Shape Of Path Research Articles

Iterative Learning-Based Path Optimization With Application to Marine Hydrokinetic Energy Systems

This article presents an iterative learning control (ILC)-based approach for optimizing the flight path geometry of a tethered marine hydrokinetic (MHK) energy system. This type of system, which replaces the tower of a conventional system with a tether and a lifting body, can capture energy either through an on-board rotor or by driving a generator with tension in the tether. In the latter mode of operation, which represents the focal point of this effort, net positive energy is generated over one cycle of high-tension spool-out followed by low-tension spool-in. Because the net energy generation is sensitive to the shape of the flown path, we employ an iterative learning update law to adapt the path shape from one lap to the next. This update law is complemented with an iterative power take-off (PTO) controller, which adjusts the spooling profile at each iteration to ensure zero net spooling. We present and validate the proposed control approach in both uniform and spatiotemporally varying turbulent flow environments, based on a realistic ocean model detailed in this article. Finally, based on simulation results across a wide range of excitation levels, we perform a simulation-based assessment of convergence properties, comparing these results against bounds derived in the authors’ prior work.

Drag-Mitigating Dynamic Flight Path Design for an Ultra-Long Tether Underwater Kite

This paper presents a computational study of an underwater kite operating in an ultra-long tether (ULT) application. Leveraging a dynamic model established in literature, we study the relationship between path shape and tether drag at varying tether lengths in order to develop meaningful insights as to the operation of systems that require ultra-long tethers in order to reach available flow resources. The results are compared to fundamental tether drag relationships developed in the airborne wind energy field, including the multi-airborne wind energy system (MAWES) proposed by Leuthold et al. (2017, 2018). It will be shown that by careful selection of path shape, these fundamental relationships break down in deep-water marine environments, and that high performance rivaling that of the MAWES system can be achieved, without the extra required mechanical complexity.

Assessment of fatigue crack growth based on 3D finite element modeling approach

Fatigue crack growth life assessment enables manufacturers to quantify damage tolerance capability of high-risk components. Reduced order models that are based on simple geometries (i.e. surface crack in a plate, corner crack at a bolt hole) and on the assumption that cracks maintain an elliptical shape during propagation, are commonly employed in the damage assessment. A more comprehensive modeling process should consider the component geometry, service loading conditions and, eliminate assumptions related to crack front shape or planarity of the crack growth path. A 3D finite element-based approach is evaluated in this study as a more accurate alternative to reduced order models. For verification purposes, an analytical solution-based model was developed and implemented in MATLAB to predict fatigue crack growth life and crack front evolution for three different crack types: surface, corner and internal. The analytical model solutions are compared against 3D finite element (FE) based approach implemented in SimModeler Crack. The 3D FE modelling approach has been further tested and validated against experimental fatigue crack growth measurements from two Al 2024-T3 specimens containing multiple cracks. The verification and validation data presented herein show that the 3D FE-based modelling approach provides an accurate and effective modelling tool for crack propagation life assessment of structural components.

Experimental study on morphological characteristics of landslide dams in different shaped valleys

Landslide dams pose enormous risks to infrastructures and communities in mountainous areas near rivers, with potential dam breaches causing catastrophic secondary hazards. The morphology of a landslide dam, essential to its stability, is highly influenced by its formation conditions, including the landslide type, material composition, and valley shape. However, the correlation between the dam morphology and these factors is poorly understood. A series of laboratory tests were conducted to investigate the damming process and deposition morphology across three different granular materials, two sliding widths, and three valley shapes. Detailed topography surveys of the dam deposits were conducted using a 3D laser scanner. The experimental results show that the width of the sliding path and valley shape have a significant effect on the morphology of a landslide dam. The dam deposits under a narrow sliding path are more concentrated and higher with steeper upstream and downstream slopes. The cross-valley profiles are dependent on the sliding width and valley shape for the well-graded gravel with sand (Soil I, GW) and poorly-graded sand with gravel (Soil II, SP) but are of the linear shape for the poorly-graded sand (Soil III, SP). The crest surface frontal angle of soil III is larger than that of the soils containing gravel (i.e., Soils I and II). The dam length increases as the valley shape changes from rectangular to trapezoidal and then to triangular, and shows opposite trends under the two sliding widths as the gradation becomes finer. The dam height decreases under the narrow sliding path as the soil changes from Soil I to Soil II to Soil III. In addition, larger particles (i.e., gravels) tend to accumulate on the surface and opposite side whereas finer particles (i.e., sand) tend to accumulate on the bottom and source side.

