Draft:Dynamic Master Logic Diagram
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The Dynamic Master Logic Diagram (DMLD) is a hierarchical functional modeling method for representing the time-dependent and uncertain behavior of complex physical and engineering systems. It extends goal tree–success tree and master logic diagram approaches by incorporating time-dependent, multistate, physical, logical, and fuzzy relationships among system objectives, functions, subsystems, and components.[1][2]
DMLD was initially developed for system-level modeling, diagnosis, and control in safety and reliability applications. Independent studies later adapted the method for multistate systems of systems, critical-infrastructure resilience, and dynamic reliability analysis.[3][4]
Background and development
[edit]Goal tree–success tree (GTST) models organize a system according to the objectives it is intended to achieve and the functions and resources required to achieve them. Master logic diagrams provide a related representation of dependencies among system functions, support functions, and physical elements.[5]
Hu and Modarres introduced DMLD as a means of extending these hierarchical representations to time-dependent system behavior. Their 1996 formulation addressed feedback, delayed dependencies, autocorrelation, trends, degrees of success or failure, and transition effects.[1] A more extensive formulation published in 1999 described the representation of partial system success and failure, logical and physical connectivity, imprecise or fuzzy relationships, multistate dynamics, uncertainty, floating thresholds, and transitions between system states.[2]
Later literature has sometimes used the shorter expression dynamic master logic (DML) for related functional-modeling and diagnostic frameworks. The terminology is not entirely uniform: some studies use DMLD, while others use combinations such as GTST–DMLD, GTST–MLD, or dynamic MLD, depending on the model formulation and application.
Model structure
[edit]A DMLD represents a system as a hierarchy linking high-level objectives to the functions, subfunctions, resources, and components that support them. The hierarchy can be examined in two directions. Downward analysis identifies the functions and elements needed to satisfy a system objective, while upward analysis examines how the state or failure of lower-level elements affects higher-level functions and objectives.[2]
The method distinguishes between functional and structural descriptions. Functional elements represent what a system or subsystem is intended to accomplish. Structural elements represent the hardware, software, human, or other resources that implement or support those functions. Connections between elements may represent logical dependencies, physical relationships, or graded relationships for which a binary true-or-false description is insufficient.[2]
Traditional Boolean operators can be used where dependencies are discrete. Fuzzy operators can instead assign intermediate degrees of membership or success, allowing a model to represent partial degradation, uncertain thresholds, and conditions that change gradually rather than instantaneously.[2]
Dynamic and uncertain behavior
[edit]The dynamic aspect of DMLD concerns relationships whose effects depend on time, sequence, duration, or previous system states. Examples described in the early literature include feedback, delayed effects, trends, autocorrelation, transition behavior, and thresholds that vary according to operating conditions.[1]
The 1999 formulation permits multiple degrees of system success or failure rather than restricting the model to two states. It also distinguishes several forms of uncertainty, including probabilistic uncertainty and imprecision represented through fuzzy or linguistic values.[2] A DMLD can therefore be used to trace both the functional consequences of an observed condition and the combinations of lower-level conditions that support a desired system state.
