Relevant bibliographies by topics / Curve extrapolation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Curve extrapolation'

Author: Grafiati
Published: 28 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Curve extrapolation"

1

Gallacher, Daniel, Peter Auguste, and Martin Connock. "How Do Pharmaceutical Companies Model Survival of Cancer Patients? A Review of NICE Single Technology Appraisals in 2017." International Journal of Technology Assessment in Health Care 35, no. 2 (2019): 160–67. http://dx.doi.org/10.1017/s0266462319000175.

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AbstractObjectivesBefore an intervention is publicly funded within the United Kingdom, the cost-effectiveness is assessed by the National Institute of Health and Care Excellence (NICE). The efficacy of an intervention across the patients’ lifetime is often influential of the cost-effectiveness analyses, but is associated with large uncertainties. We reviewed committee documents containing company submissions and evidence review group (ERG) reports to establish the methods used when extrapolating survival data, whether these adhered to NICE Technical Support Document (TSD) 14, and how uncertainty was addressed.MethodsA systematic search was completed on the NHS Evidence Search webpage limited to single technology appraisals of cancer interventions published in 2017, with information obtained from the NICE Web site.ResultsTwenty-eight appraisals were identified, covering twenty-two interventions across eighteen diseases. Every economic model used parametric curves to model survival. All submissions used goodness-of-fit statistics and plausibility of extrapolations when selecting a parametric curve. Twenty-five submissions considered alternate parametric curves in scenario analyses. Six submissions reported including the parameters of the survival curves in the probabilistic sensitivity analysis. ERGs agreed with the company's choice of parametric curve in nine appraisals, and agreed with all major survival-related assumptions in two appraisals.ConclusionsTSD 14 on survival extrapolation was followed in all appraisals. Despite this, the choice of parametric curve remains subjective. Recent developments in Bayesian approaches to extrapolation are not implemented. More precise guidance on the selection of curves and modelling of uncertainty may reduce subjectivity, accelerating the appraisal process.
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Liu, You Yu, Jiang Han, and Gou Zheng Zhang. "Research on Intelligent Extension Technology for Curves Based on Trend Extrapolation." Advanced Materials Research 482-484 (February 2012): 2596–99. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.2596.

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To solve the defect of being not extended for curves in some CAD software, the trend extrapolation principle was imported and the intelligent extension technology for curves was discussed in this paper. The methods of identifying and choosing the trend extrapolation model are provided. Three mathematical models including polynomial curve extension, Gompertz curve extension and exponential curve extension were built, which can be adopted according to the feature points in curves reasonably. This paper has solved the common and core problems, which can be applied to CAD software upgrade or re-development.
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Dias, Luanna Costa, Lindemberg Lima Fernandes, and David Franco Lopes. "Elaboração e Extrapolação de Curvas-chave na Região Amazônica." Revista Brasileira de Geografia Física 12, no. 6 (January 9, 2020): 2285. http://dx.doi.org/10.26848/rbgf.v12.6.p2285-2301.

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O estudo consiste na elaboração e extrapolação de curvas-chave localizadas na Região Amazônica. A elevada disponibilidade hídrica da Região requer hidrogramas precisos para gestão dos Recursos Hídricos. Foram escolhidas cinco estações, com período de dados de 1971 a 2015 e o uso de 463 medições de descarga, para elaboração de curvas-chave do tipo potência e relacionando “cota x vazão” empregando duas formas de calibração: utilização do programa GrafChav e da ferramenta Solver do Excel, tendo o coeficiente de Nash-Sutcliffe (NS) como validação. A extrapolação foi realizada pelos métodos: Logarítmico, Velocidade x Área e Stevens, sendo validadas pela metodologia de pseudo-extrapolação. As duas formas de calibração da curva-chave (GrafChav e Excel) são eficientes. Quanto à extrapolação, a que obteve maior erro em relação à curva-chave foi o método de Stevens. O método com menor erro é o Velocidade x Área, desde que apresente tendência linear na relação entre cota e velocidade. A curva-chave é a etapa primordial na consistência de dados fluviométricos e requer técnicas bens aplicadas para incrementar na confiabilidade dos dados gerados. Development and Extrapolation of Rating Curves in Amazon A B S T R A C TThe study consists in the development and extrapolation of rating curves located in the Amazon. The high water availability of the Region requires accurate hydrographs for water resources management. Five stations were chosen, with a data period from 1971 to 2015 and the use of 463 discharge measurements, for the elaboration of power-type rating curves and relating “stage x flow” employing two forms of calibration: using the GrafChav program and the Excel Solver tool, with the Nash-Sutcliffe (NS) coefficient as validation. The extrapolation was performed by the following methods: Logarithmic, Velocity x Area and Stevens, being validated by the pseudo-extrapolation methodology. The two forms of rating curve calibration (GrafChav and Excel) are efficient. Regarding extrapolation, the one that obtained the greatest error in relation to the key curve was the Stevens method. The method with the smallest error is Speed x Area, as long as it presents a linear trend in the relationship between dimension and speed. The rating curve is the primordial step in the consistency of fluviometric data and requires applied good techniques to increase the reliability of the generated dataKeywords: Rating Curve, Calibration, Extrapolation.
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Sato, Hiroyuki, Kosuke Omote, Akira Sato, and Kouki Ueno. "Extrapolation of Sigmoidal Creep Curve by Strain Acceleration Parameter." Key Engineering Materials 592-593 (November 2013): 606–9. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.606.