Lateral inhibition between banks of orientation selective channels predicts shape context effects: A tilt-illusion field

The perceived shapes of almost circular paths are modified by concentrically placed context paths. These induced changes have previously been attributed to curvature masking. This paper shows that, instead, they can be explained by the impacts of local tilt illusions. First, the tilt-illusion was measured over the full range of orientation differences between short test and context lines and it was shown that the resulting function can be predicted by a model based on a vectorial population response of a bank of orientation selective channels, provided lateral inhibition between channels with the same orientation selectivity and adjacent receptive fields was postulated. Subsequently, it was demonstrated that, if the perceived shape of a test path were modified to accommodate the predicted local tilt-illusion, then this could account for previously reported changes in the detectability of a path sinusoidally modulated in radius. Further, we measured points of subjective vertical in test lines and points of subjective circularity in test paths when surrounded by modulated context paths. The tilt required to null the tilt-illusion approximated the maximum orientation difference from circular measured in the modulated paths at their point of subjective circularity, supporting the proposal that the illusory shape change is due to local changes in the position of the path arising from a response to local tilt illusions induced by the orientation context. An important corollary to this result is that such effects will generalize to all paths which are adjacent.

Path Tracking and Position Control of Nonholonomic Differential Drive Wheeled Mobile Robot

Differential drive wheeled mobile robot (DDWMR) is one example of a robot with a constrained movement, Multiple Input Multiple Output (MIMO), and nonlinear system. Designing a low resource position and heading controller using linear MIMO methods such as LQR became a problem because of the linearization of robot dynamics at zero value. One of the solutions is to design a MIMO controller using a Single Input Single Output (SISO) controller. This work design a controller using PID for DDWMR Jetbot and selects the best feedback gain using different scenarios. The designed controller manipulates both motors by using calculated control signal to achieve a complex task such as path tracking with robot position in x-Axis, y-Axis, and heading angle as the feedback. The priority between position and heading angle can be adjusted by changing three feedback gains. The controller was tested, and the best gain was selected using Integral Absolute Error (IAE) metrics in a path tracking task with four different path shapes. The proposed methods can track square, circle, and two types of infinity shape paths, with the less well-formed shape being the four edges square path.

On the investment strategies in occupational pension plans

Demographic changes increase the necessity to base the pension system more and more on the second and the third pillars, namely the occupational and private pension plans; this paper deals with Target Date Funds (TDFs), which are a typical investment opportunity for occupational pension planners. TDFs are usually identified with a decreasing fraction of wealth invested in equity (a so-called glide path) as retirement comes closer, i.e. wealth is invested more riskily the younger the saver is. We investigate whether this is actually optimal in the presence of non-tradable income risk in a stochastic volatility environment. The retirement planning procedure is formulated as a stochastic optimization problem. We find it is the (random) contributions that induce the optimal path exhibiting a glide path structure, both in the constant and stochastic volatility environment. Moreover, the initial wealth and the initial contribution made to a retirement account strongly influence the fraction of wealth invested in risky assets. The risk aversion of an individual mainly determines the shape of the glide path, while the ratio of the wealth and income influences the steepness of the glide path.

How to turn the corner: Discrimination of path shapes in rats.

