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Relevant bibliographies by topics / Probabilities – Mathematical models

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Academic literature on the topic 'Probabilities – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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Journal articles on the topic "Probabilities – Mathematical models"

1

Raup, David M. "Mathematical models of cladogenesis." Paleobiology 11, no. 1 (1985): 42–52. http://dx.doi.org/10.1017/s0094837300011386.

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The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.

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Bronevich, A. G., and I. N. Rosenberg. "Applying models of imprecise probabilities in the mathematical theory of criteria importance." Automation and Remote Control 78, no. 8 (August 2017): 1460–73. http://dx.doi.org/10.1134/s0005117917080070.

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Lomeli, Luis Martinez, Abdon Iniguez, Prasanthi Tata, Nilamani Jena, Zhong-Ying Liu, Richard Van Etten, Arthur D. Lander, Babak Shahbaba, John S. Lowengrub, and Vladimir N. Minin. "Optimal experimental design for mathematical models of haematopoiesis." Journal of The Royal Society Interface 18, no. 174 (January 2021): 20200729. http://dx.doi.org/10.1098/rsif.2020.0729.

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The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.

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Loucopoulos, Constantine. "Effect of prior probabilities on the classificatory performance of parametric and mathematical programming approaches to the two-group discriminant problem." Journal of Applied Mathematics and Decision Sciences 1, no. 1 (January 1, 1997): 45–51. http://dx.doi.org/10.1155/s1173912697000047.

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A mixed-integer programming model (MIP) incorporating prior probabilities for the two-group discriminant problem is presented. Its classificatory performance is compared against that of Fisher's linear discrimininant function (LDF) and Smith's quadradic discriminant function (QDF) for simulated data from normal and nonnormal populations for different settings of the prior probabilities of group membership. The proposed model is shown to outperform both LDF and QDF for most settings of the prior probabilities when the data are generated from nonnormal populations but underperforms the parametric models for data generated from normal populations.

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Forrester, P. J., and G. E. Andrews. "Height probabilities in solid-on-solid models. II." Journal of Physics A: Mathematical and General 20, no. 13 (September 11, 1987): 4465–81. http://dx.doi.org/10.1088/0305-4470/20/13/046.

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Forrester, P. J., and G. E. Andrews. "Height probabilities in solid-on-solid models. I." Journal of Physics A: Mathematical and General 19, no. 15 (October 21, 1986): L923—L926. http://dx.doi.org/10.1088/0305-4470/19/15/011.

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Zhao, Ming-Jie, and Herbert Jaeger. "Norm-Observable Operator Models." Neural Computation 22, no. 7 (July 2010): 1927–59. http://dx.doi.org/10.1162/neco.2010.03-09-983.

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Hidden Markov models (HMMs) are one of the most popular and successful statistical models for time series. Observable operator models (OOMs) are generalizations of HMMs that exhibit several attractive advantages. In particular, a variety of highly efficient, constructive, and asymptotically correct learning algorithms are available for OOMs. However, the OOM theory suffers from the negative probability problem (NPP): a given, learned OOM may sometimes predict negative probabilities for certain events. It was recently shown that it is undecidable whether a given OOM will eventually produce such negative values. We propose a novel variant of OOMs, called norm-observable operator models (NOOMs), which avoid the NPP by design. Like OOMs, NOOMs use a set of linear operators to update system states. But differing from OOMs, they represent probabilities by the square of the norm of system states, thus precluding negative probability values. While being free of the NPP, NOOMs retain most advantages of OOMs. For example, NOOMs also capture (some) processes that cannot be modeled by HMMs. More importantly, in principle, NOOMs can be learned from data in a constructive way, and the learned models are asymptotically correct. We also prove that NOOMs capture all Markov chain (MC) describable processes. This letter presents the mathematical foundations of NOOMs, discusses the expressiveness of the model class, and explains how a NOOM can be estimated from data constructively.

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PYKACZ, JAROSŁAW, and BART D'HOOGHE. "BELL-TYPE INEQUALITIES IN FUZZY PROBABILITY CALCULUS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 02 (April 2001): 263–75. http://dx.doi.org/10.1142/s021848850100079x.

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Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved that if we use fuzzy set intersections pointwisely generated by Frank's fundamental triangular norms Ts(x,y), then the borderline between fuzzy probability models that can be distinguished from Kolmogorovian ones and these fuzzy probability models that cannot be distinguished is for [Formula: see text].

