Sequential Optimization Procedure Research Articles

Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column

This study focuses on separating a mixture consisting of 1,2-ethanediol (1,2-ED), 1,3-propanediol (1,3-PD), and 1,4-butanediol (1,4-BD). Vapor–liquid equilibrium (VLE) data for 1,2-ED + 1,4-BD and 1,3-PD + 1,4-BD are determined at 101.3 kPa using a modified Rose equilibrium still. The consistency of the VLE data is checked with both Redlich–Kister and Fredenslund tests. The VLE data are fitted by the Wilson, NRTL, and UNIQUAC activity coefficient models. All three models can effectively correlate the VLE data. Then, the separation of the mixture is designed with the NRTL model and its correlated binary interaction parameters. A liquid-only transfer dividing wall column (LDWC) is investigated on the basis of a direct conventional distillation sequence (DCDS). For a fair comparison, both DCDS and LDWC are optimized to minimize total annual cost using sequential iterative optimization procedures. After optimization, LDWC exhibits a 16.87% reduction in total annual cost, while cooling and heating utility consumptions are reduced by 28.40% and 19.24% compared to DCDS.

Energy, exergy, economic, and environmental analysis of a novel liquid-only transfer dividing wall column with vapor recompression

The Kaibel dividing wall column (KDWC) uses a thermal coupling technology for separating quaternary mixtures, which exhibits less energy consumption and more economic benefits than a conventional distillation sequence (CDS). However, it is hard to control the vapor split ratio, which limits the industrialization of KDWC. The liquid-only transfer dividing wall column (LDWC) doesn’t involve the vapor split ratio. It has been verified as equivalent to KDWC. To improve LDWC’s performance further, four novel vapor recompression-assisted LDWCs are proposed according to the column grand composite curve analysis. And CDS and LDWC are taken as the base cases for comparison. Then, the processes are optimized by the sequential iterative optimization procedures to minimize the total annual cost. The performance of optimized processes is systematically evaluated through energy, exergy, economic, and environmental (4E) analysis. The results demonstrate that the SCVRC-IR-LDWC2, equipped with a side condenser and intermediate reboiler involved in lower vapor side stream withdrawal, performs well in the total annual cost, energy consumption, gas emissions, and thermodynamic efficiency.

Linear system identification using the sequential stabilizing spline algorithm

Paradoxically, even if stability (with its many facets) is the key concept in control, including system stability constraints in an identification procedure is still an unresolved puzzle under many aspects. In fact, also in the linear setting there is no procedure proposed in the literature able to estimate the dominant pole of a dynamic system ensuring stability. In this paper, we design a new algorithm, namely the sequential stabilizing spline (SSS) algorithm, which fills this gap. Our approach determines the system’s stability radius by combining Gaussian regression and stochastic simulation, using stable spline kernels to model the one-step ahead predictor impulse responses. Then, a stable model is recovered through a novel sequential convex optimization procedure whose computational time is orders of magnitude faster than approaches based on linear matrix inequalities (LMI). Numerical experiments are included and show that SSS can return models with high long-term predictive capability. SSS performance is comparable to that achieved by classical prediction error methods equipped with an oracle that has access to the test set to tune the best model order for any prediction horizon.

Energy-saving investigation of vacuum reactive distillation for the production of ethyl acetate

Abstract Ethyl acetate (EtAc) reactive distillation (RD) configurations often use atmospheric pressure, and this operating pressure can be reduced further to conserve energy based on the condenser cooling water temperature. Using the Aspen Plus simulator, two proposed configurations, RD column with stripper and pressure swing reactive distillation (PSRD), were simulated at lower operating pressure. The impact of RD column operating pressure on total energy usage and total annual cost (TAC) was studied. All design parameters were optimized using sequential iterative optimization procedures and sensitivity analysis to minimize the energy cost while maintaining the required product purity at 99.99%. The simulation results showed that the RD column with a stripper is better than PSRD with a saving of 23.17% in TAC and 31.53% in the specific cost of EtAc per kg. Compared to literature results, the proposed configurations have lower reboiler duty requirements and lower cost per kg of EtAc.

