Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fault properties”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Superconductivity in type-II Weyl-semimetal WTe 2 induced by a normal metal contact

WTe 2 is a material with rich topological properties: it is a 2D topological insulator as a monolayer and a Weyl-semimetal and higher-order topological insulator in a bulk form. Inducing superconductivity in topological materials is a way to obtain topological superconductivity, which lays at the foundation for many proposals of fault tolerant quantum computing. Here, we demonstrate the emergence of superconductivity at the interface between WTe 2 and the normal metal palladium. The superconductivity has a critical temperature of about 1.2 K. By studying the superconductivity in a perpendicular magnetic field, we obtain the coherence length and the London penetration depth. These parameters correspond to a low Fermi velocity and a high density of states at the Fermi level. This hints to a possible origin of superconductivity due to the formation of flatbands. Furthermore, the critical in-plane magnetic field exceeds the Pauli limit, suggesting a non-trivial nature of the superconducting state.

Kononov, Artem↗

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗

The importance of properties in modeling

Casting and welding of superalloys, stainless steel and titanium alloys are processes which can be improved through modeling of heat flow, fluid flow, residual stress development, and microstructural evolution. These simulations require inputs of thermophysical data, some of which involves the partially or totally liquid state. In particular, these processes involve melting, flow in the liquid, and solidification. Modeling of such processes can lead to an improved understanding of defects such as shrinkage, inclusions, cracks, incomplete filling (or penetration), macrosegregation, improper grain structure, and deviations from dimensional specifications. Effective modeling can shorten process development time and improve quality. An approach to these problems is to develop efficient models; validate through correlations with thermal, distortion, and microstructural data; run parametric studies; extract knowledge based rules; and apply to adaptive closed loop control systems. With the appropriate pre- and post-processing, such analyses can be made 'user friendly'. This would include graphical user interfaces as well as realistic images and color maps. In such form, these models can be used for sensitivity analyses, which are useful in defining appropriate sensors and in the development of control strategies. Such modeling can be done at several levels, e.g., the MARO level, modeling large scale phenomena such as heat and fluid flow or material deformation; the MICRO level, modeling the development of dendrites, grains or precipitates; or at the NANO level, modeling point defects, dislocations, stacking faults, etc. There are many computational issues associated with these simulations, e.g. computational efficiency and accuracy. In addition, there are many materials issues, not the least of which is the availability of accurate high temperature thermophysical data for complex alloys. This would include latent heat of fusion, temperature dependent heat capacity and thermal conductivity (for liquid and solid), viscosity, surface tension, thermal expansion, mechanical properties, etc. Preliminary data is frequently gathered from the literature; however, this is often not available for modern alloys. If additional data are required, measurements can be used; however, these are costly, time consuming and can be erroneous due to a lack of testing standards or impure materials. Microstructural predictors can be extracted from thermal information, e.g. cooling rate and thermal gradient; the prediction of microstructure is dependent on solidus and liquidus temperature, mushy zone permeability, the solidification curve, volume changes, phase transformations, alloying effects (such as surface tension or viscosity), mold/metal reactions, metal/environment reactions, etc. Defect maps may be needed to predict the onset of shrinkage, hot cracking or 'freckling'. Constants may be needed for stress relaxation, dendrite coarsening, vaporization, etc. Visualization was used as a tool to better comprehend complex data sets associated with the analysis of directional solidification (including crystal growth) and welding. Examples include not only isotherms, but also cooling rate, growth rate and thermal gradient. The latter two are not single valued scalars, but rather time and space dependent vector fields. Efficient models were developed for both casting and welding to predict heat flow and the relationship to dendrite and grain growth. These codes include many of the non-linear effects, e.g. radiation, which dominate these processes. The home-built FDM code(s) were designed to be useful not only to the scientist, but also to the process engineer. Special output can be requested to compare directly to experimental data. Visualization procedures were developed to visualize critical results, e.g. fusion zone width at the surface opposite that where the arc is applied ('penetration'). Both elaborate and simplified distortion analyses were carried out. It is clear that extensive mechanical property data are critical in order to accurately predict residual stress patterns. A scheme is currently being developed to integrate these modeling tools into a set of control algorithms; however, the success of this approach is critically dependent on the availability of accurate high temperature thermophysical data.