The internal representation of a path shape is an element that constructs an internal representation of an entire route or environment. In the present study, we examined the ability of rats to discriminate path shapes. The rats learned to discriminate between an oval-shaped runway and a square-shaped one and to respond to one of two response boxes on the two sides of the runways. After the learning sessions, we tested which of the inner and outer walls the rats used as cues for discrimination using different wall shapes. The results suggest that the rats used the shape of the inner walls for the discrimination. Subsequently, the learning sessions, in which different shapes of the inner and outer walls were used, continued. There was a tendency for the rats to show better performance when the shape of the inner walls was congruent with the rule in the original learning, suggesting again that the rats used the shape of the inner wall for the discrimination. In addition, similar results were obtained when the task was conducted in the dark, suggesting that rats can discriminate path shapes using non-visual information.

Path Continuity for Multi-Wheeled AGVs

Notwithstanding the growing presence of AGVs in the industry, there is a lack of research about multi-wheeled AGVs which offer higher maneuverability and space efficiency. In this letter, we present generalized path continuity conditions as a continuation of previous research done for vehicles with more constrained kinematic capabilities. We propose a novel approach for analytically defining various kinematic modes (motion modes), that AGVs with multiple steer&drive wheels can utilize. This approach enables deriving vehicle kinematic equations based on the vehicle configuration and its constraints, path shape, and corresponding motion mode. Finally, we derive general continuity conditions for paths that multi-wheeled AGVs can follow, and show through examples how they can be utilized in layout design methods.

A novel intelligent microcatheter-shaping method for embolization of intracranial aneurysm

Objective:This study proposed and validated an intelligent microcatheter-shaping algorithm for interventional embolization of intracranial aneurysms.Methods:A stepwise microcatheter simulation algorithm constrained by a vessel center line was developed based on the geometry of aneurysms and parent arteries, and a collision correction factor of vessel walls was introduced to automatically calculate the optimal microcatheter path and tip shape. The efficacy of this intelligent shaping method was verified in an in vitro aneurysm model experiment.Results:The microcatheter path can be automatically generated using the intelligent microcatheter-shaping algorithm. Furthermore, the experiment verified that the delivery performance of an intelligently shaped microcatheter was excellent with 100% placement accuracy, superior to that of three pre-shaped microcatheters: straight (0°), 45°, and 90°. In three typical cases, the microcatheter could not be placed in the aneurysms successfully within 5 min with the aid of a microwire using a manual shaping scheme; however, it can be placed in the aneurysms successfully within 5 min using an intelligent microcatheter- shaping scheme, and the time of microcatheter placement in aneurysms was short.Conclusion:This intelligent microcatheter-shaping algorithm based on three-dimensional image data is effective and reasonable. This approach has advantages over standard pre-shaped microcatheters, with a potential clinical application value.

Experimental Investigations on Leakages in Positive Displacement Machines

The clearance gaps in positive displacement machines such as compressors, pumps, expanders, and turbines are critical for their performance and reliability. The leakage flow through these clearances influences the volumetric and adiabatic efficiencies of the machines. The extent of the leakage flow depends on the size and shape of clearance paths and pressure differences across these paths. Usually, the mass flow through the gaps is estimated using the isentropic nozzle equation with the flow coefficients applied to correct for the real flow conditions. However, the flow coefficients applied generally do not take into account the shape and size of these leakage paths. For that reason, a proper understanding of the relationship between flow coefficients and shape parameters is crucial for an accurate prediction of leakage flows. The present study investigates the influence of the various dimensionless parameters such as Reynolds number, Mach number, and pressure ratio on the flow coefficients for circular and rectangular clearance shapes. The flow coefficients are determined by comparing the experimental values obtained in an experimental test rig and the flow rates obtained from the isentropic nozzle equation. It is observed that in the case of circular clearances, the mean deviation of the experimental leakage results (in comparison to the analytical results using isotropic nozzle equations) is +9.1%, which is significantly lower than the mean deviation (+20.5%) in the case of rectangular clearance leakages. The study indicates that the isentropic nozzle equation method is more suitable for predicting the leakages through the circular clearances and needs modifications for consideration of the rectangular clearances. Using regression analysis, empirical correlations are developed to predict the flow coefficient in terms of Reynolds number, Mach number, pressure ratio, aspect ratio, and β ratio, which are found to match within ±6.4 percent of the numerical results for the rectangular clearance and within the range of -3.6 percent to +5.1 percent of the numerical result for the circular clearance. The empirical relationships presented in this study can be extended to evaluate the flow coefficients in a positive displacement machine.

