An Approach of the Grey System Modelling and Simulation for Complex Systems

Data mining with a multitude of methodologies is a good basis for the integration of intelligent systems. Small, specialised systems have a large number of feasible solutions, but developing truly adaptive, and still understandable, systems for highly complex systems require domain expertise and more compact approaches at the basic level. This paper focuses on the integration of methodologies in the smart adaptive applications. Statistical methods and arti cial neural networks form a good basis for the data-driven analysis of interactions and fuzzy logic introduces solutions for knowledge-based understanding the system behaviour and the meaning of variable levels. Efficient normalisation, scaling and decomposition approaches are the key methodologies in developing large-scale applications. Linguistic equation (LE) approach originating from fuzzy logic is an efficient technique for these problems. The nonlinear scaling methodology based on advanced statistical analysis is the corner stone in representing the variable meanings in a compact way to introduce intelligent indices for control and diagnostics. The new constraint handling together with generalised norms and moments facilitates recursive parameter estimation approaches for the adaptive scaling. Well-known linear methodologies are used for the steady state, dynamic and case-based modelling in connection with the cascade and interactive structures in building complex large scale applications. To achieve insight and robustness the parameters are de ned separately for the scaling and the interactions. Introduction EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 2 SNE 24(1) – 4/2014 ON 1 Steady-State Modelling multiple input, multiple output MIMO response surface methodology RSM multiple input, single output MISO Fuzzy set theory Extension principle Type-2 fuzzy Figure 1: Methodologies for modelling of complex system. EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 3 O N Linguistic fuzzy models Takagi-Sugeno (TS) fuzzy models Singleton models Fuzzy relational models Figure 2: Combined fuzzy modelling. Artificial neural networks ANN Linear networks multilayer perceptron MLP backpropagation learning Neurofuzzy systems Figure 3: A fuzzy neuron. function expansion Approximate reasoning 2 Decomposition Methodologies EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 4 SNE 24(1) – 4/2014 ON Decomposition Figure 4: Decomposition for modelling. Hierarchical clustering Partitioning-based clustering algorithms fuzzy clustering Fuzzy c-means (FCM) Subtractive clustering Neural clustering Robust clustering number of clusters Composite local model Linear parameter varying (LPV) models Piecewise affine (PWA) systems Fuzzy models Multiple neural network systems mixed approach EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 5 O N 3 Adaptive Nonlinear Scaling Membership 3.1 Working point and feasible ranges Figure 5: Nonlinear scaling [28] EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 6 SNE 24(1) – 4/2014 ON 3.2 Membership definitions linguistic range linguistic values • the corner points (Figure 5) are good for visualisation; • the parameters suit for tuning; • the coefficients are used in the calculations. 3.3 Adaptation of nonlinear scaling EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 7 O N 4 Intelligent Systems 4.1 LE models 4.2 Hybrid LE systems EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 8 SNE 24(1) – 4/2014 ON extension principle linguistification

An Approach of the Grey System Modelling and Simulation for Complex Systems was published in Systems Analysis and Simulation 1988, I: Theory and Foundations. Proceedings of the International Symposium held in Berlin (GDR), September 12–16, 1988 on page 117.

The context of our work is the complex systems simulation. Complex systems modelling and simulation require to take into account the interactions between the different components. For instance, an airport ground traffic simulation requires to model the planes with the pilots, the control tower, the

Regional complex system simulation optimization through linking governance and environment performance: A case study of water environmental carrying capacity based on the SDES model

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to study complex system behavior involving feedback, laments the lack of understanding of complex systems evident in short-sited decisions made by legislators -- global climate change and fiscal policies being cases in point. In order to better prepare future decision makers with tools that could allow them to make more informed decisions about issues involving complex systems efforts have been underway to increase pre-college teacher understanding of the SD method. The research described in this dissertation introduces the mathematics education community to the value of System Dynamics modeling in pre-college algebra classes, indicates a path by which a traditional mathematics curriculum could be enhanced to include small SD models as a new representation for elementary functions studied in algebra classes, and provides an empirical study regarding conceptual understanding of functions by students. Chapter 2 indicates the numerous beneficial learning outcomes that empirical studies have shown accompany model-building activities. Chapter 3 indicates the need for students to become familiar with complex systems analysis, how SD modeling (one method of complex systems analysis) aligns with the Common Core State Standards in Mathematics, and the work that has transpired over the past two decades using SD in K-12. Chapter 4 focuses on the importance of the concept of function in high school mathematics, some limitations of exclusive reliance on the closed form equation representation for mathematizing problems and the SD stock/flow representations of some of the elementary functions that are studied in algebra classes. Chapter 5 looks at the issues affecting two traditional teachers and the challenges they faced when trying to reintroduce SD modeling into their algebra classes. Chapter 6 explains the student component of the classroom experiment that was conducted by the teachers who are highlighted in Chapter 5. The analysis of the results of student model-building activities in the two classroom

