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Recent advancements in empirical observations of human psychological responses have revealed that the governing rules of human behavioral aspects can not only be predicted with adequate deterministic precision but also forged into mathematical formulations. These modeling studies enable crisis managers with reliable simulation tools to gain insights into critical facets of crowd disasters and enhance their decision-making abilities to facilitate safe egress in emergency situations. The macroscopic scale of representation in this context is often invoked to comprehend large-scale collective pattern formation in vast built environments, owing to its computational viability. The associated governing equations are typically constructed in a system of hyperbolic conservation law form, and conducting simulations in real-life complex geometric configurations can pose computational challenges. This article puts forward a high-resolution, shock-capturing meshfree particle method in an Eulerian framework for the numerical approximation of several widely adopted macroscopic pedestrian flow models. It serves as a superior alternative to traditional mesh-based methods, eliminating the need for specific mesh structures and connectivity between them. A classical Generalized Finite Difference Method (GFDM) in conjunction with several consistency conditions on spatial derivative coefficients is adopted to obtain a non-oscillatory and fairly conservative Godunov-type discretization of the governing system. The intercell flux is evaluated using a suitable Riemann solver, and a slope-limited reconstruction procedure of the corresponding Riemann states, adapted to arbitrary point distribution, is employed for improved accuracy. Moreover, the preferred direction of human motion is determined from a local density-dependent eikonal-type equation, which is solved using a generalized version of the Fast Marching Method. A thorough numerical investigation of three well-known second-order macroscopic models, namely Payne-Whitham (PW), Aw-Rascle (AR), and Aw-Rascle-Zhang (ARZ) is carried out through two hypothetical scenarios of crowd evacuation, not only to demonstrate the accuracy and applicability of the proposed approach but also to deepen understanding of their distinctive characteristics. A comparison of the flow flux with the fundamental diagram suggests that the density profile obtained with the ARZ model is equivalent to Hughes' first-order model. In contrast, the PW and AR models have proven to effectively replicate complex, unstable pedestrian phenomena such as stop-and-go waves. Finally, Helbing's counter-intuitive idea that strategically positioned barriers upstream of a bottleneck can essentially expedite evacuation is numerically investigated across various parameter choices. • A high-resolution, shock-capturing mesh-free particle method for three widely adopted pedestrian flow models. • Classical Generalized Finite Difference Method in conjunction with geometric conservation. • Complete characterization of complex, unstable crowd phenomena such as stop-and-go waves. • Investigation of bottleneck evacuation in the presence of strategically placed obstacles. [ABSTRACT FROM AUTHOR]

Medical doctors identify benign or malignant colon polyps by their size and shape. Since this identification is related to whether or not resection surgery is necessary, a technology for estimating absolute size and shape from endoscopic images is required. In previous research, the method for recovering the size and shape of polyps using a blood vessel region as a reference object has been proposed. This paper proposes a method to recover the size and shape of polyps by using a cylindrical endoscopic hood as a reference object. The experimental results confirm that the proposed method can estimate reflectance factor without using blood vessel information. [ABSTRACT FROM AUTHOR]

The well placement problem in the petroleum industry is usually solved by integrating an optimizer with a reservoir simulation model. This is a time-consuming approach requiring thousands of simulation runs depending on the complexity of the reservoir system. This paper introduces two well placement optimization models: a Fast-Marching Model (FMM) based on fluid flow physics and a Hybrid Model integrating reservoir simulations and FMM results with a gradient boosting algorithm. These models prioritize speed and accuracy when integrated with genetic algorithm optimization, demonstrated using a synthetic unconventional field. From 290 randomly selected locations across the synthetic unconventional field, simulation runs were performed to determine cumulative gas production and used as ground truth. Using reservoir properties at these locations as inputs, Relative Opportunity Ranking (ROR) maps were generated using the FMM and Hybrid Model approaches. The ROR maps were then linked with a genetic algorithm to determine optimal well locations, iteratively updating ROR maps with penalty maps until all wells were appropriately placed. Results indicated that the standalone FMM generated ROR maps were highly correlated with the simulation results. Time complexity analysis revealed that both models were significantly faster than traditional methods, with the FMM independent of simulation and the Hybrid Model requiring only about 290 simulation runs. Ultimately, these models have shown tremendous potential for integration into current reservoir engineering workflows, reducing decision-making times in both greenfield and brownfield scenarios. • The proposed model combines reduced-physics and ML models to accelerate trajectory optimization for shale reservoirs. • Using proposed methods, Relative Opportunity Ranking maps were generated, which maps well location to potential recovery. • The standalone Fast-Marching Model generated results have 0.93 correlations score compared to actual simulation results. • The Hybrid Model displayed a higher resolution with 0.97 R2 score compared to actual simulation results. • 7 sequential well trajectories are optimized using both approaches which shows consistency across results. [ABSTRACT FROM AUTHOR]

In this paper, a multilayer path planner (MPP) with global path-planning (GPP), collision avoidance (CA) and routine correction (RC) for an unmanned surface vehicle (USV) under complex marine environments including both coastal and surface constraints is presented. The main contributions of this paper are as follow: 1) An MPP framework consisting of multiple layers, i.e., backbone, CA and RC, is established, and achieves self-tuning path-planning which adapts time-varying environments. 2) To minimize yaw-cost for the USV within local path, a novel CA algorithm is developed by the B-Spline method. 3) For capturing environmental influences arisen from reefs around the coastline, a stochastic dynamic coastal environments (SDCE) model is built by virtue of Poisson distribution. In combination with the fast marching method (FMM) and the SCDE model, the RC algorithm is proposed to handle environmental uncertainties. Simulation results show that the proposed MPP achieves remarkable path-planning performance in terms of both collision avoidance and adaptability to complex environments. • A multilayer path planner (MPP) for a USV under complex environments is presented. • The MPP achieves self-tuning path planning adapting to time-varying environments. • A novel collision avoidance is developed by the B-spline method. • A stochastic dynamic coastal environments model is built. [ABSTRACT FROM AUTHOR]

A system for motion-planning, collision avoidance, guidance and control of an autonomous surface vehicles formation, navigating in complex marine environment is presented. The motion-planning unit, which is based in angle-guidance fast-marching square method, is specially developed for operation in dynamic and static environments. The collision avoidance unit is based in fuzzy-logic formulation, the guidance unit uses the vector-field guidance formulation and the control unit is composed by a PID heading controller and a speed controller. The leader-follower's configuration is used for cooperative operation. A set of numerical simulations are carried out for a team of three autonomous surface vehicles navigating in a complex maritime environment including static and dynamic obstacles and the results show good performance of the system. [ABSTRACT FROM AUTHOR]