Scaling law for velocity of domino toppling motion in curved paths

Abstract The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In this study, the finite-element analysis (FEA) program ABAQUS was used to discuss the scaling law for the propagation speed of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun [Scaling law for the propagation speed of domino toppling. AIP Adv. 2020;10(9):095124] is true. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes, but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. On one hand, the fitted amendatory function, φ revise {\varphi }_{{\rm{revise}}} , provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines; on the other hand, it is the rationale for the study of the domino effect.

Automatic recognition method of primary path for an anastomosing river based on its typical features

AbstractPrimary path recognition is a prerequisite for effective river network generalization. In a river network with a large spatial region, anastomosing rivers refer to those with intertwined river channels. Dense reaches with similar semantic information usually form complex spatial structures, which creates special challenges for accurately delineating the primary path. The recognition of the primary path for anastomosing rivers has not received much attention in the literature. Traditional methods rely on empirical thresholds to determine the basin including the primary path, and do not consider the overall spatial structure features of rivers, which lower the flexibility and accuracy of the primary path recognition. Therefore, this article proposes an automatic recognition method for the primary path of an anastomosing river based on its typical features. First, a directed topology of the river network is constructed to detect the key nodes in forming the anastomosing rivers in the river network, which are the nodes with multiple outflow reaches and are defined as redundant nodes. Second, by considering the flow direction, the effective topological boundary of each redundant node is identified to determine the basin of the anastomosing rivers automatically. Finally, a hierarchical tree is constructed to describe the spatial relationships among redundant nodes and based on the hierarchical tree and other typical features of anastomosing rivers, the optimal connection path between each redundant node and downstream node is calculated to identify the primary path. 1:10,000 topographic river data of the experimental region in Hubei Province, China, were used for validation. The experiment reveals that compared with the state‐of‐the‐art Buttenfield method, the primary path identified by the proposed method is more similar to that obtained manually. The inclination angle difference between the result obtained using the Buttenfield method and the artificial identification result is four times larger than that obtained by the proposed method; moreover, the shape of the primary path detected by the proposed method is more natural and smoother.

Crack growth models for multiaxial fatigue in a ship’s propeller shaft

A premature fatigue failure of a large intermediate propeller shaft in a shuttle tanker is discussed and analyzed. The short fatigue life consists mainly of a crack growth phase. Life predictions are carried out by crack growth modelling based on engineering fracture mechanics. The purpose of the present investigation is to identify the most likely loading modes based on the evolution of the crack propagation. A Linear Elastic Fracture Mechanics Model (LEFM) is applied with the stress intensity factor range entering the Paris law as a key parameter. Existing formulas for the geometry functions are supplemented by more detailed stress intensity factor calculations pertaining to small semi-elliptical surface cracks subjected to stress mode I. Enhanced geometry functions are proposed as a function of the relative crack depth and the crack shape aspect ratio. The ability of the fracture mechanics model to reconstruct the observed crack path and crack shape development is emphasized. Various loading modes and multi-axial stress states are applied to pursue the observed crack behavior. The observed semi-elliptical crack shapes and the shift in crack planes are included in the analysis.