Complexity science offers many theories such as chaos theory and coevolutionary theory. These theories illustrate a large set of real life systems and help decipher their nonlinear and unpredictable behaviours. Categorizing an observed Complex System among these theories depends on the aspect that we intend to study, and it can help better understand the phenomena that occur within the system. This article aims to give an overview on Complex Systems and their modelling. Therefore, we compare these theories based on their main behavioural characteristics, e.g. emergence, adaptability, and dynamism. Then we compare the methods used in the literature to model and simulate Complex Systems, and we propose and discuss simple guidelines to help understand one's Complex System and choose the most adequate model to simulate it.

Complex sociotechnical systems with multiple competing objectives and nonlinear dynamics pose significant challenges for policy optimization. Traditional simulation-based methods often struggle with high-dimensional policy spaces. This study addresses these challenges by combining genetic algorithms (GAs) with system dynamics (SD) modeling to optimize policy configurations in complex environments. Our approach merges SD’s capacity to simulate intricate system behaviors with GA’s prowess in multi-objective optimization. The SD model uses predefined decision variables to simulate system behavior, while GA iteratively adjusts these variables to find optimal policy configurations. We apply this hybrid approach to a media industry case study, focusing on balancing profit, competitiveness, and audience satisfaction. The research methodology integrates SD’s ability to capture complex system behaviors with GA’s strength in optimizing multiple objectives. An SD model simulates system behavior based on predefined decision variables representing key policy levers. GA then iteratively adjusts these variables based on fitness objectives derived from the SD model. This process evaluates performance and identifies the globally optimal policy configurations. The results show that the hybrid SD–GA framework significantly improves policy solutions compared to conventional methods. Sensitivity analysis confirms the optimized policies’ robustness and comparative assessments highlight our approach’s advantages in navigating complex policy spaces. This study introduces a new SD–GA framework that improves data-driven policy formulation in complex systems. It combines policy informatics and evolutionary algorithms to offer a comprehensive approach to multi-criteria decision-making. Future research could include long-term validation of this approach in the broadcasting industry to further refine and apply this methodology across various domains.

BackgroundMathematical modelling has been a vital research tool for exploring complex systems, most recently to aid understanding of health system functioning and optimisation. System dynamics models (SDM) and agent-based models (ABM) are two popular complementary methods, used to simulate macro- and micro-level health system behaviour. This systematic review aims to collate, compare and summarise the application of both methods in this field and to identify common healthcare settings and problems that have been modelled using SDM and ABM.MethodsWe searched MEDLINE, EMBASE, Cochrane Library, MathSciNet, ACM Digital Library, HMIC, Econlit and Global Health databases to identify literature for this review. We described papers meeting the inclusion criteria using descriptive statistics and narrative synthesis, and made comparisons between the identified SDM and ABM literature.ResultsWe identified 28 papers using SDM methods and 11 papers using ABM methods, one of which used hybrid SDM-ABM to simulate health system behaviour. The majority of SDM, ABM and hybrid modelling papers simulated health systems based in high income countries. Emergency and acute care, and elderly care and long-term care services were the most frequently simulated health system settings, modelling the impact of health policies and interventions such as those targeting stretched and under resourced healthcare services, patient length of stay in healthcare facilities and undesirable patient outcomes.ConclusionsFuture work should now turn to modelling health systems in low- and middle-income countries to aid our understanding of health system functioning in these settings and allow stakeholders and researchers to assess the impact of policies or interventions before implementation. Hybrid modelling of health systems is still relatively novel but with increasing software developments and a growing demand to account for both complex system feedback and heterogeneous behaviour exhibited by those who access or deliver healthcare, we expect a boost in their use to model health systems.

