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Fast Probability Integration
Fast probability integration (FPI) is a method of determining the probability of a class of events, particularly a failure event, that is faster to execute than Monte Carlo analysis. It is used where large numbers of time-variant variables contribute to the reliability of a system. The method was proposed by Wen and Chen in 1987. For a simple failure analysis with one stress variable, there will be a time-variant failure barrier, r(t), beyond which the system will fail. This simple case may have a deterministic solution, but for more complex systems, such as crack analysis of a large structure, there can be a very large number of variables, for instance, because of the large number of ways a crack can propagate. In many cases, it is infeasible to produce a deterministic solution even when the individual variables are all individually deterministic. In this case, one defines a probabilistic failure barrier surface, \mathbf R (t), over the vector space of the stress variables. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Analysis
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix, which allows computing in vector spaces. This provides a concise and synthetic way for manipulating and studying systems of linear eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Counting Process
A counting process is a stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ... with values that are non-negative, integer, and non-decreasing: # ''N''(''t'') ≥ 0. # ''N''(''t'') is an integer. # If ''s'' ≤ ''t'' then ''N''(''s'') ≤ ''N''(''t''). If ''s'' < ''t'', then ''N''(''t'') − ''N''(''s'') is the number of events occurred during the interval [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Reliability Method
The first-order reliability method, (FORM), is a semi- probabilistic reliability analysis method devised to evaluate the reliability of a system. The accuracy of the method can be improved by averaging over many samples, which is known as Line Sampling. The method is also known as the Hasofer-Lind Reliability Index, developed by Professor Michael Hasofer and Professor Neil Lind in 1974. The index has been recognized as an important step towards the development of contemporary methods to effectively and accurately estimate structural safety. The analysis method depends on a "Most Probable Point" on the limit state C Annis"How FORM/SORM is Supposed to Work"/ref> See also * EN 1990 En or EN may refer to: Businesses * Bouygues (stock symbol EN) * Esquimalt and Nanaimo Railway (reporting mark EN, but now known as Southern Railway of Vancouver Island) * Euronews, a news television and internet channel Language and writing * E ... * Fast probability integration * Stress–streng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding the National Advisory Committee for Aeronautics (NACA), to give the U.S. space development effort a distinctly civilian orientation, emphasizing peaceful applications in space science. NASA has since led most American space exploration, including Project Mercury, Project Gemini, the 1968-1972 Apollo Moon landing missions, the Skylab space station, and the Space Shuttle. NASA supports the International Space Station and oversees the development of the Orion spacecraft and the Space Launch System for the crewed lunar Artemis program, Commercial Crew spacecraft, and the planned Lunar Gateway space station. The agency is also responsible for the Launch Services Program, which provides oversight of launch operations and countdown management f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NESSUS Probabilistic Analysis Software
{{other uses of, Nessus NESSUS is a general-purpose, probabilistic analysis program that simulates variations and uncertainties in loads, geometry, material behavior and other user-defined inputs to compute probability of failure and probabilistic sensitivity measures of engineered systems. Because NESSUS uses highly efficient and accurate probabilistic analysis methods, probabilistic solutions can be obtained even for extremely large and complex models. The system performance can be hierarchically decomposed into multiple smaller models and/or analytical equations. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety critical and one-of-a-kind systems, and to maintain a level of quality while reducing manufacturing costs for larger quantity products. NESSUS is interfaced to all major commercial finite element programs and includes capabilities for analyzing computationally intensive real-world pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Shuttle Main Engine
The Aerojet Rocketdyne RS-25, also known as the Space Shuttle Main Engine (SSME), is a liquid-fuel cryogenic rocket engine that was used on NASA's Space Shuttle and is currently used on the Space Launch System (SLS). Designed and manufactured in the United States by Rocketdyne (later Pratt & Whitney Rocketdyne and Aerojet Rocketdyne), the RS-25 burns cryogenic liquid hydrogen and liquid oxygen propellants, with each engine producing thrust at liftoff. Although RS-25 heritage traces back to the 1960s, its concerted development began in the 1970s with the first flight, STS-1, on April 12, 1981. The RS-25 has undergone upgrades over its operational history to improve the engine's reliability, safety, and maintenance load. The engine produces a specific impulse (''I''sp) of in a vacuum, or at sea level, has a mass of approximately , and is capable of throttling between 67% and 109% of its rated power level in one-percent increments. Components of the RS-25 operate at tempera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Models
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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