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It has been widely accepted that the creep characteristics at high temperatures are mainly evaluated by a minimum creep rate and a time to fracture. Although, a shape of creep curve may vary depending on deformation conditions, the apparent minimum creep rates may become the same value. Thus, for detailed analysis and prediction of creep behavior, other values should be considered which reflects the shape of each creep curve. For the purpose, authors have proposed Satos Strain-Acceleration-Parameter (SAP) which reflects strain rate change during creep. Based on the concept of SAP, the whole creep curve can be represented by a set of small numbers of numerical parameters, and can be extrapolated from a part of creep curve [. It is also well accepted that the creep rates depend on microstructures, and microstructural changes cause strain rate change. The SAP would reflect stability and magnitude of microstructural change during deformation at high temperatures. In this paper, application of the concept of SAP to creep curves that show sigmoidal type primary creep is presented. The creep curve can be divided into two regime based on the SAP values. The sigmoidal creep curve is reasonably reproduced by the concept of Strain-Acceleration-Parameter, and reasonably agrees with experiment. Whole creep curve can be reasonably represented by a few numerical values which reflect shape of creep curve in each regime. The concept of SAP is applicable for quantitative evaluation of both normal and sigmoidal type of creep curves.
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Jansen, J. R., J. M. Bogaard, and A. Versprille. "Extrapolation of thermodilution curves obtained during a pause in artificial ventilation." Journal of Applied Physiology 63, no. 4 (October 1, 1987): 1551–57. http://dx.doi.org/10.1152/jappl.1987.63.4.1551.

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The feasibility of three mathematical models to extrapolate the tail of thermodilution curves, when flectures are present in the descending limb, was tested in anesthetized pigs. The models were a local random walk model (LDRW), a log-normal distribution, and a two-compartment model. First, the accuracy of the extrapolation of the tail by each model was tested on two undisturbed curves by taking the truncation at five different points on the descending limb. The extrapolated curve area obtained from each model was compared with total area of the undisturbed curve. Next, dilution curves obtained during inspiratory hold maneuvers and characterized by deflection points were analyzed, taking the truncation just before deflection. The estimates of cardiac output by the models were compared with electromagnetically measured flow in the pulmonary artery. The area of the dilution curve was estimated more accurately when more information on the descending limb was available. The LDRW model and the log-normal distribution were superior to the two-compartment model regarding accuracy of cardiac output estimation and root-mean-square errors of the fit. Both models estimated curve area with an error less than 5% when truncation of the descending limb occurred below 60% of the peak value. In circumstances of mechanical ventilation, where only short periods of constant flow will be present, analyses of dilution curves based on the LDRW model or the log-normal distribution are recommended.
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Constantino, Reginaldo. "Estimating Global Termite Species Richness Using Extrapolation." Sociobiology 65, no. 1 (March 31, 2018): 10. http://dx.doi.org/10.13102/sociobiology.v65i1.1845.

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Cumulative species description curves since 1758 are given for all termites of the world and for each biogeographical region (Australian, Ethiopian, Nearctic, Neotropical, Oriental, Palearctic, and Papuan). A cumulative description curve is also given for world genera. Estimation by maximum likelihood using the Michaelis-Menten model suggests a maximum of 5366 ± 175 species (p < 2.2E-16) and 704 ± 77 genera (p < 4.387E-13). Model fitting was poor for most individual biogeographical regions, with the exception of the Ethiopian region (estimate = 1295 ± 57 species, p < 2.2E-16). World War I and World War II had marked negative impacts on termite description rates. Data from China was treated separately due to the atypical rate of description of new termites in that country during the last two decades of the 20th century.
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Bruni, Carlo. "Modelling of Flow Behaviour of Magnesium Alloys." Key Engineering Materials 716 (October 2016): 360–67. http://dx.doi.org/10.4028/www.scientific.net/kem.716.360.

