Numerical Optimization Method Research Articles

Air vent shape optimization with metamaterials.

Heating, Ventilation and Air Conditioning (HVAC), are crucial in every building for the well being of the occupants. While these equipments take care of the air quality with exhausting polluted air out and bringing fresh air in, they can let a polluant in: noise. Noise can have non-physical effects like disturbed sleep, cognitive problems or even influences on heart diseases. Recent developments in the acoustic field shown the use of metamaterials that can reduce noise while keeping good ventilation. The sonic crystals, disposed in a certain pattern following the Bragg's law, can be tuned to reduce noise on a wide frequency band. The design of an air vent, known as a metacage, was made by using open source numerical simulations. Based on a numerical plan and optimization methods, this study's goal was to find the optimal solution for the HVAC to reduce noise while minimizing ventilation loss. Following the simulations results, the metacage generated was 3D printed for validation in the laboratory, showing the corroboration with the simulations. The final results show third-octave bands with a TL peak over 10dB and an average of 3dB for all the others bands up to 10kHz. All this while keeping minimal ventilation loss.

MULTI-CRITERIA NUMERICAL OPTIMIZATION OF MECHANICAL PROPERTIES IN ULTRASONIC WELDING PROCESS PARAMETERS OF PVC-COATED HYBRID TEXTILES FOR WEATHER PROTECTION

A series of research was carried out to determine the correlation between ultrasonic welding process parameters and weld seam mechanical properties. However, multi-objective numerical optimization of coated hybrid textiles for weather protection has not been addressed. To ensure a comprehensive evaluation of ultrasonic weld seams, the research investigates the optimal solution of the multi-objective function of ultrasonic welding process parameters and formulates a single criteria objective function. Lapped and superimposed types of seams were applied based on 33 factorial designs of experiments for 6 and 12 mm welding widths. Single-criteria objective functions instead of three independent problems were developed as a generalized utility function. A single-criteria optimization method was introduced through predetermined weight and normalization within the range of acceptable/unacceptable values. Numerical and graphical optimization methods were also applied to determine possible optimal solutions through generalized utility functions. The best optimal value of the generalized utility function (0.670425 and 0.944374) was attained at welding speed (2 and 2.01564 m/min), power (93.756 and 117.973 W), and pressure force (198.803 and 239.756 N) of 6 and 12 mm welding widths, respectively. The acceptable range of satisfactory values was determined for the roof and wall of awnings and camping tents through standard, in which seam performance level indicated. Nonlinear quadratic numerical models were formulated to estimate the generalized utility function, and their results were close to the regressed diagonal line against the actual points. The statistical analysis was shown a statistically significant effect of welding process parameters on the generalized utility function.

Learning Heuristics With Different Representations for Stochastic Routing.

Uncertainty is ubiquitous in real-world routing applications. The automated design of the routing policy by hyperheuristic methods is an effective technique to handle the uncertainty and to achieve online routing for dynamic or stochastic routing problems. Currently, the tree representation routing policy evolved by genetic programming is commonly adopted because of the remarkable flexibility. However, numeric representations have never been used. Considering the practicability of the numeric representations and the capability of the numeric optimization methods, in this article, we investigate two numeric representations on a representative stochastic routing problem and uncertain capacitated arc routing problem. Specifically, a linear representation and an artificial neural-network (ANN) representation are implemented and compared with the tree representation to reveal the potential of the numeric representations and the characteristics of their optimization. Experimental results show that the tree representation is the best choice, but on a majority of the test instances, the numeric representations, especially the ANN representation, can provide competitive performance. Further analyses also show that training a good ANN representation policy requires more training data than the tree representation. Finally, a guideline of representation selection is given.