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Raza, Ahmed, and Vladimir Ulansky. "Optimization of Condition Monitoring Decision Making by the Criterion of Minimum Entropy." Entropy 21, no. 12 (December 4, 2019): 1193. http://dx.doi.org/10.3390/e21121193.

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Condition-based maintenance (CBM) is a promising technique for a wide variety of deteriorating systems. Condition-based maintenance’s effectiveness largely depends on the quality of condition monitoring. The majority of CBM mathematical models consider perfect inspections, in which the system condition is assumed to be determined error-free. This article presents a mathematical model of CBM with imperfect condition monitoring conducted at discrete times. Mathematical expressions were derived for evaluating the probabilities of correct and incorrect decisions when monitoring the system condition at a scheduled time. Further, these probabilities were incorporated into the equation of the Shannon entropy. The problem of determining the optimal preventive maintenance threshold at each inspection time by the criterion of the minimum of Shannon entropy was formulated. For the first time, the article showed that Shannon’s entropy is a convex function of the preventive maintenance threshold for each moment of condition monitoring. It was also shown that the probabilities of correct and incorrect decisions depend on the time and parameters of the degradation model. Numerical calculations show that the proposed approach to determining the optimal preventive maintenance threshold can significantly reduce uncertainty when deciding on the condition of the monitoring object.

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Neustroev, S. S., V. I. Serdyukov, N. A. Serdyukova, and S. I. Shishkina. "Mathematical Modeling-based Analysis from the Great Patriotic War Events." Mathematics and Mathematical Modeling, no. 3 (August 25, 2019): 25–35. http://dx.doi.org/10.24108/mathm.0319.0000189.

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When fighting against terrorism in modern armed conflicts, combat vehicles, including tanks, are widely used. To minimise own losses of vehicles and personnel for overthrowing enemy is a relevant task. To solve it, the paper considers certain events in the history of the Great Patriotic War, which are associated with battle of tanks that spring an ambush. A mathematical model of the battle is built. The state graph of the system is given. Using this graph, a probability of tank kills and a ratio of mathematical expectations of losses have been calculated. This mathematical model generalizes the models, previously published in this journal, based on the Markov chain apparatus. The paper gives an example of calculations for this model in the particular case in which experimental data are used as a basis. The ratios of mathematical expectations of losses of the warring parties are obtained. Further, we consider the mathematical models, in which it is assumed that probabilities for tank crews to provide operations of targets detection in firing are known. With technology development and its mathematical support it becomes increasingly more real. The formulas to obtain the probability of tank kills are given according to the graph of states using the known probabilities of transition from one state to another. In each of the three mathematical models under consideration there is a graph of the system state, which allows calculation of the tank kills probability. We have analysed the models to prove a significant dependence of the loss ratio of the warring parties on the number of firing positions used by the tank in ambush in case re-siting is unnoticeable for the enemy. The authors-considered models that use the examples of historical events confirm that the tactics of organising and conducting ambushes in tank battles can be successfully used nowadays, when the technology intensiveness of the opposing forces significantly grows. The obtained results can be applied to organise and conduct tank ambushes in modern armed conflicts and fight against terrorist army.

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Dissertations / Theses on the topic "Probabilities – Mathematical models"

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Gong, Qi, and 龔綺. "Gerber-Shiu function in threshold insurance risk models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40987966.

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Wan, Lai-mei. "Ruin analysis of correlated aggregate claims models." Thesis, Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B30705708.

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Huang, Sheng, and 黄盛. "Some properties of [¯gamma*n] and error control with group network codes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46606117.

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Wei, Zhenghong. "Empirical likelihood based evaluation for value at risk models." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/896.

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Kwan, Kwok-man, and 關國文. "Ruin theory under a threshold insurance risk model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B38320034.

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Dunster, Joanne L. "Mathematical models of soft tissue injury repair : towards understanding musculoskeletal disorders." Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/27797/.