Joint Active and Passive Beamforming for IRS-Assisted Radar

Intelligent reflecting surface (IRS) is a promising technology being considered for future wireless communications due to its ability to control signal propagation. This paper considers the joint active and passive beamforming problem for an IRS-assisted radar, where multiple IRSs are employed to assist the surveillance of multiple targets in cluttered environments. Specifically, we aim to maximize the minimum target illumination power at multiple target locations by jointly optimizing the active beamformer at the radar transmitter and the passive phase-shift matrices at the IRSs, subject to an upperbound on the clutter power at each clutter scatterer. The resulting optimization problem is nonconvex and solved with a sequential optimization procedure along with semidefinite relaxation (SDR). Simulation results show that additional line-of-sight (LOS) paths created by IRSs can substantially improve the radar robustness against target blockage.

Optimization of a composite pyramidal lattice structure for the auxiliary converter cabinet

The auxiliary converter cabinet (ACC) of electric multiple unit vehicles guarantees the regular operation of electrical equipment. This article develops and optimizes a parametric model of the ACC based on lightweight composite pyramidal lattice materials to improve its performance. To make the sequential optimization procedure automatically closed-loop, an ACC model with parameter interfaces is built. A representative volume element model is adopted to obtain the physical properties of the pyramidal lattice structure. After global sensitivity analysis, three popular multi-objective optimization algorithms- multiobjective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm-III (NSGA-III) and multi-objective evolutionary algorithm based on decomposition (MOEAD)—are used to optimize the lattice ACC. MOPSO obtained the best results, and the lattice structure greatly improved the performance of the ACC in terms of random vibration and shock conditions.

Novel energy-saving methods to improve the three-column extractive distillation process for separating ethyl acetate and ethanol using furfural

• Eight energy-saving processes based on the features of the system and the flowsheet. • A novel way of partial condensation saves 8.6% TAC compared with the normal way. • A novel vapor–liquid coupling process saves 48.6% TAC compared with the base case. • Using a compressor for vapor–liquid coupling process can further save TAC by 12.8%. A mixture of ethyl acetate and ethanol is difficult to separate because of a minimum-boiling homogeneous azeotrope. The characteristics of the ethyl acetate/ethanol system are analyzed. The energy-saving potential of a three-column extractive distillation process to separate the system is explored. The effects of the distillate composition of pre-concentrator, the temperature of solvent feed and operating pressures are studied. Energy-saving processes including heat pump distillation, heat integration and partial condensation are proposed. A novel way of partial condensation is proposed and compared with the conventional way. An innovative method of vapor–liquid coupling between the per-concentrator and the extractive column is then proposed. It is more economical and energy-efficient than the above processes. Besides, based on the vapor–liquid coupling process, two further improvements are proposed through heat integration and through compressors. All processes are optimized using the sequential iterative optimization procedure with the minimum total annual cost as the target. Compared with the conventional process operated at 101.3 kPa, the two improved processes can reduce total annual cost by more than 52%, reduce energy consumption by more than 60%, and reduce CO 2 emissions by more than 61%.

Simultaneous Multi-objective Optimization of Semi-active Intermediate Isolation System and Building Structure

Recently, to reduce seismic responses, dozens of high-rise buildings in Japan and Korea have adopted the intermediate isolation system (IIS). These applications have shown successful response reduction performance for tall buildings. The important dynamic responses of building structures with the IIS are the peak intermediate isolator drift (IID), and the peak inter-story drift (ISD). The semi-active intermediate isolation system (SAIIS) was developed to more effectively reduce these seismic responses. In previous study, the authors showed that the SAIIS using magnetorheological dampers successfully reduced both the IID and the ISD. However, the optimal design of the SAIIS only was conducted, without considering the building structure. If both the SAIIS and the building structure properties are considered in the optimal design procedure, more effective optimal design for both the SAIIS and the building structure can be achieved. In this research, a simultaneous multi-objective optimization (MOO) method of the SAIIS and the building structure is proposed to achieve this. Genetic algorithm was selected for simultaneous MOO of the SAIIS and the building structure. The fuzzy inference controller was selected as a control algorithm. The authors show that in comparison to the sequential optimization procedure that practical applications generally use, the simultaneous MOO method can provide much better control capacity and structural design process.