Abstract The determination of the optimal multilateral well configuration for different kinds of reservoirs is extremely challenging due to the wide varieties of possible well type. In this paper, we propose a novel method to determine the number of laterals, lateral length and lateral spacing in the multilateral well. The objective in the design is to fully exploit the entire reservoir within a certain period of development time. A geological map is constructed based on the reservoir properties. The fast marching method is used to calculate the drainage area of each lateral in the development time. The drainage area of the designed multilateral well configuration can cover the entire reservoir. The results have been validated by analytical method and specific steps of the method are presented. The applications in both homogeneous and heterogeneous cases are studied. Longer development time can lead to less number of laterals, shorter lateral length and larger lateral spacing. The drainage area is irregular in the heterogeneous case. The algorithm can automatically determine the number of laterals, lateral length and lateral spacing based on the geological characteristics to exploit the reservoir efficiently. The proposed method is appropriate for the field application due to the short computational time. Highlights • A semi-analytical method for the design of multilateral well is presented. • The lateral number, length and spacing are optimized based on the drainage area. • Applications in homogeneous and heterogeneous reservoirs are investigated. [ABSTRACT FROM AUTHOR]

Motivated by a specific application in seismic reflection, the goal of this paper is to present a modified version of the Castillo–Grone mimetic gradient operators that allows for a high-order accurate solution of the Eikonal equation with Soner boundary conditions. The modified gradient operators utilize a non-staggered grid. In dimensions other than 1D, the modified gradient operators are expressed as Kronecker products of their corresponding 1D versions and some identity matrices. It is shown, that these modified 1D gradient operators are as accurate as the original gradient operators in terms of approximating first-order partial derivatives. It turns out, that in 1D one requires to solve two linear systems for finding a numerical solution of the Eikonal equation. Some examples show that the solution obtained by utilizing the modified operators increases its accuracy when incrementing the order of their approximation, something that does not occur when using the original operators. An iterative scheme is presented for the nonlinear 2D case. The method is of a quasi-Newton-like nature. At each iteration a linear system is built, with progressively higher-order stencils. The solution of the Fast Marching method is the initial guess. Numerical evidence indicates that high-order accurate solutions can be achieved. [ABSTRACT FROM AUTHOR]

This paper describes a method to determine the time-dependent stability of the fracture zone near the edges of tabular excavation layouts when different mining rates and face advance increment lengths are scheduled. Some analytic properties of the proposed time-dependent fracture zone evolution model are presented initially for a simplified mining geometry. The implementation of the model in a general tabular layout setting is described next including a novel scheme to allow for partially fractured elements. The reef plane stress distribution in the fracture zone is solved using a fast marching method that is coupled to a displacement discontinuity solution of the excavation and fracture zone deformations. The numerical scheme is illustrated by considering the extraction of a hypothetical deep-level mining layout. The sensitivity of the results to changes in the mining rate schedule and the face advance step size are discussed. Further extensions to the solution scheme are noted. [ABSTRACT FROM AUTHOR]

Horizontal well drilling and multistage hydraulic fracturing are essential to economic recovery of unconventional tight/shale reservoirs. Multiple transverse fractures are ideally supposed to be perpendicular to the minimum stress direction, but nonorthogonal transverse fractures might be seen in practice, which might bring a better connection between wellbore and fractures. However, for the same fracture half-length, the stimulated reservoir area might be less. Thus, the well performance with these nonorthogonal transverse fractures is full of uncertainty. Little research work is currently conducted on the nonorthogonal transverse fracture scenario. Our transient pressure analysis of horizontal well performance with nonorthogonal transverse hydraulic fractures utilizes the concept of rate-normalized pressure and transient productivity index. The novel Fast Marching Method (FMM) is adopted to characterize the drainage volume evolution for multi-stage horizontal wells and validate the proposed methodology. Sensitivity studies contrast transient pressure behavior and productivity index for azimuth angles from 15 to 90°, e.g. from nearly longitudinal to truly transverse fracture angles. Additionally, transient pressure behavior and long-term reservoir performance of horizontal well for different scenarios are investigated, such as reservoir anisotropy and different proppant allocation strategies under the constraints of given horizontal well spacing and total proppant amount. Contrast to what we are usually expecting, results show that for the same fracture spacing, and the same total proppant amount, the well with nonorthogonal transverse fractures will have a higher productivity index than that for truly transverse fractures. Different from productivity index, the long-term reservoir performance, however, turns out to play a different game, given specific horizontal well spacing and the same total proppant amount. Reservoir performance for horizontal well with nonorthogonal transverse fractures can be significantly improved by optimally allocating the proppant and designing hydraulic fracture placement strategies through this research. [ABSTRACT FROM AUTHOR]

An efficient path planning algorithm is required for the robot to move in a complex known and unknown environments. In the present research, the authors made an attempt to develop a path planning algorithm, that is, fast marching method (FMM) for the biped robot to move in a static environment. Once the path planning algorithm is developed, a simulation study is conducted to determine the path for the environment that consists of different number of obstacles that from different configurations for the terrain. The path planning algorithm is successfully seen to derive collision-free shortest paths in all the cases. Further, experiments are conducted on a real biped robot to test the effectiveness of the algorithm in deriving on-line collision-free path for the robot. [ABSTRACT FROM AUTHOR]

Integral Non-Local (INL) formulations are often used to regularize Continuum Damage computations, in the presence of stress softening for instance. The introduction of a characteristic/internal length allows for avoiding pathological mesh dependency. Some questions concerning the identification of the characteristic length, its possible evolution during damage process and the need for special treatments of non-locality operators near boundaries (e.g. edges, cracks) are however still open. A physical request is that material points separated by a crack (or an highly damaged zone) should not interact. Despite what is done in standard Integral Non-Local theories, this can be obtained by allowing non-local interactions to evolve depending on mechanical fields (e.g. damage, strain, stress). The Eikonal Non-Local (ENL) formulation provides a novel interpretation of damage dependent non-local interactions. Based on the Wentzel–Kramers–Brillouin (WKB) approximation for high-frequency wave propagation in a damaged medium, this formulation defines the interaction distances as the solution of a stationary damage dependent Eikonal equation. It allows for the modeling of non-local interactions which gradually vanish in damaged zones, thus ensuring a progressive transition from diffuse damage to fracture in a natural way. The numerical implementation and properties of this regularization technique are investigated and discussed. From a numerical viewpoint, a Fast Marching method is used to compute non-local interaction distances between Gauss integration points. Geodesic distances are then used to define the kernel of weighting function to be used in integral non-local averaging. Several numerical results of quasi-statics simulations of quasi-brittle fracture in isotropic media are presented. [ABSTRACT FROM AUTHOR]