Ball-End Cutting Tool Posture Optimization for Robot Surface Milling Considering Different Joint Load

Robots with openness and flexibility have attracted a large number of researchers to conduct in-depth studies in the field of surface machining. However, there is a redundant degree of freedom (DOF) in 6-DOF robot machining: when a ball end milling cutter is used to process curved parts, the tool point needs to strictly follow the planned milling trajectory, but the tool axis vector only needs to be within a certain range. During the machining process, the rotation of the tool around its axis is not constrained. Therefore, it is necessary to optimize the redundant DOF. Aiming at the redundant DOF of the tool axis vector in ball end milling for surface parts, a Redundancy Optimization strategy for Minimum Joint trajectory (ROMJ) is proposed. It takes the shortest trajectory of robot joints as the optimization objective, and the numerical optimization method is adopted to carry out the optimal design of tool axis vector trajectory in the milling process. Before optimization, to decrease the data volume, the number of track points is sampled and adjusted based on curve characterization errors. In the optimization process, considering the obvious difference in the load quality characteristics of the robot joints, a Redundancy Optimization strategy for Minimum Joint trajectory considering the different Load of joints (ROMJ-L) is proposed. The load difference coefficients of each joint are introduced into the optimization objective of the trajectory of robot joints. By using this method, the optimal design of each joint trajectory of the robot is realized. In order to verify the methods proposed in this paper, a comparison experiment is carried out. The results show that under the same tool point trajectory, the proposed methods can significantly reduce the robot joint trajectory, and the joint trajectory is influenced by the load difference of each joint. Finally, an Eflin-10 robot is used to process the butterfly trajectory tool path by the trajectory planned by the ROMJ-L method, and the results show that the method is practical.

An attention-driven nonlinear optimization method for CS-based hyperspectral image reconstruction

Hyperspectral images contain both spatial and spectral information, which makes it has great advantages in the field of target identification, material determination, etc. However, hyperspectral image acquisition systems usually output massive amounts of data. Compressed sensing (CS) and single dispatchers coded aperture snapshot spectral imaging (SD-CASSI) were proposed to compress the amount of data. These systems usually use numerical optimization methods to do image reconstruction by finding the optimal reconstructed image. This method generates a large number of iterative calculations, which is time-consuming. In this paper, we modeled the image reconstruction for SC-CASSI as a non-linear optimization problem and proved that the number of iterations of the solution process is exponential. We proposed an attention-driven reconstruction algorithm for SD-CASSI systems. The algorithm mainly consists of an initial convolution block and residual attention modules. A channel attention module is also introduced to mine spectrally correlated features in raw signals. Experimental results show that the proposed algorithm is superior to three states-of-art reconstruction algorithms for CS-based systems. The reconstruction speed of the system is also increased by 94% compared with the numerical method.

Efficient GaN-on-Si Power Amplifier Design Using Analytical and Numerical Optimization Methods for 24–30 GHz 5G Applications

This paper presents the design procedure of an efficient compact monolithic microwave integrated circuit power amplifier (MMIC PA) in a 0.1 μm GaN-on-Si process for 5G millimeter-wave communication. Load/source-pull simulations were conducted to correctly create equivalent large-signal matching models for stabilized power cells and to determine the optimal impedance domain. The shorted stub with bypass capacitors minimizes the transistor’s output reactance, simplifying the matching objective to an approximate real impedance transformation (IT). With miniaturization as the implementation guide, explicit formulas and tabulated methods based on mathematical analysis were applied to synthesize the filtering matching networks (MNs) for the input and output stages. In addition, a CAD-dependent numerical optimization approach was used for the interstage MN that needs to cope with high IT ratio and complex loads. The continuous-wave (CW) characterization for the proposed two-stage PA demonstrated 19.8 ± 0.7 dB of small-signal gain, very flat output power (Pout) and power-added efficiency (PAE) at 4 dB gain compression of 32–32.4 dBm and 34–34.6%, respectively, over 24–30 GHz, with 37.1% of peak PAE at mid-frequency.

