Optimization Constraints Research Articles

Enhancing the wind farm‐based power system stability with coordinated tuned supplementary controller

SummaryThe effects of the wind farm on the low‐frequency oscillations of interconnected power systems have become a significant problem with extensive apprehension. These low‐frequency oscillations are undesirable, malfunctioning and resulting in system instability. This paper studies the influence of various factors on stability, with varying wind penetration, a different combination of controllers, wind farm (WF) integration and replacement of synchronous generators. To enhance the stability, it is integrated and analyzed significance of the controller by considering the power oscillation damper for WF, power system stabilizer for synchronous generators and supplementary controller of flexible AC transmission system devices for the system. The rotor speed deviation is considered an objective function with various constraints for particle swarm optimization to provide the controller's optimized value and combination. The small‐signal and transient stability problems were examined using eigenvalue analysis and time‐domain simulation. The state‐space formulation is derived for eigenvalue analysis for small signal stability assessment with system variables. The nonlinear dynamic simulation results for transient stability analysis are obtained using a three‐phase fault. From stability analysis, coordinated controllers intensify the capability of SGs and WF under extreme disturbances. The effectiveness and robustness of the proposed approaches have been verified using the IEEE‐9 bus test system. All the analysis and simulations are performed using real time digital simulation (RTDS) with interfacing between MATLAB/SIMULINK‐2018a software and RT‐LAB (an OP5600 RT‐LAB).

Body trajectory optimisation of walking gait for a quadruped robot

AbstractTo ensure that the robot can follow the planned trajectory, smooth switching between swinging legs and a smooth transition of motion process is realised. The previous motion planning work is analysed, and a method for improving the optimisation objective function and constraint conditions is proposed to eliminate the sudden change of acceleration and reduce the peak value of acceleration change. This method eliminates the impact phenomenon in the motor drive process and reduces the motor drive energy consumption, thus ensuring the smooth and consistent movement of the robot. The results show that the improved optimisation method has a better motion effect than the previous approach in terms of centre of mass motion speed, trajectory fitting and body posture change, and realises more robust motion of quadruped robots in a senseless state.

Neuromuscular control: from a biomechanist's perspective.

Understanding neural control of movement necessitates a collaborative approach between many disciplines, including biomechanics, neuroscience, and motor control. Biomechanics grounds us to the laws of physics that our musculoskeletal system must obey. Neuroscience reveals the inner workings of our nervous system that functions to control our body. Motor control investigates the coordinated motor behaviours we display when interacting with our environment. The combined efforts across the many disciplines aimed at understanding human movement has resulted in a rich and rapidly growing body of literature overflowing with theories, models, and experimental paradigms. As a result, gathering knowledge and drawing connections between the overlapping but seemingly disparate fields can be an overwhelming endeavour. This review paper evolved as a need for us to learn of the diverse perspectives underlying current understanding of neuromuscular control. The purpose of our review paper is to integrate ideas from biomechanics, neuroscience, and motor control to better understand how we voluntarily control our muscles. As biomechanists, we approach this paper starting from a biomechanical modelling framework. We first define the theoretical solutions (i.e., muscle activity patterns) that an individual could feasibly use to complete a motor task. The theoretical solutions will be compared to experimental findings and reveal that individuals display structured muscle activity patterns that do not span the entire theoretical solution space. Prevalent neuromuscular control theories will be discussed in length, highlighting optimality, probabilistic principles, and neuromechanical constraints, that may guide individuals to families of muscle activity solutions within what is theoretically possible. Our intention is for this paper to serve as a primer for the neuromuscular control scientific community by introducing and integrating many of the ideas common across disciplines today, as well as inspire future work to improve the representation of neural control in biomechanical models.