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The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a role. The coagulation cascade and the subsequent formation of the enzyme thrombin are central to the creation of blood clots. By focusing on a subset of reactions that occur within the coagulation cascade, we develop a model that exhibits a rich asymptotic structure. Using singular perturbation theory we produce a sequence of simpler time-dependent model which enable us to elucidate the physical mechanisms that underlie the cascade and the formation of thrombin. There is considerable interest in identifying new therapeutic targets within the coagulation cascade, as current drugs for treating pathological coagulation (thrombosis) target multiple factors and cause the unwelcome side effect of excessive bleeding. Factor XI is thought to be a potential therapeutic target, as it is implicated in pathological coagulation but not in haemostasis (the stopping of bleeding), but its mechanism of activation is controversial. By extending our previous model of the coagulation cascade to include the whole cascade (albeit in a simplistic way) we use numerical methods to simulate experimental data of the coagulation cascade under normal as well as specific-factor-deficient conditions. We then provide simulations supporting the hypothesis that thrombin activates factor XI. The interest in inflammation is now increasing due to it being implicated in such diverse conditions as Alzmeimer's disease, cancer and heart disease. Inflammation can either resolve or settle into a self-perpetuating condition which in the context of soft tissue repair is termed chronic inflammation. Inflammation has traditionally been thought gradualIy to subside but new biological interest centres on the anti-inflammatory processes (relating to macrophages) that are thought to promote resolution and the pro-inflammatory role that neutrophils can provide by causing damage to healthy tissue. We develop a new ordinary differential equation model of the inflammatory process that accounts for populations of neutrophils and macrophages. We use numerical techniques and bifurcation theory to characterise and elucidate the physiological mechanisms that are dominant during the inflammatory phase and the roles they play in the healing process. There is therapeutic interest in modifying the rate of neutrophil apoptosis but we find that increased apoptosis is dependent on macrophage removal to be anti-inflammatory. We develop a simplified version of the model of inflammation reducing a system of nine ordinary equations to six while retaining the physical processes of neutrophil apoptosis and macrophage driven anti-inflammatory mechanisms. The simplified model reproduces the key outcomes that we relate to resolution or chronic inflammation. We then present preliminary work on the inclusion of the spatial effects of chemotaxis and diffusion.

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Venter, Rudolf Gerrit. "Pricing options under stochastic volatility." Diss., Pretoria : [s.n.], 2003. http://upetd.up.ac.za/thesis/available/etd09052005-120952.

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Sirkin, Jeffrey M. "Quantifying the probabilities of selection of surface warfare officers to executive officer." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2006. http://library.nps.navy.mil/uhtbin/hyperion/06Sep%5FSirkin.pdf.

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Thesis (M.S. in Operations Research)--Naval Postgraduate School, September 2006.
Thesis Advisor(s): Robert A. Koyak. "September 2006." Includes bibliographical references (p. 51). Also available in print.

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Przybyla, Craig Paul. "Microstructure-sensitive extreme value probabilities of fatigue in advanced engineering alloys." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34780.

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A novel microstructure-sensitive extreme value probabilistic framework is introduced to evaluate material performance/variability for damage evolution processes (e.g., fatigue, fracture, creep). This framework employs newly developed extreme value marked correlation functions (EVMCF) to identify the coupled microstructure attributes (e.g., phase/grain size, grain orientation, grain misorientation) that have the greatest statistical relevance to the extreme value response variables (e.g., stress, elastic/plastic strain) that describe the damage evolution processes of interest. This is an improvement on previous approaches that account for distributed extreme value response variables that describe the damage evolution process of interest based only on the extreme value distributions of a single microstructure attribute; previous approaches have given no consideration of how coupled microstructure attributes affect the distributions of extreme value response. This framework also utilizes computational modeling techniques to identify correlations between microstructure attributes that significantly raise or lower the magnitudes of the damage response variables of interest through the simulation of multiple statistical volume elements (SVE). Each SVE for a given response is constructed to be a statistical sample of the entire microstructure ensemble (i.e., bulk material); therefore, the response of interest in each SVE is not expected to be the same. This is in contrast to computational simulation of a single representative volume element (RVE), which often is untenably large for response variables dependent on the extreme value microstructure attributes. This framework has been demonstrated in the context of characterizing microstructure-sensitive high cycle fatigue (HCF) variability due to the processes of fatigue crack formation (nucleation and microstructurally small crack growth) in polycrystalline metallic alloys. Specifically, the framework is exercised to estimate the local driving forces for fatigue crack formation, to validate these with limited existing experiments, and to explore how the extreme value probabilities of certain fatigue indicator parameters (FIPs) affect overall variability in fatigue life in the HCF regime. Various FIPs have been introduced and used previously as a means to quantify the potential for fatigue crack formation based on experimentally observed mechanisms. Distributions of the extreme value FIPs are calculated for multiple SVEs simulated via the FEM with crystal plasticity constitutive relations. By using crystal plasticity relations, the FIPs can be computed based on the cyclic plastic strain on the scale of the individual grains. These simulated SVEs are instantiated such that they are statistically similar to real microstructures in terms of the crystallographic microstructure attributes that are hypothesized to have the most influence on the extreme value HCF response. The polycrystalline alloys considered here include the Ni-base superalloy IN100 and the Ti alloy Ti-6Al-4V. In applying this framework to study the microstructure dependent variability of HCF in these alloys, the extreme value distributions of the FIPs and associated extreme value marked correlations of crystallographic microstructure attributes are characterized. This information can then be used to rank order multiple variants of the microstructure for a specific material system for relative HCF performance or to design new microstructures hypothesized to exhibit improved performance. This framework enables limiting the (presently) large number of experiments required to characterize scatter in HCF and lends quantitative support to designing improved, fatigue-resistant materials and accelerating insertion of modified and new materials into service.