An improved passive tuned mass damper assisted by dual stiffness

A tuned mass damper (TMD) is one of the oldest and most commonly used passive control devices attached to structures to absorb lateral loads of energy from main systems. In the last decades, several novel tuned mass dampers have been designed to increase the performance of TMDs in decreasing the structural responses during excitation vibrations. Moreover, several formulations and numerical optimization methods have been developed to optimize the TMDs parameters. This paper proposes a novel passive tuned mass damper with dual stiffness (DSTMD). The DSTMD includes mass, primary and secondary springs, dashpot, and motion limiting chamber. The performance of DSTMDs depends on their properties such as mass, primary and secondary stiffness, damping coefficient, and the length of the motion limiting chamber. Thus, a metaheuristic optimization algorithm, called the Mouth Brooding Fish algorithm, was used to optimize the DSTMDs parameters. The effectiveness of the optimum DSTMD on two different linear ten-story structures under several earthquakes has been studied and compared with the effectiveness of classical optimum TMDs. According to the study, optimum DSTMDs generally show better effects for certain excitations, and as an average performance, they are superior compared to the classical optimum TMDs in reducing maximum displacement of the buildings. At last, structural yielding is considered, and the performance analysis on this structure shows that the DSTMD has a superior effect in reducing the maximum displacement and is among the best methods for the calculated absolute yielding amount.

Optimization of extraction parameters for pectin from guava pomace using response surface methodology

Pectin is being used more often in industrial settings even though there is a large gap between supply and demand, placing further strain on the sources of pectin that are already available. The objective of the current study is to extract pectin from guava pomace, and the central composite design (CCD) in conjunction with a numerical optimization method of the response surface methodology (RSM) was used to optimize the processing parameters, including temperature (75, 85, and 95 °C), pH (1.5, 2.0, and 2.5), and extraction time (50, 60, and 70 min). The findings showed that the parameters studied substantially impacted the pectin yield. The resulting second-order polynomial model thoroughly explains the relationship between the input and output variables and how the data varied. Ideal conditions were achieved: temperature: 87.43 °C; pH: 1.83; and extraction time: 69.46 min, which predicted 16.59% pectin and was verified by the validation experiments. Numerous food and pharmaceutical products can be made using extracted pectin, which may also help relieve some of the pressure on the presently accessible pectin sources.

Simulation and optimum control of a two-stage compression air source heat pump system: A comparison of two kinds of variable volume approaches

Two-stage vapor compression technology can effectively improve the performance of an air source heat pump, and a staged compression system with two separate compressors has a highly flexible modulation capacity. However, the effect of different volume modulation approaches on the heating COP requires further analysis. In this study, a Modelica-based dynamic simulation model of a two-stage air-source heat pump was developed and verified with experimental data. A numerical optimization method was used to obtain the optimum frequencies and low- or high-stage cylinder volumes of the compressors that maximize the COP. The results show that the three optimization approaches have different effects. At lower ambient temperatures, varying the high-stage compressor cylinder volume can yield the maximum COP among the three optimization methods, followed by varying the low-stage compressor cylinder volume and compressor frequencies. At higher ambient temperatures, varying low-stage cylinder volume can yield the maximum COP, followed by varying the compressor frequencies and high-stage cylinder volume. The further the working condition deviates from the design point, the greater the improvement in the COP. The maximum improvements in the COP achieved with optimization in this study were 8.23%, 6.39% and 5.39% by varying the high-stage cylinder volume, low-stage cylinder volume, and frequencies, respectively.

