scholarly journals Spectral Characterization of Hierarchical Modularity in Product Architectures1

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Somwrita Sarkar ◽  
Andy Dong ◽  
James A. Henderson ◽  
P. A. Robinson
Keyword(s):  
Adjacency Matrix ◽  
Product Architecture ◽  
Modular Organization ◽  
Design Management ◽  
Spectral Approach ◽  
Graph Theoretic ◽  
Complex Engineered Systems ◽  
System Resilience ◽  
Engineered Systems

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

Resilient Design of Complex Engineered Systems

2013 ◽  
Author(s):  
Hoda Mehrpouyan ◽  
Brandon Haley ◽  
Andy Dong ◽  
Irem Y. Tumer ◽  
Chris Hoyle
Keyword(s):  
Complex Network ◽  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Algebraic Connectivity ◽  
Graph Spectra ◽  
Complex Engineered Systems ◽  
Resilient Design ◽  
Spectra Properties ◽  
Key Driver ◽  
Engineered Systems

This paper presents a complex network and graph spectral approach to calculate the resiliency of complex engineered systems. Resiliency is a key driver in how systems are developed to operate in an unexpected operating environment, and how systems change and respond to the environments in which they operate. This paper deduces resiliency properties of complex engineered systems based on graph spectra calculated from their adjacency matrix representations, which describes the physical connections between components in a complex engineered systems. In conjunction with the adjacency matrix, the degree and Laplacian matrices also have eigenvalue and eigenspectrum properties that can be used to calculate the resiliency of the complex engineered system. One such property of the Laplacian matrix is the algebraic connectivity. The algebraic connectivity is defined as the second smallest eigenvalue of the Laplacian matrix and is proven to be directly related to the resiliency of a complex network. Our motivation in the present work is to calculate the algebraic connectivity and other graph spectra properties to predict the resiliency of the system under design.

Model Validation in Early Phase of Designing Complex Engineered Systems

2018 ◽  
Author(s):  
Elham Keshavarzi ◽  
Kai Goebel ◽  
Irem Y. Tumer ◽  
Christopher Hoyle
Keyword(s):  
Model Simulation ◽  
Early Stage ◽  
Design Stage ◽  
Early Design ◽  
The Real ◽  
Early Design Stage ◽  
Complex Engineered Systems ◽  
Search Tool ◽  
Engineered Systems

In design process of a complex engineered system, studying the behavior of the system prior to manufacturing plays a key role to reduce cost of design and enhance the efficiency of the system during its lifecycle. To study the behavior of the system in the early design phase, it is required to model the characterization of the system and simulate the system’s behavior. The challenge is the fact that in early design stage, there is no or little information from the real system’s behavior, therefore there is not enough data to use to validate the model simulation and make sure that the model is representing the real system’s behavior appropriately. In this paper, we address this issue and propose methods to validate the model developed in the early design stage. First we propose a method based on FMEA and show how to quantify expert’s knowledge and validate the model simulation in the early design stage. Then, we propose a non-parametric technique to test if the observed behavior of one or more subsystems which currently exist, and the model simulation are the same. In addition, a local sensitivity analysis search tool is developed that helps the designers to focus on sensitive parts of the system in further design stages, particularly when mapping the conceptual model to a component model. We apply the proposed methods to validate the output of failure simulation developed in the early stage of designing a monopropellant propulsion system design.

scholarly journals Classes of graphs with restricted interval models

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Andrzej Proskurowski ◽  
Jan Arne Telle
Keyword(s):  
Maximum Clique ◽  
Interval Graphs ◽  
Induced Subgraph ◽  
Graph Theoretic ◽  
Graph Classes ◽  
International Audience ◽  
Forbidden Induced Subgraph ◽  
Nested Hierarchy ◽  
Graph Families

