On preventing the dripping effect of overhang constraints in topology optimization for additive manufacturing

This article falls within the scope of topology optimization for Additive Manufacturing processes and proposes an alternative strategy to prevent the phenomenon known as the Dripping Effect. The Dripping Effect is when an overhang constraint is imposed on topology optimization processes for Additive Manufacturing and is defined as the formation of oscillatory contour trends within the prescribed threshold angle. Although these drop-like formations constitute local minimizers of the constraint function, they do not provide a printable feature, and, therefore, they neither eliminate the need to form temporary support structures. So far, there has been no general agreement on how to prevent the Dripping Effect, so this work aims to introduce a strategy that effectively prevents it, and that at the same time may be easy to extrapolate to other types of geometric overhang restrictions. This paper provides a study of the origin of the Dripping Effect and gives detailed instructions on how the proposed prevention strategy is applied. In addition, several benchmark examples where the Dripping Effect is prevented are shown.

Research on the Impact of Relationship Networks on Farmers’ Formal Credit Constraints: The Case of China

Based on the survey data of Lishui City, Zhejiang Province, this paper uses the Heckman two-stage model to construct a credit constraint function without selection bias, and explores the relationship between the scale and quality of the relationship network and the credit constraints of rural households. Research shows that the scale of the relationship network is affected adversely by urbanization and networking, having a weaker impact on the formal credit constraints of rural households. The quality of the relationship networks can improve farmers’ awareness of formal credit, reduce transaction exposure, regulate farmers’ behavior and act as a “guarantee”, thereby effectively alleviating farmers’ formal credit constraints. At the same time, the relationship network of farmers is gradually becoming more structured, where farmers' social interests are becoming more purposeful. Additionally, formal financial institutions have set a threshold for farmers’ credit, which requires a certain amount of securities for money.

Research on ARKFCM Algorithm Based on Membership Constraint and Bias Field Correction in Neonatal HIE Image Segmentation Method

First, this paper presents the algorithm of adaptively regularized kernel-based fuzzy C-means based on membership constraint (G-ARKFCM). Under the idea of competitive learning based on penalizing opponents, a new membership constraint function penalty item is introduced for each sample point in the segmented image, so that the ARKFCM algorithm is no longer limited to the fuzzy index m = 2. Secondly, the multiplicative intrinsic component optimization (MICO) is introduced into G-ARKFCM to obtain the GM-ARKFCM algorithm, which can correct the bias field when segmenting neonatal HIE images. Compared with other algorithms, the GM-ARKFCM algorithm has better segmentation quality and robustness. The GM-ARKFCM algorithm can more completely segment the neonatal ventricles and surrounding white matter and can retain more information of the original image.

A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.

A Preliminary Investigation Into the Feasibility of Semi-Autonomous Surgical Path Planning for a Mastoidectomy Using LSTM-Recurrent Neural Networks

Path planning algorithms for robotics can be as simple as having an operator program waypoints into a robot's controller and having the robot perform a simple task such as welding. This works well in an industrial setting but will not work for complicated tasks such as performing surgery. Another approach would be to use a constraint function in programing a robot to perform surgery, but it would be difficult to capture and represent all of the surgeon's information in the mathematical terms required for a cost function. A third approach, and the one utilized in this study, is to train a set of artificial neural networks (ANNs) using recorded surgeons' motions when manipulating a surgical instrument during procedure training using a surgery simulator. This has the advantage of indirectly capturing the surgeon's abilities and intentions without needing to explicitly capture all of the motion information that must be encoded from their trajectory planning and decision-making, and then, say, creating a complex constraint function using that information. In this research effort, virtually captured surgical trajectories from trained surgeons were used to train ANNs, after being preprocessed into three subtasks. Each set of subtask data was used to train a separate ANN. Each of the ANNs was trained using a custom cost function and evaluated using custom metrics. During the training, the positions of fiducial markers, recorded during procedure attempts, were used to orient the recorded path relative to the patient's anatomy. Although the ANN-generated trajectories were not used to perform surgery on a live patient in this study, the fiducial marker position information is intended to be exploited during a real procedure to position, orient, and scale a tool trajectory to suit a patient's specific anatomy. The trained ANNs were subjected to several tests to assess their safety and robustness. We found that even when trained on a small number of datasets, the ANNs converged and could generate output trajectories that were still assessed to be safe even when slight changes in the fiducial marker placement locations were given.

Calculation accuracy of mathematical homogenization method for thermo-mechanical coupling problems

The paper analyzes the thermo-mechanical couplinag phenomenon under the condition of sliding contact, establishes the finite element analysis continuous model of thermo-mechanical coupling, and proposes the system dynamic equilibrium equation and thermodynamic equilibrium equation. The article analyzes the contact conditions between the objects in the system and obtains the objects? contact conditions? mathematical expression. On this basis, the constraint function is used to express the mathematical homogenization. We apply the variation principle to the constraint function and form a non-linear equation group with the system balance equation solve the thermal-mechanical coupling problem. The example shows that we use the constraint function method to solve the thermo-mechanical coupling problem, which has good convergence, stable algorithm, and the calculation result can reflect the actual situation.

Appointed-Time Integral Barrier Lyapunov Function-Based Trajectory Tracking Control for a Hovercraft with Performance Constraints

This paper develops a totally new appointed-time integral barrier Lyapunov function-based trajectory tracking algorithm for a hovercraft in the presence of multiple performance constraints and model uncertainties. Firstly, an appointed-time performance constraint function is skillfully designed, which proposes to pre-specify the a priori transient and steady performances on the system tracking errors. Secondly, a new integral barrier Lyapunov function is constructed, which combines with the appointed-time performance constraint function to guarantee that the performance constraints on the system tracking errors are never violated. On this basis, an adaptive trajectory tracking controller is derived using the appointed-time integral barrier Lyapunov function technique in the combination of neural networks. According to Lyapunov’s stability theory, it can be shown that the proposed controller is capable of ensuring transient and steady performances on the output tracking errors. In particular, the position and speed tracking can be fulfilled in a user-appointed time without requiring complex control parameters selection. Finally, results from a comparative simulation study verify the efficacy and advantage of the proposed control approach.

Data-Driven Additive Manufacturing Constraints for Topology Optimization

The topology optimization (TO) of structures to be produced using additive manufacturing (AM) is explored using a data-driven constraint function that predicts the minimum producible size of small features in different shapes and orientations. This shape- and orientation-dependent manufacturing constraint, derived from experimental data, is implemented within a TO framework using a modified version of the moving morphable components (MMC) approach. Because the analytic constraint function is fully differentiable, gradient-based optimization can be used. The MMC approach is extended in this work to include a “bootstrapping” step, which provides initial component layouts to the MMC algorithm based on intermediate solid isotropic material with penalization (SIMP) topology optimization results. This “bootstrapping” approach improves convergence compared with reference MMC implementations. Results from two compliance design optimization example problems demonstrate the successful integration of the manufacturability constraint in the MMC approach, and the optimal designs produced show minor changes in topology and shape compared to designs produced using fixed-radius filters in the traditional SIMP approach. The use of this data-driven manufacturability constraint makes it possible to take better advantage of the achievable complexity in additive manufacturing processes, while resulting in typical penalties to the design objective function of around only 2% when compared with the unconstrained case.