Correlations between product distribution and feedstock composition in thermal cracking processes for mixed plastic waste

Thermal conversion can transform the carbon-based waste into valuable chemicals to be further used in the petrochemical industry for a polymeric carbon circular economy. This work’s aim was to identify chemical correlations between the thermal-cracking products and the feedstock polymer composition when using highly blended waste streams. The challenges addressed were to: (i) access a pool of experimental data on the monomer recovery potential of real-life, highly blended waste streams; (ii) estimate the polymer constituents of the mixed waste streams; and (iii) formulate a generic and systematic method to identify correlations between feedstock constituents and cracking products. Different post-consumer waste streams were investigated, including cardboard, automotive shredder residues, cable stripping waste, and textile waste. The cracking experiments were performed in a 2–4MWth industrial-scale Dual Fluidized Bed system at 800 °C using steam as fluidization agent. The polymeric constituents of the feedstocks were estimated using a numerical convex optimization method. To identify correlations between the feedstocks and products, a carbon bond-based classification was introduced. The experimental monomer yield ranged from 0.08 kg/kgf to 0.3 kg/kgf (f = feedstock) for the evaluated materials, corresponding to a carbon feedstock conversion rate between 14 % and 44 %. High yields of valuable monomers were obtained for the materials with the highest polyolefin content. The olefin monomer production correlated positively to the amount of aliphatic carbon in the original material and negatively to the carbon contents of the aromatic rings. From the trends observed, it was concluded that a framework based on carbon bond types is a promising approach to identify such correlations, which could serve as predictive tools for monomer recovery based on material’s composition and overall process conditions.

Bayesian inference of admixture graphs on Native American and Arctic populations.

Admixture graphs are mathematical structures that describe the ancestry of populations in terms of divergence and merging (admixing) of ancestral populations as a graph. An admixture graph consists of a graph topology, branch lengths, and admixture proportions. The branch lengths and admixture proportions can be estimated using numerous numerical optimization methods, but inferring the topology involves a combinatorial search for which no polynomial algorithm is known. In this paper, we present a reversible jump MCMC algorithm for sampling high-probability admixture graphs and show that this approach works well both as a heuristic search for a single best-fitting graph and for summarizing shared features extracted from posterior samples of graphs. We apply the method to 11 Native American and Siberian populations and exploit the shared structure of high-probability graphs to characterize the relationship between Saqqaq, Inuit, Koryaks, and Athabascans. Our analyses show that the Saqqaq is not a good proxy for the previously identified gene flow from Arctic people into the Na-Dene speaking Athabascans.

Two-stage ANN based intelligent technique for optimal positioning and sizing of DERs in distribution system

Recent years have examined large transformational implications due to integration of highly intermittent renewable sources of energy. Therefore, initiatives must be explored to enhance the operational flexibility of distributed energy resources (DER) for bringing a new viewpoint to the planning and operation of future distribution system. Also, despite the economic, environmental and societal advantages of DERs, their adoption is limited and markets are yet to realize its full potential to address the operational challenges of the system. The solution to these is integration of multiple DERs in the system of appropriate size at optimal location in the system. Currently, numerous optimization methods based on rigorous mathematical calculation are used to solve this issue. This inevitably increases the complexity of such algorithms. Therefore, this paper proposes a two-stage artificial neural network (ANN) based intelligent technique to solve the problem. In this work, first stage ANN is used for screening the critical buses rank wise based on voltage, line and power stability index to find the optimal location. In second stage ANN, screening the size of DER based on the location of critical bus is accomplished to find the optimal sizing of DER. The intelligent technique proposed in this work is applicable to both radial as well as networked system. The solution is extensively evaluated through simulation in MATLab for a set of operational scenarios and performance verification of the proposed technique is provided for IEEE 33 and 69 bus systems for radial and IEEE 14 and 118 bus systems for mesh networked systems. The results validate the efficacy of the proposed technique.

A USV-UAV Cooperative Trajectory Planning Algorithm with Hull Dynamic Constraints.