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The present investigation aims at studying the flow behaviour of magnesium alloys under different conditions in terms of temperature, deformation velocities and deformation. The modelling approach was based on a proposed equation to model the shape of each flow curve through different variables. The modelled flow curves were subsequently compared with those obtained with experiments. The models were validated on flow curves not used in the building stage. It was observed that, for low temperature values, high deformation velocities and deformations the final part of the flow curve has to be adapted in order to be adopted for the description of material in the numerical simulation. In other words it needs to be extrapolated. Also for the high temperature, the flow softening has to be limited in order to allow the extrapolation queue required for elevated deformations. The deformation value at which the extrapolation can start can be predicted with an other proposed equation detailed in the paper.
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Quetting, Florian, Pavel Hora, and Karl Roll. "Modelling of Strain Hardening Behaviour of Sheet Metals for Stochastic Simulations." Key Engineering Materials 504-506 (February 2012): 41–46. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.41.

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In current forming simulations, Ghosh or Hockett-Sherby extrapolation functions are used to model strain hardening effects of sheet metals. When it comes to stochastic simulations, the respective parameters have to be recalculated according to the scattering of the mechanical material properties like yield or tensile strength. As present stochastic samplings for deep drawing simulations only consider yield strength and tensile strength, it is non-trivial securing the extrapolated area of strain hardening curves due to lack of data beyond uniform strain. It is current practice to improve the description of the flow curve beyond uniform elongation point by using the maximum force criterion, which takes into account the gradient of the yield curve at the last known point. The corresponding system of equations has to be solved numerically. We propose a method for adjusting parameters of the Ghosh or Hockett-Sherby extrapolation functions, which overcomes the need of numerical calculations and keeps flow curve information from the extrapolated interval, even if the stochastic sampling doesn’t incorporate any data regarding that area.
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Sato, Hiroyuki. "Extrapolation of Imaginal Minimum Creep Rate in Compression by a Concept of SATO-Index." Key Engineering Materials 741 (June 2017): 99–104. http://dx.doi.org/10.4028/www.scientific.net/kem.741.99.

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Creep characteristics of alloys and compounds have been evaluated mainly by the minimum creep rate or the steady-state creep rate, and by its stress and temperature dependences. In some cases, however, direct comparison of the minimum creep rate or the steady-state creep rate are not practically easy due to difficulties of experiment, i.e., a long duration of primary stage of creep deformation. The minimum creep rates are not always precise representative value, which is directly evaluated from experiments. It should be valuable, if one could estimate the minimum creep rate from creep curve in primary stage. I have proposed a method of quantitative evaluation of creep curve based on the evaluation of strain rate change and its strain dependence during creep [1-3]. The value that reflects a shape of creep curve is named “Strain Acceleration and Transition Objective-Index (SATO-Index)” [4]. SATO-Index and related differential equation show a strain dependence of strain rate and lead entre creep curve by numerical integration. This concept provides quantitative information of shape of each creep curve, and information of the entire creep curve. In this paper, examples of evaluation and extrapolation of creep rate from primary stage in compression are presented. It is concluded that the extrapolation with the concept of SATO-Index reasonably provides imaginal minimum creep rate. Usability of extrapolation of creep curve by the concept is presented.
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Chen, Junfu, Zhiping Guan, Pinkui Ma, Zhigang Li, and Dan Gao. "Experimental extrapolation of hardening curve for cylindrical specimens via pre-torsion tension tests." Journal of Strain Analysis for Engineering Design 55, no. 1-2 (November 16, 2019): 20–30. http://dx.doi.org/10.1177/0309324719887863.

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The hardening curve for cylindrical specimens determined by conventional uniaxial tension tests generally corresponds to a relatively narrow strain range due to the occurrence of necking. To achieve the hardening curve within a large strain range, in this study, the multi-specimen tension tests with pre-torsion are developed through extrapolating the hardening curve from the stress–strain data of cylindrical specimens with various magnitudes of pre-torsion strains. The calculation of pre-strain of twisted specimen needs to be addressed for the multi-specimen tension tests. The three calculation methods on the multi-specimen tension tests are proposed, leading to their individual hardening curves for Q345 specimens. An optimal strategy for the multi-specimen tests with pre-torsion is presented by comparison with the inverse method for a single specimen tension test. The results for Q345 specimen show the strain range (0–0.6) of the hardening curve determined by the multi-specimen tension tests is significantly larger than one (0–0.04) from conventional tension test, with reasonable accuracy. Compared with the current multi-specimen tests with pre-extrusion/drawing, the proposed multi-specimen tests with pre-torsion is possessed of stronger applicability and generality, lower cost, and higher efficiency.
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Dissertations / Theses on the topic "Curve extrapolation"

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Thomas, Michael Patrick. "Long term extrapolation and hedging of the South African yield curve." Diss., Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-06172009-085254.

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Šooš, Marek. "Segmentace 2D Point-cloudu pro proložení křivkami." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444985.