International audience We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs. We initiate a graph-theoretic study of subgraphs of q-proper interval graphs with maximum clique size k+1 and give an equivalent characterization of these graphs by restricted path-decomposition. By allowing the parameter q to vary from 0 to k, we obtain a nested hierarchy of graph families, from graphs of bandwidth at most k to graphs of pathwidth at most k. Allowing both parameters to vary, we have an infinite lattice of graph classes ordered by containment.

scholarly journals Forensic Engineering Use Of Fault Tree Analysis

2006 ◽  
Vol 23 (2) ◽  
Author(s):  
Frank H. Johnson ◽  
DeWitt William E.
Keyword(s):  
Fault Tree ◽  
Fault Tree Analysis ◽  
Tree Analysis ◽  
Complex Engineered Systems ◽  
Track Record ◽  
Forensic Engineering ◽  
Fire And Explosion ◽  
Engineered Systems ◽  
Analytical Tools

Analytical Tools, Like Fault Tree Analysis, Have A Proven Track Record In The Aviation And Nuclear Industries. A Positive Tree Is Used To Insure That A Complex Engineered System Operates Correctly. A Negative Tree (Or Fault Tree) Is Used To Investigate Failures Of Complex Engineered Systems. Boeings Use Of Fault Tree Analysis To Investigate The Apollo Launch Pad Fire In 1967 Brought National Attention To The Technique. The 2002 Edition Of Nfpa 921, Guide For Fire And Explosion Investigations, Contains A New Chapter Entitled Failure Analysis And Analytical Tools. That Chapter Addresses Fault Tree Analysis With Respect To Fire And Explosion Investigation. This Paper Will Review The Fundamentals Of Fault Tree Analysis, List Recent Peer Reviewed Papers About The Forensic Engineering Use Of Fault Tree Analysis, Present A Relevant Forensic Engineering Case Study, And Conclude With The Results Of A Recent University Study On The Subject.

Evaluation of supply chain resilience index: a graph theory based approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nishtha Agarwal ◽  
Nitin Seth ◽  
Ashish Agarwal
Keyword(s):  
Supply Chain ◽  
Adjacency Matrix ◽  
Theoretic Approach ◽  
Worst Case ◽  
Content Type ◽  
Supply Chain Resilience ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Resilience Index ◽  
Index Value

PurposeThe present study aims at developing a model to quantify supply chain resilience as a single numerical value. The numerical value is called resilience index that measures the resilience capability of the case company's supply chain. The model calculates the index value based on the interactions between the enablers of supply chain resilience and its dimensions.Design/methodology/approachGraph theoretic approach (GTA) is used to evaluate the resilience index for the case company's supply chain. In GTA, the dimensions of resilience enablers and their interdependencies are modelled through a digraph. The digraph depicting the influence of each dimension is converted into an adjacency matrix. The permanent function value of the adjacency matrix is called the resilience index (RI).FindingsThe proposed approach has been illustrated in context of an Indian automobile organization, and value of the RI is evaluated. The best case and the worst-case values are also obtained with the help of GTA. It is noted from the model that strategic level dimension of enablers is most important in contributing towards supply chain resilience. They are followed by tactical and operational level enablers. The GTA framework proposed will help supply chain practitioners to evaluate and benchmark the supply chain resilience of their respective organizations with the best in the industry.Originality/valueA firm can compare the RI of its own supply chain with other's supply chain or with the best in the industry for benchmarking purpose. Benchmarking of resilience will help organizations in developing strategies to compete in dynamic market scenario.

Uniform asymptotic stability, an initial treatment

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Single Point ◽  
Fundamental Property ◽  
Uniform Asymptotic Stability ◽  
Closed Set ◽  
Long Term Trends ◽  
Engineered Systems

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered systems. It provides qualitative information about solutions, especially a characterization of the solutions' long-term trends. The asymptotic stability of a closed set, rather than of an equilibrium point, is significant since the solutions of a hybrid system often do not settle down to an equilibrium point. Furthermore, the asymptotic stability of an equilibrium point is a special case of asymptotic stability of a closed set. Namely, an equilibrium point is a closed set containing a single point.

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