On modern manufacturing production lines, Non-Destructive Testing (NDT) is frequently a bottleneck which could greatly be alleviated by integrating the inspection of components as they are manufactured. By moving inspection to the point of manufacture, greater economic and productivity benefits are realised in terms of reduced rework and schedule slippage, however, new technical challenges emerge. For welded components, high temperatures and the resulting thermal gradients, present challenges when performing ultrasonic inspection at the point of manufacture. The thermal gradients introduce positional misalignment due to "beam bending" effects arising from refraction as the material properties change with temperature. This paper presents for the first time, through simulation and practical experiments, a novel thermal compensation strategy to mitigate for thermal effects when performing ultrasonic inspection of welded components at the point of manufacture. To understand the thermal gradients experienced during standard Tungsten Inert Gas (TIG) welding, 3-dimensional thermal simulations were developed and experimentally-validated with an average error of 1.80% (mean error: 4.1oC, max error: 19.2oC). The output from the thermal simulations in combination with material properties that vary over temperature, allowed for generalised time of flight maps to be created via the Multi-Stencils Fast Marching Method (MSFMM) and the ultrasonic data to be imaged by the Total Focusing Method (TFM). The thermal compensation strategy was initially proved on synthetically generated finite element Full Matrix Capture (FMC) datasets, and it was shown that reflector positional accuracy could be increased by ∼ 3 mm. Experimental results also showed marked improvements with reflector positional accuracy also being increased by ∼3 mm. Over both simulated and experimental datasets, the SNR was shown to be negligibly altered between uncompensated and compensated images. The results show how high-quality ultrasonic images can be generated in-process and help bring inspection closer to the point of manufacture. [ABSTRACT FROM AUTHOR]

Recent research into transient reservoir response has developed a novel formulation of the diffusivity equation to model pressure, rate, and production, especially for unconventional reservoirs. This formulation characterizes the geometry of pressure propagation through a reservoir taking into account the heterogeneity of the reservoir and the boundary conditions which arise from multiple fractures and complex well completions. The formulation is derived from the asymptotic (high frequency) limit of the diffusivity equation for the impulse pressure solution. The formulation requires the solution of the Eikonal equation for the Diffusive Time of Flight (DToF) and the corresponding pore volume geometry contained within a Diffusive Time of Flight contour. Once the pore volume geometry is constructed, it may be used as the basis for either numerical or analytic solution. While numerical solutions are more general, the analytic approach is more readily applicable to production data analysis. The analytic approach may be used to determine two important field characteristics: the drainage volume of a well and the ratio of the produced volume to the drainage volume. In the pseudo steady state (PSS) limit, the latter would be the recovery factor for a reservoir. These quantities may be predicted from a model (for calibration purposes) or calculated directly from production data without resorting to any modeling. In this paper, we work directly with field production and pressure data to infer the drainage volume, and the instantaneous recovery ratio, defined as the ratio of the produced volume to the drainage volume. We also introduce a new w ( τ ) function that is related to a combined fracture and reservoir surface area. Our work draws upon the commonly used pressure transient and Rate Normalized Pressure (RNP) concepts. However, it specifically generalizes the concept of the drainage volume from PSS flow to transient flow, as is required for unconventional reservoirs, and then infers the underlying flow geometry to help differentiate and analyze different reservoir and fracture properties. The proposed formulation is applied to the analysis of the production data from shale oil reservoirs. The field data has been interpreted to describe the variations in performance characteristics seen in a number of wells. [ABSTRACT FROM AUTHOR]

Finding optimum well locations is still among the most challenging reservoir engineering problems. Reservoir simulators are routinely used to evaluate different configuration of well locations in the reservoirs. However, simulation of giant field models is computationally demanding and time consuming. In the current study, a novel proxy with the objective function that is based on volumetric pressure approximation provided by Fast Marching Method (FMM) is introduced. This proxy calculates the wells bottom-hole pressure at the end of unsteady state period. The locations where the calculated bottom-hole pressure are maximum will likely leads to maximum Net Present Value (NPV). Foremost, The FMM-based approach is applied on the single production well placement problem and the correlation between results provided by this approach and the conventional simulator-based method is calculated. Thereafter, FMM-based approach is coupled with Particle Swarm Optimization (PSO) algorithm and applied to multiple production well placement in two standard reservoir model. Results provided by the new approach is compared with simulator-based approach in terms of performance and time efficiency. Results reveal that FMM-based approach can provide satisfactory results while significantly reducing computational cost. [ABSTRACT FROM AUTHOR]

Unmanned surface vehicles (USVs) have obtained increasing interests in recent decades. Because of the features of improved mission efficiency and decreased resource costs, applications of USVs can been seen in both civilian and naval areas. In order to efficiently and effectively achieve missions without any human intervention, a robust and intelligent navigation, guidance and control (NGC) system is vital for USV. This paper has therefore presented a novel NGC system designed for a USV named Springer . The system is developed by integrating multiple functional modules, which include a reliable navigation module that provides reliable position and heading information, a robust autopilot module enabling Springer tracking well the waypoints and an intelligent path planning module that is capable of generating feasible and practical waypoints. The path planning algorithm has been developed based upon the angle guidance fast marching square method, which is able to calculate the optimal path according to vehicle's motion constraints. The designed NGC system has been validated in both real field trials and computer based simulations proving that Springer USV is able to autonomously navigate in different maritime environments with the guidance of the NGC system. [ABSTRACT FROM AUTHOR]

In the last decade, Unmanned Aerial Vehicles (UAVs) have been a research focus for many purposes. Many of these studies require a path planning to perform autonomous flights, as well as the maintenance of a fixed flight level with respect to the ground to capture videos or overlying images. This article presents an approach to plan a mission for UAVs keeping a fixed flight level constraint. The 3D environment where the planning is carried out is an open field with non-uniform terrain. The approach proposed is based on the Fast Marching Square (FM 2 ) method, which generates a path free from obstacles. Our approach includes two adjustment parameters. Depending on the values of these parameters, the restriction of flight level can be modified, as well as the smoothness and safety of the generated paths. Simulated experiments carried out in this work demonstrate that the proposed approach generates trajectories respecting a fixed flight level over the ground with successful results. [ABSTRACT FROM AUTHOR]