Applications
[edit]Safety and resilience assessment
[edit]Ferrario and Zio adapted the goal tree–success tree–dynamic master logic diagram to a multistate system-of-systems framework for evaluating the safety and physical resilience of a critical plant exposed to external events. Their method represented different levels of component damage and system safety and combined the hierarchical model with Monte Carlo simulation.[3]
Ferrario, Pedroni, and Zio subsequently used GTST–DMLD to model dependencies within and between critical infrastructures. Their case study included an electric power system, a gas network, and a supervisory control and data acquisition system. The study incorporated multistate component performance and epistemic uncertainty in transition probabilities and state holding times.[4]
Dynamic reliability analysis
[edit]Jenab, Sarfaraz, Dhillon, and Seyed Hosseini developed a probabilistic method for analyzing a dynamic master logic diagram by translating its dependency matrix into a flow graph. Their formulation modeled functions with failure detection, recovery, and self-healing mechanisms and was used to estimate system failure probability and time-to-failure measures.[6]
Related GTST–MLD models have also been investigated for the dynamic reliability assessment of cyber-physical energy systems.[7]
Knowledge-based diagnosis
[edit]DMLD has also been used as a knowledge-representation and inference structure for diagnostic systems. The original publications described applications to model-based diagnosis and dynamic-system control.[1][2] Later research applied fuzzy-logic-based functional hierarchies to manufacturing-process diagnosis.[8]
Relationship to other methods
[edit]DMLD belongs to a broader family of functional and hierarchical system-modeling methods. Unlike fault tree analysis, which begins with an undesired top event and decomposes its possible causes, a functional hierarchy begins with system objectives and identifies the functions and resources required to achieve them. DMLD extends this type of hierarchy with representations of graded, dynamic, and time-dependent relationships.[2]
The method is related to goal tree–success tree modeling, master logic diagrams, multistate-system modeling, fuzzy inference, and knowledge-based diagnostic systems. Related publications use terms including dynamic MLD, GTST–MLD, and GTST–DMLD, depending on the formulation discussed.
See also
[edit]- Event tree analysis
- Fault detection and isolation
- Fault tree analysis
- Functional analysis
- Fuzzy logic
- Knowledge graph
- Knowledge representation
- Probabilistic risk assessment
- Reliability engineering
- Systems engineering
References
[edit]- ^ a b c d Hu, Yu-Shu; Modarres, Mohammad (1996). "Time-dependent system knowledge representation based on dynamic master logic diagrams". Control Engineering Practice. 4 (1): 89–98. doi:10.1016/0967-0661(95)00211-5.
- ^ a b c d e f g h Hu, Yu-Shu; Modarres, Mohammad (1999). "Evaluating system behavior through Dynamic Master Logic Diagram (DMLD) modeling". Reliability Engineering & System Safety. 64 (2): 241–269. doi:10.1016/S0951-8320(98)00066-0.
- ^ a b Ferrario, Elisa; Zio, Enrico (2014). "Goal Tree Success Tree–Dynamic Master Logic Diagram and Monte Carlo simulation for the safety and resilience assessment of a multistate system of systems". Engineering Structures. 59: 411–433. doi:10.1016/j.engstruct.2013.11.001.
- ^ a b Ferrario, Elisa; Pedroni, Nicola; Zio, Enrico (2015). "Analysis of the Robustness and Recovery of Critical Infrastructures by Goal Tree–Success Tree: Dynamic Master Logic Diagram, Within a Multistate System-of-Systems Framework, in the Presence of Epistemic Uncertainty". ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering. 1 (3): 031001. doi:10.1115/1.4030439.
- ^ Modarres, Mohammad; Cheon, Se Woo (1999). "Function-centered modeling of engineering systems using the goal tree–success tree technique and functional primitives". Reliability Engineering & System Safety. 64 (2): 181–200. doi:10.1016/S0951-8320(98)00062-3.
- ^ Jenab, Kouroush; Sarfaraz, Ali; Dhillon, Balbir S.; Seyed Hosseini, Seyed Mohammad (2012). "Dynamic MLD analysis with flow graphs". Reliability Engineering & System Safety. 106: 80–85. doi:10.1016/j.ress.2012.05.008.
- ^ Hao, Z.; Di Maio, F.; Zio, E. (2021). "Dynamic Reliability Assessment of Cyber-Physical Energy Systems by GTST-MLD". 2021 5th International Conference on System Reliability and Safety. IEEE. pp. 98–102. doi:10.1109/ICSRS53853.2021.9660671.
- ^ Hu, Yu-Shu; Modarres, Mohammad (2005). "Apply fuzzy-logic-based functional-center hierarchies as inference engines for self-learning manufacture process diagnoses". Fuzzy Systems and Knowledge Discovery. Lecture Notes in Computer Science. Vol. 3614. Springer. pp. 1012–1021. doi:10.1007/11540007_129.
Category:Reliability engineering Category:Risk analysis methodologies Category:Systems engineering Category:Knowledge representation Category:Fuzzy logic
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