Preface

This book examines some problems and current trends relating to the theory of dynamical systems. It also discusses some significant advances made in this field in the last several years, including new models, computer algorithms, and applications in various scientific areas.

The book includes six chapters. Chapter 1 presents an innovative methodology that integrates physical devices and machinery with text mining technologies to identify anomalous behaviors, even of minimal entity, rarely perceived by other strategies in a machine tool. Chapter 2 presents a vibrations analysis of elastic beams based on the constitutive equation of Kelvin-Voigt type, which contains fractional derivatives of real order. Chapter 3 discusses the emergence of chaos and complex behavior in real and physical systems, reviewing problems such as the complexity of Child's swing dynamics, chaotic neuronal dynamics, complex food-web dynamics, financial models, and others. Chapter 4 considers the invariant method theory for stochastic systems with strong perturbations, representing modern approaches to describe dynamical systems having a set of invariant functions. Chapter 5 presents a study of a mesoscopic stochastic process derived from deterministic dynamics studied by Kolmogorov and others in the stationary case, and extends their methods and some of their results considering the non-stationary process, which stems from a non-invariant initial measure. Finally, Chapter 6 introduces recent developments on the stability analysis of dynamical systems using the powerful tool of control Lyapunov functions.

Researchers, engineers, and graduate students in both pure and applied mathematics may benefit from the chapters collected in this volume. We express appreciation to IntechOpen for their professional support and to Author Service Manager Mr. Josip Knapić for his tireless help in the preparation of this book.

> **Bruno Carpentieri** Free University of Bozen-Bolzano (Faculty of Computer Science), Bolzano, Italy

**Chapter 1**

**Abstract**

mining, efficient algorithm

**1. Introduction**

**1**

Text Mining for Industrial

with Multiple Data Sources

*Giancarlo Nota and Alberto Postiglione*

Machine Predictive Maintenance

This paper presents an innovative methodology, from which an efficient system prototype is derived, for the algorithmic prediction of malfunctions of a generic industrial machine tool. It integrates physical devices and machinery with Text Mining technologies and allows the identification of anomalous behaviors, even of minimal entity, rarely perceived by other strategies in a machine tool. The system works without waiting for the end of the shift or the planned stop of the machine. Operationally, the system analyzes the log messages emitted by multiple data sources associated with a machine tool (such as different types of sensors and log files produced by part programs running on CNC or PLC) and deduces whether they can be inferred from them future machine malfunctions. In a preliminary offline phase, the system associates an alert level with each message and stores it in a data structure. At runtime, three algorithms guide the system: pre-processing, matching and analysis: Preprocessing, performed only once, builds the data structure; Matching, in which the system issues the alert level associated with the message; Analysis, which identifies possible future criticalities. It can also analyze an entire historical series of stored messages The algorithms have a linear execution time and are independent of the size of the data structure, which does not need to

be sorted and therefore can be updated without any computational effort.

**Keywords:** industrial machine tool, predictive maintenance, log message, text

tenance activities before the equipment failure. The primary goal of predictive maintenance is to reduce the frequency of equipment failures by preventing the failure before it actually occurs [5]. This strategy helps to minimize breakdown costs and downtime (loss of production) and increase product quality, well known thanks to [6] and recently reiterated by [4]. Obviously [7] predictive maintenance is different from corrective maintenance, as action will be taken here to "anticipate" the error before it actually occurs. Predictive maintenance is primarily about detecting hidden and potential failures. It does not replace, but joins the Preventive Maintenance in the strict sense, which is linked to the execution of a specific protocol (often agreed with the machine manufacturer) intended to periodically

The concept of Predictive Maintenance [1–4] foresees the carrying out of main-
