Основы теории сложности

<i>Introduction to the Modeling and Analysis of Complex Systems.</i> H. Sayama (Ed.). (2015, Open SUNY Textbooks). Free open access PDF, 498 pp. ISBN 978-1-942341-06-2 (deluxe color edition). ISBN 978-1-942341-08-6 (print edition). ISBN 978-1-942341-09-3 (ebook).

Aim. For complex highly-integrated technical systems that contain elements that vary in their physical nature and operating principles (combination of mechanical, electrical and programmable electronic components), complex dependability analysis appears to be challenging due to both qualitative and quantitative reasons (large number of elements and performed functions, poorly defined boundaries of interfunctional interaction, presence of hidden redundancy, static and dynamic reconfiguration, etc.). The high degree of integration of various subsystems erodes the boundaries of responsibility in the cause-and-effect link of failures. Thus, the definition of the strength and boundaries of interfunctional and cross-system interaction is of great value in the context of complex system analysis from the standpoint of locating bottlenecks, as well as reliable evaluation of the complex dependability level. Methods. In order to solve the tasks at hand, the authors propose a method that is based on the research of the behavior of the centroid of an area bounded above by the failure density function graph, below by the coordinate axis, from the right and left by the boundaries of the considered operation interval. Graphical analysis with construction of centroids is performed for each subsystem or structural unit of a complex technical system. After that, based on the partial centroids of the respective subsystems/units, the average centroid for the whole complex system is constructed. The authors suggest using the average centroid as a conditional universal measure of the average dependability level of highly-integrated technical systems that can be used in the development of specific design solutions. In this case, in particular, it is suggested to use the presented method for identification of the subsystem that, when redundant, ensures the highest all-around growth of dependability of the complex technical system as a whole. This condition is fulfilled by the subsystem/unit of which the partial centroid is situated at the longest distance from the average centroid. The assumptions presented in this article and the results obtained are tested by means of a short verification consisting in the calculation of the probability of no-failure of the system and subsystems, construction and analysis of respective graphs. Results. The method’s implementation is presented using the example of a conventional mechatronic system. For the sake of briefness and focus the information is given in a simplified and abstract form. The application of the proposed method for analyzing complex technical systems dependability through the research of density function centroid introduced in this article was the target criterion of the method’s development, i.e. identification of bottlenecks and areas with the highest potential for increasing the overall dependability. Further publications will be dedicated to proving the applicability of such entity as a centroid as a dependability evaluation criterion, as well as other applications of the presented method in complex technical systems dependability analysis.

System reliability is important for systems engineers, since it is directly related to a company's reputation, customer satisfaction, and system design costs. Improving system reliability has been an important task for the system engineers and a number of studies have been published to discuss methods for improving system reliability. For this purpose sensitivity analysis and fault diagnosis has been used in various studies, where identification of significant and problematic components plays an important role. Both sensitivity analysis and fault diagnosis require understanding the system structure and component relationships; and Bayesian networks (BN) have been shown to be an effective tool for modeling the systems and quantifying the component interactions. In this study, we use BN for sensitivity analysis and fault diagnosis to improve system reliability. We focus on the complex systems, where the number of components and component interactions can be very large. In this study, we first discuss sensitivity analysis in complex systems using BN, which can be used for identification of significant system components. Sensitivity analysis using BN is concerned with the question of how sensitive system reliability is to possible changes in the nodes in BN. In this paper we demonstrate that BN can be efficiently and effectively used for sensitivity analysis in complex system reliability. This study is the first that considers component reliabilities and uses BN for sensitivity analysis in complex systems. In this paper as a part of our method for sensitivity analysis, an efficient algorithm (SA) is introduced to perform sensitivity analysis in complex systems. Our SA algorithm is based on a graph traversal algorithm that can be effectively used in BN. The SA algorithm traverses the BN through the connected nodes and evaluates the reliabilities to perform sensitivity analysis. Our method helps the systems engineers understand the cause and effect relationships between system components and their reliability and discover the key components that have significant effects on system reliability. Once the key components are identified, system structure can be revised to improve the overall system reliability. Next we discuss fault diagnosis in complex systems and show how fault diagnosis can be used to improve complex system reliability. Due to component aging and environmental factors, the system components in real-life complex systems may fail or not function as expected. Such failures may cause unprecedented changes in the system reliability values and affect the reliability of not only the failed component, but also the overall system. One important issue in complex systems is that, the system engineers must process large amounts of information before making operational decisions. Since BN combine expert knowledge of the system with probabilistic theory for construction of effective diagnosis methodologies, they have been applied to fault diagnosis in various studies. In this paper, we present a new method for fault diagnosis in complex systems. Our method uses the complex system reliability to detect the faulty components. We continuously monitor the overall system reliability value, and our fault diagnosis mechanism is only triggered when significant changes to system reliability are detected. As part of our method, an efficient search algorithm is designed specifically for BN. This algorithm is empowered with popular heuristics. In this paper, we discuss how our method can be efficiently applied to complex systems since our search algorithm needs to check only a small portion of the system's components before detecting the failed one. We believe that our method provides system engineers with invaluable information to diagnose the faulty component and improve reliability in complex systems.