Layout Embedding via Combinatorial Optimization

AbstractWe consider the problem of injectively embedding a given graph connectivity (a layout) into a target surface. Starting from prescribed positions of layout vertices, the task is to embed all layout edges as intersection‐free paths on the surface. Besides merely geometric choices (the shape of paths) this problem is especially challenging due to its topological degrees of freedom (how to route paths around layout vertices). The problem is typically addressed through a sequence of shortest path insertions, ordered by a greedy heuristic. Such insertion sequences are not guaranteed to be optimal: Early path insertions can potentially force later paths into unexpected homotopy classes. We show how common greedy methods can easily produce embeddings of dramatically bad quality, rendering such methods unsuitable for automatic processing pipelines. Instead, we strive to find the optimal order of insertions, i.e. the one that minimizes the total path length of the embedding. We demonstrate that, despite the vast combinatorial solution space, this problem can be effectively solved on simply‐connected domains via a custom‐tailored branch‐and‐bound strategy. This enables directly using the resulting embeddings in downstream applications which cannot recover from initializations in a wrong homotopy class. We demonstrate the robustness of our method on a shape dataset by embedding a common template layout per category, and show applications in quad meshing and inter‐surface mapping.

A one-step optimization method for a compressor wheel of a microturbine engine

The work deals with the design acceleration of optimal turbomachines. For its solution, it is proposed to apply mathematical optimization methods at the initial design stage. The goal of the study was to develop a one-step algorithm for optimal compressor wheel design. The application of the algorithm has a decisive advantage in comparison to the traditional iterative method for turbomachines design. The task of designing a turbomachine is multi-parameter and interdisciplinary and involves different requirements, which often contradict each other, consequently several optimality criteria can be used simultaneously. The traditional method consists in performing one-dimensional thermal and gas-dynamic calculations with subsequent refinement using numerical study. Further fine-tuning of the wheel geometry includes variation of the blade angle at the exit from the impeller, as well as of the height of the flow path at the exit from the wheel. One-step global optimization was performed by using a particle swarm algorithm involving eleven variable parameters. The objective function is thermodynamic efficiency, calculated by stagnation parameters. The authors compare the results of calculating the geometry of the centrifugal compressor wheel by the traditional sequential method and by the newly developed global optimization method. The compressor wheel has an outer diameter of 200 mm, the diameter of the hub is 52 mm, the rotational speed is 60,000 rpm and the required compression ratio is 3.7. In the traditional optimization method, the blade angles and the profile thickness are varied in three or four blade cross sections. The novelty of the developed one-step algorithm consists in the optimization of the initially three-dimensional shape of the flow path. Testing has shown that the one-step global optimization method provides an efficiency gain of about 2 %. Compared to the traditional method, the required time decreased 6 to 18 times. The proposed method can be applied to the design of turbomachines of various dimensions. The developed algorithm can be used as a basis for external modules in various existing packages, such as Ansys, Comsol and SolidWorks.

Optimal Smooth Paths Based on Clothoids for Car-like Vehicles in the Presence of Obstacles

Automated Guided Vehicles are increasingly used for material transfer in factory and warehouse environments amongst humans and human operated vehicles. Safe and efficient operation is challenging when there is a mix of human and automated traffic as fixed guide paths can become blocked more frequently. In this work we aim to show smooth and efficient paths based on clothoid curves can be used to automatically plan diversions which can be traversed at high speed by automated fork-lift vehicles, which are car-like in the sense they have a limited turning radius and angular acceleration. The approach, based on numerical optimisation within convex region constraints is described in detail, and numerical results for curvature and sharpness are compared to a cubic spline on a small number of simulated environments. The clothoid spline is less affected, in terms of its objective function, by a shift in the obstacle boundaries than a cubic spline, for obstacle shifts below 0.5m. The clothoid spline takes longer to converge for but the output path has attractive qualities like lower peak sharpness, enabling high speed operation. The method is therefore most useful for applications where path quality is important and updates are required less frequently. Changing the objective function by increasing weighting parameter b allowed the path shape to be tuned to reduce the peak sharpness, at the cost of increasing the total length. With b > 100, convergence was poor because parts of the spline were pushed outside the assigned region, an artefact arising from the constraints only being enforced at the start and end of each segment. The analytical Jacobian of the constraints was effective at reducing the number of function evaluations to reach convergence.

