Analytical Optimization Approach Research Articles

Optimization of Weight Matrices for the Linear Quadratic Regulator Problem Using Algebraic Closed-Form Solutions

This work proposes an analytical gradient-based optimization approach to determine the optimal weight matrices that make the state and control input at the final time close to zero for the linear quadratic regulator problem. Most existing methodologies focused on regulating the diagonal elements using only bio-inspired approaches or analytical approaches. The method proposed, contrarily, optimizes both diagonal and off-diagonal matrix elements based on the gradient. Moreover, by introducing a new variable composed of the steady-state and time-varying terms for the Riccati matrix and using the coordinate transformation for the state, one develops algebraic equationsbased closed-form solutions to generate the required states and numerical partial derivatives for an optimization strategy that does not require the computationally intensive numerical integration process. The authors test the algorithm with one- and two-degrees-of-freedom linear plant models, and it yields the weight matrices that successfully satisfy the pre-defined requirement, which is the norm of the augmented states less than 10−5. The results suggest the broad applicability of the proposed algorithm in science and engineering.

A Two-Storage Inventory Model with Trade Credit Policy and Time-Varying Holding Cost under Quantity Discounts

Background: What are the cumulative influences of pricing, promotions of commodities, order size-based discount opportunities, and alternative warehousing scenarios on effective decision-making concerning inventory management? It is observed that the prices and promotion of products influence the demand rate. The shortage can be partially backlogged, and the backlogging rate depends on the waiting time. Also, discount and trade credit facilities may be available when purchasing items. This paper describes a novel inventory control model regarding optimal warehousing decision-making scenarios. Methods: This paper includes the facts in its hypothesis and examines the overall impact of the mentioned issues on profitability. The inventory carrying scheme associated with the proposed model consists of both rented and owned warehouse facilities in which the cost increases linearly with time. The numerical and visual simulation succeeds the mathematical approach to analyze the proposed inventory model in Mathematica software. Results: The results show that a price hike enhances profit despite the negative impact on demand creation. Also, promotion frequency favors profitability, suppressing the corresponding costs. Another managerial intuition is revealed through the numerical result that the stock should be held in a rented warehouse when deterioration in the owned warehouse increases, despite the cost of a rented warehouse. Conclusions: Besides several mentioned management insights, this study includes several existing models as particular cases and tackles challenges in the analytical optimization approach. This study leads toward the consequences of future research scopes with industry-based raw data.

Review on Laser Shock Peening Effect on Fatigue of Powder Bed Fusion Materials

The ability to manufacture parts with complex geometry by sending a model from CAD directly to the manufacturing machine has attracted much attention in the industry, driving the development of additive manufacturing technology. However, studies have shown that components manufactured using additive manufacturing technology have several problems, namely high tensile residual stresses, cracks, and voids, which are known to have a major impact on material performance (in service). Therefore, various post-treatment methods have been developed to address these drawbacks. Among the post-treatment techniques, laser shock peening (LSP) is currently considered one of the most efficient post-treatment technologies for improving the mechanical properties of materials. In practice, LSP is responsible for eliminating unfavorable tensile residual stresses and generating compressive residual stresses (CRS), which result in higher resistance to crack initiation and propagation, thus increasing component life. However, since CRS depends on many parameters, the optimization of LSP parameters remains a challenge. In this paper, a general overview of AM and LSP technology is first provided. It then describes which parameters have a greater influence during powder bed melting and LSP processing and how they affect the microstructure and mechanical properties of the material. Experimental, numerical, and analytical optimization approaches are also presented, and their results are discussed. Finally, a performance evaluation of the LSP technique in powder bed melting of metallic materials is presented. It is expected that the analysis presented in this review will stimulate further studies on the optimization of parameters via experimental, numerical, and perhaps analytical approaches that have not been well studied so far.

