Model-based decision-making in oilfield development often involves hundreds of computationally demanding reservoir simulation runs. In particular, well placement optimization under uncertainty in the geologic representation of the reservoir model is an overly time-consuming procedure as the performance of any proposed well configuration needs to be evaluated over multiple realizations, using computationally expensive flow simulations. To reduce computation, we propose an efficient robust optimization procedure in which at each iteration of the optimization procedure, instead of evaluating the well configuration over all available realizations, we approximate the expected performance using a small subset of randomly selected model realizations. Since the samples are selected randomly, all the realizations are expected to eventually be included in the performance evaluation after a certain number of iterations. However, using only a few random realizations to compute the expected cost function introduces noise in the estimated objective function, necessitating the use of a stochastic optimizer. In this paper, we use the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, which is known to be robust against noise in the objective function. We first evaluate the performance of different forms of the SPSA algorithm (including discrete, continuous, and adaptive) using several numerical experiments, followed by a discussion of the properties of the proposed reduced random sampling approach and comparison with global optimization techniques. The method is applied to several numerical experiments, including case studies involving vertical, horizontal, and lateral wells, to evaluate its performance. The results from these experiments indicate that the reduced random sampling approach can provide significant computational gain with minimal impact on the attained optimization performance.

Robust trajectory optimization using polynomial chaos and convex optimization

The polynomial chaos (PC) theory and direct collocation method have been integrated to solve a lot of robust trajectory optimization problems. However, the computational cost and memory consumption increase significantly with the increase of the dimension of uncertain factors, and the nonlinearity of dynamic equations. To address this issue, a novel robust trajectory optimization procedure combining PC with the convex optimization technique is proposed in this paper. With the proposed procedure, the trajectory optimization can be implemented with high accuracy and efficiency, by taking advantage of the high accuracy of PC in addressing UP for highly nonlinear dynamics and the high efficiency of convex optimization in solving optimal control. The proposed robust trajectory optimization procedure is applied to two examples and compared with the existing method employing PC and the pseudospectral method. The results show that the proposed procedure can obtain highly accurate results similar to the existing method. Moreover, with the increase of random dimension, the optimal trajectory can still be generated very efficiently without significant increase of computational cost. These results demonstrates the effectiveness of the proposed procedure.

An efficient robust cost optimization procedure for rice husk ash concrete mix

As rice husk ash (RHA) is not produced in controlled manufacturing process like cement, its properties vary significantly even within the same lot. In fact, properties of Rice Husk Ash Based Concrete (RHABC) are largely dictated by uncertainty leading to huge deviations from their expected values. This paper proposes a Robust Cost Optimization (RCO) procedure for RHABC, which minimizes such unwanted deviation due to uncertainty and provides guarantee of achieving desired strength and workability with least possible cost. The RCO simultaneously minimizes cost of RHABC production and its deviation considering feasibility of attaining desired strength and workability in presence of uncertainty. RHA related properties have been modeled as uncertain-but-bounded type as associated probability density function is not available. Metamodeling technique is adopted in this work for generating explicit expressions of constraint functions required for formulation of RCO. In doing so, the Moving Least Squares Method is explored in place of conventional Least Square Method (LSM) to ensure accuracy of the RCO. The efficiency by the proposed MLSM based RCO is validated by experimental studies. The error by the LSM and accuracy by the MLSM predictions are clearly envisaged from the test results. The experimental results show good agreement with the proposedMLSMbased RCO predicted mix properties. The present RCO procedure yields RHABC mixes which is almost insensitive to uncertainty (i.e., robust solution) with nominal deviation from experimental mean values. At the same time, desired reliability of satisfying the constraints is achieved with marginal increment in cost.