Efficient trajectory generation in complex dynamic environments remains an open problem in the operation of an unmanned surface vehicle (USV). The perception of a USV is usually interfered by the swing of the hull and the ambient weather, making it challenging to plan optimal USV trajectories. In this paper, a cooperative trajectory planning algorithm for a coupled USV-UAV system is proposed to ensure that a USV can execute a safe and smooth path as it autonomously advances through multi-obstacle maps. Specifically, the unmanned aerial vehicle (UAV) plays the role of a flight sensor, providing real-time global map and obstacle information with a lightweight semantic segmentation network and 3D projection transformation. An initial obstacle avoidance trajectory is generated by a graph-based search method. Concerning the unique under-actuated kinematic characteristics of the USV, a numerical optimization method based on hull dynamic constraints is introduced to make the trajectory easier to be tracked for motion control. Finally, a motion control method based on NMPC with the lowest energy consumption constraint during execution is proposed. Experimental results verify the effectiveness of the whole system, and the generated trajectory is locally optimal for USV with considerable tracking accuracy.

Utility of Particle Swarm Optimization in Statistical Population Reconstruction

Statistical population reconstruction models based on maximum likelihood and minimum chi-square objective functions provide a robust and versatile approach to estimating the demographic dynamics of harvested populations of wildlife. These models employ numerical optimization techniques to determine which set of model parameters best describes observed age-at-harvest, catch-effort, and other auxiliary field data. Although numerous optimization methods have been used in the past, the benefits of using particle swarm optimization (PSO) have yet to be explored. Using a harvested population of North American river otter (Lontra canadensis) in Indiana as a case study, we investigated the performance of population reconstruction using particle swarm optimization, spectral projected gradient (SPG), Nelder–Mead, and Broyden–Fletcher–Goldfarb–Shanno (BFGS) methods. We used Monte Carlo studies to simulate populations under a wide range of conditions to compare the relative performance of population reconstruction models using each of the four optimization methods. We found that using particle swarm optimization consistently and significantly improved model stability and precision when compared with other numerical optimization methods that may be used in statistical population reconstruction. Given that these models are frequently used to guide management decisions and set harvest limits, we encourage management agencies to adopt this more precise method of estimating model parameters and corresponding population abundance. These results illustrate the benefits of using particle swarm optimization, caution against relying on the results of population reconstruction based on optimization methods that are highly dependent on initial conditions, and reinforce the need to ensure model convergence to a global rather than a local maximum.

Comparative Analysis of Eight Numerical Methods Using Weibull Distribution to Estimate Wind Power Density for Coastal Areas in Pakistan

Currently, Pakistan is facing severe energy crises and global warming effects. Hence, there is an urgent need to utilize renewable energy generation. In this context, Pakistan possesses massive wind energy potential across the coastal areas. This paper investigates and numerically analyzes coastal areas’ wind power density potential. Eight different state-of-the-art numerical methods, namely an (a) empirical method, (b) graphical method, (c) wasp algorithm, (d) energy pattern method, (e) moment method, (f) maximum likelihood method, (g) energy trend method, and (h) least-squares regression method, were analyzed to calculate Weibull parameters. We computed Weibull shape parameters (WSP) and Weibull scale parameters (WCP) for four regions: Jiwani, Gwadar, Pasni, and Ormara in Pakistan. These Weibull parameters from the above-mentioned numerical methods were analyzed and compared to find an optimal numerical method for the coastal areas of Pakistan. Further, the following statistical indicators were used to compare the efficiency of the above numerical methods: (i) analysis of variance (R2), (ii) chi-square (X2), and (iii) root mean square error (RMSE). The performance validation showed that the energy trend and graphical method provided weak performance for the observed period for four coastal regions of Pakistan. Further, we observed that Ormara is the best and Jiwani is the worst area for wind power generation using comparative analyses for actual and estimated data of wind power density from four regions of Pakistan.