Quantum computing for a profusion of postman problem variants

In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally varying weights, number of parties involved in routing, among others. We put emphasis on the explanation of how to convert such problems into quadratic unconstrained binary optimization (QUBO) problems. QUBO is one of two equivalent natural paradigms for quantum annealing devices, the other being the Ising Model. We also expand upon a previously discovered algorithm for solving the Chinese Postman Problem on a closed undirected graph to decrease the number of constraints and variables used in the problem. Optimal annealing parameter settings and constraint weight values are discussed based on results from implementation on the D-Wave 2000Q and Advantage. Results from classical, purely quantum, and hybrid algorithms are compared.

Data-Driven Security and Stability Rule in High Renewable Penetrated Power System Operation

Power systems around the world are experiencing an energy revolution that substitutes fossil fuels with renewable energy. Such a transition poses two significant challenges: highly variable generators that add short-term and long-term difficulties for supply–demand balance, and a high proportion of convertor-based devices that may jeopardize power system security and stability. At the same time, machine learning techniques provide more opportunities to study the complex power system security and stability problems. This article summarizes the machine learning framework to embed security rules into power system operation optimization under high renewable energy penetration. First, we explore how high penetration renewable energy impacts power system security and stability. Then, we review how the complex security and stability boundary of power systems is modeled using various machine learning techniques. Finally, we show how the machine learning model is transformed into optimization constraints that can be embedded into the power system operation model. The framework is substantiated through case studies of practical power systems.

Accuracy improvement of cooperative localization using UAV and UGV

In a simultaneous localization and mapping (SLAM) system, in general, distribution estimation based on a particle filter is used for localization of Unmanned Ground Vehicle (UGV) with a laser rangefinder, and point estimation based on optimization is used for Unmanned Aerial Vehicle (UAV) with a monocular camera. In order for such robots to perform cooperative localization to improve accuracy, it is necessary to convert the localization results of point estimation and distribution estimation into a format that can be introduced to each other. In this paper, we propose an integration method of estimation results for cooperative localization by UAV and UGV. The UAV point estimation result is converted to a normal distribution by giving a fixed covariance matrix in order to introduce it as the observation likelihood of the UGV. On the other hand, the particle pose with maximum weight obtained from the UGV distribution estimation result is added to the current pose constraint in UAV optimization. As a result, this allows stable localization of both by correcting with the estimation result of the other even in an environment where either one is disadvantageous for localization.

Harmonic Injection Strategy Considering Multiplane Iron Loss Impact With Optimal Magnetizing Flux Distribution for Multiphase Induction Machines

Lagging orientation error detuning induced by iron losses for multi-planes of multiphase IM under non-sinusoidal supply control triggers error in determination of calculated harmonic, fundamental air-gap flux advance angles and harmonic slip frequency. This in-turn leads to inaccurate harmonic injected currents, which are dependent on harmonic multiple of frequency for the corresponding plane with respect to fundamental plane frequency. This paper proposes the novel harmonic injection strategy considering the detuned impact of iron losses by keeping in view the complete iron loss modeling for both harmonic magnetizing flux orientation control (MFOC) and fundamental rotor flux orientation control (RFOC) planes. Furthermore, satisfaction of complete optimal flux distribution constraints for multiphase IM are taken into account which results in preserving optimal flux patterns throughout the mechanical loading particularly at low and medium load conditions. Contrary to other traditional orientation schemes, this paper adopts the MFOC and RFOC for harmonic and fundamental plane respectively for acquiring the aligned and synchronized control of harmonic and fundamental air-gap flux distribution. Detailed experimental results incorporating seven phase induction machine as prototype are utilized to evaluate the harmonic injected currents, advance angles, slip frequencies and induced EMF waveforms which validate the effectiveness of proposed scheme.

