Relevant bibliographies by topics / Multivariate Operator Theory

Academic literature on the topic 'Multivariate Operator Theory'

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Published: 6 September 2023

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Journal articles on the topic "Multivariate Operator Theory"

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Xu, Yuan. "Multivariate orthogonal polynomials and operator theory." Transactions of the American Mathematical Society 343, no. 1 (January 1, 1994): 193–202. http://dx.doi.org/10.1090/s0002-9947-1994-1169912-x.

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Anastassiou, George A. "Multivariate and abstract approximation theory for Banach space valued functions." Demonstratio Mathematica 50, no. 1 (August 28, 2017): 208–22. http://dx.doi.org/10.1515/dema-2017-0020.

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Abstract Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.
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Filipiak, Katarzyna, Daniel Klein, and Erika Vojtková. "The properties of partial trace and block trace operators of partitioned matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 3–15. http://dx.doi.org/10.13001/1081-3810.3688.

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The aim of this paper is to give the properties of two linear operators defined on non-square partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positive-definiteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multi-level multivariate models or in the theory of experiments for the determination of an optimal designs under the linear models.
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Fuchs, David, Steven Sherwood, and Daniel Hernandez. "An Exploration of Multivariate Fluctuation Dissipation Operators and Their Response to Sea Surface Temperature Perturbations." Journal of the Atmospheric Sciences 72, no. 1 (January 1, 2015): 472–86. http://dx.doi.org/10.1175/jas-d-14-0077.1.

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Abstract The fluctuation–dissipation theorem (FDT) has been proposed as a method of calculating the mean response of the atmosphere to small external perturbations. This paper explores the application of the theory under time and space constraints that approximate realistic conditions. To date, most applications of the theory in the climate context used univariate, low-dimensional-state representations of the climate system and an arbitrarily long sample size. The authors explore high-dimensional multivariate FDT operators and the lower bounds of sample size needed to construct skillful operators. It is shown that the skill of the operator depends on the selection of variables and features representing the climate system and that these features change once memory (slab ocean) is added to the system. In addition, it is found that the FDT operator has skill in estimating the response to realistic sea surface temperature (SST) patterns, such as El Niño–Southern Oscillation (ENSO), despite the fact that these patterns were not part of the data used to produce the operator. The response of clouds is also studied; for variables that represent cloud properties, the decrease in skill in relation to decrease in sample size still maintains the key features of the response.
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Hiai, Fumio, Yuki Seo, and Shuhei Wada. "Ando–Hiai type inequalities for multivariate operator means." Linear and Multilinear Algebra 67, no. 11 (June 27, 2018): 2253–81. http://dx.doi.org/10.1080/03081087.2018.1488938.

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Neretin, Yury A. "Multi-operator colligations and multivariate characteristic functions." Analysis and Mathematical Physics 1, no. 2-3 (August 2, 2011): 121–38. http://dx.doi.org/10.1007/s13324-011-0009-y.

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Reich, Nils. "Anisotropic Operator Symbols Arising From Multivariate Jump Processes." Integral Equations and Operator Theory 63, no. 1 (December 22, 2008): 127–50. http://dx.doi.org/10.1007/s00020-008-1645-y.

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Zizler, Peter. "The spectral radius of a multivariate sampling operator." Linear Algebra and its Applications 385 (July 2004): 463–74. http://dx.doi.org/10.1016/j.laa.2003.12.042.

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Chen, Zhong Yin. "The Traits of Two-Directional Orthogonal Multivariate Small-Wave Packages with Finite Support." Advanced Materials Research 430-432 (January 2012): 543–46. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.543.

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In this paper, we introduce the notion of vector-valued multiresolution analysis and two-directional vector-valued multivariate wavelet packages associated with an integer-valued dilation matrix. A novel method for constructing multi-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are establ- lished. Orthogonality decomposition relation formulas of the space are derived by constru- cting a series of subspaces of wavelet packets.
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Xia, Yin Hong, and Hua Li. "The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix." Key Engineering Materials 439-440 (June 2010): 932–37. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.932.

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In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.
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Dissertations / Theses on the topic "Multivariate Operator Theory"

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Park, Baeil P. "Canonical forms for time-varying multivariable linear systems and periodic filtering and control applications." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/16734.