Multi-stage hydraulic fracturing in horizontal wells is a crucial technology driving the economic production from unconventional resources. Multi-stage transverse fracture treatments provide significant reservoir stimulation, but recent industry study estimates that as high as one third fracture clusters are not performing as expected. This is due to the complexity of the fracture and reservoir characteristics and large number of possible design variables, such as the number of transverse fracture stages, the fracture spacing, horizontal well length, proppant concentration, and the fluid and proppant injection history. A systematic and efficient fracture design procedure is needed to provide a more optimal design. This paper focuses on the optimization of the number of fracture stages, their spacing, and the allocation of proppant during multistage hydraulic fracturing. Our optimization will rely on a novel approach for drainage volume calculations using a Fast Marching Method (FMM). The FMM is a recently introduced method that relies on a high frequency asymptotic solution of the diffusivity equation to extend the concept of depth of investigation to heterogeneous and fractured media. The approach has been shown to be computationally efficient, physically intuitive and can rigorously account for the interactions between the hydraulic and natural fractures during the computation of drainage volume. Our optimization approach will attempt to maximize the Net Present Value (NPV) from the engineering perspective, by selecting the optimal number and placement of fracture stages. Optimum fracture spacing need not necessarily be uniformly distributed along the horizontal wellbore, especially when prior reservoir properties, for example natural fracture density, are available from well logs and other sources. A systematic and efficient approach to fracture design will be demonstrated, constrained by long-term well performance while accounting for specific economic parameters. The power and practical utility of the proposed approach is demonstrated using a three-dimensional synthetic example. We find that there are an optimum number of fracture stages for a given reservoir. If adequate geological, geophysical, and engineering data are available to estimate reservoir heterogeneity before hydraulic fracturing, fracturing spacing can be further optimized instead of evenly spaced. If there is uncertainty associated with reservoir heterogeneity, multiple realizations can be integrated in the proposed optimization workflow. [ABSTRACT FROM AUTHOR]

Primary geological model of reservoirs provided by geo-modeler usually contains complex structures and millions of grid cells. Despite the recent advances in computational resources, these highly detailed models are not suitable for flow simulation purposes due to enormous simulation costs. Upscaling is necessary to reduce the number of grid blocks in geological model while preserving the static and the dynamic properties of the fine grid model. Upscaling is dependent on the flow process and it is often difficult to ensure that all the fine scale details are preserved in the upscaling process. This adds to another level of uncertainty in dynamic performance. Since so much effort has been put in constructing the detailed geological model, it is often desirable that the simulation be carried out in the fine scale model. This work proposes a new strategy regarding the simulation of fine grid models using a single well modeling concept. The proposed method is currently suited for primary depletion process. The approach is relatively straight forward. We first identify the drainage Volume associated with each well using Fast Marching method. Fast Marching Method is extremely fast and can determine the drainage volume in large geological model within minutes. We then assume that the drainage volume does not change significantly over the life of the well. We then model each well separately as an independent well within a drainage volume and predict the performance of the well. Because the simulation model size is significantly reduced, the well performance can be predicted very quickly and is amenable to parallel simulations. By adding individual well performances, we can then combine performance to predict the field performance. This method is also suitable for history matching since by observing the drainage volumes of individual wells, we can reasonably determine if the model is suitable for history matching before the history matching process starts. We have tested the methodology for both the synthetic and the field cases and we have observed that the method works well while significantly reducing the computational costs. [ABSTRACT FROM AUTHOR]

• The FMM-based method is applied to the faulted rock mass to improve location accuracy of MS events. • The FMM-based method performs better than the UVM-based method in several 3D velocity models. • The wave paths from the method agree well with the analytical solution obtained by the Snell law. • The MS source mechanisms of location results are analyzed through moment tensor inversion. Understanding the temporospatial distribution of microseismic events is critical for the early warning of induced geohazards during deep rock excavation. However, the accuracy of microseismic source location can be influenced by many geological and engineering factors, such as rock discontinuities and excavated openings. This study addresses the application of fast marching method (FMM) to improve the location accuracy in faulted rock masses and takes a case of powerhouse excavation in the Shuangjiangkou hydropower project as an example. The FMM-based method includes five steps, such as inputs, gridding, velocity assignment, calculation, and output, and can be readily processed using a travel time database. Our results exhibit that the wave paths obtained from the FMM-based method are consistent with those from the analytical solution based on the Snell law and better than those from the commonly used uniform velocity model. The results also signify that the FMM-based method can improve the location accuracy for P-wave propagating across a low-velocity layer and an excavated opening. Moreover, this method can be further improved, such as reasonable determination of grid spacing and thorough detection of major discontinuities. [ABSTRACT FROM AUTHOR]

We derive and apply a methodology for the initialization of velocity and transport fields in complex multiply-connected regions with multiscale dynamics. The result is initial fields that are consistent with observations, complex geometry and dynamics, and that can simulate the evolution of ocean processes without large spurious initial transients. A class of constrained weighted least squares optimizations is defined to best fit first-guess velocities while satisfying the complex bathymetry, coastline and divergence strong constraints. A weak constraint towards the minimum inter-island transports that are in accord with the first-guess velocities provides important velocity corrections in complex archipelagos. In the optimization weights, the minimum distance and vertical area between pairs of coasts are computed using a Fast Marching Method. Additional information on velocity and transports are included as strong or weak constraints. We apply our methodology around the Hawaiian islands of Kauai/Niihau, in the Taiwan/Kuroshio region and in the Philippines Archipelago. Comparisons with other common initialization strategies, among hindcasts from these initial conditions (ICs), and with independent in situ observations show that our optimization corrects transports, satisfies boundary conditions and redirects currents. Differences between the hindcasts from these different ICs are found to grow for at least 2–3 weeks. When compared to independent in situ observations, simulations from our optimized ICs are shown to have the smallest errors. [ABSTRACT FROM AUTHOR]

Unmanned surface vehicles (USVs) have been deployed over the past decade. Current USV platforms are generally of small size with low payload capacity and short endurance times. To improve effectiveness there is a trend to deploy multiple USVs as a formation fleet. This paper presents a novel computer based algorithm that solves the problem of USV formation path planning. The algorithm is based upon the fast marching (FM) method and has been specifically designed for operation in dynamic environments using the novel constrained FM method. The constrained FM method is able to model the dynamic behaviour of moving ships with efficient computation time. The algorithm has been evaluated using a range of tests applied to a simulated area and has been proved to work effectively in a complex navigation environment. [ABSTRACT FROM AUTHOR]

Gas flow in shale gas reservoirs occurs primarily from ultra low permeability shale rocks through a complex network of natural and induced hydraulic fractures. Consequently, fracture parameters (conductivity and half length), fracture location and distribution are the dominant factors influencing well drainage volumes and shale gas well performance. Stimulated reservoir volume or SRV, estimated from microseismic event clouds or rate/pressure transient analysis, describes a measurement of overall reservoir volume impacted by fracture treatments. With SRV as well as the dynamic production/pressure response, reservoir simulation models can be calibrated to actual well performance in shale gas reservoirs leading to improved understanding, forecasting and future well placement. In this paper, we first introduce a novel approach for computing well drainage volume for shale gas wells with multistage fractures and fracture clusters. Next, we calibrate the shale gas reservoir model by matching the drainage volume with the SRV within specified confidence limits. The matching of the SRV is done in addition to the traditional history matching of production/pressure response and further constrains the estimation of fracture parameters. An evolutionary algorithm with design of experiments is used for the assisted history matching. Sensitivities to various parameters such as fracture conductivity, fracture half lengths and rock compaction have also been investigated. The proposed approach has been applied to a generic shale gas well designed after a real field case. The results clearly indicate the benefits of including SRV during history matching, leading to improved fracture/matrix parameter estimation and performance forecasting. Our proposed approach provides an important tool that can be used to optimize well placement, fracture treatments and improve the economics of shale gas plays. [ABSTRACT FROM AUTHOR]