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The presented diploma thesis deals with the division of points into homogeneous groups. The work provides a broad overview of the current state in this topic and a brief explanation of the main segmentation methods principles. From the analysis of the articles are selected and programmed five algorithms. The work defines the principles of selected algorithms and explains their mathematical models. For each algorithm is also given a code design description. The diploma thesis also contains a cross comparison of segmentation capabilities of individual algorithms on created as well as on measured data. The results of the curves extraction are compared with each other graphically and numerically. At the end of the work is a comparison graph of time dependence on the number of points and the table that includes a mutual comparison of algorithms in specific areas.
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Moudiki, Thierry. "Interest rates modeling for insurance : interpolation, extrapolation, and forecasting." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1110/document.

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L'ORSA Own Risk Solvency and Assessment est un ensemble de règles définies par la directive européenne Solvabilité II. Il est destiné à servir d'outil d'aide à la décision et d'analyse stratégique des risques. Dans le contexte de l'ORSA, les compagnies d'assurance doivent évaluer leur solvabilité future, de façon continue et prospective. Pour ce faire, ces dernières doivent notamment obtenir des projections de leur bilan (actif et passif) sur un certain horizon temporel. Dans ce travail de thèse, nous nous focalisons essentiellement sur l'aspect de prédiction des valeurs futures des actifs. Plus précisément, nous traitons de la courbe de taux, de sa construction et de son extrapolation à une date donnée, et de ses prédictions envisagées dans le futur. Nous parlons dans le texte de "courbe de taux", mais il s'agit en fait de construction de courbes de facteurs d'actualisation. Le risque de défaut de contrepartie n'est pas explicitement traité, mais des techniques similaires à celles développées peuvent être adaptées à la construction de courbe de taux incorporant le risque de défaut de contrepartie
The Own Risk Solvency and Assessment (ORSA) is a set of processes defined by the European prudential directive Solvency II, that serve for decision-making and strategic analysis. In the context of ORSA, insurance companies are required to assess their solvency needs in a continuous and prospective way. For this purpose, they notably need to forecast their balance sheet -asset and liabilities- over a defined horizon. In this work, we specifically focus on the asset forecasting part. This thesis is about the Yield Curve, Forecasting, and Forecasting the Yield Curve. We present a few novel techniques for the construction, the extrapolation of static curves (that is, curves which are constructed at a fixed date), and for forecasting the spot interest rates over time. Throughout the text, when we say "Yield Curve", we actually mean "Discount curve". That is: we ignore the counterparty credit risk, and consider that the curves are risk-free. Though, the same techniques could be applied to construct/forecast the actual risk-free curves and credit spread curves, and combine both to obtain pseudo- discount curves incorporating the counterparty credit risk
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Gazzotti, Giulia. "Corrosion resistance of aluminium alloys for civil and industrial applications." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.

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Considering the long service life which is normally expected for buildings, the maintenance cost, the quality and durability of construction materials are strongly affected by triggering of spontaneous degradation processes. As regards specifically metallic materials, awareness of their corrosion behaviour in service condition, in every environment they can get in contact during life, is essential, for maintenance and cleaning operations as well. Corrosion rate measurements can be obtained from electrochemical tests. Corrosion mechanism of metallic alloy is a spontaneous phenomenon, but some factors, as alloying elements, microstructure, surface treatments and environments, may enhance this degradation process. This thesis focuses on understanding corrosion behaviour of three aluminium alloys, Al5083, Al6082 and Al7075, with different surface treatments, tested in two aqueous solutions at different pH conditions (one environment simulating a cleaning detergent and the second environment simulating a strong alkaline solution). The corrosion rate was obtained from corrosion current densities, measured by electrochemical laboratory tests. Results, in terms of Open-Circuit Potential (OCP) and potentiodynamic measurements are reported and discussed. Lastly, SEM and EDX analysis have been used as characterization techniques for microstructure analysis.
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Dotlačilová, Petra. "Demografický vývoj zemí Evropské Unie." Master's thesis, Vysoká škola ekonomická v Praze, 2011. http://www.nusl.cz/ntk/nusl-113483.

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The aim of this Master's thesis is to describe the past and future demographic development of selected EU countries. The second aim is to utilize methods for multicriteria evaluation of alternatives in the demography. The last aim is to describe methods used to extrapolate mortality curves. The theoretical part describes demographic indicators, methods used to extrapolate mortality curves and computational processes for methods for multicriteria evaluation of alternatives. The practical part includes the computation of demographic indicators and describes the progress of the indicators in the future. The methods for multicriteria evaluation of alternatives are used for ranking selected EU countries according to the demographic indicators. The last part of the thesis includes the application of methods used for extrapolating mortality curves and compares the achieved results with the actual progress.
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Hsu, Feng-Ju, and 許鳳如. "Statistical estimation of rarefaction and extrapolation curve for Beta diversity." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/54138180233188947727.