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Bhattacharjee, Monojit. "Analytic Models, Dilations, Wandering Subspaces and Inner Functions." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4241.

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This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main contribution of this thesis is twofold: dilation and analytic model theory for n-tuples of (1) commuting contractions (in the setting of the unit polydisc), and (2) commuting row contractions (in the setting of the unit ball). On n-tuples of commuting contractions: We study analytic models of operators with some positivity assumptions and quotient modules of function Hilbert spaces over polydisc. We prove that for an m-hypercontraction T 2 C¢0 on a Hilbert space H, there exist Hilbert spaces E and E¤, and a partially isometric multiplier µ 2M ¡H2 E (D), A2 m(E¤) ¢ such that H » Æ Qµ Æ A2 m(E¤)ªµH2 E (D), and T » Æ PQµMz jQµ , where A2 m(E¤) is the E¤-valued weighted Bergman space and H2 E (D) is the E -valued Hardy space over the unit disc D. We then proceed to study and develop analytic models for doubly commuting n-tuples of operators and investigate their applications to joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over polydisc. In particular, we completely analyze doubly commuting quotient modules of a large class of reproducing kernel Hilbert modules, in the sense of Arazy and Englis, over the unit polydisc Dn. On commuting row contractions: We study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. We prove that for a large class of analytic functional Hilbert spaces HK on the unit ball in Cn, wandering subspaces for restrictions of the multiplication tupleMz Æ (Mz1 , . . . ,Mzn ) can be described in terms of suitable HK -inner functions. We prove that, HK -inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogenous polynomials as an application. Along the way we prove a refinement of a result of Arveson on the uniqueness of minimal dilations of pure row contractions.
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Sarkar, Santanu. "Some Problems in Multivariable Operator Theory." Thesis, 2014. http://etd.iisc.ac.in/handle/2005/2897.

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In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals with the wandering subspaces of the Bergman space and the Dirichlet space over the polydisc. These are described in thefollowing two sections. (I) The Defect Sequence for ContractiveTuples LetT=(T1,...,Td)bead-tuple of bounded linear operators on some Hilbert space H. We say that T is a row contraction, or, acontractive tuplei f the row operator (Pl refer the abstract pdf file)
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Sarkar, Santanu. "Some Problems in Multivariable Operator Theory." Thesis, 2014. http://etd.iisc.ernet.in/handle/2005/2897.

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In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals with the wandering subspaces of the Bergman space and the Dirichlet space over the polydisc. These are described in thefollowing two sections. (I) The Defect Sequence for ContractiveTuples LetT=(T1,...,Td)bead-tuple of bounded linear operators on some Hilbert space H. We say that T is a row contraction, or, acontractive tuplei f the row operator (Pl refer the abstract pdf file)
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Books on the topic "Multivariate Operator Theory"

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Curto, Raúl E., Ronald G. Douglas, Joel D. Pincus, and Norberto Salinas, eds. Multivariable Operator Theory. Providence, Rhode Island: American Mathematical Society, 1995. http://dx.doi.org/10.1090/conm/185.

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Unitary invariants in multivariable operator theory. Providence, R.I: American Mathematical Society, 2009.

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1954-, Curto Raúl E., ed. Multivariable operator theory: A Joint Summer Research Conference on Multivariable Operator Theory, July 10-18, 1993, University of Washington, Seattle. Providence, R.I: American Mathematical Society, 1995.

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1953-, Spitkovskiĭ Ilya M., and Woerdeman Hugo J. 1962-, eds. Abstract band method via factorization positive and band extensions of multivariable almost periodic matrix functions, and spectral estimation. Providence, RI: American Mathematical Society, 2002.

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Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. New York, USA: John Wiley & Sons, 2001.

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Habib, Ammari, Capdeboscq Yves 1971-, and Kang Hyeonbae, eds. Multi-scale and high-contrast PDE: From modelling, to mathematical analysis, to inversion : Conference on Multi-scale and High-contrast PDE:from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom. Providence, R.I: American Mathematical Society, 2010.

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Arov, Damir Z. Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems. Birkhäuser, 2018.

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Dym, Harry, and Damir Z. Arov. Multivariate Prediction, de Branges Spaces, and Related Extension and Inverse Problems. Birkhäuser, 2018.