There have been several attempts to reduce the computational costs associated with well placement optimization under geological uncertainty by selecting a representative subset of realizations or by reducing the number of function evaluations to speed up the optimization. Although previous researchers have studied this issue, they have used static or dynamic properties of the reservoir to select a reduced subset of realizations or shrank the search space of the optimizer to reduce the computational burden of the task. Using static parameters is fast but lacks the accuracy of the dynamic approach. On the other hand, dynamic parameters require a computationally expensive full flow simulation. In this paper, a workflow based on the Reservoir Opportunity Index (ROI) maps was proposed to address the two issues mentioned above. The ROI maps were constructed using both the static and dynamic reservoir properties. The dynamic feature was obtained by the computationally efficient Fast Marching Method instead of full reservoir simulation. In this workflow, ROI density (DROI) maps were constructed by averaging the ROI values of adjacent cells to incorporate the effect of neighboring cells in finding potential regions to constrain the search space of the optimizer. In addition, these DROI maps were used to select a representative subset of realizations. Furthermore, the effect of re-selection of the representative realizations was investigated in this study. The proposed workflow was applied to optimize the location of production wells under geological uncertainty and was compared with the Full Case (using all realizations in optimization) in terms of three criteria, namely the expected value, the standard deviation, and the cumulative distribution function (CDF) of the objective function. Results of optimization showed that the constrained search with a fixed number of realizations and the statistical clustering technique outperformed other approaches with minimum differences of 1.5% and 8.9% from the objective function and its standard deviation of the values obtained from the Full Case, respectively. Also, it had 28.64% less difference between its CDF and the Full Case in comparison to the second-best technique. In addition, it was shown that the constrained search required fewer function evaluations to achieve similar results as the global search with approximately three times fewer function evaluations. The results of this paper can be used as a guidance for reservoir engineers to select a proper approach for optimization (constrained or unconstrained), clustering the geological realizations (statistical or K-means), and proper implementation of ROI maps for shrinking the search space of the optimizer and selecting a representative subset of realizations. • ROI maps were used to speed up the convergence of robust well location optimization. • The optimizer was limited to sweet spots determined by statistical ROI density maps. • Static and dynamic properties were used to calculate the ROI maps. • ROI density maps were used to select the representative subset of realizations. • The proposed workflow could facilitate the optimization and reach better results. [ABSTRACT FROM AUTHOR]

Path following is one of the indispensable tools for autonomous ships, which ensures that autonomous ships are sufficiently capable of navigating in specified collision-free waters. This study proposes a novel path following approach for autonomous ships based on the fast marching (FM) method and deep reinforcement learning (DRL). The proposed approach is capable of controlling a ship to follow different paths and ensuring that the path tracking errors are always within a set range. With the help of the FM method, a grid-based path deviation map is specially produced to indicate the minimum distance between grid points and the path. Besides, a path deviation perceptron is specifically designed to simulate a range sensor for sensing the set path deviation boundaries based on the path deviation map. Afterwards, an agent is trained to control a ship following a circular path based on the DRL. Particularly, the approach is validated and evaluated through simulations. The obtained results show that the proposed method is always capable of maintaining high overall efficiency with the same strategy to follow different paths. Moreover, the ability of this approach exhibits a significant contribution to the development of autonomous ships. • A path deviation map is proposed based on the fast marching method. • A path deviation perceptron is designed for path following. • The deep reinforcement learning is introduced into path following. • A novel path following approach is put forward for autonomous ships. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) simulations are useful to optimize the lithography process of thick photoresists, however, less efficient models and etching surface advancement algorithms limits current application of various simulation tools. This paper presents a comprehensive aerial image model based on Fresnel diffraction to simulate the 3D inclined/vertical UV light intensity distribution into the SU-8 with the diffraction, refraction, absorbance and reflection during light transmission efficiently considered simultaneously. The aerial image model are solved by using adaptable element size in x , y and z direction to speed up the calculation. The improved two-dimensional (2D) Dill exposure model, the post exposure bake (PEB) model and the Enhanced Notch model are also extended to three dimensions. Furthermore, a 3D hash fast marching method is developed to calculate the final development profiles with less required memory elements. Thus various large scale 3D simulations of thick SU-8 lithography process can be well implemented, and the simulated development profiles have been verified by experimental results. [ABSTRACT FROM AUTHOR]

Abstract: The fast marching method is widely used to solve the eikonal equation. By introducing a new way of managing propagation interfaces which avoid the use of expensive data structures, the fast iterative method reveals to be a faster variant with a higher parallel potential compared to the fast marching method. We investigate in this paper a multi-level parallel approach for the fast iterative method which is well fitted for today heterogenous and hierarchical architectures. We show experiment results which focus on the fine-grained parallel level of the algorithm and we give a performance analysis. [Copyright &y& Elsevier]

Highlights: [•] Dynamic upscaling is one of the key factors in reservoir simulation. [•] We proposed new dynamic method for permeability upscaling using Fast Marching Method. [•] Pressure propagation time is calculated using Fast Marching Method in a matter of seconds for multimillion cells. [•] New method is able to capture connectivity of reservoir very efficiently. [Copyright &y& Elsevier]

In this study, we propose a multi-stencils fast marching method to solve the factored eikonal equations for media with quadratic anisotropy, also known as Riemannian anisotropy. Compared with the conventional fast marching method, the new method has an improved accuracy in tracing moving wavefronts via computing the solution at each grid point along several stencils. To deal with the source singularity, we solve for the viscosity solution iteratively by factorize the unknown traveltime function into a function that captures the singularity and a multiplicative factor which is differentiable at the source location. By leveraging the strengths of multi-stencils and factorisation, the newly developed algorithm is highly accurate in solving anisotropic eikonal equations. Through a series of numerical examples, we explicitly show that the algorithm (1) has an obvious first (second) order convergence rate with the first (second) order finite-difference scheme, and (2) is unconditionally stable as long as the initial time table around the source is specified. Finally, we design an eikonal-based anisotropic ray tracing technique. We test the anisotropic ray tracing technique on both radial and azimuthal anisotropy cases and the numerical results demonstrate that the usage of multi-stencils scheme increase the accuracy of the anisotropic ray paths especially for azimuthal anisotropy case. This high-accurate eikonal solver and the associated ray tracing technique can be used in high-resolution seismic anisotropic tomography and other researches in the future. [ABSTRACT FROM AUTHOR]

