There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Additive manufacturing of metallic components – Process, structure and properties

Spatial and temporal variation of hardness of a printed steel part

Structure and properties of steel welds are affected by their cooling rates in the 800 to 500°C range. The available cooling rate correlations are based mostly on heat conduction equation that ignores convective heat transfer and are inaccurate or empirical in nature and valid only for a limited range of welding conditions. Numerical heat and fluid flow models can accurately calculate cooling rates, but they are not widely available. In the present paper, the authors propose and test a generalised correlation for cooling rate developed through dimensional analysis, valid for a wide range of welding processes, operating parameters and material properties.

Cooling rate in 800 to 500°C range from dimensional analysis

Mathematical model for stainless steelmaking - 1. argon-oxygen and argon-oxygen-steam mixtures.

A desired weld feature such as geometry can be produced using multiple sets of welding variables, i.e., different combinations of arc current, voltage, welding speed, and wire feed rate. At present, there is no systematic methodology that can determine, in a realistic time frame, these multiple paths based on scientific principles. Here we show that the various combinations of welding variables necessary to achieve a target gas metal arc (GMA) fillet weld geometry can be systematically and quickly computed by a real-number-based genetic algorithm and a neural network that has been trained with the results of a heat transfer and fluid flow model. The neural network is computationally efficient and, because of its origin, its input and the output obey the equations of conservation of mass, momentum, and energy. A genetic algorithm is used to determine a population of solutions by minimizing an objective function that represents the difference between the calculated and the desired values of the penetration, throat, and leg length. The model proposed here is different from traditional reverse models, since they cannot provide a choice of solutions and usually do not confirm to any phenomenological laws. The computational methodology provided a choice among various sets of current, voltage, welding speed, and wire feed rate for achieving a given fillet weld geometry specified by a set of leg length, penetration, and throat. The computed results were adequately verified by comparing with experimental results. The results provide hope that other weld attributes can also be tailored based on scientific principles in the future.

Tailoring fillet weld geometry using a genetic algorithm and a neural network trained with convective heat flow calculations

In recent years, significant progress has been made toward understanding the development of the weld pool shape and size from the numerical calculations of heat transfer and fluid flow in the weld pool. Although such calculations have provided detailed information about the welding processes, no efforts have been made to understand the development of fusion zone microstructures from the fundamentals of transport phenomena. The aim of this work is to address this. Heat transfer and fluid flow during manual metal arc welding of low-alloy steels containing different concentrations of vanadium and manganese were investigated by solving the equations of conservation of mass, momentum and energy in three-dimensional transient form. The computed microstructures are found to be in good agreement with the experimentally observed microstructures. The agreement indicates significant promise for predicting weld metal microstructure from the fundamentals of transport phenomena.

Tarasankar Debroy

Papers

Spatial and temporal variation of hardness of a printed steel part

Cooling rate in 800 to 500°C range from dimensional analysis

Mathematical model for stainless steelmaking - 1. argon-oxygen and argon-oxygen-steam mixtures.

Tailoring fillet weld geometry using a genetic algorithm and a neural network trained with convective heat flow calculations

Weld metal microstructure calculations from fundamentals of transport phenomena in the arc welding of low-alloy steels