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Entropy and Multivariable Interpolation (Memoirs of the American Mathematical Society) (Memoirs of the American Mathematical Society). American Mathematical Society, 2006.

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Romain, Yves. An Invitation to Operator-Based Statistics. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.16.

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This article deals with operator-based statistics and its advantages. It first provides an overview of the historical and pedagogical aspects of operator-based statistics before explaining the underlying practical and theoretical motivations, along with synthetic and conceptual arguments. In particular, it develops the operator-based approach for factor multivariate analysis (and for their asymptotic studies) and offers several examples that show the value of operators in statistics. The discussion focuses on covariance operators, Hankel and Toeplitz operators, regression operators, measure-associated operators, tensor operators, and some other important categories. The article also describes noncommutative or quantum statistics and concludes with some reflections on the key notions and formulations of a "unified statistics" and projectors in (classical) statistics.
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Book chapters on the topic "Multivariate Operator Theory"

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Mai, Tobias, and Roland Speicher. "Operator-Valued and Multivariate Free Berry-Esseen Theorems." In Limit Theorems in Probability, Statistics and Number Theory, 113–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36068-8_7.

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Holbrook, John A. "Schur norms and the multivariate von Neumann inequality." In Recent Advances in Operator Theory and Related Topics, 375–86. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8374-0_20.

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Sarkar, Jaydeb. "Applications of Hilbert Module Approach to Multivariable Operator Theory." In Operator Theory, 1035–91. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_69.

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Sarkar, Jaydeb. "Applications of Hilbert Module Approach to Multivariable Operator Theory." In Operator Theory, 1–52. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_69-1.

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Sarkar, Jaydeb. "An Introduction to Hilbert Module Approach to Multivariable Operator Theory." In Operator Theory, 969–1033. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_59.

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Sarkar, Jaydeb. "An Introduction to Hilbert Module Approach to Multivariable Operator Theory." In Operator Theory, 1–58. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_59-1.

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Anastassiou, George A., and Sorin G. Gal. "Shift Invariant Multivariate Integral Operators." In Approximation Theory, 297–323. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1360-4_11.

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Ball, Joseph A., and Sanne ter Horst. "Multivariable Operator-valued Nevanlinna-Pick Interpolation: a Survey." In Operator Algebras, Operator Theory and Applications, 1–72. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0174-0_1.

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Lenze, Burkhard. "On Multidimensional Lebesgue-Stieltjes Convolution Operators." In Multivariate Approximation Theory IV, 225–32. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-7298-0_24.

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Upmeier, Harald. "Multivariable Toeplitz Operators and Index Theory." In Mappings of Operator Algebras, 275–88. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0453-4_16.

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Conference papers on the topic "Multivariate Operator Theory"

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Scheianu, Dorin, and Phillip A. Farrington. "Development of a Companion Set of Charts—Soft Sensor and Directional Moving Range—for Fault Monitoring, Detection and Diagnosis With Application to Gas Turbine Engines." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-50962.

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Gas turbines monitoring for fault detection and diagnosis is long desired to be embedded within control systems. Yet the general approach is to have alarms and shut downs when critical parameters exceed certain limits, and fault diagnosis is initiated on the behalf of experienced professionals and testing apparatus during scheduled maintenance time. Statistical methods for monitoring univariate and multivariate processes have been developed and publicized in the research literature. A gas turbine can be treated as a complex multivariate process with parameters depending both on control variables imposed by operator and on independent ambient parameters. The authors propose a set of companion charts that can be implemented on line and allows continuous monitoring both for fault amplitude — represented by a newly introduced soft sensor — and for process variability in the direction of interest. The control limits are introduced using multivariate statistical theory. The set of charts was applied at Wood Group LIT in a test cell, for monitoring process variability and for diagnosis and characterization of engine faults during tests. A second application is used for early detection of faults at the current serviced fleet of turbines.
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Priezzhev, Ivan, Dmitry Danko, and Uwe Strecker. "New-Age Kolmogorov Full-Function Neural Network KNN Offers High-Fidelity Reservoir Predictions via Estimation of Core, Well Log, Map and Seismic Properties." In Abu Dhabi International Petroleum Exhibition & Conference. SPE, 2021. http://dx.doi.org/10.2118/207575-ms.