Giamei, A. F.↗

Evolution of Pore Structure and Permeability of Rocks Under Hydrothermal Conditions (Final Report)

The physical and transport properties of porous rocks can be altered by a variety of diagenetic, metamorphic, and tectonic processes, and the changes that result are of critical importance to such industrial applications as resource recovery, carbon dioxide sequestration, and waste isolation in geologic formations. The associated interrelationships between rocks, pore fluids and deformation are also key to understanding many natural processes, including dynamic metamorphism, fault mechanics, fault stability and pressure solution creep. In this project, we investigated the changes of permeability and pore geometry owing to inelastic deformation by solution-transfer, brittle fracturing and dislocation creep. In particular, we studied the coupling between pore fluids and deformation in fluid-filled quartz, calcite, mudstones and ultramafic rocks and examine the effects of coupled mechanical and chemical processes on the evolution of porosity and permeability under hydrothermal conditions. The investigations used a combination of techniques, that included triaxial laboratory experiments; uniaxial compressive loading with in situ observations of microstructure; permeability under hydrostatic compression; observations of microstructure using optical and electron microscopes, and micro-CT imaging; and numerical calculations. Laboratory experiments were designed to provide mechanical and transport data under conditions that isolate the particular mechanisms responsible for the changes. The data obtained were used to quantify changes in surface roughness, porosity, pore dimensions and their spatial fluctuations. The results of the experiments and data from image analyses were compared to the results of network, finite-difference and other numerical models to verify the validity of experimentally established relations between permeability and other rock properties. A bibliography for the period from 2015-2019 is appended below. New results obtained in the final year and the unfunded extension period are detailed below.

58 GEOSCIENCES↗

Experimental study of fracture slip due to stress perturbation in fractured geo-resources

Anthropogenic activities such as underground fluid injection/extraction, well stimulation, and dam impoundment will perturb the state-of-stress in the subsurface, which could activate critically stressed pre-existing fractures and faults. Fault and fracture activation can induce seismicity, change flow behavior, and damage asperities on the fracture surface to alter reservoir permeability. Here, in this study, triaxial shear tests were conducted on saw cut and rough fracture Barre granite specimens to better characterize how a decrease in normal stress and increase in shear stress will influence crystalline rock fracture hydromechanical properties. In a triaxial set up, confining pressure (CP) and differential stress (DS) were used to induce normal and shear stress on a 45° oriented fracture. Fracture slip and the corresponding stress relaxation was observed when the confining stress decreased. Fracture permeability increased when the fracture slipped. Moreover, new micro-cracks observed by x-ray images indicated the creation of new flow paths for fluid movement. The experimental outcomes of this study indicate that decrease in normal stress due to stress perturbations along the faults/fractures in the extensional stress regime can induce the slip along the fracture. This could have a significant influence on slope stability in quarries, stimulation and injection strategy in deep geo-resources, and potentially minimize the risk of induced seismicity. The observed stress dependency of hydraulic aperture in rough fracture during pre- and post-slip stages could provide key inputs for field-scale simulation of geo-resources.

58 GEOSCIENCES↗

Structure-dependent clustering-to-declustering solute segregation transitions near disconnections

Grain-boundary disconnections, characterized by a step and a dislocation, are pervasive interfacial line defects that play a critical role in governing the properties and performance of nanocrystalline alloys. Although segregation of alloying elements is frequently observed at GB disconnections, the underlying mechanisms remain poorly understood, particularly at elevated temperatures and non-dilute conditions. In this study, we employ atomistic simulations to study the segregation behavior of Ag at various faulted disconnections in Cu as a model material system. Our results demonstrate a pronounced size and compactness effect on the segregation behavior: more compact faulted disconnection structures promote the formation of Ag segregation clusters due to a highly localized tensile field, whereas more spread faulted disconnection structures (i.e., with wider partial dislocation spacing) exhibit much weaker clustering tendencies. Furthermore, with increasing temperature, Ag clustering in small disconnections initially intensifies and then disappears, indicating a thermally driven transition from clustering to declustering segregation behavior.