Efficient temperature regulation through power optimization for arbitrary paths in Laser Based Additive Manufacturing

This study presents a temperature regulation methodology for Laser Based Additive Manufacturing. A Surrogate Model based on Artificial Neural Networks is trained by Finite Element simulations to predict peak temperature on the powder bed under a moving laser beam. The beam may follow a discretized trajectory of arbitrary shape, while laser power is allowed to change between each simulation step. The Surrogate Model exhibits extreme efficiency, being designed to process an entire trajectory at once. The shape of the laser path causes instabilities on the trace of peak temperature for constant laser power. A recursive control law is implemented which gradually modifies the power profile to counteract these instabilities. To maintain efficiency the control law is also designed to be applied to the entire power vector, i.e. along the entire trajectory, in a parallel manner. The result is a highly efficient framework which produces an optimized power profile for smooth peak temperature output.

Estimating transition path times and shapes from single-molecule photon trajectories: A simulation analysis.

In a two-state molecular system, transition paths comprise the portions of trajectories during which the system transits from one stable state to the other. Because of their low population, it is essentially impossible to obtain information on transition paths from experiments on a large sample of molecules. However, single-molecule experiments such as laser optical tweezers or Förster resonance energy transfer (FRET) spectroscopy have allowed transition-path durations to be estimated. Here, we use molecular simulations to test the methodology for obtaining information on transition paths in single-molecule FRET by generating photon trajectories from the distance trajectories obtained in the simulation. Encouragingly, we find that this maximum likelihood analysis yields transition-path times within a factor of 2-4 of the values estimated using a good coordinate for folding, but tends to systematically underestimate them. The underestimation can be attributed partly to the fact that the large changes in the end-end distance occur mostly early in a folding trajectory. However, even if the transfer efficiency is a good reaction coordinate for folding, the assumption that the transition-path shape is a step function still leads to an underestimation of the transition-path time as defined here. We find that allowing more flexibility in the form of the transition path model allows more accurate transition-path times to be extracted and points the way toward further improvements in methods for estimating transition-path time and transition-path shape.

Interpreting SMFRET-Based Calculation of Transition Path Time with Molecular Simulations

Folding transition paths are fleeting events that occur when a protein crosses between unfolded and folded states. The ensemble of folding transition paths for a given protein contains a wealth of information regarding the barrier crossing pathways, i.e. the folding mechanism. Due to their typical durations and vanishing equilibrium probability, transition paths are extremely challenging to resolve experimentally. Recent advances in smFRET confer the time resolution necessary to capture at least the duration of these fast transitions (∼10∧(-5)s). However, measuring transition path durations by FRET presents a problem: a maximum likelihood model based on simplifying assumptions must be used to infer the duration because of the relatively low rate of photon detection. Here we use molecular simulation trajectories, in which all information is known to compute simulated photon trajectories with similar mean photon detection rates to those of real experiments. We then determine transition path times by passing the photon trajectory from simulation through a maximum likelihood algorithm identical to that employed for analysis of smFRET data. Specifically, we use a coarse-grained Go-model as an approximate representation of proteins alpha 3D, CspTm and GB1. We compare transition path times directly calculated from a reaction coordinate based on native contacts and transition path times calculated from a likelihood analysis of photon trajectory realizations of molecular simulations. We find that while the likelihood analysis of photon trajectories estimates transition path times within a factor of three of the true transition path time, it systematically underestimates true transition path times due to the oversimplified model of the transition path shape. Seeing as transition path shapes vary across proteins, we propose searching for the most likely transition path time with tunable transition path shape.