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Abstract Instead of relying on analytical functions to approximate property relationships, this innovative hybrid neural network technique offers highly adaptive, full-function (!) predictions that can be applied to different subsurface data types ranging from (1.) core-to-log prediction (permeability), (2.) multivariate property maps (oil-saturated thickness maps), and, (3.) petrophysical properties from 3D seismic data (i.e., hydrocarbon pore volume, instantaneous velocity). For each scenario a separate example is shown. In case study 1, core measurements are used as the target array and well log data serve training. To analyze the uncertainty of predicted estimates, a second oilfield case study applies 100 iterations of log data from 350 wells to obtain P10-P50-P90 probabilities by randomly removing 40% (140 wells) for validation purposes. In a third case study elastic logs and a low-frequency model are used to predict seismic properties. KNN generates a high level of freedom operator with only one (or more) hidden layer(s). Iterative parameterization precludes that high correlation coefficients arise from overtraining. Because the key advantage of the Kolmogorov neural network (KNN) is to permit non-linear, full-function approximations of reservoir properties, the KNN approach provides a higher-fidelity solution in comparison to other linear or non-linear neural net regressions. KNN offers a fast-track alternative to classic reservoir property predictions from model-based seismic inversions by combining (a) Kolmogorov's Superposition Theorem and (b) principles of genetic inversion (Darwin's "Survival of the fittest") together with Tikhonov regularization and gradient theory. In practice, this is accomplished by minimizing an objective function on multiple and simultaneous outputs from full-function (via look-up table) Kolmogorov neural network runs. All case studies produce high correlations between actual and predicted properties when compared to other stochastic or deterministic inversions. For instance, in the log to seismic prediction better (simulated) resolution of neural network results can be discerned compared to traditional inversion results. Moreover, all blind tests match the overall shape of prominent log curve deflections with a higher degree of fidelity than from inversion. An important fringe benefit of KNN application is the observed increase in seismic resolution that by comparison falls between the seismic resolution of a model-based inversion and the simulated resolution from seismic stochastic inversion.
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Hussain, Nur Afande Ali, Syed Saad Azhar Ali, Mohamad Naufal Mohamad Saad, and Mark Ovinis. "Nonlinear adaptive control synthesis using U-model for multivariable underwater remotely operated vehicle." In 2017 IEEE 7th International Conference on Underwater System Technology: Theory and Applications (USYS). IEEE, 2017. http://dx.doi.org/10.1109/usys.2017.8309442.

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Tsai, Alex, David Tucker, and Craig Groves. "Improved Controller Performance of Selected Hybrid SOFC-GT Plant Signals Based on Practical Control Schemes." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22470.

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This paper compares and demonstrates the efficacy of implementing two practical Single Input Single Output (SISO) multi-loop control schemes on the dynamic performance of selected signals of a Solid Oxide Fuel Cell Gas Turbine (SOFC-GT) hybrid simulation facility. The hybrid plant, located at the U.S. Department of Energy National Energy Technology Laboratory (NETL) in Morgantown WV, is capable of simulating the interaction between a 350kW SOFC and a 120kW GT using a Hardware-in-the-Loop (HIL) configuration. Previous studies have shown that the thermal management of coal based SOFC-GT hybrid systems is accomplished by the careful control of the cathode air stream within the fuel cell (FC). A decoupled centralized and dynamic de-centralized control scheme is tested for one critical airflow bypass loop to regulate cathode FC airflow and modulation of turbine electric load to maintain synchronous turbine speed during system transients. Improvements to the studied multivariate architectures include: feed-forward (FF) control for disturbance rejection, anti-windup (AW) compensation for actuator saturation, gain scheduling for adaptive operation, bumpless transfer (BT) for manual to auto switching, and adequate filter design for the inclusion of derivative action. Controller gain tuning is accomplished by Skogestad’s Internal Model Control (SIMC) tuning rules derived from empirical First Order Plus Delay Time (FOPDT) Transfer Function {TF} models of the hybrid facility. Avoidance of strong Input-Output (IO) coupling interactions is achieved via Relative Gain Array (RGA), Niederlinski Index (NI), and Decomposed Relative Interaction Analysis (DRIA), following recent methodologies in PID control theory for multivariable processes.
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Abdenouri, Naji, A. Zoukit, H. Elferouali, I. Salhi, and S. Doubabi. "Multivariable modeling of an innovative hybrid solar-gas dryer." In 21st International Drying Symposium. Valencia: Universitat Politècnica València, 2018. http://dx.doi.org/10.4995/ids2018.2018.7523.