Sequential semidefinite optimization for physically and statistically consistent robot identification

This work considers the problem of dynamic identification for robotic mechanisms given noisy measurements of configuration variables and applied torques. Conventionally, this problem is solved via least-squares, exploiting linearity properties of the inverse dynamics model for rigid-body systems. However, the nonlinear dependency of this model on configurations and velocities gives rise to bias in the resultant estimates when using noisy or even filtered data. Further, these biases can cause parameters of best fit to be non-physical, potentially leading to an ill-posed forward dynamic model. The main contribution of this paper is to propose a sequential semidefinite optimization procedure to both (1) ensure the physical consistency of the identified model and (2) maintain the statistical consistency of the estimator. The new method validates both a direct and inverse dynamic identification model (DIDIM), and also ensures that intermediate iterates of the algorithm remain physically valid. Due to these favorable properties, the method is named a Physically-Consistent DIDIM (PC-DIDIM) approach. Recent statistical hypothesis tests for instrumental variable approaches are generalized for application with a PC-DIDIM approach. Experimental results with a six-degree-of-freedom industrial robot supported by Monte Carlo simulations show the effectiveness of the new method and robustness benefits in comparison to conventional least-squares and the vanilla DIDIM method.

Joint design of the transmit and receive beamforming for multi-mission MIMO radar

This paper jointly designs the transmit and receive beamforming vectors for a multi-mission multiple-input multiple-output (MIMO) radar. The radar searches for potential targets within a prescribed region while tracking multiple targets with known locations. To improve the performance of search mission and track mission, we aim to maximize the transmit energy in the prescribed region and ensure that the received signal to interference plus noise ratio (SINR) of each target is not less than a preset threshold. To tackle the resulting NP-hard problem, we introduce an iterative algorithm based on the sequential optimization procedure. In each iteration, the receive beamforming vectors are first updated by resolving the unconstrained maximization problems. Then, a fractional quadratic constrained quadratic programming (QCQP) is developed for updating the transmit beamforming vector and is solved with semidefinite relaxation (SDR) technique. Numerical simulations verify the convergence performance of the proposed algorithm. The ability of the radar to simultaneously implement the required two tasks is also demonstrated through the synthesized transmit and receive beampatterns.

Zn/Al-layered double hydroxide–graphene oxide nanocomposite use in the solid-phase extraction–preconcentration and HPLC determination of diclofenac

A rapid and inexpensive hydrothermal process was employed for the synthesis of a nanocomposite composed of zinc/aluminum-layered double hydroxide with carbonate interlayer anions and graphene oxide (Zn/Al LDH-GO). Fourier-transform infrared spectroscopy, scanning electron microscopy, Brunauer–Emmett–Teller area analysis, and X-ray diffraction technique were employed for the characterization of the prepared nanocomposite. Considering the possible cooperative adsorption effect of LDH and GO moieties, a column packed with this adsorbent has been used, for the first time, in the solid-phase extraction (SPE) of diclofenac. The analysis of DCF was carried out by employing high-performance liquid chromatography (HPLC). The parameters influencing the SPE and elution processes were optimized by the univariate sequential optimization procedure. Under optimized experimental conditions, the linear calibration plots for the determination of DCF in hospital wastewater and human serum samples were obtained in the ranges of 1–730 µg L−1 (R2 = 0.999) and 4–625 µg L−1 (R2 = 0.998), respectively. The limits of detections were correspondingly 0.12 and 0.5 µg L−1, with the preconcentration factors of 68 and 59. The column stability was excellent, and its efficiency was almost constant, even after 192 adsorption/desorption cycles. The results confirmed the abilities of the developed method for the efficient preconcentration and thus precise trace analysis of DCF in real samples.

Application of zinc/aluminum layered double hydroxide nanosorbent in a fixed-bed column for SPE-preconcentration followed by HPLC determination of diclofenac in biological and hospital wastewater samples