Disconnections↗

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS) Milestone 6.0: Evaluation of Class VI Readiness

Introduction. Project OASIS is approximately 30 miles southeast of Birmingham, Alabama, and approximately 5 miles north-northwest of Alabama Power Company's Plant Gaston. Geologically, the Project area is in the Alabama fold and thrust belt province. This work builds on the initiatives of the Southeast Regional Carbon Utilization and Storage Acceleration Partnership (SECARB-USA, DE-FE0031830) that identified nearly 500 million metric tonnes of CO 2 emitted on an annual basis that is not collocated with prospective storage geology (the Coastal Plain of the Southeastern US in this context). This observation suggests costly investments in connective infrastructure (e.g., pipelines) or exploratory well drilling campaigns to identify CO 2 storage opportunities in under explored areas. While not traditionally thought of for saline storage, these studies suggest that storage prospects in the Valley and Ridge Province occur in relatively flat lying structural panels between thrust faults. For the Project OASIS region, available geologic studies related to hydrocarbon exploration suggest that Cambro-Ordovician carbonates and Cambrian clastic units offer multiple potential storage intervals, and that regional confining systems are present, such as the tectonically thickened Floyd-Parkwood Shale. The Project OASIS surface property is owned by a timber and land stewardship company, The Westervelt Company, Inc., who worked with the Project Team to select and prepare adequate sites for geologic assessment. The purpose of drilling the Westover Stratigraphic Test Well #2 was to collect geologic data to model the feasibility of commercial scale CO 2 injection and storage in an under explored region. This initiative benefits the regions emitters as the data generated from this study can inform their own internal decision making. The field program included geological and geophysical evaluations, reservoir engineering analyses, and risk assessments. This report evaluates existing data, as well as a variety of modeling scenarios to evaluate project readiness. Importantly, the impact of this study is not limited to Alabama as there are numerous large emitters throughout Appalachia, in similar geologic settings, contemplating their decarbonization options.

20 FOSSIL-FUELED POWER PLANTS↗

Optimizing Alabama’s CO 2 Storage in Shelby County (Project OASIS), Task 5.0 Deliverable: Infrastructure Assessment Report

The “Optimizing Alabama’s CO 2 Storage in Shelby County: Project OASIS” CarbonSAFE Phase II Project seeks to build on regional data sets that demonstrate that the subsurface within Shelby County, Alabama has the potential to store commercial volumes of CO 2 safely, permanently, and economically. This work builds on the initiatives of the Southeast Regional Carbon Utilization and Storage Acceleration Partnership (SECARB-USA, DE-FE0031830) that identified nearly 500 million metric tonnes of CO 2 emitted on an annual basis that is not collocated with prospective storage geology (the Coastal Plain of the Southeastern U.S. in this context). This observation suggests costly investments in connective infrastructure (e.g., pipelines) or exploratory well drilling campaigns to identify CO 2 storage opportunities in under explored areas. While not traditionally thought of for saline storage, these studies suggest that storage prospects in the Valley and Ridge Province occur in relatively flat lying structural panels between thrust faults. For the Project OASIS region, available geologic studies related to hydrocarbon exploration suggest that Cambro-Ordovician carbonates and Cambrian clastic units offer multiple potential storage intervals, and that regional confining systems are present, such as the tectonically thickened Floyd-Parkwood Shale. The Project OASIS surface property is owned by a timber and land stewardship company, The Westervelt Company, Inc., who worked with the Project Team to select and prepare adequate sites for geologic assessment.

20 FOSSIL-FUELED POWER PLANTS↗

Co-introduction of precipitate hardening and TRIP in a TWIP high-entropy alloy using friction stir alloying

Tuning deformation mechanisms is imperative to overcome the well-known strength-ductility paradigm. Twinning-induced plasticity (TWIP), transformation-induced plasticity (TRIP) and precipitate hardening have been investigated separately and have been altered to achieve exceptional strength or ductility in several alloy systems. In this study, we use a novel solid-state alloying method—friction stir alloying (FSA)—to tune the microstructure, and a composition of a TWIP high-entropy alloy by adding Ti, and thus activating site-specific deformation mechanisms that occur concomitantly in a single alloy. During the FSA process, grains of the as-cast face-centered cubic matrix were refined by high-temperature severe plastic deformation and, subsequently, a new alloy composition was obtained by dissolving Ti into the matrix. After annealing the FSA specimen at 900 °C, hard Ni–Ti rich precipitates formed to strengthen the alloy. An additional result was a Ni-depleted region in the vicinity of newly-formed precipitates. The reduction in Ni locally reduced the stacking fault energy, thus inducing TRIP-based deformation while the remaining matrix still deformed as a result of TWIP. Our current approach presents a novel microstructural architecture to design alloys, an approach that combines and optimizes local compositions such that multiple deformation mechanisms can be activated to enhance engineering properties.

