Method of lines and runge-kutta method in solving partial differential equation for heat equation

Solving the differential equation for Newton’s cooling law mostly consists of several fragments formed during a long time to solve the equation. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This research will try to overcome such problems and compare results from two classes of numerical methods for heat equation problems. The heat or diffusion equation, an example of parabolic equations, is classified into Partial Differential Equations. Two classes of numerical methods which are Method of Lines and Runge-Kutta will be performed and discussed. The development, analysis and implementation have been made using the Matlab language, which the graphs exhibited to highlight the accuracy and efficiency of the numerical methods. From the solution of the equations, it showed that better accuracy is achieved through the new combined method by Method of Lines and Runge-Kutta method

Life jacket

Anyone who cannot swim well should wear life jacket whether they are in the water or around the water. Even those who are can swim well should wear the life jacket when they are doing activity such as swimming, fishing, boating or while doing any water-related activity. Life jacket is a kind of safety jacket that keeping the wearer float the in the water. The wearer may be in the conscious or unconscious condition but by wearing the life jacket we can minimize the risk of drowning because life jacket assist the wearer to keep floating in the water

Detecting and quantifying causal associations in large nonlinear time series datasets

Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields

Recognition of Process Disturbances for an SPC/EPC Stochastic System Using Support Vector Machine and Artificial Neural Network Approaches

Because of the excellent performance on monitoring and controlling an autocorrelated process, the integration of statistical process control (SPC) and engineering process control (EPC) has drawn considerable attention in recent years. Both theoretical and empirical findings have suggested that the integration of SPC and EPC can be an effective way to improve the quality of a process, especially when the underlying process is autocorrelated. However, because EPC compensates for the effects of underlying disturbances, the disturbance patterns are embedded and hard to be recognized. Effective recognition of disturbance patterns is a very important issue for process improvement since disturbance patterns would be associated with certain assignable causes which affect the process. In practical situations, after compensating by EPC, the underlying disturbance patterns could be of any mixture types which are totally different from the original patterns. This study proposes the integration of support vector machine (SVM) and artificial neural network (ANN) approaches to recognize the disturbance patterns of the underlying disturbances. Experimental results revealed that the proposed schemes are able to effectively recognize various disturbance patterns of an SPC/EPC system

Information and Control ICIC International c ⃝2011 ISSN

Abstract. The statistical process control (SPC) chart is effective in detecting proces

Recent Advances in Spatial Data Analysis

This article views spatial analysis as a research paradigm that provides a unique set of specialised techniques and models for a wide range of research questions in which the prime variables of interest vary significantly over space. The heart of spatial analysis is concerned with the analysis and modeling of spatial data. Spatial point patterns and area referenced data represent the most appropriate perspectives for applications in the social sciences. The researcher analysing and modeling spatial data tends to be confronted with a series of problems such as the data quality problem, the ecological fallacy problem, the modifiable areal unit problem, boundary and frame effects, and the spatial dependence problem. The problem of spatial dependence is at the core of modern spatial analysis and requires the use of specialised techniques and models in the data analysis. The discussion focuses on exploratory techniques and model-driven [confirmatory] modes of analysing spatial point patterns and area data. In closing, prospects are given towards a new style of data-driven spatial analysis characterized by computational intelligence techniques such as evolutionary computation and neural network modeling to meet the challenges of huge quantities of spatial data characteristic in remote sensing, geodemographics and marketing. (author's abstract)Series: Discussion Papers of the Institute for Economic Geography and GIScienc

ACERAC: Efficient reinforcement learning in fine time discretization

We propose a framework for reinforcement learning (RL) in fine time discretization and a learning algorithm in this framework. One of the main goals of RL is to provide a way for physical machines to learn optimal behavior instead of being programmed. However, the machines are usually controlled in fine time discretization. The most common RL methods apply independent random elements to each action, which is not suitable in that setting. It is not feasible because it causes the controlled system to jerk, and does not ensure sufficient exploration since a single action is not long enough to create a significant experience that could be translated into policy improvement. In the RL framework introduced in this paper, policies are considered that produce actions based on states and random elements autocorrelated in subsequent time instants. The RL algorithm introduced here approximately optimizes such a policy. The efficiency of this algorithm is verified against three other RL methods (PPO, SAC, ACER) in four simulated learning control problems (Ant, HalfCheetah, Hopper, and Walker2D) in diverse time discretization. The algorithm introduced here outperforms the competitors in most cases considered.Comment: Submitted to IEEE Transactions on Neural Networks and Learning Systems. arXiv admin note: text overlap with arXiv:2009.0477

A modelling-oriented scheme for control chart pattern recognition

Control charts are graphical tools that monitor and assess the performance of production processes, revealing abnormal (deterministic) disturbances when there is a fault. Simple patterns belonging to one of six types can be observed when a fault is occurring, and a Normal pattern when the process is performing under its intended conditions. Machine Learning algorithms have been implemented in this research to enable automatic identification of simple patterns. Two pattern generation schemes (PGS) for synthesising patterns are proposed in this work. These PGSs ensure generality, randomness, and comparability, as well as allowing the further categorisation of the studied patterns. One of these PGSs was developed for processes that fulfil the NIID (Normally, identically and independently distributed) condition, and the other for three first-order lagged time series models. This last PGS was used as base to generate patterns of feedback-controlled processes. Using the three aforementioned processes, control chart pattern recognition (CCPR) systems for these process types were proposed and studied. Furthermore, taking the recognition accuracy as a performance measure, the arrangement of input factors that achieved the highest accuracies for each of the CCPR systems was determined. Furthermore, a CCPR system for feedback-controlled processes was developed