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Books on the topic "Curve extrapolation"

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Skinner, F. Interpretation of ultimate biochemical oxygen demand data via kinetic curve extrapolation models. Vegreville, Alta: Environmental Technology Division, Alberta Environmental Centre, 1990.

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U.S. Nuclear Regulatory Commission. Office of Nuclear Regulatory Research. Division of Engineering., University of Tennessee Knoxville, and Oak Ridge National Laboratory, eds. Extrapolation of the J-R curve for predicting reactor vessel integrity. Washington, DC: Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1992.

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U.S. Nuclear Regulatory Commission. Office of Nuclear Regulatory Research. Division of Engineering., University of Tennessee Knoxville, and Oak Ridge National Laboratory, eds. Extrapolation of the J-R curve for predicting reactor vessel integrity. Washington, DC: Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1992.

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U.S. Nuclear Regulatory Commission. Office of Nuclear Regulatory Research. Division of Engineering., University of Tennessee Knoxville, and Oak Ridge National Laboratory, eds. Extrapolation of the J-R curve for predicting reactor vessel integrity. Washington, DC: Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1992.

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Joyce, J. A. Extension and extrapolation of J-R curves and their application to the low upper shelf toughness issue. Supt. of Docs., U.S. G.P.O. [distributor], 1991.

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Book chapters on the topic "Curve extrapolation"

1

Böck, J., A. Hoeft, H. Korb, J. Steinmann, H. G. Wolpers, and G. Hellige. "A Comparison of Extrapolation and Deconvolution of Thermo-Dye Dilution Curve, with Special Emphasis on States with Early Indicator Recirculation." In Practical Applications of Fiberoptics in Critical Care Monitoring, 87–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75086-1_12.

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Hosaka, Mamoru. "Curves Through Given Points, Interpolation and Extrapolation." In Modeling of Curves and Surfaces in CAD/CAM, 103–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-76598-8_8.

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Klemyatsionok, Peter, Svetlana Kolmogorova, and Sergey Kolmogorov. "Compression Curves’ Extrapolation to High Pressures for Soft Clay Soils." In Lecture Notes in Civil Engineering, 233–38. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0454-9_25.

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Chandrashekaran, Akshay, and Ian R. Lane. "Speeding up Hyper-parameter Optimization by Extrapolation of Learning Curves Using Previous Builds." In Machine Learning and Knowledge Discovery in Databases, 477–92. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71249-9_29.

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Chen, Xiao, Guan-Nian Chen, Bate Bate, and Yu-Chao Li. "Extrapolating Kd or Rd from Breakthrough Curves of Cesium Cations Transporting Through a Soil Column." In Environmental Science and Engineering, 602–11. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2221-1_66.

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Jakóbczak, Dariusz Jacek. "Data Extrapolation via Curve Modeling in Analyzing Risk." In Analyzing Risk through Probabilistic Modeling in Operations Research, 1–31. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9458-3.ch001.

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Risk analysis needs suitable methods of data extrapolation and decision making. Proposed method of Hurwitz-Radon Matrices (MHR) can be used in extrapolation and interpolation of curves in the plane. For example quotations from the Stock Exchange, the market prices or rate of a currency form a curve. This chapter contains the way of data anticipation and extrapolation via MHR method and decision making: to buy or not, to sell or not. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional data are represented by the set of curve points. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of data foreseeing and extrapolation. MHR method is interpolating and extrapolating the curve point by point without using any formula or function.
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Jakóbczak, Dariusz Jacek. "Data Extrapolation via Curve Modeling in Analyzing Risk." In Natural Language Processing, 1379–407. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-0951-7.ch067.

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Risk analysis needs suitable methods of data extrapolation and decision making. Proposed method of Hurwitz-Radon Matrices (MHR) can be used in extrapolation and interpolation of curves in the plane. For example quotations from the Stock Exchange, the market prices or rate of a currency form a curve. This chapter contains the way of data anticipation and extrapolation via MHR method and decision making: to buy or not, to sell or not. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional data are represented by the set of curve points. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of data foreseeing and extrapolation. MHR method is interpolating and extrapolating the curve point by point without using any formula or function.
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Jakóbczak, Dariusz Jacek. "The Method of Probabilistic Nodes Combination in Decision Making and Risk Analysis." In Analyzing Risk through Probabilistic Modeling in Operations Research, 32–60. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9458-3.ch002.

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Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Nodes can be treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter ? as probability distribution function enables value anticipation in risk analysis and decision making. Two-dimensional curve is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.
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"Creep." In Damage Mechanisms and Life Assessment of High-Temperature Components, 59–110. ASM International, 1989. http://dx.doi.org/10.31399/asm.tb.dmlahtc.t60490059.