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Reischman, Diann. "Order restricted inferences on parameters in generalized linear models with emphasis on logistic regression /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9842560.

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Books on the topic "Probabilities – Mathematical models"

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Probabilities in physics. Oxford: Oxford University Press, 2011.

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Ross, Sheldon M. Applied probability models with optimization applications. New York: London, 1992.

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Ross, Sheldon M. Applied probability models with optimization applications. New York: Dover Publications, 1992.

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Puppe, Clemens. Distorted probabilities and choice under risk. Berlin: Springer-Verlag, 1991.

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Reeb, J. E. An introduction to models and probability concepts. Corvallis, Or: Oregon State University Extension Service, 1998.

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Reeb, J. E. An introduction to models and probability concepts. Corvallis, Or: Oregon State University Extension Service, 1998.

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Finite mathematics for the managerial, life, and social sciences. Belmont, CA: Brooks/Cole, Cengage Learning, 2012.

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Tan, Soo Tang. Finite mathematics for the managerial, life, and social sciences. 9th ed. Belmont, CA: Brooks/Cole Cengage Learning, 2009.

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Tan, Soo Tang. Finite mathematics for the managerial, life, and social sciences. 7th ed. Pacific Grove, CA: Thomson-Brooks/Cole, 2003.

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Tan, Soo Tang. Finite mathematics for the managerial, life, and social sciences. 6th ed. Pacific Grove, CA: Brooks/Cole, 2000.

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Book chapters on the topic "Probabilities – Mathematical models"

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Hendry, David F. "Mathematical Models and Economic Forecasting: Some Uses and Mis-Uses of Mathematics in Economics." In Probabilities, Laws, and Structures, 319–35. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-3030-4_23.

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Vicig, Paolo. "Conditional and Comparative Probabilities in Artificial Intelligence." In Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, 271–80. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1424-8_19.

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Moral, Serafín, and Nic Wilson. "Revision Rules for Convex Sets of Probabilities." In Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, 113–27. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1424-8_7.

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Kordzakhia, Nino, Alexander Novikov, and Gurami Tsitsiashvili. "On ruin probabilities in risk models with interest rate." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 245–53. Milano: Springer Milan, 2012. http://dx.doi.org/10.1007/978-88-470-2342-0_29.

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Lafuente, Miguel, David Ejea, Raúl Gouet, F. Javier López, and Gerardo Sanz. "Approximations of $$\delta $$-Record Probabilities in i.i.d. and Trend Models." In Trends in Mathematical, Information and Data Sciences, 73–81. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04137-2_8.

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Di Biase, Giuseppe, and Antonio Maturo. "Checking the Coherence of Conditional Probabilities in Expert Systems: Remarks and Algorithms." In Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, 191–200. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1424-8_11.

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Aslett, Louis J. M. "Sampling from Complex Probability Distributions: A Monte Carlo Primer for Engineers." In Uncertainty in Engineering, 15–35. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83640-5_2.

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AbstractModels which are constructed to represent the uncertainty arising in engineered systems can often be quite complex to ensure they provide a reasonably faithful reflection of the real-world system. As a result, even computation of simple expectations, event probabilities, variances, or integration over utilities for a decision problem can be analytically intractable. Indeed, such models are often sufficiently high dimensional that even traditional numerical methods perform poorly. However, access to random samples drawn from the probability model under study typically simplifies such problems substantially. The methodologies to generate and use such samples fall under the stable of techniques usually referred to as ‘Monte Carlo methods’. This chapter provides a motivation, simple primer introduction to the basics, and sign-posts to further reading and literature on Monte Carlo methods, in a manner that should be accessible to those with an engineering mathematics background. There is deliberately informal mathematical presentation which avoids measure-theoretic formalism. The accompanying lecture can be viewed at https://www.louisaslett.com/Courses/UTOPIAE/.