Design and optimization study of a resistance structure for an industrial storage platform supporting injection molding tools for the automotive industry

The paper offers an optimized solution for an industrial storage platform supporting injection molding tools used to produce thermoplastic components in the automotive sector. After analyzing the current situation for storing the massive tools, a work platform was proposed in order to ensure the conditions imposed by the extension of the company’s implementation of LEAN methods to streamline the production flow. The design of the resistance structure was modeled in the program Autodesk Inventor Professional 2020, taking into account realistic loads and their statistical distribution in the construction of the static and loading scheme of the main beam. The analysis of stress and strain in the main beam under the action of external loads was performed using the finite element method of the program Autodesk Inventor Nastran. The optimized solution for the main beam has been found by analyzing the optimization possibilities in three steps: structural optimization, dimensional optimization and the validation of the proposed optimization options, by verifying the safety of the structure. This paper presents in detail the choice of optimization criteria, decision variables, constraints and objective function. Based on the numerical analysis of mechanical stress and safety coefficient in operation, an optimal variant was chosen from the analyzed models: recessed articulated structure simple and with intermediate support, using laminated profiles IPE 200 and IPE 140.

DDPG-Based Joint Resource Management for Latency Minimization in NOMA-MEC Networks

In this letter, we consider the latency minimization problem in NOMA-MEC networks. Each user offloads partial tasks to the MEC server for remote execution and processes the remaining tasks locally. An iterative two-user NOMA scheme is proposed for task offloading. Obviously, users’ tasks partition ratios and offloading power impose a great effect on system performance, which can be further optimized based on the deep deterministic policy gradient (DDPG) method. Specifically, we derive an upper bound for users’ offloading power, and all the power variables can be normalized to fall between zero and one. In this way, the ratio and power variables lie in the same range, which can be obtained via a single DDPG actor network. Moreover, the optimization objective and constraints are both incorporated into the design of the reward function, which assists DDPG to learn desired strategies. Simulation results show that the proposed algorithm can effectively reduce the task processing latency.

Design, Topology Optimization, and Additive Manufacturing of a Pneumatically Actuated Lightweight Robot

Soft robotics research has rapidly incorporated Additive Manufacturing (AM) into its standard prototyping repertoire. While numerous publications have highlighted the suitability of AM for producing soft pneumatic actuators, fluidic components, and lightweight structures, their integration into an industry-like robotic arm has not yet been shown. Against this background, a pneumatically actuated robot was developed that incorporates additively manufactured soft structures into rigid articulated hinges that generally allow for integration into today’s industrial production lines. The development of the robot, including pneumatic soft rotary bellows and rotary vane actuators (RVAs), is summarized, and its functionality is proven. It was found that using AM can increase the structural stiffness of robot links to a significant degree as manufacturing-related constraints in topology optimization are largely eliminated. Moreover, it was found that multi-material polyjet printing of soft rotary bellows actuators allows for highly integrated designs that provide low leakage and friction. However, these soft rotary actuators are still inferior in terms of endurance and performance if compared to AM replicas of RVAs. Our work narrows the gap between soft robotics research and today’s industrial applications, may realign research directions, and may provide impulses for the industry towards soft robotics and AM.

Optimal Demand Response Using Battery Storage Systems and Electric Vehicles in Community Home Energy Management System-Based Microgrids

Demand response (DR) strategies are recieving much attention recently for their applications in the residential sector. Electric vehicles (EVs), which are considered to be a fairly new consumer load in the power sector, have opened up new opportunities by providing the active utilization of EVs as a storage unit. Considering their storage capacities, they can be used in vehicle-to-grid (V2G) or vehicle-to-community (V2C) options instead of taking power in peak times from the grid itself. This paper suggests a community-based home energy management system for microgrids to achieve flatter power demand and peak demand shaving using particle swarm optimization (PSO) and user-defined constraints. A dynamic clustered load scheduling scheme is proposed, including a method for managing peak shaving using rules specifically designed for PV systems that are grid-connected alongside battery energy storage systems and electric vehicles. The technique being proposed involves determining the limits of feed-in and demand dynamically, using estimated load demands and profiles of PV power for the following day. Additionally, an optimal rule-based management technique is presented for the peak shaving of utility grid power that sets the charge/discharge schedules of the battery and EV one day ahead. Utilizing the PSO algorithm, the optimal inputs for implementing the rule-based peak shaving management strategy are calculated, resulting in an average improvement of about 7% in percentage peak shaving (PPS) when tested using MATLAB for numerous case studies.