A zinc/aluminum layered double hydroxide (Zn/Al LDH) with carbonate interlayer anions was synthesized by the co-precipitation method. The prepared sorbent was examined for the solid phase extraction (SPE) and high performance liquid chromatography (HPLC) determination of the trace amounts of diclofenac (DCF) in human serum, as a complex matrix, and hospital wastewater samples. The first step of the procedure was the extraction of DCF by the synthesized Zn/Al LDH via an anion exchange mechanism, in which the interlayer carbonate anions were involved. A univariate sequential optimization procedure was conducted to find the optimal value of the parameters affecting the extraction process. The second step was the elution of the adsorbed DCF by a sodium hydroxide solution (2 mol L−1), followed by HPLC analysis of DCF. Under the optimal experimental conditions, the calibration plots for the determination of DCF in hospital wastewater and human serum samples were linear in the ranges of 3–415 (R2 = 0.999) and 9–300 (R2 = 0.997) μg L−1, respectively. The corresponding limits of detection were found to be as 0.16, 1.5 μg L−1, and the evaluated preconcentration factors were 41 and 37. The stability of the studied LDH allowed using a column packed with this adsorbent for 185 adsorption-desorption cycles. The results demonstrated the potentials of the developed method for efficient preconcentration and thus precise trace analysis of DCF in real samples.

Convex optimization based adjustable robust dispatch for integrated electric-gas systems considering gas delivery priority

With the mushrooming deployment of volatile renewable energy sources as well as the intrinsic uncertainty from the demand side, secure and economic energy dispatch has become increasingly challenging for energy systems, especially for the emerging and promising integrated electric-gas system. Aside from the aforementioned uncertainties, the dispatch of the integrated electric-gas system suffers from two inherent obstacles, which are model nonconvexities, originating from the Weymouth equations in the gas network, and the demand-side differentiated gas delivery priorities according to current industrial practice, respectively. To deal with the conundrum, an adjustable robust dispatch method is proposed for operating the integrated electric-gas system, where uncertain wind generation outputs and gas loads are described by intervals. In contrast to existing work employing pre-determined intervals, the admissible wind output intervals in this paper are optimized, reflecting the interdependencies between the regulation capabilities of gas-fired generation and the gas delivery adequacy. By this means, gas delivery priority is considered in comply with gas industrial practice, and it also provides a more flexible mechanism to maintain robustness of the dispatch strategy. Through analyzing the feasibility impact of uncertain variables, a deterministic robust counterpart is derived, in which uncertainties are eliminated based on affine generator dispatch and estimation of total line pack. Furthermore, nonconvex quadratic terms in the Weymouth equations are expressed as difference-of-convex functions. A sequential convex optimization procedure is developed, and a heuristic method is suggested to initiate the sequential algorithm. The proposed models and methods are tested on three test systems. Key impact factors on the dispatch strategy, such as gas prices, wind generation forecast accuracy and gas network initial operation conditions, are analyzed, and the computational benefits brought by convex programming are validated by scalability tests.

A New Sequential Optimization Procedure and Its Applications to Resource Allocation for Wireless Systems

A novel optimization framework for resource allocation in wireless networks and radar systems is proposed, which merges the methods of maximum block improvement (MBI) and of sequential optimization. A detailed convergence proof is provided, showing that the proposed algorithm is able to monotonically increase the objective value while ensuring that every limit point of the generated variable sequence fulfills the problem first-order optimality conditions under very mild hypothesis. These results extend available convergence results on MBI and sequential optimization, significantly widening the range of applications that can be handled by the proposed framework compared to available approaches. This point is illustrated in detail presenting relevant applications from both the cellular and radar context, which fall under the umbrella of the developed optimization method.

Compared novel thermally coupled extractive distillation sequences for separating multi-azeotropic mixture of acetonitrile/benzene/methanol

In this paper, extractive distillation applies to separate acetonitrile/benzene/methanol, the medicine is a compounding of multi-azeotropes via introducing chlorobenzene as a solvent. In order to achieve the purpose of energy saving and CO2 emission reduction, ten novel thermally coupled separation sequences including direct sequences, indirect sequences, hybrid sequences and solvent splitting sequences are established and explored based on extractive dividing wall column (EDWC) and side-stream extractive distillation column (SSED). The corresponding optimal parameters are determined by effective and convenient sequential iterative optimization procedures on the basis of minimized total annual cost (TAC) and meanwhile CO2 emissions are calculated to evaluate environmental impact. The comparison results illustrate that the solvent splitting SSED sequence has more advantages in energy consumption, environment impact and economic cost than others, reducing at most 38.44%, 32.84% and 38.41% in terms of total reboiler duty, TAC and CO2 emissions.

Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures

This paper presents a topology optimization method for the sequential design of material layout and fiber orientation in functionally graded fiber-reinforced composite structures. Specifically, the proposed method can find the optimal structural layout of matrix and fiber materials together with optimal discrete fiber orientations. In this method, an orientation design variable in the Cartesian coordinate system is employed with a conventional density design variable. The orientation design variable controls not only the fiber orientation, but also fiber volume fraction. The fiber volume fraction control can be used to relax the orientation design problem and simultaneously design a functionally graded structural layout of fiber material. To avoid intermediate fiber orientations and achieve discrete fiber orientation design, a penalization scheme is applied to the orientation design variable. For solving the optimization problem which involves multiple design variables such as the density variable, fiber orientation variable, and target discrete orientation set, a three-step sequential optimization procedure is proposed. In this procedure, the result for each step provides the isotropic design, continuous fiber orientation design, and functionally graded discrete orientation design, respectively. To validate the effectiveness of the proposed approach, numerical examples for structural compliance minimization and compliant mechanism design are provided.

A trajectory‐based sampling strategy for sequentially refined metamodel management of metamodel‐based dynamic optimization in mechatronics

SummaryDynamic optimization problems based on computationally expensive models that embody the dynamics of a mechatronic system can result in prohibitively long optimization runs. When facing optimization problems with static models, reduction in the computational time and thus attaining convergence can be established by means of a metamodel placed within a metamodel management scheme. This paper proposes a metamodel management scheme with a dedicated sampling strategy when using computationally demanding dynamic models in a dynamic optimization problem context. The dedicated sampling strategy enables to attain dynamically feasible solutions where the metamodel is locally refined during the optimization process upon satisfying a feasibility‐based stopping condition. The samples are distributed along the iterate trajectories of the sequential direct dynamic optimization procedure. Algorithmic implementation of the trajectory‐based metamodel management is detailed and applied on two case studies involving dynamic optimization problems. These numerical experiments illustrate the benefits of the presented scheme and its sampling strategy on the convergence properties. It is shown that the acceleration of the solution time of the dynamic optimization problem can be achieved when evaluating the metamodel that is lower than 90% compared to the computationally expensive model.

Estimation of the second heart sound split using windowed sinusoidal models

Abstract Knowing the time difference between the onsets of the aortic part (A2) and the pulmonic part (P2) of the second heart sound (S2), also referred to as the time split (TS) of S2, can assist in the diagnosis of a variety of heart diseases. However, estimating the TS is a non-trivial task due to the potential overlap between A2 and P2. In this paper, a model-based approach is proposed where both A2 and P2 are modeled as windowed sinusoids with their sum forming the S2 signal. Estimation of the model parameters and the S2 split form a non-convex optimization problem, where a local minimum is obtained using a sequential optimization procedure. First, the window parameters are found as the solution to a regularized least squares problem. Then, the frequencies and phases of the sinusoids are found by locating the maximal peaks of the heart signals’ frequency magnitudes, and using the corresponding phases. Finally, the TS is estimated as the time difference between the peaks of the cross-correlations between the measured S2 signal and the modeled A2/P2 signals. The algorithm is able to estimate the TS for synthetic signals with a root-mean-square error (RMSE) of 7.6 ms for equidistantly placed TSs between −70 ms and 70 ms. The RMSE increases for small TSs in the interval −30 ms to 10 ms, and at increased noise levels. The algorithm was applied to phonocardiograms recorded from 146 patients, where the average estimated TS was 29.6 ms, in conformance with the average TS of healthy subjects as found in the literature.

A classification approach to efficient global optimization in presence of non-computable domains

Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the non-computable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

A Mathematical Programming Method for Optimizing the Single-Contaminant Regeneration Heat-Integrated Water Networks

A superstructure-based mathematical model is established for single-contaminant heat-integrated water networks (HIWN), and the water loss of both wastewater regeneration recycling and regeneration reuse is considered. Furthermore, a sequential optimization procedure is established to achieve multi-objective optimization. The loss rate of water is taken into the mathematical model as there must have water loss in regeneration process, so that the optimization would be more realistic. Two cases are optimized using proposed model with regeneration recycling and regeneration reuse considered, respectively; the results show the differences between these two modes. Compared with the optimization method in the literature, the proposed method is more realistic.