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Boumans, Marcel. "Mathematics as Quasi-matter to Build Models as Instruments." In Probabilities, Laws, and Structures, 307–18. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-3030-4_22.

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Bacharoudis, Konstantinos, Atanas Popov, and Svetan Ratchev. "Application of Advanced Simulation Methods for the Tolerance Analysis of Mechanical Assemblies." In IFIP Advances in Information and Communication Technology, 153–67. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72632-4_11.

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AbstractIn the frame of a statistical tolerance analysis of complex assemblies, for example an aircraft wing, the capability to predict accurately and fast specified, very small quantiles of the distribution of the assembly key characteristic becomes crucial. The problem is significantly magnified, when the tolerance synthesis problem is considered in which several tolerance analyses are performed and thus, a reliability analysis problem is nested inside an optimisation one in a fully probabilistic approach. The need to reduce the computational time and accurately estimate the specified probabilities is critical. Therefore, herein, a systematic study on several state of the art simulation methods is performed whilst they are critically evaluated with respect to their efficiency to deal with tolerance analysis problems. It is demonstrated that tolerance analysis problems are characterised by high dimensionality, high non-linearity of the state functions, disconnected failure domains, implicit state functions and small probability estimations. Therefore, the successful implementation of reliability methods becomes a formidable task. Herein, advanced simulation methods are combined with in-house developed assembly models based on the Homogeneous Transformation Matrix method as well as off-the-self Computer Aided Tolerance tools. The main outcome of the work is that by using an appropriate reliability method, computational time can be reduced whilst the probability of defected products can be accurately predicted. Furthermore, the connection of advanced mathematical toolboxes with off-the-self 3D tolerance tools into a process integration framework introduces benefits to successfully deal with the tolerance allocation problem in the future using dedicated and powerful computational tools.

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Bernhard, Pierre, Jacob C. Engwerda, Berend Roorda, J. M. Schumacher, Vassili Kolokoltsov, Patrick Saint-Pierre, and Jean-Pierre Aubin. "Emergence of Risk-Neutral Probabilities from a Game-Theoretic Origin." In The Interval Market Model in Mathematical Finance, 221–47. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-0-8176-8388-7_12.

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Conference papers on the topic "Probabilities – Mathematical models"

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Ma, Jin, and Xiaodong Sun. "Sharp Estimates of Ruin Probabilities for Insurance Models Involving Investments." In Proceedings of the International Conference on Mathematical Finance. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799579_0007.

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Bruns, Morgan, and Christiaan J. J. Paredis. "Numerical Methods for Propagating Imprecise Uncertainty." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99237.

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Since engineering design requires decision making under uncertainty, the degree to which good decisions can be made depends upon the degree to which the decision maker has expressive and accurate representations of his or her uncertain beliefs. Whereas traditional decision analysis uses precise probability distributions to represent uncertain beliefs, recent research has examined the effects of relaxing this assumption of precision. A specific example of this is the theory of imprecise probability. Imprecise probabilities are more expressive than precise probabilities, but they are also more computationally expensive to propagate through mathematical models. The probability box (p-box) is an alternative representation that is both more expressive than precise probabilities, and less computationally expensive than general imprecise probabilities. In this paper, we introduce a method for propagating p-boxes through black box models. Based on two example models, a new method, called p-box convolution sampling (PCS), is compared with three other p-box propagation methods. It is found that, although PCS is less expensive than the alternatives, it is still relatively expensive and therefore only justifiable when the expected benefits are large. Several directions for further improving the efficiency of PCS are discussed.

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Zheng, Liyu, Janis Terpenny, Peter Sandborn, and Raymond Nelson. "Design Refresh Planning Models for Managing Obsolescence." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70743.