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The main goal of this paper, is to propose a multivariable control model (MM) issued from CFD study of an innovative hybrid solar-gas dryer to simulate the drying chamber temperature in three modes of operation: Solar mode, Gas mode and hybrid mode. There is an indirect heating of drying air instead of direct heating inside the drying chamber. The air temperature obtained by CFD is still closed to one obtained by multivariable model (MM) with an RMSE under 2.31. the proposed multivariable model leads to a quick output parameters estimation related to each clilmate conditions and so, to an easy control of a hybrid solar dryer. Keywords: Hybrid dryer; Multivariable model; solar dryer simulation; solar dryer control; Least square methods
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Woodruff, Matthew J., Timothy W. Simpson, and Patrick M. Reed. "Diagnostic Analysis of Metamodels’ Multivariate Dependencies and Their Impacts in Many-Objective Design Optimization." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13125.

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While computers are continually getting faster, physical models of complex systems grow more sophisticated and keep pace. Using metamodels can dramatically reduce the time it takes to evaluate a solution for a complex system; however, while the chief virtue of metamodels is that they approximate more computationally expensive models, this is also their main drawback. Metamodels are approximations, and as such they behave differently than the more sophisticated models they approximate. While the metamodels may be accurate approximations, they may also introduce new interdependencies in the response outputs that may hinder search algorithms during optimization. Understanding the impact of the approximation on the subsequent search thus becomes an important part of the problem as models that were computationally expensive ten to fifteen years ago may now run fast enough for use in optimization. In this paper, we use Sobol′ global sensitivity analysis to compare the search performance of a new auto-adaptive many objective evolutionary algorithm solving a challenging product family design problem with both the original analysis and a second-order response surface approximation of the original analysis. Interdependencies in the response outputs are found to result from the problem formulation used rather than the underlying model in this case. Search operator selection by the auto-adaptive evolutionary algorithm is shown to be consistent with the model sensitivities found by global sensitivity analysis.
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Fan, Muwei, Yang Wu, Wenhui Kong, and Jing Gong. "The Reliability Estimation of Simplified Natural Gas Pipeline Compressor Stations Based on Statistics Principles." In 2016 11th International Pipeline Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/ipc2016-64084.

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With the rapid economic and rigorous requirement of environmental governance, natural gas serves as important energy source in industry consumption. In 2015, the total consumption of natural gas in China is approximately 142 billion m3. As the primary mode of natural gas transport, early pipeline operated for more than 20 years in China, and its reliability also attracts abundant concerns by the increasing potential risks. However, the process of pipeline reliability evaluating and estimation in China is still located under development. To solve the problem, a simplified reliability estimation method is introduced in this article. To begin with the main equipment of a compressing station, the filter, air cooler and compressors are three research objectives. Because of redundant design for enhancing reliability, the major equipment usually operates with a same spare unit. Thus, the simplified station is consisted by 3 main sections with multiple units as filter section, compressing section and cooling section. By assuming their reliability following normal distribution, the multivariate normal distribution model is available. Each unit is characterized by one dimension of the multivariate normal distribution. This article considers both relevant and irrelevant processes while the equipment is operating simultaneously and illustrates the results via two and three dimensions normal distribution calculation. Due to the model being singular function because of be established based on multivariate normal distribution and parameter estimation principles, the analytical solution is not available. Therefore, numerical computation is the compulsory solution. However, the reliability analysis of pipe is different from equipment and it has been studied for years in details from theory to experiments. Consequently, the reliability of pipe is analyzed by statistics method from collected operating data. A pipeline with 25-years operating data in China is applied in the case study chapter for reliability estimation and analysis. According to the operating data collected by China National Petroleum Corporation, the failure rate of major equipment is estimated by determining the parameters of each distribution and fitted a curve like bathtub curve. Similarly, the failure rate of pipe is indicated as failures per 103 km • year. For comparing, the operating data is also fitted a curve to validate the result of the model with the purpose of reasonably estimating the whole period reliability. The result demonstrates that the model is available in practice if the parameters are determined properly.
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Castillo-Dura´n, Rogelio, Javier Ortiz-Villafuerte, Raymundo Go´mez-Herrera, and Gabriel Calleros-Micheland. "Autoregressive Multivariate Analysis of BWR Bistable Flow." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48730.

