A FRAMEWORK TO MANAGE UNCERTAINTY IN THE COMPUTATION OF WASTE COLLECTION ROUTES AFTER A FLOOD

In this paper, we describe a framework to find a good quality waste collection tour after a flood, without having to solve a complicated optimization problem from scratch in limited time. We model the computation of a waste collection tour as a capacitated routing problem, on the vertices or on the edges of a graph, with uncertain waste quantities and uncertain road availability. Multiple models have been conceived to manage uncertainty in routing problems, and we build on the ideas of discretizing the uncertain parameters and computing master solutions that can be adapted to propose an original method to compute efficient solutions. We first introduce our model for the progressive removal of the uncertainty, then outline our method to compute solutions: our method first considers a low-dimensional set of random variables that govern the behaviour of the problem parameters, discretizes these variables and computes a solution for each discrete point before the flood, and then uses these solutions as a basis to build operational solutions when there are enough information about the parameters of the routing problem. We then give computational tools to implement this method. We give a framework to compute the basis of solutions in an efficient way, by computing all the solutions simultaneously and sharing information (that can lead to good quality solutions) between the different problems based on how close their parameters are, and we also describe how real solutions can be derived from this basis. Our main contributions are our model for the progressive removal of uncertainty, our multi-step method to compute efficient solutions, and our intrusive framework to compute solutions on the discrete grid of parameters.

Tracking Fluorescent Dye Dispersion from an Unmanned Aerial Vehicle

Commercial unmanned aerial vehicles continue to gain popularity and their use for collecting image data and recording new phenomena is becoming more frequent. This study presents an effective method for measuring the concentration of fluorescent dyes (fluorescein and Rhodamine WT) for the purpose of providing a mathematical dispersion model. Image data obtained using a typical visible-light camera was used to measure the concentration of the dye floating on water. The reference measurement was taken using a laboratory fluorometer. The article presents the details of three extensive measurement sessions and presents elements of a newly developed method for measuring fluorescent tracer concentrations. The said method provides tracer concentration maps presented on the example of an orthophoto within a 2 × 2 m discrete grid.

Adaptation of energy methods to automated calculation of mobile machines frame constructions

The paper shows that the adaptation of energy methods to automated calculation of mobile machines frame constructions consists of developing a single algorithm applicable to different construction schemes. The calculation outset still remains the idea of getting a function of potential energy of deformation as a function with unknown inner power factors. Search for local function minimum of potential power of deformation has been based on the function’s discrete grid-surface. We managed to reach tactical flexibility of coordinate descent method in an attempt to continue approaching local minimum in cases of a dead end situation by changing the discrete course. The paper suggests extending the implemented algorithm from 3-D surface dealing only with two power factors, to n-D one with many unknown values.

A Precision Evaluation Index System for Remote Sensing Data Sampling Based on Hexagonal Discrete Grids

With the rapid development of earth observation, satellite navigation, mobile communication, and other technologies, the order of magnitude of the spatial data we acquire and accumulate is increasing, and higher requirements are put forward for the application and storage of spatial data. As a new form of data management, the global discrete grid can be used for the efficient storage and application of large-scale global spatial data, which is a digital multiresolution georeference model that helps to establish a new model of data association and fusion. It is expected to make up for the shortcomings in the organization, processing, and application of current spatial data. There are different types of grid systems according to the grid division form, including global discrete grids with equal latitude and longitude, global discrete grids with variable latitude and longitude, and global discrete grids based on regular polyhedrons. However, there is no accuracy evaluation index system for remote sensing images expressed on the global discrete grid to solve this problem. This paper is dedicated to finding a suitable way to express remote sensing data on discrete grids, as well as establishing a suitable accuracy evaluation system for modeling remote sensing data based on hexagonal grids to evaluate modeling accuracy. The results show that this accuracy evaluation method can evaluate and analyze remote sensing data based on hexagonal grids from multiple levels, and the comprehensive similarity coefficient of the images before and after conversion is greater than 98%, which further proves the availability of the hexagonal-grid-based remote sensing data of remote sensing images. This evaluation method is generally applicable to all raster remote sensing images based on hexagonal grids, and it can be used to evaluate the availability of hexagonal grid images.