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Fast moving technologies have caused high-tech components to have shortened life cycles, rendering them obsolete quickly. Obsolescence is a significant problem for systems with operational and support life that are much longer than the procurement lifetimes of their constituent components. Design refresh planning is a strategic way of managing obsolescence. Mathematical models are presented herein to determine the design refresh plan that minimizes total cost. The plan includes guidance on when to execute design refreshes (dates) and what obsolete/non-obsolete system components should be replaced at a specific design refresh. When data uncertainty is considered and obsolescence dates of the components are assumed to follow specific probability distributions, different solutions for executing design refreshes and the probabilities of adopting these solutions can be obtained. The final optimal cost becomes an expected value. An example of an electronic engine control unit (ECU) is included for demonstration of the developed models.

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Sandquist, Gary M., and D. Shannon Sentell. "Assessing Aircraft Hazards to Nuclear Facilities." In 12th International Conference on Nuclear Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/icone12-49384.

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The methodology and selected models used for assessing the frequency of aircraft crashes to critical surface facilities are examined. The DOE Standard model is the basis for comparing other models, particularly those used to assess risk to DOE facilities. The NRC methodology is relevant for nuclear power plants. A rigorous physical model that describes the Markov chain of events and their related probabilities that lead to aircraft hazards to ground facilities is developed. The chain of events is then quantified to provide a basis for comparison and evaluation of mathematical models. It is evident that all quantitative models for aircraft crash frequency assessments are constrained by the limited statistical database available for supporting such risk assessments. Aircraft crashes to critical facilities are rare events, and this condition limits experimental data and verification efforts.

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Kupciuniene, Kristina, and Robertas Alzbutas. "External Events Importance for Safety of the Ignalina Nuclear Power Plant." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48230.

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Probabilistic risk analysis of external events impact on the safety important systems of Ignalina nuclear power plant (NPP) is performed. At first, the methodology was established for screening out external events, which impact on Ignalina NPP safety is not significant. In order to estimate probabilities of external events occurrences the statistical data were collected, mathematical models were constructed and probabilities of these events occurrences were determined. For risk estimation, the following external events were studied: forest fires, external floods, aircraft crash, seismic events, extreme winds, fall of frequency in electricity network and loss of an external electricity supply. The aircraft crash event was modeled and analyzed in more detail. The crash probability estimation model is improved considering uncertain data. The aircraft crash probability on the territory of the Ignalina NPP with the radius r is expressed by the derived analytical formula. This formula is used to calculate the aircraft crash probability applying the most recent statistical data. The aircraft crash dependencies upon the amount of flights and crashes in the different radius territories were analyzed. Relationship of non-flying zone around Ignalina NPP and aircraft crash frequency was investigated. As a part of the initial conditions and parameters of aircraft crash model are not well-known or have different values for various types of aircrafts, the sensitivity analysis was performed for the model. This analysis determines the parameters that have the greatest influence on the model results. Conclusions about the importance of the parameters and sensitivity of the results are obtained using a sensitivity measures of the model under analysis.

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Salanova Grau, Josep Maria, and Miquel Estrada Romeu. "Social optimal shifts and fares of taxi services." In CIT2016. Congreso de Ingeniería del Transporte. Valencia: Universitat Politècnica València, 2016. http://dx.doi.org/10.4995/cit2016.2016.3254.

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This paper presents a mathematical model for supporting the decision and policy making related to the optimal determination of shifts and fares of taxi services in a major city. The model is based on the system’s generalized cost function and uses continuous approximations and geometric probabilities for estimating the key performance indicators of the taxi market, which are waiting and access time for the customers (in-vehicle travel time does not depend on the offer side) and benefits for the drivers. The model is based on an econometric model with the inclusion of an elastic demand, which allows the estimation of the optimal values for the two decision variables of the problem: fare structure and the taxi fleet size. The model also accounts for a full-day time period instead of the one-hour time frame models used in most of the taxi models, which allows for providing insights on the daily duration and distribution of the shifts that should be defined by the policy makers.DOI: http://dx.doi.org/10.4995/CIT2016.2016.3254

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Wang, Qian, and Jun Ji. "Reliability Analysis of Underground Structures Using Metamodels and FORM." In IABSE Congress, New York, New York 2019: The Evolving Metropolis. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE), 2019. http://dx.doi.org/10.2749/newyork.2019.1163.