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Bi-stable flow patterns can induce flow oscillations possibly leading to power fluctuations. In other cases, bi-stable flow can generate loads on components, so that structural stresses may become a potential cause of failure. This type of flow occurs in BWRs at different operation conditions, so there is no an absolute methodology for detection and prediction of such phenomenon. In this work, a multivariate autoregressive (MAR) analysis is performed to different signals related to a bi-stable flow event that occurred in one of the BWR Units at the Laguna Verde Nuclear Power Plant. The signal analysis was performed with the home-developed NOISE computer program, which, among several other applications, computes the autoregressive coefficients which contain the information of the dynamics of the signal, and that later are used to determine the relative power contribution (RPC) ratio, which in turn allows establishing the influence of the different signals on each other. From the signal analysis, among the important results obtained, it was found that no new frequencies appeared during the event. Also, it was determined through the Relative Power Contribution ratios that the most probable cause of reactor power change was the flow variation in the recirculation flow of loop B. Maximum variations (both above and below) from the initial average reactor power were 0.5%, so the bi-stable flow impact was of no safety concern.
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Williams, Brandon, Brian Weaver, and Leen Weijers. "Completing the Second Target: Finding Optimal Completion Practices for the Three Forks Formation in the Williston Basin Using Multivariate Statistical Analysis." In SPE Hydraulic Fracturing Technology Conference. SPE, 2015. http://dx.doi.org/10.2118/spe-173377-ms.

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Abstract The Three Forks Formation in the Williston Basin has started to see a large increase in activity in the past six years. This is largely due to the shallower Bakken Formation transitioning into an infill development mode and operators looking at finding incremental reserves from the Three Forks Formation below. The objective of this paper is to evaluate the geological and completion variables of Three Forks horizontal wells in the North Dakota portion of the Williston Basin, and show which factors impact production performance using multivariate statistics. A financial evaluation of the completion factors will also be presented to show which variables have the biggest impact on production. A database of available completion and geological data has been assembled from the North Dakota Industrial Commission (NDIC) website. To date there are roughly 2,400 horizontal wells targeting the Three Forks Formation on the North Dakota side of the Williston Basin. Some of the variables collected include number of fracture stages, amount and type of proppant, total volume and type of frac fluid, lateral length, max treatment pressure and rate, API oil gravity, formation thickness (from formation tops) and production. The data was subjected to multivariate nonlinear statistical analysis. This type of analysis allows for simultaneously comparing multiple variables to one outcome variable. In this case study the outcome variable is 180-day production. Using multivariate analysis in the Three Forks Formation of the Williston Basin will aid in predicting production in different parts of the basin and finding which controllable completion variables have the most significant impact on production. The output can also aid in production forecasting based on changes to treatment designs.
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10

McDowell, Neil, Geoff McCullough, Xun Wang, Uwe Kruger, and George W. Irwin. "Application of Auto-Associative Neural Networks to Transient Fault Detection in an IC Engine." In ASME 2007 Internal Combustion Engine Division Fall Technical Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/icef2007-1728.

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The tailpipe emissions from automotive engines have been subject to steadily reducing legislative limits. This reduction has been achieved through the addition of sub-systems to the basic four-stroke engine which thereby increases its complexity. To ensure the entire system functions correctly, each system and / or sub-systems needs to be continuously monitored for the presence of any faults or malfunctions. This is a requirement detailed within the On-Board Diagnostic (OBD) legislation. To date, a physical model approach has been adopted by the automotive industry for the monitoring requirement of OBD legislation. However, this approach has restrictions from the available knowledge base and computational load required. A neural network technique incorporating Multivariant Statistical Process Control (MSPC) has been proposed as an alternative method of building interrelationships between the measured variables and monitoring the correct operation of the engine. Building upon earlier work for steady state fault detection, this paper details the use of non-linear models based on an Auto-associate Neural Network (ANN) for fault detection under transient engine operation. The theory and use of the technique is shown in this paper with the application to the detection of air leaks within the inlet manifold system of a modern gasoline engine whilst operated on a pseudo-drive cycle.
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