Hybrid analytical H-norm optimization approach for dynamic vibration absorbers

Conventionally, single-targeted H∞ or H2 optimization methods are adopted to determine the optimal parameters of different Dynamic Vibration Absorbers (DVAs) individually. A generic analytical framework for various DVAs considering a dual-target of H∞ and H2 norms is lacking. Addressing these issues, a hybrid analytical H∞-H2 optimization approach is proposed, leading to closed-form optimal solutions characterized by equal-height fixed points and conditional minimum H2-norms, combining the advantages of H∞ and H2 solutions. The proposed method is completely based on arbitrary filter coefficients of the targeted transfer function. Therefore, it can be generically applied for various DVAs. With the proposed method, the analytical optimal parameters of Negative-Stiffness Inerter-based Tuned Mass Systems (NS-ITMSs) are obtained based on an extended generic representation model considering multiple parameters. In extension, the method is illustratively applied on three complicated DVAs, including a Lever-type Inerter-based Vibration Absorber with Negative Stiffness (NS-LIVA) considering a leverage effect, a Piezoelectric Shunt Damping System (PSDS) considering an electro-mechanical coupling effect, and a Negative-Stiffness Tuned Viscous Mass Damper (NS-TVMD) for vibration isolator considering a transmissibility target. The closed-form solutions for these advanced DVAs are obtained for engineering reference. Furthermore, this method can be extended for more complicated energy dissipation or harvesting techniques.

Development of 150 Mpixel lens-coupled X-ray imaging detectors equipped with diffusion-free transparent scintillators based on an analytical optimization approach

X-ray microscopy experiments at synchrotron radiation facilities generally require X-ray imaging detectors with high spatial resolution and a wide field of view. For such purposes, lens-coupled X-ray imaging detectors are widely used. The SPring-8 X-ray microscopy beamlines require detectors that satisfy a 200 nm spatial resolution and over 50 mm field of view. We have carried out a systematic optical design based on an analytical optimization approach and elucidated that a set of five detector systems is able to meet these requirements. Their objective lenses have magnifications of 20x, 7x, 5.2x, 3.5x, and 1x. All the systems are designed to be equipped with 150 Mpixel CMOS image sensors. To verify our optimization approach, we have built a detector system with a magnification of 3.5x. The detector has successfully resolved 1.2 µm line-and-space patterns for the entire field of view, which is close to the optical diffraction-limited resolving power of 1.0 µm line-and-space patterns.

Light trapping gratings for solar cells: an analytical period optimization approach.

Solar cells can harvest incident sunlight very efficiently by utilizing grating-based light trapping. As the working principle of such gratings strongly depends on the number as well as the propagation directions of the diffraction orders, the grating period is a key parameter. We present an analytical model for optimizing the grating period, focusing on its impact on light path enhancement and outcoupling probability. Based on the presented model, we formulate guidelines to maximize light trapping in state-of-the-art high-end solar cells. The model increases the understanding of the grating performance in systems like the III-V//Si triple junction solar cell achieving record efficiency.

An analytical approach for optimization of computer network design considering the integration of the communication and power infrastructures

SummaryNowadays, computer networks are critical to the success of small and large businesses. They connect people, support applications and services, and provide access to the resources that keep the businesses running. Our work proposes analytical models and a methodology for supporting the optimization of the network infrastructure design, considering both technical and business oriented metrics, such as availability, reliability, and total cost. The integration of communication and power infrastructures is supported by this methodology. The dependability (availability/reliability) models were created using the Reliability Block Diagram and Stochastic Petri Net modeling mechanisms following a hierarchical approach. A case study considering the design of a real‐world network infrastructure is presented to illustrate the proposed methodology. The results showed a significant reduction in the design complexity as well as an improvement in the relationship between technical and business aspects.

Toward ATM Resiliency: A Deep CNN to Predict Number of Delayed Flights and ATFM Delay

The European Air Traffic Management Network (EATMN) is comprised of various stakeholders and actors. Accordingly, the operations within EATMN are planned up to six months ahead of target date (tactical phase). However, stochastic events and the built-in operational flexibility (robustness), along with other factors, result in demand and capacity imbalances that lead to delayed flights. The size of the EATMN and its complexity challenge the prediction of the total network delay using analytical methods or optimization approaches. We face this challenge by proposing a deep convolutional neural network (DCNN), which takes capacity regulations as the input. DCNN architecture successfully improves the prediction results by 50 percent (compared to random forest as the baseline model). In fact, the trained model on 2016 and 2017 data is able to predict 2018 with a mean absolute percentage error of 22% and 14% for the delay and delayed traffic, respectively. This study presents a method to provide more accurate situational awareness, which is a must for the topic of network resiliency.