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<p>An engineering reliability analysis method of underground structures using metamodels and a first-order reliability method (FORM) was studied. Surrogate models, or metamodels are approximate models that can be constructed to replace implicit response functions that involve finite element analyses. The radial basis functions (RBFs) are suitable for creating metamodels for general linear or nonlinear responses and they are locally and globally adaptive. After a performance function was replaced by an augmented RBF metamodel, an alternative FORM was applied. The method was tested using mathematical functions and applied to a tunnel engineering example. Different numbers of samples were tested and reliability analyses were performed. The failure probabilities and reliability indices were found to have a good accuracy. The proposed method combining RBFs and FORM is useful for practical engineering problems involving expensive response simulations.</p>

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Kupciuniene, Kristina, and Robertas Alzbutas. "Updated Probabilistic Analysis of External Events Data and Safety of the Nuclear Power Plant in Lithuania." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75736.

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The main purpose of performed work is the probabilistic analysis of extreme external events, which have a potential influence on safety of the present nuclear power plant (NPP) in Lithuania. This analysis can also be related to the future NPP in Lithuania at the same site. At first, the methodology was established for screening out hazardous events, which impact on the present Ignalina NPP safety is not significant. For risk estimation, the following external events were considered in detail: forest fire, external flood, airplane crash, extreme wind. In order to estimate probabilities of hazards occurrence the statistical data related to various external events were collected, mathematical models were constructed and probabilities of these events occurrence were determined. Statistical, meteorological and other updated data from the Republic of Lithuania has been used to estimate probability of the most important hazardous events. Due to many factors affecting the inaccuracy of any result it is not enough to calculate only the estimate of the probability of the event. There is a need also to evaluate errors or variations of result made by such estimation. For such purpose uncertainty and sensitivity analysis was performed for a probability estimate, i.e. frequency of the event. This analysis determines the parameters that have the greatest influence on the probabilistic model results. The modelling of external events occurrence and its impact on the NPP is significant in order to evaluate the safety of NPP and to prevent failure of the systems important to the safety.

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Loboda, Igor, and Sergey Yepifanov. "A Mixed Data-Driven and Model Based Fault Classification for Gas Turbine Diagnosis." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23075.

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In modern gas turbine health monitoring systems, the diagnostic algorithms based on gas path analysis may be considered as principal. They analyze gas path measured variables and are capable of identifying different faults and degradation mechanisms of gas turbine components (e.g. compressor, turbine, and combustor) as well as malfunctions of the measurement system itself. Gas path mathematical models are widely used in building fault classification required for diagnostics because faults rarely occur during field operation. In that case, model errors are transmitted to the model-based classification, which poses the problem of rendering the description of some classes more accurate using real data. This paper looks into the possibility of creating a mixed fault classification that incorporates both model-based and data-driven fault classes. Such a classification will combine a profound common diagnosis with a higher diagnostic accuracy for the data-driven classes. A gas turbine power plant for natural gas pumping has been chosen as a test case. Its real data with cycles of compressor fouling were used to form a data-driven class of the fouling. Preliminary qualitative analysis showed that these data allow creating a representative class of the fouling and that this class will be compatible with simulated fault classes. A diagnostic algorithm was created based on the proposed classification (real class of compressor fouling and simulated fault classes for other components) and artificial neural networks. The algorithm was subjected to statistical testing. As a result, probabilities of a correct diagnosis were determined. Different variations of the classification were considered and compared using these probabilities as criteria. The performed analysis has revealed no limitations for realizing a principle of the mixed classification in real monitoring systems.

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Doraiswamy, Srikanth, and Sundar Krishnamurty. "Bayesian Analysis in Engineering Model Assessment." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dtm-14546.

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Abstract Engineering design decisions often need to be made when complete knowledge of the system is not available. Getting such complete deterministic information may be impossible or impractical as the resources required to get the information may be unaffordable. The challenge then is to identify and construct an information-gathering strategy, one that can be expected to yield most reliable results in an efficient manner during design. In this context, an engineering model can be viewed as an information-gathering strategy, using which predictive information regarding the performance of a design can be acquired by means of mathematical simulation studies. Focusing on this issue, this paper presents the development of a Bayesian analysis based model selection strategy to understand and deal with the uncertainty inherent in engineering models. Specifically, this work offers a basis for assessing engineering models under conditions of uncertainty through a methodical generation of the required probabilities in a Bayesian tree format, and subsequently using it in the selection of the best analysis model from a design decision perspective. The selection of the best model is made under conditions of uncertainty by considering the models’ performance on each design attribute, and based on the payoffs resulting from the design outcomes. The modeling of a windshield-wiper arm is used to illustrate the application of the proposed methodology.

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