Optimization with manufacturing constraints for composite laminates reinforced by curvilinear fibers through a parametric level set method

This paper presents the design optimization with manufacturing constraints for composite laminates reinforced by curvilinear fibers by using a parametric level set method. In each layer of the composite laminate, a level set function is defined by using the compactly supported radial basis functions (CS-RBFs), and the iso-contours of each level set function represent the fiber paths in one layer of the laminate. By this means, the fiber orientation at an arbitrary point in a layer can be computed by the orientation of the tangent vector of the iso-contour passing through this point. To avoid structure defects (such as gap/overlap, wrinkling and delamination) that would arise if the fiber paths are not parallel or their curvature is too large, the gradient norm and contour curvature radius of the level set functions are considered as constraints in the design optimization. The p-norm method is used to aggregate the constraints to improve the optimization efficiency. The coefficients of CS-RBFs are considered as design variables. Several numerical examples of compliance minimization and eigen-frequency maximization are investigated to verify the proposed method.

On the derivation of inequality constraints for independent component optimization maintaining a minimum system eigenfrequency

The lowest eigenfrequency of a structure depends on the local distributions of stiffness and inertia. When components of a structural system are designed separately, which is typical, e.g., in the aerospace industry, design targets for stiffness and mass of components support independent design work: they can be chosen such that realizing them ensures a minimum system eigenfrequency. However, meeting design targets exactly may be difficult, e.g., due to unforeseen restrictions such as requirements from other disciplines or limitations with respect to manufacturing. This paper uses Rayleigh’s Quotient to derive inequality constraints as limits on the spatial distributions of stiffness and mass, rather than target distributions without tolerance. They serve as component requirements with design freedom and help to decompose the system for independent design.A general formulation based on limit functionals for deformation energy and kinetic energy is proposed for arbitrary structures. For the special case of simply connected systems with rigid interfaces between components and mass-less support elements, limit functionals for support stiffness can be expressed using limit stiffness matrices. A particular choice for them is motivated assuming rigid body motion of the main body. This is then relaxed to produce limit stiffness matrices for arbitrary deformable main bodies.The approach is applied to the structural design of a space payload instrument, the ATHENA Wide Field Imager, enabling independent mass optimization of the so-called primary structure and the support elements. The resulting total mass is 7% larger than the one obtained by monolithic optimization. This could be further reduced to 3% by appropriately adjusting the requirements.

Policy-Based Primal-Dual Methods for Convex Constrained Markov Decision Processes

We study convex Constrained Markov Decision Processes (CMDPs) in which the objective is concave and the constraints are convex in the state-action occupancy measure. We propose a policy-based primal-dual algorithm that updates the primal variable via policy gradient ascent and updates the dual variable via projected sub-gradient descent. Despite the loss of additivity structure and the nonconvex nature, we establish the global convergence of the proposed algorithm by leveraging a hidden convexity in the problem, and prove the O(T^-1/3) convergence rate in terms of both optimality gap and constraint violation. When the objective is strongly concave in the occupancy measure, we prove an improved convergence rate of O(T^-1/2). By introducing a pessimistic term to the constraint, we further show that a zero constraint violation can be achieved while preserving the same convergence rate for the optimality gap. This work is the first one in the literature that establishes non-asymptotic convergence guarantees for policy-based primal-dual methods for solving infinite-horizon discounted convex CMDPs.