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Abstract This chapter provides a detailed overview of the creep behavior of metals and how to account for it when determining the remaining service life of components. It begins with a review of creep curves, explaining how they are plotted and what they reveal about the operating history, damage mechanisms, and structural integrity of the test sample. In the sections that follow, it discusses the effects of stress and temperature on creep rate, the difference between diffusional and dislocation creep, and the use of time-temperature-stress parameters for data extrapolation. It explains how to deal with time dependent deformation in design, how to estimate cumulative damage under changing conditions, and how to assess the effect of multiaxial stress based on uniaxial test data. It also includes information on rupture ductility, creep fracture, and creep-crack growth and their effect on component life and performance.
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Cornish-Bowden, Athel. "Steady-state kinetics." In Spectrophotometry and Spectrofluorimetry. Oxford University Press, 2000. http://dx.doi.org/10.1093/oso/9780199638130.003.0010.

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All of chemical kinetics is based on rate equations, but this is especially true of steady-state enzyme kinetics: in other applications a rate equation can be regarded as a differential equation that has to be integrated to give the function of real interest, whereas in steady-state enzyme kinetics it is used as it stands. Although the early enzymologists tried to follow the usual chemical practice of deriving equations that describe the state of reaction as a function of time there were too many complications, such as loss of enzyme activity, effects of accumulating product etc., for this to be a fruitful approach. Rapid progress only became possible when Michaelis and Menten (1) realized that most of the complications could be removed by extrapolating back to zero time and regarding the measured initial rate as the primary observation. Since then, of course, accumulating knowledge has made it possible to study time courses directly, and this has led to two additional subdisciplines of enzyme kinetics, transient-state kinetics, which deals with the time regime before a steady state is established, and progress-curve analysis, which deals with the slow approach to equilibrium during the steady-state phase. The former of these has achieved great importance but is regarded as more specialized. It is dealt with in later chapters of this book. Progress-curve analysis has never recovered the importance that it had at the beginning of the twentieth century. Nearly all steps that form parts of the mechanisms of enzyme-catalysed reactions involve reactions of a single molecule, in which case they typically follow first-order kinetics: . . . v = ka . . . . . . 1 . . . or they involve two molecules (usually but not necessarily different from one another) and typically follow second-order kinetics: . . . v = kab . . . . . . 2 . . . In both cases v represents the rate of reaction, and a and b are the concentrations of the molecules involved, and k is a rate constant. Because we shall be regarding the rate as a quantity in its own right it is not usual in steady-state kinetics to represent it as a derivative such as -da/dt.
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Conference papers on the topic "Curve extrapolation"

1

Sato, Hiroyuki. "Extrapolation of Creep Curve and Creep Life Prediction From Secondary Creep by Evaluation of Strain Rate Change." In ASME 2010 Power Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/power2010-27336.

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New method of creep life prediction by Strain-Acceleration-Parameter, SAP, is presented. Sato has found that shapes of creep curves can be characterized by the SAP that reflects magnitude of strain-rate change in secondary creep [1–4]. The SAP values are defined at minimum creep rates, and show the shapes of a creep curve, that depends on stress and temperature. Reconstruction of creep curves by a combination of SAP and a minimum-creep rate is successfully performed, and the extrapolated curves agree well with experiment. The predicted life times also reasonably agree with that obtained by experiment. The possibility of precise life prediction by SAP is pronounced. One of an important advantage of the proposed method is that the required parameters evaluated by individual creep curve are simpler than that are used in methods previously proposed, i.e., the theta projection concept, for example. Possibilities of wide application on many kinds of heat resistant materials should be investigated with the method of SAP.
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Sracic, Michael W., and William J. Elke. "Predicting Finite Element Submodel Boundary Conditions for Contact Models Using Richardson Extrapolation." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98070.

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Abstract This paper considers an efficient way to apply submodeling methods to finite element models using Richardson Extrapolation. A problem is considered where a rigid cylindrical indenter contacts an elastic half plane (RCEHP). A submodeling method is introduced where the errors of the displacements on the boundaries of the submodel are controlled by employing a best-fit Richardson Extrapolation curve. Specifically, the curve is fit to the convergence relationship of various estimates of submodel boundary displacements. The method is tested on the RCEHP problem, and the results of the model predictions for maximum contact pressure are compared to an analytical and converged global model result. The submodeling method predicted the maximum contact pressure of the RCEHP contact interface to be about 7% higher than the analytical prediction and 5% higher than the converged global model prediction. The error is likely due to the selection of the global and submodel domains, the numerical algorithm used to estimate the Richardson Extrapolation Curve Fits, and the mesh refinements used for the various models. The proposed method solved in about 42.6 minutes while the converged global model solved in 11.19 hours. Future work will aim to provide best practices to reduce error and maximize computational time savings when using the method.
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Friedman, Jeffrey R., and David Keyser. "ASME PTC 19.5 Procedures for Application of Laboratory Calibrations of Differential Pressure Flow Meters." In ASME 2008 Power Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/power2008-60151.