This paper describes a multi-level system dynamics (SD) / discrete event simulation (DES) approach for assessing planning and scheduling problems within an aviation training continuum. The aviation training continuum is a complex system, consisting of multiple aviation schools interacting through interschool student and instructor flows that are affected by external triggers such as resource availability and the weather. SD was used to model the overall training continuum at a macro level to ascertain relationships between system entities. SD also assisted in developing a shared understanding of the training continuum, which involves constructing the definitions of the training requirements, resources and policy objectives. An end-to-end model of the continuum is easy to relate to, while dynamic visualisation of system behaviour provides a method for exploration of the model. DES was used for micro level exploration of an individual school within the training continuum to capture the physical aspects of the system including resource capacity requirements, bottlenecks and student waiting times. It was also used to model stochastic events such as weather and student availability. DES has the advantage of being able to represent system variability and accurately reflect the limitations imposed on a system by resource constraints. Through sharing results between the models, we demonstrate a multi-level approach to the analysis of the overall continuum. The SD model provides the school’s targeted demand to the DES model. The detailed DES model is able to assess schedules in the presence of resource constraints and variability and provide the expected capacity of a school to the high level SD model, subjected to constraints such as instructor availability or budgeted number of training systems. The SD model allows stakeholders to assess how policy and planning affect the continuum, both in the short and the long term. The development of this approach permits moving the analysis of the continuum between SD and DES models as appropriate for given system entities, scales and tasks. The resultant model outcomes are propagated between the continuum and the detailed DES model, iteratively generating an assessment of the entire set of plans and schedule across the continuum. Combining data and information between SD and DES models and techniques assures relevance to the stakeholder needs and effective problem scoping and scaling that can also evolve with dynamic architecture and policy requirements. An example case study shows the combined use of the two models and how they are used to evaluate a typical scenario where increased demand is placed on the training continuum. The multi-level approach provides a high level indication of training requirements to the model of the new training school, where the detailed model indicates the resources required to achieve those particular student levels.

The StarCraft II game has become the main experimental environment in the field of intelligent combat decision-making, and system dynamics is suitable for macro modeling and simulation of complex systems. This paper proposes a general model of "unified planning-delayed output" supplemented by C language extended external functions to solve the difficulty of system dynamics modeling in the field of combat decision-making, and realize the refined modeling and simulation of StarCraft II, which verified the effectiveness of this method. This paper can lay the foundation for the research of intelligent combat decision-making based on deep reinforcement learning.

Water, energy and the environment are inextricably linked. Complex and volatile global situations pose serious challenges to long-term stable and sustainable social development, resulting in many uncertainties in maintaining regular water and energy supplies and avoiding environmental degradation. Based on the nexus theory, it has become an urgent global and regional need for policy makers and scientists to consider water, energy, and the environment nexus (WEEN) as a complex system in order to deal with the water and energy issues brought about by rapid urbanization, the synergistic response of the environment under climate change, and the corresponding potential risks. Aiming at these problems, a simulation and optimization framework for WEEN complex systems is proposed by combining the system dynamics model, Gaussian white noise, and NSGA-II method. A system dynamics model integrated with Gaussian white noise is used to characterize the feedback relationships among the elements within the different subsystems of water resources, energy, and environment under uncertainty. Taking the city cluster in the middle reaches of the Yangtze River (CCMRYR) in China as the research object, the evolution of the WEEN complex system is simulated under different uncertainty conditions such as climate change conditions and policy backgrounds. In addition, an optimization method based on NSGA-II algorithm is constructed for solving the optimal development strategy of WEEN complex system. The results show that: Following the current development path, by increasing the proportion of energy conservation and environmental protection expenditures by 0.033%, as well as adjusting the ratio of the primary, secondary, and tertiary industries from 5.8:29.0:59.1 to 6.9:28.3:59.7, it is possible for CCMRYR to achieve a reduction of 1.31 billion tons of total water consumption, a reduction of 12.17 million tce of total energy consumption, and a decrease of 0.13×106 of total pollution equivalent in 2035.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of Simulinkand Matlab. These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of SimulinkTM and MatlabTM . These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

Overview: New directions for simulation and modeling of complex systems

168 Impact of Connecticut’s Good Samaritan Laws in Preventing Opioid Overdose Deaths – An Applied System Dynamics Approach