Highlights: [•] We detail and unify a two-stage freehand 3D ultrasound reconstruction framework. [•] A fast marching method (FMM) based reconstruction algorithm is proposed to interpolate the missing voxels. [•] A direction-weighted function is designed to ensure that the structural details around the empty voxel could be well propagated from its surrounding local neighborhood. [•] The FMM reconstruction algorithm could preserve relatively sharper edges and more texture patterns in the reconstructed image slices. [•] The FMM reconstruction algorithm runs efficiently and requires less computation time. [ABSTRACT FROM AUTHOR]

Abstract: Range imaging sensors such as Kinect and time-of-flight cameras can produce aligned depth and color images in real time. However, the depth maps captured by such sensors contain numerous invalid regions and suffer from heavy noise. These defects more or less influence the use of depth information in practical applications. In order to enhance the depth maps, this paper proposes a new inpainting approach based on the fast marching method (FMM). We extend the inpainting model and the propagation strategy of FMM to incorporate color information for depth inpainting. An edge-preserving guided filter is further applied for noise reduction. To validate our algorithm, we perform experiments on both Kinect data and Middlebury dataset which, respectively, provide qualitative and quantitative results. Meanwhile, we also compare it to the original FMM and other two state-of-the-art depth enhancement methods. Experimental results show that our method performs better than the local methods in terms of both visual and metric qualities, and it achieves visually comparable results to the time-consuming global method. [Copyright &y& Elsevier]

Abstract: An endoscope is a medical instrument that acquires images inside the human body. This paper proposes a new approach to recover 3-D shape under conditions of both point light source illumination and perspective projection. Previous approaches recovered shape based on a Fast Marching Method under conditions of parallel light source and orthographic projection. The new approach uses optimization based on constraints provided by geometry and by a suitable image irradiance equation. Experiments with endoscope images are demonstrated to confirm that the recovered shape is improved. [Copyright &y& Elsevier]

Abstract: In order to reconstruct a surface which has specular reflection from the grayscale information contained in a single two-dimensional (2D) image, a specular shape from shading (SFS) using the fast marching method is presented. Under assumptions that the camera performs an orthographic projection whose direction is equal to the direction of the light source and that the Phong model is used to depict the reflectance property of the surface, the image irradiance equation for specular surface is derived and it is a first-order nonlinear partial differential equation (PDE). By transforming it into a standard Eiknoal PDE, the fast marching method is applied to compute a solution of the resultant Eiknoal equation. Experiments are tested on both a synthetic vase image and a sphere image and the results demonstrate the effectiveness of the presented specular SFS method. [Copyright &y& Elsevier]

Abstract: We propose a new mathematical formulation for perspective shape from shading (PSFS) problems. Our approach is based on representing the unknown surface as a spherical surface, expressed by Euclidean distance to the optical centre, as opposed to the traditional representation by distance from the image plane. We show that our parameterization is better suited for perspective camera models and results in simpler models and equations for classical PSFS problems with a light source in the optical centre. The unknown distance field satisfies a simple isotropic Eikonal equation on the unit sphere in the case of a Lambertian surface reflection model. This is in contrast to previous methods with depth field parameterization, which result in anisotropic equations. Adding light attenuation to the model, we show that the distance field satisfies an Eikonal type of equation with a zero order term. We show how both Eikonal equations can be approximated by very efficient Fast Marching methods. A number of numerical tests and examples are provided to demonstrate our approach, and to compare with previous work. Our results indicate competitive accuracy and computational time that are several orders of magnitude faster than state-of-the-art iterative algorithms. A preliminary investigation indicates that our method could be used in more general PSFS problems. [Copyright &y& Elsevier]

Abstract: A fundamental requirement in realistic ocean simulations and dynamical studies is the optimal estimation of gridded fields from the spatially irregular and multivariate data sets that are collected by varied platforms. In this work, we derive and utilize new schemes for the mapping and dynamical inference of ocean fields in complex multiply-connected domains and study the computational properties of these schemes. Specifically, we extend a Bayesian-based multiscale Objective Analysis (OA) approach to complex coastal regions and archipelagos. Such OAs commonly require an estimate of the distances between data and model points, without going across complex landforms. New OA schemes that estimate the length of shortest sea paths using the Level Set Method (LSM) and Fast Marching Method (FMM) are thus derived, implemented and utilized in idealized and realistic ocean cases. An FMM-based methodology for the estimation of total velocity under geostrophic balance in complex domains is also presented. Comparisons with other OA approaches are provided, including those using stochastically forced partial differential equations (SPDEs). We find that the FMM-based OA scheme is the most efficient and accurate. The FMM-based field maps do not require postprocessing (smoothing). Mathematical and computational properties of our new OA schemes are studied in detail, using fundamental theorems and illustrations. We find that higher-order FMM’s schemes improve accuracy and that a multi-order scheme is efficient. We also provide solutions that ensure the use of positive-definite covariances, even in complex multiply-connected domains. [Copyright &y& Elsevier]

Abstract: Probing the lateral heterogeneity of the upper mantle seismic velocity structure beneath southern and central Taiwan is critical to understanding the local tectonics and orogeny. A linear broadband array that transects southern Taiwan, together with carefully selected teleseismic sources with the right azimuth provides useful constraints. They are capable of differentiating the lateral heterogeneity along the profile with systematic coverage of ray paths. We implement a scheme based on the genetic algorithm to simultaneously determine the relative delayed times of the teleseismic first arrivals of array data. The resulting patterns of the delayed times systematically vary as a function of the incident angle. Ray tracing attributes the observed variations to a high velocity anomaly dipping east in the mantle beneath the southeast of Taiwan. Combining the ray tracing analysis and a pseudo-spectral method to solve the 2-D wave propagations, we determine the extent of the anomaly that best fits the observations via the forward grid search. The east-dipping fast anomaly in the upper mantle beneath the southeast of Taiwan agrees with the results from several previous studies and indicates that the nature of the local ongoing arc–continent collision is likely characterized by the thin-skinned style. [ABSTRACT FROM AUTHOR]

Abstract: In oblique shape from shading (SfS), the illumination direction is essential for recovering the 3D surface of a shaded image. On the other hand, fast marching methods (FMM) are SfS algorithms that use the mechanism of wave propagation to reconstruct the surface. In this paper, the estimation of illumination direction is addressed and we model it as an optimization problem. The idea is to minimize the inconsistency of wave propagation of FMM during the reconstruction. As the consistency of wave propagation is a multi-modal function of illumination direction, genetic algorithm (GA) is utilized. The proposed algorithm is examined on four synthetic models and a real world object. The experimental results show that the proposed algorithm is superior to benchmark methods. [Copyright &y& Elsevier]