36 MATERIALS SCIENCE↗

Strength, deformation, and the fcc–hcp phase transition in condensed Kr and Xe to the 100 GPa pressure range

The rare gas solids exhibit systematic differences in crystal structure, phase transition conditions, bond strength, and other physical properties. The physical properties of heavy rare gas solids krypton and xenon are modified by the martensitic phase transition from face-centered cubic to hexagonal close packed structure over a broad pressure range. Crystal structure, strength, and plastic deformation of krypton and xenon have been investigated at 300 K using compression in the diamond-anvil cell with synchrotron angle-dispersive x-ray diffraction and complementary ruby fluorescence spectroscopy for Xe. Stacking faults indicative of the fcc–hcp phase transition are observed at pressures at and above 1.23 ± 0.05 and 1.9 ± 0.6 GPa in Kr and Xe, respectively. The transition remains incomplete in both solids to pressures greater than 100 GPa. Strength determined from stress measurements in Pt and ruby standards at pressures up to 111 GPa and complemented by observations of strain and texture measurements obtained by x-ray diffraction in the radial geometry to 100 GPa indicates similar or higher strength than Ar at all conditions, with significant stiffening at 15–20 GPa. Radial diffraction data reveal the persistence of broad highly textured fcc diffraction lines to 101 GPa in Xe, suggesting that the axial measurements may underestimate the metastable persistence of the fcc phase due to biased sampling of hcp crystallites resulting from preferred crystallite orientation. Kr and Xe are compared with He, Ne, and Ar for a systematic understanding of physical properties and phase equilibria of rare gas solids.

Compressive stress↗

Stacking disorder and thermal transport properties of α-RuCl 3

α-RuCl 3 , a well-known candidate material for Kitaev quantum spin liquid, is prone to stacking disorder due to the weak van der Waals bonding between the honeycomb layers. After a decade of intensive experimental and theoretical studies, the detailed correlation between stacking degree of freedom, structure transition, magnetic, and thermal transport properties remains unresolved. In this work, we reveal the effects of a small amount of stacking disorder inherent even in high quality α-RuCl 3 crystals. This small amount of stacking disorder results in the variation of the magnetic ordering temperature, and it suppresses the structure transition and thermal conductivity. Crystals with a minimal amount of stacking disorder have a T N > 7.4 K and exhibit a well-defined structure transition around 140 K upon cooling. For those with more stacking faults and a T N below 7 K, the structure transition occurs well below 140 K upon cooling and is incomplete, manifested by the diffuse streaks and the coexistence of both high-temperature and low-temperature phases down to the lowest measurement temperature. Both types of crystals exhibit oscillatory field-dependent thermal conductivity and a plateaulike feature in thermal Hall resistivity in the field-induced quantum spin liquid state. However, α-RuCl 3 crystals with a minimal amount of stacking disorder have a higher thermal conductivity that pushes the thermal Hall conductivity to be closer to the half-integer quantized value. Importantly, these findings demonstrate a strong correlation between layer stacking, structure transition, magnetic, and thermal transport properties, underscoring the importance of interlayer coupling in α-RuCl3 despite the weak van der Waals bonding.

36 MATERIALS SCIENCE↗

Foreshock properties illuminate nucleation processes of slow and fast laboratory earthquakes

Understanding the connection between seismic activity and the earthquake nucleation process is a fundamental goal in earthquake seismology with important implications for earthquake early warning systems and forecasting. We use high-resolution acoustic emission (AE) waveform measurements from laboratory stick-slip experiments that span a spectrum of slow to fast slip rates to probe spatiotemporal properties of laboratory foreshocks and nucleation processes. We measure waveform similarity and pairwise differential travel-times (DTT) between AEs throughout the seismic cycle. AEs broadcasted prior to slow labquakes have small DTT and high waveform similarity relative to fast labquakes. We show that during slow stick-slip, the fault never fully locks, and waveform similarity and pairwise differential travel times do not evolve throughout the seismic cycle. In contrast, fast laboratory earthquakes are preceded by a rapid increase in waveform similarity late in the seismic cycle and a reduction in differential travel times, indicating that AEs begin to coalesce as the fault slip velocity increases leading up to failure. These observations point to key differences in the nucleation process of slow and fast labquakes and suggest that the spatiotemporal evolution of laboratory foreshocks is linked to fault slip velocity.