Experimentally validated numerical model of multi-spectral bands radiative transport in solar receiver/reactor with photo-active porous absorber reacting media

Solar energy efficient utilization such as solar thermal energy storage and thermochemical conversion technologies is an effective way of closing carbon cycles with systematic green environmental remediation. Understanding the complexity of induced light with its spectrum and intensity feature is crucial for the further optimization of the solar system using a more advanced concept such as photothermal catalysis. This study discussed the radiation transfer processes in detail and clarified the principles and assumptions underlying the photothermal effect in the solar receiver/reactor. In addition, the phenomenon of radiation absorption through the porous interface is discussed and the solution of the equivalent surface is given out. Based on the above discussion, a two-bands numerical model is established with various numerical methods to adapt the properties of different surfaces and irradiation sources. The numerical model is validated by experimental data and used to estimate both spectra and intensity transfer characteristics through the solar reactor. The analysis of optimal operation condition, distribution coefficient, spectral feature of glasses, and thermal-optical performance are presented based on advanced numerical model. This study deepens the understanding of radiative transfer mechanisms in solar energy conversion systems and provides pioneering theoretical guidance with an advanced numerical method for the further optimization of a system-level photothermal catalysis process.

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

Optimal Control of Dynamical Systems using Calculus of Variations

This paper explores the application of calculus of variations techniques for optimizing the control of complex dynamical systems. Determining control strategies that minimize cost metrics and satisfy constraints is critical across engineering disciplines like robotics, aerospace, and process operations. Classical optimal control methods, such as Pontryagin's Maximum Principle, transform an optimal control problem into a calculus of variations framework amenable to analytical and numerical optimization. We present a unified framework for applying these techniques, enabling dynamical systems defined by ordinary and partial differential equations to be optimized by conversion into a nonlinear programming form. Analytical approaches provide theoretical guarantees on control performance while numerical methods, like direct collocation and transcription, enable large-scale optimal control problems to be efficiently solved. The connections between dynamical systems, calculus of variations, and modern numerical optimization methods establish a holistic methodology for control engineers and applied mathematicians to design optimal controllers for physical systems. Case studies on real-time trajectory optimization, adaptive path planning, and dynamic process operations demonstrate the efficacy of the proposed optimal control framework across robotics, aerospace, power systems, and other applications.

A probability density model of stress amplitude under bimodal vibration response

In order to improve the fatigue life prediction of engineering structures under bimodal vibration response stress power spectra, a new probability density model of stress amplitude is proposed in this paper, which is composed of an exponential distribution and a two-parameter Weibull distribution. Under ideal bimodal response stress power spectra with different bandwidths, the connection between the first three order moments of rain-flow amplitude distributions and the spectral parameters is found. Then, according to the equations between the first three order moments of stress amplitude distributions of the model and those of rain-flow amplitude distributions, combined with the numerical optimization method, the relationship between model parameters and spectral parameters is established. Through comparative studies, the model in this paper leads to more accurate stress amplitude distributions and fatigue damage, which is very close to those obtained from time domain approach. Through the stochastic vibration fatigue test of aluminum alloy notched specimens, the high accuracy of the proposed model for estimating fatigue life is further verified.

Numerical matching of supercharger for gasoline engine based on three-line working condition method

The traditional study of matching gasoline engine and supercharger mainly focuses on the external characteristic conditions, but the reasonable matching of external characteristic conditions cannot guarantee the reasonable matching of supercharger and gasoline engine in the whole operating range. Therefore, to address the limitation of studying only the external characteristic conditions in the supercharger matching process, a thermodynamic model of a direct injection supercharged gasoline engine was established, based on which the matching between the supercharger and the gasoline engine in the whole operating range was studied by the three-line condition method. The results show that the matching performance of the supercharger in the whole engine operating range can be significantly improved by using the three-line working condition method to match the supercharger. The three-line method takes into account both full-load and part-load engine conditions, and can visually evaluate the operating efficiency of the supercharger over the entire engine operating range, as well as predict the likelihood of surging, blocking and overspeeding of the supercharger over the entire engine operating range, overcoming the limitation of studying only the external characteristic conditions and providing a numerical evaluation method for pre-selection and optimization of the supercharger.