Optimal Railway Disruption Bridging Using Heterogeneous Bus Fleets

Mass Rapid Transit (MRT) systems, i.e. subway systems, all over the world, are experiencing an increase in ridership. This also means that in case of an unplanned MRT service disruption, the number of affected passengers is larger, requiring a fast and comprehensive response. In this paper, we thus study the disruption management of MRT systems. We develop an optimization model to identify the optimal bridging plan in response to an MRT disruption, so that the negative effects of a disruption could be minimized. Our approach supports deployment of multiple types of bridging buses, reflecting the diversity of vehicle types in a typical public transportation provider's vehicle fleet. The optimization objective of our approach is to decrease the travel delay of passengers and increase the number of passengers who can be served. We demonstrate the effectiveness of our approach on a hypothetical case study in the central business district of Singapore. Moreover, we validate our analytical results with microscopic simulation, showing that our simplified analytical optimization approach can be used for disruption response planning. Some deviations indicate, however, that a combined simulation and optimization approach yields better results to obtain an effective bridging plan.

Analytical Optimization Approach for Simultaneous Design and Operation of Water Distribution–Systems Optimization

AbstractThis paper presents an analytical algorithm for simultaneous least-cost design and operation of looped water distribution systems (WDSs). This method could be used to replace evolutionary m...

Parameter Development via In Situ Residual Stress Measurement and Post-deposition Analysis of Cold Spray CuNi Coatings

Developing dense, well-adhered coatings with minimal heterogeneity via cold spray deposition has been a challenge because in-flight and layer-by-layer diagnostics has not yet been adequately adapted to complement existing post-deposition analyses and parameter process mapping. This study presents an empirical and analytical approach for development and optimization of requisite spray parameters via the cold spray solid-state consolidation process using the in situ beam curvature technique to assess particle dynamics during deposition, in conjunction with post-deposition analyses. Here, CuNi (62/38) powder was deposited onto CuNi (70/30) substrates and monitored with an in situ beam curvature sensor to provide real-time feedback of the coating’s evolving stress states during the deposition process and subsequent residual stress determination immediately after deposition. The resulting beam curvature compressive and tensile stress amplitudes detected layer-by-layer coating variations during deposition resulting from adjusted carrier gas flow rates, substrate surface preparations, nozzle deposition angle, robot raster speeds, powder feed rate, substrate preheat, as well as identifying nozzle clogging. The acquired stress-state data enhanced post-deposition analyses that directed and accelerated the downselection process to define and optimize cold spray parameters, as it pertained to coating adhesion, cohesion, and the corresponding microstructure.

Design of High-Efficiency Matching Networks for Capacitive Wireless Power Transfer Systems

Matching networks are an efficient means of providing large voltage or current gain and reactive compensation in high-frequency wireless power transfer (WPT) systems. This article introduces an analytical optimization approach for the design of L-section matching networks in capacitive WPT systems, which maximizes the network efficiency while achieving the required overall gain and compensation. The proposed approach identifies the optimal number of matching network stages and the optimal distribution of gains and compensations among these stages. Compared with the conventional approach to designing matching networks for capacitive WPT systems, the proposed approach results in higher and flatter efficiency for a wide range of air-gap voltages. The proposed approach also offers a better tradeoff between efficiency and power transfer density while meeting electric field safety requirements. The efficiency predictions of the proposed design approach are experimentally validated using three 6.78-MHz 100-W prototype capacitive WPT systems: one with single-stage matching networks, one with two-stage matching networks, and another with three-stage matching networks. The measured matching network efficiencies of the prototype systems are in close agreement with the theoretical predictions. The prototype system with two-stage matching networks is also compared with a prototype system designed using the conventional approach and is shown to achieve significantly higher efficiency.