58 GEOSCIENCES↗

Discontinuous Galerkin discretization for quantum simulation of chemistry

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations—on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O(N 4.5 ) in molecular orbital representations to O(N 2.6 ) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1–2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deformation modeling and constitutive modeling for anisotropic superalloys

A study of deformation mechanisms in the single crystal superalloy PWA 1480 was conducted. Monotonic and cyclic tests were conducted from 20 to 1093 C. Both (001) and near-(123) crystals were tested, at strain rates of 0.5 and 50 percent/minute. The deformation behavior could be grouped into two temperature regimes: low temperatures, below 760 C; and high temperatures, above 820 to 950 C depending on the strain rate. At low temperatures, the mechanical behavior was very anisotropic. An orientation dependent CRSS, a tension-compression asymmetry, and anisotropic strain hardening were all observed. The material was deformed by planar octahedral slip. The anisotropic properties were correlated with the ease of cube cross-slip, as well as the number of active slip systems. At high temperatures, the material was isotropic, and deformed by homogeneous gamma by-pass. It was found that the temperature dependence of the formation of superlattice-intrinsic stacking faults was responsible for the local minimum in the CRSS of this alloy at 400 C. It was proposed that the cube cross-slip process must be reversible. This was used to explain the reversible tension-compression asymmetry, and was used to study models of cross-slip. As a result, the cross-slip model proposed by Paidar, Pope and Vitek was found to be consistent with the proposed slip reversibility. The results were related to anisotropic viscoplastic constitutive models. The model proposed by Walter and Jordan was found to be capable of modeling all aspects of the material anisotropy. Temperature and strain rate boundaries for the model were proposed, and guidelines for numerical experiments were proposed.

Milligan, Walter W.↗

Estimation in a discrete tail rate family of recapture sampling models

In the context of recapture sampling design for debugging experiments the problem of estimating the error or hitting rate of the faults remaining in a system is considered. Moment estimators are derived for a family of models in which the rate parameters are assumed proportional to the tail probabilities of a discrete distribution on the positive integers. The estimators are shown to be asymptotically normal and fully efficient. Their fixed sample properties are compared, through simulation, with those of the conditional maximum likelihood estimators.

Gupta, Rajan↗

Formal Methods for Verification and Validation of Partial Specifications: A Case Study

This paper describes our work exploring the suitability of formal specification methods for independent verification and validation (IV&V) of software specifications for large, safety critical systems. An IV&V contractor often has to perform rapid analysis on incomplete specifications, with no control over how those specifications are represented. Lightweight formal methods show significant promise in this context, as they offer a way of uncovering major errors, without the burden of full proofs of correctness. We describe a case study of the use of partial formal models for V&V of the requirements for Fault Detection Isolation and Recovery on the space station. We conclude that the insights gained from formalizing a specification are valuable, and it is the process of formalization, rather than the end product that is important. It was only necessary to build enough of the formal model to test the properties in which we were interested. Maintenance of fidelity between multiple representations of the same requirements (as they evolve) is still a problem, and deserves further study.

Easterbrook, Steve↗

Algorithms for Spectral Decomposition with Applications to Optical Plume Anomaly Detection

The analysis of spectral signals for features that represent physical phenomenon is ubiquitous in the science and engineering communities. There are two main approaches that can be taken to extract relevant features from these high-dimensional data streams. The first set of approaches relies on extracting features using a physics-based paradigm where the underlying physical mechanism that generates the spectra is used to infer the most important features in the data stream. We focus on a complementary methodology that uses a data-driven technique that is informed by the underlying physics but also has the ability to adapt to unmodeled system attributes and dynamics. We discuss the following four algorithms: Spectral Decomposition Algorithm (SDA), Non-Negative Matrix Factorization (NMF), Independent Component Analysis (ICA) and Principal Components Analysis (PCA) and compare their performance on a spectral emulator which we use to generate artificial data with known statistical properties. This spectral emulator mimics the real-world phenomena arising from the plume of the space shuttle main engine and can be used to validate the results that arise from various spectral decomposition algorithms and is very useful for situations where real-world systems have very low probabilities of fault or failure. Our results indicate that methods like SDA and NMF provide a straightforward way of incorporating prior physical knowledge while NMF with a tuning mechanism can give superior performance on some tests. We demonstrate these algorithms to detect potential system-health issues on data from a spectral emulator with tunable health parameters.

Srivastava, Askok N.↗

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