Abstract: A method for removing arteries that appear bright with intensities similar to white matter in Magnetized Prepared Rapid Gradient Echo images of the ventral medial prefrontal cortex is described. The Fast Marching method is used to generate a curve within the artery. Then, the largest connected component is selected to segment the artery which is used to mask the image. The surface reconstructed from the masked image yielded cortical thickness maps similar to those generated by manually pruning the arteries from surfaces reconstructed from the original image. The method may be useful in masking vasculature in other cortical regions. [Copyright &y& Elsevier]

In this paper, we present an efficient visibility-based algorithm for determining a locally exact shortest path (LESP) from a source point to a destination point on a (triangulated) polyhedral surface. Our algorithm, of a finitely-iterative scheme, evolves an initial approximately shortest path into a LESP. During each iteration, we first compute the exact shortest path restricted on the current face sequence according to Fermat’s principle which affirms that light always follows the shortest optical path, and then optimize the face sequence where the path is not locally shortest on the polyhedral surface. Since the series of paths we obtained are monotonic decreasing in length, the algorithm gives a LESP which is shorter than the initial path, at conclusion. For comparison, we use various methods to provide an initial path. One of the methods is Dijkstra’s algorithm, and the others are the Fast Marching Method (FMM) and its improved version. Our intention for improvement is to overcome the limitation of acute triangulations in the original version. To achieve this goal, we classify all the edges into seven types according to different wavefront propagation manners, and dynamically determine the type of each edge for controlling the subsequent wavefront expansion. Furthermore, we give two approaches for backtracing the approximately shortest paths directed at the improved FMM. One exploits the known propagation manners of the edges as well as the Euler’s method. This is another contribution in this paper. [Copyright &y& Elsevier]

Abstract: A fast marching method (FMM) using the line-of-site calculation to solve the eikonal equation is applied to an adaptive mesh. The criteria for refinement are the curvature of the propagating front. It is shown empirically that for cases involving an initial front initiated from a single point in an open three dimensional domain and constant front propagating speed that the FMM with adaptive mesh refinement (AMR) uses roughly an order of magnitude less CPU time and an order of magnitude less CPU memory than the non-AMR FMM to attain a similar level of accuracy. It is also shown that the AMR-FMM refines when the curvature is caused by boundary irregularities and also non-constant front propagating speed. [Copyright &y& Elsevier]

Image registration is an important procedure for medical diagnosis. Since the large inter-site retrospective validation study led by Fitzpatrick at Vanderbilt University, voxel-based methods and more specifically mutual information-based registration methods (see for instance [IEEE Trans. Med. Imag. 22 (8) (2003) 986] for a review on these methods) have been regarded as the method of choice for rigid-body intra-subject registration problems. In this study we propose a method that is based on the Iterative Closest Point algorithm and a pre-computed closest point map obtained with a slight modification of the fast marching method proposed by Sethian. Pre-computing the closest point map speeds up the process because at each iteration point correspondence can be established by table lookup. We also show that because the closest point map is defined on a regular grid it introduces a registration error and we propose an interpolation scheme that addresses this issue. The method has been tested both on synthetic and real images, and registration results have been assessed quantitatively using the data set provided by the Retrospective Registration Evaluation Project. For these volumes, MR and CT head surfaces were extracted automatically using a level-set technique. Results show that on these data sets this registration method leads to accuracy numbers that are comparable to those obtained with voxel-based methods. [Copyright &y& Elsevier]

A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modeled by finite elements with no explicit meshing of the crack surfaces. The initial crack geometry is represented by level set functions, and subsequently signed distance functions are used to compute the enrichment functions that appear in the displacement-based finite element approximation. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. Stress intensity factors for planar three-dimensional cracks are computed, and fatigue crack growth simulations for planar cracks are presented. Good agreement between the numerical results and theory is realized. [Copyright &y& Elsevier]

• A methodology combining the Langevin equation, the lattice-gas cellular automata and the fast marching method is proposed. • Stochastic rule of evolution based on geological parameters is formulated • The workflow is applied to the study of an outcrop from Jandaíra Formation, Potiguar Basin, Brazil. • 3D karstic networks are generated considering epigenic, hypogenic, and hybrid karstification processes. In this work, the formation of karstic networks is modeled through the phenomenological stochastic differential Langevin equation. The solution of this equation follows through the application of the lattice-gas cellular automata formalism in terms of spatial and temporal discretization. The flow velocity vector is computed using a stochastic dimensionless equation where permeability, porosity, facies, and fracture persistence are the input parameters. Fluid flow is assumed to follow minimum effort paths in a heterogeneous medium from sinkholes or dolines towards springs. The shortest path search is performed using a fast marching algorithm in which fracture persistence is used as a proxy for a velocity field. Additionally, the Langevin equation's memory effect allows the coupling of the widening of the conduits with the amount of flowing water, taking into account dissolution phenomena. As conduits widen, more particles tend to run through them. This work presents a workflow for the modeling of karst generation in carbonate reservoirs. The workflow is applied to the study of an outcrop from Jandaíra Formation, Potiguar Basin, Brazil. High-resolution aerial images of the area, scanlines, and karst facies stacking pattern of an outcrop near this area are the primary data to define the three-dimensional model. Three feasible scenarios of karstification were generated: epigenic, hypogenic, and hybrid karst. As a result, 3D karstic networks form, considering the regional geology, flow conditions, and local heterogeneities. [ABSTRACT FROM AUTHOR]

Well placement is one of the challenging steps in field development optimization. Finding optimal locations with fewer function evaluations and less time is crucial when dealing with giant models. In this study, we propose a method based on the combination of Fast Marching Method and Particle Swarm Optimization to decrease the number of function evaluations in optimizing the location of vertical injection wells. The idea is to restrict the optimization algorithm's search space to a region around the drainage boundary of producers. Thereby, the optimization algorithm can find good locations with fewer function evaluations compared to direct optimization. Drainage boundaries are predicted based on the diffusive time of flight (arrival time) calculated by the Fast Marching Method. First, the performance of the proposed method in predicting the drainage boundaries is evaluated by verifying the drainage boundary of four producers on two synthetic models using the fast marching method and streamline simulator which showed a good match. Next, the approach is applied to two- and three-dimensional example cases, including four synthetic models and a real field case to test the robustness and efficiency of the proposed method. Results are compared with the direct optimization approach and showed that the proposed approach can provide higher Net Present Values with fewer function evaluations most of the time. Finally, a comparison between the computational efficiency of the fast marching method and streamline simulator showed that the time needed by the fast marching method to predict the drainage boundary of the wells was orders of magnitude lower than the streamline simulator. • PSO-FMM is used to facilitate the process of finding good positions for injection wells. • PSO-FMM could find appropriate locations for the injectors with fewer function evaluations compared to direct optimization. • FMM could predict the drainage boundary of producers with satisfactory accuracy compared to streamline simulation. • Computational time required by FMM to estimate the drainage boundary was much lower than streamline simulation. [ABSTRACT FROM AUTHOR]