An analytical optimization approach to the joint trajectory and signal optimization problem for connected automated vehicles

Traffic conflict points (e.g., intersections, work-zones) cause travel delay, stop-and-go traffic, and excessive energy consumption. Efforts have been taken to improve traffic conflict point performance via trajectory control of connected automated vehicles (CAV) as the CAV technology emerges. One major challenge to these efforts is the complexity in optimization of CAV trajectories, particularly with joint signal timing optimization. This challenge poses barriers to real-time application requirements, scaling them up to address network level problems and drawing analytical insights into problem structures. To overcome this challenge, this paper aims to seek for an efficient and analytical solution to a joint vehicle trajectory and signal timing optimization problem. This problem simultaneously optimizes CAV trajectories and signal timing to minimize travel delay and energy consumption at a conflicting point with two traffic approaches. This study modifies the original complex formulation in two ways. First, the vehicle trajectory shape is simplified into a piece-wise quadratic function with no more than five segments. Second, instead of using the highly non-linear instantaneous fuel consumption function, a simplified macroscopic measure is proposed to approximate fuel consumption as an analytical quadratic function of signal red interval. These simplifications provide elegant theoretical properties that enable solving an analytical exact solution to this complex problem with parsimonious analytical insights. Numerical examples reveal that the proposed model can significantly reduce travel delay and fuel consumption. Moreover, it is demonstrated that the presented algorithm is highly efficient and appropriate for real-world traffic applications.

Correntropy-Induced Discriminative Nonnegative Sparse Coding for Robust Palmprint Recognition

Palmprint recognition has been widely studied for security applications. However, there is a lack of in-depth investigations on robust palmprint recognition. Regression analysis being intuitively interpretable on robustness design inspires us to propose a correntropy-induced discriminative nonnegative sparse coding method for robust palmprint recognition. Specifically, we combine the correntropy metric and l1-norm to present a powerful error estimator that gains flexibility and robustness to various contaminations by cooperatively detecting and correcting errors. Furthermore, we equip the error estimator with a tailored discriminative nonnegative sparse regularizer to extract significant nonnegative features. We manage to explore an analytical optimization approach regarding this unified scheme and figure out a novel efficient method to address the challenging non-negative constraint. Finally, the proposed coding method is extended for robust multispectral palmprint recognition. Namely, we develop a constrained particle swarm optimizer to search for the feasible parameters to fuse the extracted robust features of different spectrums. Extensive experimental results on both contactless and contact-based multispectral palmprint databases verify the flexibility and robustness of our methods.

Heuristic self-photography approach for flat-top beam generation with arbitrary beam intensity distribution

Flat-top beam (FTB) is a type of laser illumination with broad applications. To achieve an easily accessible and cost-effective flat-top intensity profile, a self-photography approach was developed in this study. Utilizing the linear region of the Hurter–Driffield (H&D) curve, we developed an analytical formulation and simulation approach for FTB power optimization with a Gaussian beam (GB) and other intensity profiles. Notably, when a GB profile was used, the maximum transmission efficiency of an FTB depended on the lowest photographic density within the linear region of the H&D curve. Various beam profiles and experimental conditions were evaluated through numerical simulations. We performed experiments to verify the simulation results, which exhibited power efficiency of up to 14.89 % when using a GB. Current beam reshaping techniques use phase modulation; our self-photography method provides an alternative approach to generating uniform illumination with arbitrary intensity profiles, regardless of beam coherence properties. This newly developed cost-effective film approach can be easily incorporated into systems without excessive additional components. This straightforward implementation can be adapted for various illumination needs, such as high-order beam modes and multiple beam sources.

Evaluation of PMSG‐based drivetrain technologies for 10‐MW floating offshore wind turbines: Pros and cons in a life cycle perspective

AbstractThis paper presents an in depth evaluation and comparison of three different drivetrain choices based on permanent‐magnet synchronous generator (PMSG) technology for 10‐MW offshore wind turbines. The life cycle approach is suggested to evaluate the performance of the different under consideration drivetrain topologies. Furthermore, the design of the drivetrain is studied through optimized designs for the generator and gearbox. The proposed drivetrain analytical optimization approach supported by numerical simulations shows that application of gearbox in 10‐MW offshore wind turbines can help to reduce weight, raw material cost, and size and simultaneously improve the efficiency. The possibility of resonance with the first torsional natural frequency of drivetrain for the different designed drivetrain systems, the influence of gear ratio, and the feasibility of the application for a spar floating platform are also discussed. This study gives evidence on how gearbox can mitigate the torque oscillation consequences on the other components and how the latter can influence the reliability of drivetrain.