System reliability is important for systems engineers, since it is directly related to a company's reputation, customer satisfaction, and system design costs. Improving system reliability has been an important task for the system engineers and a number of studies have been published to discuss methods for improving system reliability. For this purpose sensitivity analysis and fault diagnosis has been used in various studies, where identification of significant and problematic components plays an important role. Both sensitivity analysis and fault diagnosis require understanding the system structure and component relationships; and Bayesian networks (BN) have been shown to be an effective tool for modeling the systems and quantifying the component interactions. In this study, we use BN for sensitivity analysis and fault diagnosis to improve system reliability. We focus on the complex systems, where the number of components and component interactions can be very large. In this study, we first discuss sensitivity analysis in complex systems using BN, which can be used for identification of significant system components. Sensitivity analysis using BN is concerned with the question of how sensitive system reliability is to possible changes in the nodes in BN. In this paper we demonstrate that BN can be efficiently and effectively used for sensitivity analysis in complex system reliability. This study is the first that considers component reliabilities and uses BN for sensitivity analysis in complex systems. In this paper as a part of our method for sensitivity analysis, an efficient algorithm (SA) is introduced to perform sensitivity analysis in complex systems. Our SA algorithm is based on a graph traversal algorithm that can be effectively used in BN. The SA algorithm traverses the BN through the connected nodes and evaluates the reliabilities to perform sensitivity analysis. Our method helps the systems engineers understand the cause and effect relationships between system components and their reliability and discover the key components that have significant effects on system reliability. Once the key components are identified, system structure can be revised to improve the overall system reliability. Next we discuss fault diagnosis in complex systems and show how fault diagnosis can be used to improve complex system reliability. Due to component aging and environmental factors, the system components in real-life complex systems may fail or not function as expected. Such failures may cause unprecedented changes in the system reliability values and affect the reliability of not only the failed component, but also the overall system. One important issue in complex systems is that, the system engineers must process large amounts of information before making operational decisions. Since BN combine expert knowledge of the system with probabilistic theory for construction of effective diagnosis methodologies, they have been applied to fault diagnosis in various studies. In this paper, we present a new method for fault diagnosis in complex systems. Our method uses the complex system reliability to detect the faulty components. We continuously monitor the overall system reliability value, and our fault diagnosis mechanism is only triggered when significant changes to system reliability are detected. As part of our method, an efficient search algorithm is designed specifically for BN. This algorithm is empowered with popular heuristics. In this paper, we discuss how our method can be efficiently applied to complex systems since our search algorithm needs to check only a small portion of the system's components before detecting the failed one. We believe that our method provides system engineers with invaluable information to diagnose the faulty component and improve reliability in complex systems.

What is a complex system? Although “complexity science” is used to understand phenomena as diverse as the behavior of honeybees, the economic markets, the human brain, and the climate, there is no agreement about its foundations. In this introduction for students, academics, and general readers, the authors develop an account of complexity that brings the different concepts and mathematical measures applied to complex systems into a single framework. The book begins with an overview and a brief history of complexity science. Complexity science is relatively new but already indispensable. Many of the most important problems in engineering, medicine, and public policy are now addressed with the ideas and methods of complexity science. The conceptual foundations of complexity science are disputed, and there are many and diverging views among scientists about what complexity and complex systems are. Its origins lie in cybernetics and systems theory and it is related to dynamical systems theory and the study of cellular automata. The book introduces the different features of complex systems and discusses different conceptions of complexity with the authors documenting their own account. In do so, they explain why complexity science is so important in today's world.