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Performance Test Codes require primary mass flow accuracies that in many applications require the laboratory-quality calibration of differential pressure meters. It is also true that many performance tests are conducted at Reynolds numbers and flows well above the laboratories’ capacities, and sound extrapolation methods had to be developed. Statistical curve-fits and regression analyses by themselves, absent fluid-dynamic foundations, are not valid procedures for extrapolation. The ASME PTC 19.5-2004 discharge coefficient equations presented in this paper are suitable for use and extrapolation of laboratory calibration data.
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Menon, M. N., P. T. Kantzos, and D. J. Greving. "An Isothermal Model for Creep Rupture Prediction of Gas Turbine Airfoils With Thickness Effect." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56072.

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An isothermal model for creep rupture prediction of equiaxed gas turbine airfoils is presented. It provides a family of curves linear in log-log space between applied tensile stress and rupture time. Each curve represents a specific temperature. The model accommodates changes in slope with temperature by a temperature-time interaction term. In addition, it can capture phenomena that are solely temperature dependent such as thickness (grain size) effect observed in rupture of equiaxed turbine blade alloys. It represents an improvement over Larson-Miller (LM) formulation in which time and temperature are combined into a single parameter and assumed to have a unique value dependent only on the applied stress. It is also more accurate and less conservative than the LM model when extrapolating to lower stresses at a specific temperature, if the LM model shape is non-linear, curving downward. The isothermal formulation better preserves the accuracy of extrapolation and can model phenomena affecting stress rupture which are exclusively temperature dependent.
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Tveiten, Ba˚rd Wathne, Stig Berge, and Xiaozhi Wang. "Fatigue Assessment of Aluminum Ship Details by Hot-Spot Stress Approach." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50201.

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This paper presents a robust methodology for fatigue assessment of aluminum ship details using a hot-spot stress range approach. A series of fatigue tests of a typical aluminum ship detail was carried out to obtain a design S-N curve. The test detail was analyzed by the finite element method (FEM) using several modeling techniques and element types. Recommendations are given on finite element modeling practice, extrapolation methods and design S-N curves.
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Steiner, D. "Real Time Curve Extrapolator for Fixtureless Inspection of Freeform Surfaces." In ASME 2006 International Manufacturing Science and Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/msec2006-21103.

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The inspection of free-form surfaces is an important task in manufacturing process control. This task motivated researchers to develop methodologies and technologies for fixtureless inspection. The motivation for performing fixtureless inspection rises from the fact that a datum or an exact fixture is not always available for free-form objects. When datum and fixtures are not present, the location and rotation of the object in space relative to the sensor coordinate system are unknown. Thus, scanning along a proper trajectory is not trivial especially when dealing with high precision sensors with small depth of field (DOF). In this paper we introduce a theoretical scheme for real time curve extrapolation. This scheme performs real time automatic adjustment to the sensor depth of field by smoothly changing the position of the sensor. The proposed scheme can handle local C1 discontinuity (C0 continuity). In the proposed scheme, the velocity of the motion stages can be controlled by the curvature of the extrapolated curve, thus controlling the density of the sampled data. Also, no knowledge of the surface orientation and location is needed nor any reference plane or other datum. The scheme was tested using computer simulation that was developed for this purpose. The robustness of the scheme is shown at the end of this paper through simulation results using high order polynomial surfaces as test cases.
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Özgenel, Çağlar Fırat, and Arzu Gönenç Sorguç. "A New Method of Curve Fitting for Calculation of Reverberation Time From Impulse Responses With Insufficient Length." In ASME 2012 Noise Control and Acoustics Division Conference at InterNoise 2012. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ncad2012-1349.

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Most of the room acoustics evaluation parameters are calculated from the energy decay curve obtained from the room impulse response. Schroeder’s backwards integration method is one of the most commonly used methods to obtain room impulse response. Although, the method holds its validity since 1964 and used extensively, obtaining room impulse response with sufficient length to observe total energy decay requires high computational cost especially in highly reverberant rooms. In such cases, present acoustical analysis and simulation tools either use data extrapolation and linear fitting methods or they fail to provide any reliable output. Hence, in order to provide reliable data based on such an impulse response, high computational cost and effort are required. In this context, a modification for acoustical analysis methods based on impulse response is proposed, comprising a linear fitting algorithm and extrapolation together with data culling. Proposed method is based on the linear energy decay assumption of Schroeder and ideal energy decay according to global reverberation time estimates. Method is proposed for diffuse field conditions regardless of the length of room impulse response. Validity of the proposed method is checked via a developed room acoustics tool, namely RAT, and case studies conducted with the mentioned tool.
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Solin, Jussi, Tommi Seppänen, and Wolfgang Mayinger. "Fatigue Performance of Austenitic Stainless Steel: Enforced Endurance Limit and Questionable Design Curve." In ASME 2020 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/pvp2020-21050.