Weighing the Sun with five photographs

Using only five photographs of the Sun at different dates, we show that the mass of the Sun can be calculated using a telescope, a camera, and Kepler’s third law. With these photographs we are able to calculate the distance between the Sun and the Earth at different dates over a period of time of about three months. These distances allow us to obtain the correct elliptical orbit of Earth, proving Kepler’s first law. Analysis of the data extracted from the photographs is performed using an analytical optimization approach that allows us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using a geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth’s orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun’s mass by applying Kepler’s third law and Newton’s law for gravitation. This method gives a result which is in excellent agreement with the correct value for the Sun’s mass. Thus, over a time span of about three months, any student is capable to calculate the mass of the Sun with only five photographs, a telescope and a camera.

An optimized self-sensing piezoelectric cantilever for micro-robotic applications

Quasi-static piezoelectric actuators are used in micro-robotics due to the small displacements they can achieve, and they have been proven to be suitable for Self-Sensing Actuation (SSA) applications. The morphology and material of an actuator, and therefore its characteristics (i.e. stiffness, capacitance), all have an impact on the performance of the SSA implementation. This article presents a methodology that can be used to optimize the design parameters for a piezoelectric quasi-static bimorph cantilever for micro-robotic applications with sub-mN manipulation forces and sub-μ m positioning resolutions in mind. A model is established for this type of actuator, from which an objective function aiming to maximize β, the charge accumulation coefficient, is defined. Boundary conditions are set on the optimization study by imposing constraints on the design. An analytical optimization approach is then adopted to study the evolution of the objective function across the design space. The study evidences the existence of a subset of solutions satisfying the constraints and maximizing the objective function, and the partial derivatives of this subset are studied, leading to conclusions for an optimized design strategy. Experimental results show that inaccuracies in the prediction of the β parameter lie within the self-sensing actuator model due to the omission of the thin electrode layers inserted between each piezoelectric layer. Nonetheless, the presented optimization methodology has proven to be suitable to maximize the potential SSA performance of a design, with the fabricated optimized actuator having a higher β coefficient than a commercial actuator of similar external dimensions by a factor of approximately 7.

Periodic High-Sensitive Beam-Steering Leaky-Wave Antenna With Circular Polarization

This article proposes an analytical optimization approach in order to optimize the frequency-dependent beam-steering capability of a 1-D serial-fed leaky-wave antenna under the constraint of circular polarization. In the presented approach, the high beam-steering sensitivity is achieved by a circular patch approach. The circular polarization constraint, the impedance matching across unit cells, and open stopband problem are reduced to a mode rotation condition of the electric field within the circular patch. It is further shown that the mode rotation condition is achieved by a single optimization parameter. Measurements proof the beam-steering sensitivity, the circular polarization, and open stopband suppression.

Hybrid analytical and simulation optimization approach for production and distribution supply chain planning

Supply chain planning consists of designing an optimal and feasible production and distribution plan for the whole supply chain. Traditionally, two common methods of optimization are analytical and simulation-based optimization, and each of them has pros and cons. In this paper, both methods are combined to consolidate the strengths of each, also known as the hybrid analytical and simulation approach. A case study of a multi-period, multi-echelon, and multi-product production and distribution problem that maximizes the whole supply chain’s profit is introduced, to demonstrate the proposed hybrid approach. The analytical model is solved to find the optimal production-distribution plan, and then the plan is inputted into a simulation model, where uncertainties are incorporated. The proposed algorithm is then applied to identify a feasible plan that meets makespan limitation and service level requirements. Safety stock is incorporated to satisfy the service level requirements and maximize the supply chain’s profit. This procedure continues iteratively until the production-distribution plan is feasible and optimized. The results show that the proposed approach can solve for a near or possibly optimal as well as feasible solution with relatively fast computational time.