VARYING THE SHAPE OF A SURFACE WHICH IS DISCRETE PRESENTED BY AN IRREGULAR BALANCED GRID

The article discusses a problem, the solution of which is related to the research previously described in previous publications. This paper demonstrates the solution of the problem of forming a discrete frame, in the form of a balanced irregular grid, discretely represented surface. The described problem is solved by one of the methods of discrete modeling, using the static-geometric method of Professor Kovalev S.N. (SGM). The initial conditions for the formation of such irregular balanced discrete networks are the coordinates of the nodes of the reference loop, the topological organization of the grid and the z-coordinate of one of the internal nodes. Note that irregular grids are characterized by different node and cell topologies. This fact can greatly complicate the modeling process, namely, performing the necessary calculations when calculating the coordinates of discrete grid nodes. To facilitate calculations and simplify numbering of discrete grid nodes, it is proposed to use a topological grid scheme based on a regular grid. For regular grids, each node has a specific number, which greatly facilitates the calculation of node coordinates. The operative change in the shape of the grid can be carried out by connecting the classical coordinate calculations of the discrete SGM grid, that is, by solving the system of equilibrium equations of nodes, with an affine transformation, namely the introduction of the scaling factors of coordinates. The disadvantage of this synthesis of the two methods will be the change in the preassigned reference of contour of the mesh, due to the fact that all coordinates of absolutely all grid nodes are multiplied by the corresponding transformation coefficients. To avoid changing the shape of a given reference contour, it is proposed to use a synthesis of three methods in the work, namely SGM, affine coordinate transformation and a method of functional addition of coordinates. This synthesis of methods will maintain the balance of the discrete grid during the modeling process, and will allow you to simply vary (change) the shape of the simulated surface.

A COVID-19 Spread Model of the Discrete Grid to Assess the Potential of Non-pharmaceutical Interventions

Background: The outbreak of COVID-19 posed a serious threat to human health, economic development, and social stability worldwide, and many countries had taken different interventions to control the deterioration of the epidemic. Although many studies have evaluated the effectiveness of these interventions, there were few reasonable explanations for the practical geographic significance of the model parameters. Our aim was to evaluate the potential of different interventions to mitigate the spread of the epidemic, including discussion about the different time and intensity of implementation, and map parameters of model to the practical application meanings of the special interventions.Methods: In this study, a COVID-19 spread model based on the discrete grid was proposed from perspective of geography. A multi-level grid was introduced to describe the quarantine status and intensity in different spaces, which also combined with the model of medical reception-cured and self-protection, and the spatiotemporal evolution process of early COVID-19 spread was simulated based on the spatial correlation, finally, the effect of interventions was quantitatively analyzed by the dynamic transmission model of COVID-19.Results: Quarantine measure were the most effective interventions, which could effectively reduce the peak value of infection, advance the arrival time of the peak, and shorten the duration of the epidemic, but it only played a role under sufficient intensity; the medical reception-cured and self-protection measure could effectively fatten the infection curve and slowed the spread of the epidemic in the early stage, which could provide more buffer time for the relevant government departments, but the practical effect was not obvious because of the limitation of actually invested resources. The role of the medical reception-cured measure was more reflected in the reduction of the number of deaths, and the effect of the self-protection measure could be reduced in strict quarantine measure.Conclusions: Results of the study indicated that the quarantine, medical reception-cured and self-protection measures were effective, and mitigating the spread of COVID-19 by achieving strong interventions was necessary. Strict quarantine should be implementing as soon as possible in countries with serious development of COVID-19.

A Precision Evaluation Method for Remote Sensing Data Sampling Based on Hexagon Discrete Grid

With the rapid development of earth observation, satellite navigation, mobile communication and other technologies, the order of magnitude of the spatial data we acquire and accumulate is increasing, and higher requirements are put forward for the application and storage of spatial data. Under this circumstance, a new form of spatial data organization emerged-the global discrete grid. This form of data management can be used for the efficient storage and application of large-scale global spatial data, which is a digital multi-resolution the geo-reference model that helps to establish a new model of data association and fusion. It is expected to make up for the shortcomings in the organization, processing and application of current spatial data. There are different types of grid system according to the grid division form, including global discrete grids with equal latitude and longitude, global discrete grids with variable latitude and longitude, and global discrete grids based on regular polyhedrons. However, there is no accuracy evaluation index system for remote sensing images expressed on the global discrete grid to solve this problem. This paper is dedicated to finding a suitable way to express remote sensing data on discrete grids, and establishing a suitable accuracy evaluation system for modeling remote sensing data based on hexagonal grids to evaluate modeling accuracy. The results show that this accuracy evaluation method can evaluate and analyze remote sensing data based on hexagonal grids from multiple levels, and the comprehensive similarity coefficient of the images before and after conversion is greater than 98%, which further proves that the availability hexagonal grid-based remote sensing data of remote sensing images. And among the three sampling methods, the image obtained by the nearest interpolation sampling method has the highest correlation with the original image.