Robust Reliability in the Mechanical Sciences

Inhaltsangabe1 Preview of Robust Reliability.- 1.1 Flexible Solar Panel.- 1.2 Quality Control of Thin Shells.- 1.3 Fatigue Failure and Reliability.- 1.4 Plastic Extrusion Manufacturing.- 1.5 Summary.- 2 Convexity and Uncertainty.- 2.1 Complex Uncertainty and Limited Information: Four Examples.- 2.2 Some Convex Models.- 2.3 Expansion of Convex Models.- 2.4 The Structure of Convex Sets.- 2.4.1 Definition of Convexity.- 2.4.2 Extreme Points and Convex Hulls.- 2.4.3 Extrema of Linear Functions on Convex Sets.- 2.4.4 Hyperplane Separation of Convex Sets.- 2.4.5 Linear Systems Driven by Convex Input Sets.- 2.5 Clustering of Uncertain Events: The Convexity Theorem.- 2.6 Problems.- 3 Robust Reliability of Static Systems.- 3.1 Introduction.- 3.2 Beam With An Uncertain Distributed Load.- 3.2.1 Uniform Load Uncertainty.- 3.2.2 Shifted Uniform Load Uncertainty.- 3.2.3 Load-Uncertainty Envelope.- 3.2.4 Fourier Ellipsoid-Bound Uncertainty.- 3.3 Cooling Fin in an Uncertain Flow Field: Reliability and Design.- 3.3.1 Uniform Blade.- 3.3.2 Optimal Thickness Profile.- 3.3.3 Optimal Width and Thickness Profiles.- 3.3.4 Minimum Weight Design.- 3.3.5 Parameter Sensitivity of the Reliability.- 3.4 Beam in Compression With Uncertain Initial Imperfections.- 3.4.1 Band-Limited Energy-Bound Convex Model.- 3.4.2 Fourier Representation of Y (?, N0, N1).- 3.4.3 Maximum Additional Bending Moment.- 3.4.4 Critical-Energy Failure Criterion.- 3.5 Radial Buckling of Thin-Walled Shells; Reliability and Quality Control.- 3.5.1 Localized Imperfections.- 3.5.2 Fourier Ellipsoid-Bound.- 3.6 Reliability of Serial and Parallel Networks.- 3.7 Problems.- 4 Robust Reliability of Time-Varying Systems.- 4.1 Mass and Spring System.- 4.2 Seismic Safety of Secondary Equipment.- 4.2.1 Dynamics.- 4.2.2 Reliability with the Fourier-Envelope Model.- 4.3 Multi-Dimensional Vibrating Structures.- 4.3.1 Formulation.- 4.3.2 Reliability: Hyperplane Separation.- 4.3.3 Input Reliability.- 4.4 Modal Reliability.- 4.4.1 Formulation.- 4.4.2 Coordinate Transformations.- 4.5 Axially Loaded Thin-Walled Shell With Imperfect Initial Shape.- 4.5.1 Dynamics.- 4.5.2 Fourier Ellipsoid Bound.- 4.6 Fatigue Failure and Reliability With Uncertain Loading.- 4.6.1 Damage Evolution.- 4.6.2 Uncertain Load Histories and Maximum Damage Increment.- 4.6.3 The Least-Lifetime Recursion.- 4.6.4 Least-Lifetime With Uncertain Harmonic Loads.- 4.6.5 Fatigue Reliability With Uncertain Harmonic Loads.- 4.6.6 Fatigue Reliability With Complex Uncertain Loads.- 4.7 Problems.- 5 Fault Diagnosis, System Identification and Reliability Testing.- 5.1 Benchmark Diagnostic Resolution: Simple Examples.- 5.1.1 Formulation.- 5.1.2 Single Measurement.- 5.1.3 Variable Measurement Position.- 5.1.4 Multiple Measurements.- 5.1.5 Hyperplane Separation.- 5.1.6 Reliability With Two Measurements.- 5.2 Multi-Hypothesis Diagnosis of Anomalous Inputs.- 5.2.1 Multi-Hypothesis Diagnosis.- 5.2.2 Criterion for Successful Diagnosis 1ll.- 5.2.3 Example.- 5.2.4 Robust Reliability.- 5.3 Least-Squares Estimation.- 5.3.1 Formulation of the Least-Squares Problem.- 5.3.2 Variation of the Least-Squares Solution.- 5.3.3 Estimating a Spectral Centroid.- 5.3.4 Reliability of „Regularized “ Solution.- 5.4 Multi-Hypothesis Diagnosis of a Crack.- 5.4.1 The Eigenvalue Equation.- 5.4.2 The Multi-Hypothesis Algorithm.- 5.4.3 Performance Criterion for the Diagnosis.- 5.4.4 A Useful Theorem.- 5.4.5 Reliability of the Diagnosis.- 5.5 Robust Reliability of Model-Order Determination.- 5.5.1 Formulation.- 5.5.2 Examples.- 5.6 Ill-Posed Problems.- 5.6.1 Column-Space Analysis.- 5.6.2 Multiplicity of Solutions.- 5.7 Selective Sensitivity.- 5.7.1 Basic Concept of Selective Sensitivity.- 5.7.2 Example: 2-Dimensional System.- 5.7.3 Example: Structural Integrity of a Building.- 5.8 Problems.- 6 Reliability of Mathematical Models.- 6.1 Models, Decisions and Reliability.- 6.2 Cooling Fin With Uncertain Geometry.- 6.3 Modal Truncation of a High-Dimensional Model.- 6.4 Robust Multi-Hypothesis Sy

The book deals with analysis of reliability of mechanical systems, structures and devices. It addresses design for reliability, as well as quality assurance and quality control in mechanical manufacturing. This book is unique and non-classical, and reliability is defined non-probalistically as robustness to uncertainty. Convex-set models of uncertainty are described and used, rather than probabilistic models. This approach is particularly suited to the limited information typically available about uncertainties of complex mechanical systems. Static as well as dynamic systems, linear processes such as elastic vibration, and non-linear processes like damage evolution and fatigue failure are studied. Robust reliability is applied to evaluating the reliability of mathematical and convex models of uncertainty are combined in a hybrid reliability analysis applicable in those situations where prior information supports both types of uncertainty models. In short, a widely-applicable theory is developed through general discussion and many examples. Fachgebiet: Mechanical Engineering Zielgruppe: Research and Development