A Probabilistic Model for LCF

Fatigue life of components or test specimens often exhibit a significant scatter. Furthermore, size effects have a non-negligible influence on fatigue life of parts with different geometries. We present a new probabilistic model for low-cycle fatigue (LCF) in the context of polycrystalline metal. The model takes size effects and inhomogeneous strain fields into account by means of the Poisson point process (PPP). This approach is based on the assumption of independently occurring LCF cracks and the Coffin-Manson-Basquin (CMB) equation. Within the probabilistic model, we give a new and more physical interpretation of the CMB parameters which are in the original approach no material parameters in a strict sense, as they depend on the specimen geometry. Calibration and validation of the proposed model is performed using results of strain controlled LCF tests of specimens with different surface areas. The test specimens are made of the nickel base superalloy RENE 80.Comment: 20 pages, 6 figure

Probabilistic Model-Based Safety Analysis

Model-based safety analysis approaches aim at finding critical failure combinations by analysis of models of the whole system (i.e. software, hardware, failure modes and environment). The advantage of these methods compared to traditional approaches is that the analysis of the whole system gives more precise results. Only few model-based approaches have been applied to answer quantitative questions in safety analysis, often limited to analysis of specific failure propagation models, limited types of failure modes or without system dynamics and behavior, as direct quantitative analysis is uses large amounts of computing resources. New achievements in the domain of (probabilistic) model-checking now allow for overcoming this problem. This paper shows how functional models based on synchronous parallel semantics, which can be used for system design, implementation and qualitative safety analysis, can be directly re-used for (model-based) quantitative safety analysis. Accurate modeling of different types of probabilistic failure occurrence is shown as well as accurate interpretation of the results of the analysis. This allows for reliable and expressive assessment of the safety of a system in early design stages

Lazy Probabilistic Model Checking without Determinisation

The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic B\"uchi automata is the inclusion of a determinisation step of the automaton under consideration. In this paper, we show that full determinisation can be avoided: subset and breakpoint constructions suffice. We have implemented our approach---both explicit and symbolic versions---in a prototype tool. Our experiments show that our prototype can compete with mature tools like PRISM.Comment: 38 pages. Updated version for introducing the following changes: - general improvement on paper presentation; - extension of the approach to avoid full determinisation; - added proofs for such an extension; - added case studies; - updated old case studies to reflect the added extensio

Probabilistic Model Counting with Short XORs

The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique solutions. While theoretically sound, the random parity constraints in that construction have the following drawback: each constraint, on average, involves half of all variables. As a result, the branching factor associated with searching for models that also satisfy the parity constraints quickly gets out of hand. In this work we prove that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added. Our work is based on the realization that the essential feature for random systems of parity constraints to be useful in probabilistic model counting is that the geometry of their set of solutions resembles an error-correcting code.Comment: To appear in SAT 1