Self-Supervised Primal-Dual Learning for Constrained Optimization

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must balance optimality and feasibility conditions. Supervised learning methods often approach this challenge by training the model on a large collection of pre-solved instances. This paper takes a different route and proposes the idea of Primal-Dual Learning (PDL), a self-supervised training method that does not require a set of pre-solved instances or an optimization solver for training and inference. Instead, PDL mimics the trajectory of an Augmented Lagrangian Method (ALM) and jointly trains primal and dual neural networks. Being a primal-dual method, PDL uses instance-specific penalties of the constraint terms in the loss function used to train the primal network. Experiments show that, on a set of nonlinear optimization benchmarks, PDL typically exhibits negligible constraint violations and minor optimality gaps, and is remarkably close to the ALM optimization. PDL also demonstrated improved or similar performance in terms of the optimality gaps, constraint violations, and training times compared to existing approaches.

FROM EXPERIENCE-BASED TO KNOWLEDGE-DRIVEN DESIGN: A CASE STUDY OF A 3D-PRINTED PRODUCT

AbstractIn this paper, a case study of a redesign process for 3D-printed parts has been analysed. The purpose was to compare the implementation of specialist knowledge in hands-on engineering tasks with the previous experience-based approach. Here, specialist knowledge refers to systematic experimental work as a basis for Computer Aided Engineering (CAE). The case involves a set of compliant arms for an oil extraction device developed by a start-up company. Tensile tests of 3D printed dog-bone were performed to characterise the Young's modulus, tensile strength, and orthotropic behaviour of the material to build a material model based on Finite Element Analysis (FEA). With the material characteristics and three simple tests to estimate the optimisation constraints, the existing solution was disproven. Then, new solution candidates were generated and evaluated with input from the start-up company. The process resulted in a feasible solution as well as a reduction of maximum stress from 54MPa to 20MPa. The case highlights the value of specialist knowledge for characterisation of new technologies and design space constraints to reduce and improve iterations to solve a practical design problem.

Advantages and robustness of partial VMAT with prone position for neoadjuvant rectal cancer evaluated by CBCT-based offline adaptive radiotherapy

Background and purposeThis study aims to explore the advantages and robustness of the partial arc combined with prone position planning technique for radiotherapy in rectal cancer patients. Adaptive radiotherapy is recalculated and accumulated on the synthesis CT (sCT) obtained by deformable image registration between planning CT and cone beam CT (CBCT). Full and partial volume modulation arc therapy (VMAT) with the prone position on gastrointestinal and urogenital toxicity, based on the probability of normal tissue complications (NTCP) model in rectal cancer patients were evaluated.Materials and methodsThirty-one patients were studied retrospectively. The contours of different structures were outlined in 155 CBCT images. First, full VMAT (F-VMAT) and partial VMAT (P-VMAT) planning techniques were designed and calculated using the same optimization constraints for each individual patient. The Acuros XB (AXB) algorithm was used in order to generate more realistic dose distributions and DVH, considering the air cavities. Second, the Velocity 4.0 software was used to fuse the planning CT and CBCT to obtain the sCT. Then, the AXB algorithm was used in the Eclipse 15.6 software to conduct re-calculation based on the sCT to obtain the corresponding dose. Furthermore, the NTCP model was used to analyze its radiobiological side effects on the bladder and the bowel bag.ResultsWith a CTV coverage of 98%, when compared with F-VMAT, P-VMAT with the prone position technique can effectively reduce the mean dose of the bladder and the bowel bag. The NTCP model showed that the P-VMAT combined with the prone planning technique resulted in a significantly lower complication probability of the bladder (1.88 ± 2.08 vs 1.62 ± 1.41, P = 0.041) and the bowel bag (1.28 ± 1.70 vs 0.95 ± 1.52, P < 0.001) than the F-VMAT. In terms of robustness, P-VMAT was more robust than F-VMAT, considering that less dose and NTCP variation was observed in the CTV, bladder and bowel bag.ConclusionThis study analyzed the advantages and robustness of the P-VMAT in the prone position from three aspects, based on the sCT fused by CBCT. Whether it is in regards to dosimetry, radiobiological effects or robustness, P-VMAT in the prone position has shown comparative advantages.

