Application of reinforcement learning for the optimization of clinch joint characteristics

Due to increasing challenges in the area of lightweight design, the demand for time- and cost-effective joining technologies is steadily rising. For this, cold-forming processes provide a fast and environmentally friendly alternative to common joining methods, such as welding. However, to ensure a sufficient applicability in combination with a high reliability of the joint connection, not only the selection of a best-fitting process, but also the suitable dimensioning of the individual joint is crucial. Therefore, few studies already investigated the systematic analysis of clinched joints usually focusing on the optimization of particular tool geometries against shear and tensile loading. This mainly involved the application of a meta-model assisted genetic algorithm to define a solution space including Pareto optima with all efficient allocations. However, if the investigation of new process configurations (e. g. changing materials) is necessary, the earlier generated meta-models often reach their limits which can lead to a significantly loss of estimation quality. Thus, it is mainly required to repeat the time-consuming and resource-intensive data sampling process in combination with the following identification of best-fitting meta-modeling algorithms. As a solution to this problem, the combination of Deep and Reinforcement Learning provides high potentials for the determination of optimal solutions without taking labeled input data into consideration. Therefore, the training of an Agent aims not only to predict quality-relevant joint characteristics, but also at learning a policy of how to obtain them. As a result, the parameters of the deep neural networks are adapted to represent the effects of varying tool configurations on the target variables. This provides the definition of a novel approach to analyze and optimize clinch joint characteristics for certain use-case scenarios.

Coverage Path Planning Using Reinforcement Learning-Based TSP for hTetran—A Polyabolo-Inspired Self-Reconfigurable Tiling Robot

One of the critical challenges in deploying the cleaning robots is the completion of covering the entire area. Current tiling robots for area coverage have fixed forms and are limited to cleaning only certain areas. The reconfigurable system is the creative answer to such an optimal coverage problem. The tiling robot’s goal enables the complete coverage of the entire area by reconfiguring to different shapes according to the area’s needs. In the particular sequencing of navigation, it is essential to have a structure that allows the robot to extend the coverage range while saving energy usage during navigation. This implies that the robot is able to cover larger areas entirely with the least required actions. This paper presents a complete path planning (CPP) for hTetran, a polyabolo tiled robot, based on a TSP-based reinforcement learning optimization. This structure simultaneously produces robot shapes and sequential trajectories whilst maximizing the reward of the trained reinforcement learning (RL) model within the predefined polyabolo-based tileset. To this end, a reinforcement learning-based travel sales problem (TSP) with proximal policy optimization (PPO) algorithm was trained using the complementary learning computation of the TSP sequencing. The reconstructive results of the proposed RL-TSP-based CPP for hTetran were compared in terms of energy and time spent with the conventional tiled hypothetical models that incorporate TSP solved through an evolutionary based ant colony optimization (ACO) approach. The CPP demonstrates an ability to generate an ideal Pareto optima trajectory that enhances the robot’s navigation inside the real environment with the least energy and time spent in the company of conventional techniques.

Equilibrium, Efficiency, and Welfare

Competitive equilibria are studied in both partial-equilibrium and general-equilibrium settings for economies characterized by consumers with incomplete preference structures. Market equilibrium determination is developed as solving a zero-maximum problem for a supremal convolution whose dual, by Fenchel's Duality Theorem, coincides with a zero-minimum for an infimal convolution that characterizes Pareto optima. The First and Second Welfare Theorems are natural consequences. The maximization of the sum of consumer surplus and producer surplus is studied in this analytic setting, and the implications of nonsmooth preference structures or technologies for equilibrium determination are discussed.

Distributive Justice for Behavioural Welfare Economics

The incompleteness of behavioural preferences can lead many or even all allocations to qualify as Pareto optimal. But the incompleteness does not undercut the precision of utilitarian policy recommendations. Utilitarian methods can be applied to groups of goods or to the multiple social welfare functions that arise when individual preferences are incomplete, and policymakers do not need to provide the preference comparisons that individuals are unable to make for themselves. The utilitarian orderings that result, although also incomplete, can generate a unique optimum. Non-separabilities in consumption reduce this precision but in all cases the dimension of the utilitarian optima drops substantially relative to the Pareto optima.

Optimal Magnetic Spring for Compliant Actuation – Validated Torque Density Benchmark

Magnetic springs are a fatigue-free alternative to mechanical springs that could enablecompliant actuation concepts in highly dynamic industrial applications. The goals of this article are:(1) to develop and validate a methodology for the optimal design of a magnetic spring and (2) tobenchmark the magnetic springs at the component level against conventional solutions, namely,mechanical springs and highly dynamic servo motors. We present an extensive exploration of themagnetic spring design space both with respect to topology and geometry sizing, using a 2D finiteelement magnetostatics software combined with a multi-objective genetic algorithm, as a part of aMagOpt design environment. The resulting Pareto-optima are used for benchmarking rotationalmagnetic springs back-to-back with classical industrial solutions. The design methodology has beenextensively validated using a combination of one physical prototype and multiple virtual designs.The findings show that magnetic springs possess an energy density 50% higher than that of stateof-the-art reported mechanical springs for the gigacycle regime and accordingly a torque densitysignificantly higher than that of state-of-the-practice permanently magnetic synchronous motors.

Equilibrium and Efficiency

Pareto optima and competitive equilibria are defined. Allocations are functions of market wealth (sharing rules) in Pareto optima, which means that all risks except market wealth are perfectly shared. Equilibria in complete markets are shown to be equivalent to Arrow‐Debreu equilibria and to be Pareto optimal. If investors all have linear risk tolerance with the same cautiousness parameter, then equilibria are Pareto optimal, equilibrium prices are independent of the initial wealth allocation (Gorman aggregation), and two‐fund separation holds (all investors hold the risk‐free asset and the market portfolio).