The fast marching method is commonly used in expanding front simulations in various fields, such as, fluid dynamics, computer graphics, and in microelectronics, to restore the signed-distance field property of the level-set function, also known as re-distancing. To improve the performance of the re-distancing step, parallel algorithms for the fast marching method as well as support for hierarchical meshes have been developed; the latter to locally support higher resolutions of the simulation domain whilst limiting the impact on the overall computational demand. In this work, the previously developed multi-mesh fast marching method is extended by a so-called block-based decomposition step to improve serial and parallel performance on hierarchical meshes. OpenMP tasks are used for the underlying coarse-grained parallelization on a per mesh basis. The developed approach offers improved load balancing as the algorithm employs a high mesh partitioning degree, enabling to balance mesh partitions with varying mesh sizes. Various benchmarks and parameter studies are performed on representative geometries with varying complexities. The serial performance is increased by up to 21% whereas parallel speedups ranging from 7.4 to 19.1 for various test cases on a 24-core Intel Skylake computing platform have been achieved, effectively doubling the parallel efficiency of the previous approach. [ABSTRACT FROM AUTHOR]

To achieve efficient recovery of subsurface energy resources, a suitable trajectory needs to be identified for the production well. In this study, a new approach is presented for automated identification of optimum well trajectories in heterogeneous oil/gas reservoirs. The optimisation procedures are as follows. First, a productivity potential map is generated based on the site characterisation data of a reservoir (when available). Second, based on the fast-marching method, well paths are generated from a number of entrance positions to a number of exit points at opposite sides of the reservoir. The well trajectory is also locally constrained by a prescribed maximum curvature to ensure that the well trajectory is drillable. Finally, the optimum well trajectory is selected from all the candidate paths based on the calculation of a benefit-to-cost ratio. If required, a straight directional well path, may also be derived through a linear approximation to the optimised non-linear trajectory by least squares analysis. Model performance has been demonstrated in both 2D and 3D. In the 2D example, the benefit-to-cost ratio of the optimised well is much higher than that of a straight well; in the 3D example, laterals of various curvatures are generated. The applicability of the method is tested by exploring different reservoir heterogeneities and curvature constraints. This approach can be applied to determine the entrance/exit positions and the well path for subsurface energy system development, which is useful for field applications. • A novel well optimisation approach is developed based on the fast marching method. • The optimum well path maximises the productivity whilst reducing the drilling length. • A curvature constraint ensures the drillability of the well trajectory in the field. • The method is applied to optimise well trajectory in heterogeneous reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, collision avoidance (CA) scheme for unmanned surface vehicles (USVs) under complex shallow sea environments which contain static sea surface (Static), undersea obstacles (UO) and surface island with reefs (IR) is proposed. The main challenge of this paper is that CA objects not only include surface obstacles, UO and IR, but more importantly, they will be affected by dynamic water level. It is difficult, if not impossible, to employ conventional CA schemes for USVs. The salient features of the proposed scheme are: 1) A UO model which incorporates time-varying water level is developed. 2) The smoothing edge (SE) method of island of IR that is based on fuzzy Gauss mixture model is enhanced by introducing fuzzy membership to Gaussian mixture model. 3) A real-time collision probability (RTCP) algorithm under IR with time-varying water level which obeys the Poisson and Gauss distribution is developed. By combining the UO-FMM and the SE-RTCP, the proposed CA scheme is able to handle uncertainties in complex shallow sea environments. Comparative studies with the state of the art demonstrate that the proposed CA scheme is superior in terms of safety and yaw cost consumption. • An underwater obstacle (UO) model which incorporates time-varying water level is developed. • The smoothing edge (SE) method is enhanced by introducing fuzzy membership to Gaussian mixture model. • A real-time collision probability (RTCP) algorithm which obeys the Poisson and Gaussian distribution is developed. [ABSTRACT FROM AUTHOR]

• We analyze the minimum cost problem of path planning. • We design an oval shape speed profile for anisotropic fast marching method. • We propose a novel potential field model for both static and dynamic obstacles. • We propose a novel path planning approach for smart cargo ships. Path planning is an essential tool for smart cargo ships that navigate in coastal waters, inland waters or other crowded waters. These ships require expert and intelligent systems to plan safe paths in order to avoid collision with both static and dynamic obstacles. This research proposes a novel path planning approach based on the anisotropic fast marching (FM) method to specifically assist with safe operations in complex marine navigation environments. A repulsive force field is specially produced to describe the safe area distribution surrounding obstacles based on the knowledge of human. In addition, a joint potential field is created to evaluate the travel cost and a gradient descent method is used to search for appropriate paths from the start point to the end point. Meanwhile, the approach can be used to constantly optimize the paths with the help of the expert knowledge in collision avoidance. Particularly, the approach is validated and evaluated through simulations. The obtained results show that it is capable of providing a reasonable and smooth path in a crowded waters. Moreover, the ability of this approach exhibits a significant contribution to the development of expert and intelligent systems in autonomous collision avoidance. [ABSTRACT FROM AUTHOR]

In this research, a hybrid approach for global path planning for Maritime Autonomous Surface Ship (MASS) is proposed, which generates the shortest path considering the collision risk and the proximity between path and obstacles. The collision risk concerning obstacles is obtained using Time-Varying Collision Risk (TCR) concept, taking into account the velocity constraint of the ship that can achieve during operation. The influence of proximity from obstacles is measured with the Fast Marching (FM) algorithm. A new cost function is proposed allowing to combine the influence of obstacle proximity and collision risk in the region. Finally, the Fast Marching Square algorithm is applied to generate the globally optimal path that can reach the pre-set destination. The contribution of this work is two-fold: 1) considering the velocity constraint of the own ship, together with its influences of collision risk into the global path planning stage of autonomous navigation. 2) measuring the collision risk induced by the obstacles from their comprehensive influences on the achievable velocity range using TCR concept, instead of numerical integration of risk measurement. The results of the case study indicate that the proposed approach can find an optimal path considering the collision risk and proximity from the obstacles. • New approach for global path planning of autonomous ship considering both collision risk and path length. • Collision risk is measured with TCR using velocity obstacle algorithm. • Fast marching algorithm is applied to integrate the influence of collision risk and generate the optimal path. [ABSTRACT FROM AUTHOR]