Tracking Control Method for Greenhouse Environment Prediction Model Based on Real-Time Optimization Error Constraints

Model predictive control, without strict constraints on the control model, effectively overcomes problems, such as poor system dynamic quality caused by time delay, can improve control accuracy to a certain extent, and can directly process input and output constraints of the system online. It is applied in greenhouse system control. The appropriate objective optimization function and its corresponding constraint conditions have a direct impact on the solution of the optimal control rate of the model predictive control. In response to this issue, this paper proposes a simple and fast optimal predictive tracking control method. Based on the current prediction model of the greenhouse system, which reflects the dynamic relationship between various control equipment actions and greenhouse environmental factors, a multi degree of freedom discrete time state space model with tracking errors is established. Based on this model, in establishing the corresponding objective optimization function, the gradient descent theory and the two-norm definition are applied, and combined with actual constraints, iterative constraint conditions for real-time error tracking updates are established. Compared with traditional constraint ranges, a constraint function with real-time update characteristics is formed, achieving more accurate constraint conditions. By using rolling optimization and iterative methods, the optimal control rate corresponding to the minimum value of the objective optimization function within a finite time is solved. Through simulation examples, it is demonstrated that the model predictive control with optimization constraints can achieve a more accurate prediction and tracking control of indoor environmental parameters. This method has the advantages of simple control, energy-saving optimization, stable control, and accurate tracking, providing a reference for online real-time prediction and tracking control of future greenhouse environmental parameters.

Synthesizing MILP Constraints for Efficient and Robust Optimization

While mixed integer linear programming (MILP) solvers are routinely used to solve a wide range of important science and engineering problems, it remains a challenging task for end users to write correct and efficient MILP constraints, especially for problems specified using the inherently non-linear Boolean logic operations. To overcome this challenge, we propose a syntax guided synthesis (SyGuS) method capable of generating high-quality MILP constraints from the specifications expressed using arbitrary combinations of Boolean logic operations. At the center of our method is an extensible domain specification language (DSL) whose expressiveness may be improved by adding new integer variables as decision variables, together with an iterative procedure for synthesizing linear constraints from non-linear Boolean logic operations using these integer variables. To make the synthesis method efficient, we also propose an over-approximation technique for soundly proving the correctness of the synthesized linear constraints, and an under-approximation technique for safely pruning away the incorrect constraints. We have implemented and evaluated the method on a wide range of benchmark specifications from statistics, machine learning, and data science applications. The experimental results show that the method is efficient in handling these benchmarks, and the quality of the synthesized MILP constraints is close to, or higher than, that of manually-written constraints in terms of both compactness and solving time.

Covariance Estimation for Pose Graph Optimization in Visual-Inertial Navigation Systems

Pose graph optimization helps reduce drift accumulated in pure odometry of visual simultaneous localization and mapping (SLAM) systems by solving a nonlinear least square problem, including both sequential constraints and loop-closing constraints. However, the covariances of all constraints are set to constant matrices or by manual setting. In this paper, we propose a novel approach to approximate covariances of constraints in pose graph optimization to better represent the true uncertainty of the underlying visual-inertial navigation system (VINS) that fuses inertial measurements and visual observations. Specifically, for sequential constraints, we propose to utilize nonlinear factor recovery to optimally extract covariance matrices from the accumulated visual-inertial odometry (VIO). For loop-closing constraints, we propose a dynamic scale estimation method to approximate the scales of the information matrices. To evaluate the effectiveness and robustness of the proposed method, we conduct extensive experiments on public and self-collected datasets in various environments. Results show that our proposed method achieves higher accuracy compared with naively-formulated pose graph optimization adopted by several state-of-the-art visual-inertial navigation systems.