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Abstract Design codes and standards are used for new designs and also for management of operation and in service inspection of existing NPP primary circuit pressure boundaries. The current codes — ASME, KTA, RCC-M, PNAE-G and JSME — have been originally rooted to the ASME Boiler and Pressure Vessel Code, Section III, Nuclear Vessels, which was published in 1963. Article 4, N-415 “Analysis for cyclic operation” instructed calculation of stress intensities for fatigue transients and provided two design curves for basic material types — one for ferritic, the other for austenitic steels. The design curves were based on strain-controlled LCF tests, which measured the allowable numbers of cycles as function of plastic strain. The obtained material performance was then processed to strain-life and design curves (Sa = Ex εa). This local strain fatigue approach was found applicable for both ferritic and austenitic steels though their elastic plastic cyclic responses are much different. Fatigue data for stainless steels extended to ¼ million cycles and the design curve was extrapolated to one million cycles. Later on — supported by load-controlled HCF tests — the original LCF approach has been extended even beyond HCF to VHCF regime. Our strain-controlled HCF results for alloy types 347 and 304L are in conflict with the reference mean curve behind current ASME curve for stainless steels. We assume that this reflects a generic issue related to extrapolation of the LCF methodology by Coffin, Langer and other pioneers. Furthermore, analysis of cyclic responses and variable amplitude testing to millions of cycles give reasons to assume that the concept of an endurance limit (Se) is applicable also for variable amplitude straining. Variable amplitude HCF straining was not studied for ferritic steels and we propose the concept of enforced endurance limit to austenitic stainless steels only. We propose a critical review on relevance of the current ASME III design curve for stainless steels.
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Williams, Logan T. "Methodology for the Evaluation of Gear Pump Performance." In BATH/ASME 2020 Symposium on Fluid Power and Motion Control. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/fpmc2020-2763.

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Abstract Currently, most performance curves of gear pumps present volumetric efficiency as a function of one or more operating conditions. However, the nature of gear pumps is that volumetric efficiency is dependent on pump speed, pump pressure rise, and fluid viscosity. This dependency on multiple parameters impedes direct comparisons between pumps tested at disparate operating conditions or on different testbeds. A new method has been developed that formulates the volumetric efficiency as a function of a single parameter that captures pump speed, pressure, and fluid viscosity. The characteristics of the pump is then captured by curve fitting two constants to empirical data. This method allows extrapolation of pump performance beyond empirical data and direct comparison of the volumetric efficiency curves of two pumps tested under disparate conditions within a single plot. This work describes the analytical derivation of the methodology and the empirical data used for validations. Additionally, several possible applications of this method are presented.
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10

Hiraguchi, Hideo. "New Numerical Analysis Method for Creep Lifetime of Gas Turbine Materials by Using the Discrete Cosine Transform." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14029.

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Abstract Recently the Discrete Cosine Transform[1], [2], [3] which is a modified Fourier Transform has begun to be used to express coefficients of creep equations using the power law or the exponential law such as Bailey-Norton law[4], [5] and θ Projection[6], [7], [8], [9], [10]. In addition, the Discrete Cosine Transform has begun to be used to express a creep equation itself. We have already found that the Discrete Cosine Transform can express the temperature and stress dependence property of the coefficients of the creep equations at the same time by the two-dimensional Discrete Cosine Transform using 8 × 8 discrete signals[11]. Furthermore, we have already found that the Discrete Cosine Transform can fit measured creep strain values very well from the primary creep region to the tertiary creep region using 8 discrete signals and it can estimate creep strain values between the measured points by interpolation very well[12]. However it has not been known if the Discrete Cosine Transform can predict the long term creep curve by using the short term creep data yet. Therefore, as a next stage, we tried to estimate the long term creep curve from the short term creep data of gas turbine materials by extrapolation using the Discrete Cosine Transform. As a result, we were able to obtain a useful numerical analysis method by utilizing the Discrete Cosine Transform Coefficients and others as a new extrapolation method. It is found that this new numerical method would be able to predict the configuration of 150,000-hour creep curve by using 500-hour to 13,000-hour short term creep data.
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Reports on the topic "Curve extrapolation"

1

Staack, G. DEVELOPMENT OF A HYDROGEN ISOTOPE EXTRAPOLATION CURVE FOR PLATINUM CATYLIZED ZEOLITE. Office of Scientific and Technical Information (OSTI), July 2010. http://dx.doi.org/10.2172/983399.

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