The complexity of problems facing society continues to grow, and decision-makers and problem-solvers are finding many of today's emerging problems to be beyond their capability to adequately address. There is agreement in the literature that problems of this nature are complex system problems, inextricably linked to some highly complex system of systems. Establishing a clear understanding of the specific complex system context is fundamental to the process of understanding and analyzing complex systems and complex system problems across all of the different systems-based disciplines. While complex system context is widely referred to in systems literature, there is no clear characterization of exactly what system context is, making this foundational system concept ambiguous. This research addressed this gap in the systems body of knowledge by providing the needed detail and clarity to the concept of complex system context. A rigorous research methodology, employing the grounded theory method, was used to analyze data collected through a series of semi-structured interviews conducted with individuals reflecting a wide range of systems education and practical experience. Two research questions were identified as integral to increasing the understanding of context within complex systems. (1) What are the constituent elements of complex system context, and what attributes and dimensions characterize these elements? (2) What systems-based framework can be developed for constructing and articulating complex system context? Using the grounded theory method, a theory of system context was constructed, adding to the systems body of knowledge and substantiating a comprehensive and unambiguous theoretical construct for system context within complex systems. Then, based on this theory, a conceptual model to articulate and capture system-specific complex system context was developed---the Complex System Contextual Framework (CSCF). The CSCF shows significant promise for contribution to systems practitioners by supporting the future development of tools to help practitioners capture system context as a part of complex system problem formulation. The research also made a contribution in the area of research methodologies by furthering the use of the grounded theory method in the engineering management and systems engineering domain, an area where its application has been very limited.

In popular dialogues, describing a system as "complex" is often the point of resignation, inferring that the system cannot be sufficiently described, predicted nor managed. Transport networks, management infrastructure and supply chain logistics are all often described in this way. Academic dialogues have begun to explore the collective behaviors of complex systems to define a complex system specifically as an adaptive one; i.e. a system that demonstrates 'self organising' principles and 'emergent' properties. Based upon the key principles of interaction and emergence in relation to adaptive and self organising systems in cultural artifacts and processes, this paper will argue that complex systems are cultural systems. By introducing generic principles of complex systems, and looking at the exploration of such principles in art, design and media research, this paper argues that a science of cultural systems as part of complex systems theory is the post modern science for the digital age. Furthermore, that such a science was predicated by post structuralism and has been manifest in art, design and media practice since the late 1960s.

This introductory chapter provides an overview and a brief history of complexity science, which is the study of complex systems. All living systems and all intelligent systems are complex systems. Complexity science is relatively new but already indispensable. Many of the most important problems in engineering, medicine, and public policy are now addressed with the ideas and methods of complexity science. However, there is no agreement about the definition of 'complexity' or 'complex system', nor even about whether a definition is possible or needed. The conceptual foundations of complexity science are disputed, and there are many and diverging views among scientists about what complexity and complex systems are. Even the status of complexity as a discipline can be questioned given that it potentially covers almost everything. The origins of complexity science lie in cybernetics and systems theory, both of which began in the 1950s. Complexity science is related to dynamical systems theory, which matured in the 1970s, and to the study of cellular automata, which were invented at the end of the 1940s. By then computer science had become established as a new scientific discipline.

Chapter 2 - Theory of complexity, origin and complex systems

Risk assessment is the key and core technologies ensuring IT system security. Based on the comprehensive analysis to complex information systems, this paper first summarizes the typical characters of complex information systems and then gives new risk factors that complex system need to face. Furthermore, a new risk assessment method is proposed to evaluate the complex information systems. The method takes full account of the effect of complexity of complex information systems in each process of risk assessment, and utilizes multi-level risk views to carry out in-depth analysis to the risk of complex system.

The paper describes the process of choosing the optimal design option for a complex technical system under conditions of interval uncertainty and incomplete information about the parameters and the phase state. Problems of this kind are extremely relevant at the initial stage of designing complex systems, when from a variety of possible options it is necessary to select those that are more consistent with the heterogeneous quality criteria and do not always meet the ambiguous preferences of the decision maker.&#x0D; The aim of the study is to develop effective methods for comparing various design options for complex systems at the initial design stage under conditions of interval uncertainty. The objectives of the study include the construction of a mathematical model for the functioning of a complex system under conditions of uncertainty, as well as the analysis of the main methods for comparing alternatives with heterogeneous quality criteria.&#x0D; Materials and Methods. The article provides a description of the functioning model of a complex technical system under conditions of uncertainty, and also describes the main methods for comparing various options for the system design at the initial stages of design in conditions of incompleteness and uncertainty of information, as well as ambiguity of the preferences of the decision maker.&#x0D; Results. The scientific novelty of the implemented approach lies in the use of interval data statistics, which allow the most correct consideration of possible errors associated with measuring the values of the characteristics of the studied technical systems at all stages of the control process.&#x0D; The scientific novelty of the implemented approach lies in the use of the interval analysis apparatus, which makes it possible to most correctly take into account the possible errors associated with measuring the values of the characteristics of the studied technical systems at all stages of the design process.&#x0D; Discussion and Conclusions. The mathematical model of the process of functioning of a complex technical system under conditions of interval uncertainty developed in the course of the study allows selection of system design options at the initial stages of design, taking into account possible errors and inaccuracies arising from the deviation of values from the calculated nominal values.

The following news item is taken in part from the July 27, 2011 issue of Science titled ''9 Billion?,@ by Leslie Roberts.

Aim. The paper aims to research the methods of evaluating dependability indicators based on the analysis of Big Data obtained in the course of monitoring the operation of technical systems and their components. A comparative analysis is performed of the efficiency of robust statistical methods of evaluating the dependability indicators of complex technical systems based on operation data.Methods. The paper uses methods of mathematical statistics, specifically robust methods of evaluating the translation parameter of a noisy sample and numerical methods of statistical modeling. The authors consider five methods of evaluating the translation parameter: sample mean as a nonrobust method used for comparison; sample median as the simplest robust method of evaluating the translation parameter; two-stage evaluation procedure with truncation of outliers according to the three sigma rule; two-stage evaluation procedure with truncation of outliers using Tukey’s box-and-whisker plot; Huber’s robust method. The comparative analysis of the methods of evaluating system dependability indicators was conducted by means of statistical modeling in the R statistical computation package. Five distribution laws for generating an element’s time-to-failure and recovery time samples were considered: exponential distribution, Weibull distribution, log-normal distribution, gamma distribution and uniform distribution.Results. Statistical analysis of Big Data associated with the operation of technical systems is complicated by the heterogeneity and noisiness of such data, as well as the presence of errors and outliers of varied nature. That is primarily due to the varied loads and operating conditions of each object. Herein this problem is examined as regards the problem of evaluating the dependability indicators of a structurally complex monotonic system with independent element recovery. The paper examines methods of rejecting anomalous data and robust evaluation of the sample position parameter and performs a comparative analysis of the efficiency of such methods for various distribution laws. It is shown that robust methods of evaluation enable significantly higher accuracy as compared to the standard sample mean. The two-stage procedure based on the truncation of outliers and Tukey’s box-and-whisker plot proved to be the most efficient.Conclusions. The paper’s findings allow improving the accuracy of evaluation of dependability indicators based on complex technical system operation data. They can be used in Big Data processing and complex system dependability theory.

Machinic Heterogenesis and Evolution

Genomics, proteomics, and metabolomics have all vastly advanced our understanding of human biology and disease. But the functioning of even a simple system such as a single yeast cell or bacterium is much more complicated than the sum of its genes or proteins or metabolites; it’s the activity of all those components and their relationships to one another that add up to a living organism. Recognizing that complexity, the emerging field of systems biology attempts to harness the power of mathematics, engineering, and computer science to analyze and integrate data from all the “omics” and ultimately create working models of entire biological systems. “Traditionally, scientists—toxicologists included—have relied on a reductionist approach to biology,” says William Suk, director of the NIEHS Center for Risk and Integrated Sciences. Even now, many studies examine complex systems by looking at cellular components in isolation. For instance, a common experiment involves using DNA microarrays to observe the effect of a chemical exposure on thousands of genes at once. This technique can quickly tell a scientist which genes may be vulnerable to that exposure. But a systems biology approach would attempt to model not only the chemical’s effect on gene expression but also how that expression will affect protein function, and in turn how the exposure will affect cell signaling. “There’s nothing wrong with what we’ve been doing,” Suk says. “But systems biology is going to take it to another level.”