Journal articles: 'Curve extrapolation'

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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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Lu, Li Bin, Ding Xin Chen, Guo Dong Jin, Rong Ming Li, and Ying Jie Gao. "Ultrasonic Positioning Using Curve-Fitting Extrapolation and Redundant Information Fusion." Applied Mechanics and Materials 105-107 (September 2011): 1851–55. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.1851.

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To study the problem of high precision, the reason why error appears in the ultrasonic positioning process is analyzed. To decrease the effect of error, this paper raises the algorithm of curve-fitting extrapolation and redundant information fusion. The experiment and contrast on precision between this algorithm and other classical ones demonstrate that, the new algorithm could effectively control measurement errors and raise the precision of ultrasonic positioning.

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Wang, Zhi Tao, Bing Bai, Shu Ying Li, Qing Cai Yang, and Meng Qi Wang. "Compressor Performance Curve Extrapolation Method Based on the Similarity Theory." Applied Mechanics and Materials 672-674 (October 2014): 1545–49. http://dx.doi.org/10.4028/www.scientific.net/amm.672-674.1545.

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Due to the fact that the low speed pump similarity theory is only applicable to incompressible fluid, this theory cannot be used for extrapolation of compressor performance curve. Considering the compressibility of working medium; therefore, this paper has modified the similarity theory and put forward a new index relationship equation. The two low speed performance lines which are already known were used to get the similar working points and extrapolate the performance lines through the optimization method. Compared with the existing performance lines, the results show that the method is simple, convenient and qualified with practicability and accuracy. This method plays an important role on studying startup process of a gas turbine and improving the accuracy of the simulation of startup process.

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Kim, Choongrak, Changkon Hong, and Meeseon Jeong. "Simulation-Extrapolation via the Bezier Curve in Measurement Error Models." Communications in Statistics - Simulation and Computation 29, no. 4 (January 2000): 1135–47. http://dx.doi.org/10.1080/03610910008813657.

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Farouki, Rida T. "Accurate Real-time CNC Curve Interpolators Based Upon Richardson Extrapolation." Computer-Aided Design 135 (June 2021): 103005. http://dx.doi.org/10.1016/j.cad.2021.103005.

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Maruyama, K., and H. Oikawa. "An Extrapolation Procedure of Creep Data for St Determination: With Special Reference to Cr-Mo-V Steel." Journal of Pressure Vessel Technology 109, no. 1 (February 1, 1987): 142–46. http://dx.doi.org/10.1115/1.3264846.

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A predictive rule for long-term creep data, necessary to determine St of the ASME Code, was proposed with special reference to a Cr-Mo-V steel. This rule can predict long-term creep curves as well as rupture lives. A creep curve three hundred times longer than the longest test was estimated without unreasonable extrapolation.

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Sato, Hiroyuki, Kosuke Omote, and Akira Sato. "Extrapolation of Creep Curve and Creep Rate by Strain Acceleration Parameter in Al-Mg Solid Solution Alloys." Materials Science Forum 794-796 (June 2014): 307–12. http://dx.doi.org/10.4028/www.scientific.net/msf.794-796.307.

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It has been widely accepted that the creep characteristics at high temperatures are mainly evaluated by a minimum creep rate. Although, a shape of creep curve may vary depending on deformation conditions, the apparent steady state or minimum creep rates be the same. Thus,for detailed analysis and prediction of creep behavior, other values which reflect the shape of each creep curve should be considered. For the purpose, authors have proposed Sato’s strain- acceleration-parameter (Strain Acceleration and Transition Objective index, SATO-index) which reflects strain rate change during creep deformation. Based on the concept of SATO-index, the whole creep curve can be represented by a set of small number of numerical parameters, and can be extrapolated from a part of creep curve. In this paper, application of the concept of SATO-index to the creep curves of aluminum-magnesium solid solutions that the creep behavior of the alloys are well investigated and analyzed. The creep curve can be extrapolated by the concept from transient part of creep curve, and the extrapolated creep rates at the minimum creep rate agree well with experiment. Efficiency of the concept of SATO-index to creep experiments is pronounced.

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WHITE, P. A., and D. M. SCOTT. "EXAMINATION OF SOUNDING CURVE EXTRAPOLATION USED BY THE OFFSET WENNER SYSTEM1." Geophysical Prospecting 36, no. 2 (February 1988): 194–200. http://dx.doi.org/10.1111/j.1365-2478.1988.tb02159.x.

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Kordonskii, Kh B., and M. M. Larin. "Substantiation of extrapolation of the fatigue curve to longer test bases." Strength of Materials 18, no. 11 (November 1986): 1458–61. http://dx.doi.org/10.1007/bf01524251.

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Kim, J., J. Suh, Hartmut Hoffmann, and Roland Golle. "Determination of Uniaxial Flow Stress Curve Using Aero-Bulge Test for Very Thin Copper Sheet." Advanced Materials Research 264-265 (June 2011): 608–13. http://dx.doi.org/10.4028/www.scientific.net/amr.264-265.608.

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Determination of the flow stress curve is an important step for precisely describing material behavior in Finite Element simulations. The flow stress curve is generally determined by taking a uniaxial tensile test as a standard. In the case of very thin sheet, since the fracture is generated at a low strain, there is not enough uniaxial data obtained to be applied in the FE simulation. The reason for this is that charactering plastic deformation at a large strain values by extrapolating a flow stress curve which is based on insufficient measurement data is highly susceptible to error. Bulge test is useful method for determining the equivalent biaxial flow stress curve up to a large strain. In this paper, the biaxial flow stresses curve for very thin copper sheet with thickness 35 and 50 μm were determined using the aero-bulge test. A new empirical model was derived for the estimation of the sheet thickness at the pole. After the compatibility between uniaxial and biaxial flow stresses was verified, the uniaxial flow stress curve was determined from the aero-bulge test using reverse engineering. The methodology of extrapolation of the flow stress curve at a large strain was finally proposed for application in FE simulations.

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LEONARD, J., M. MIETTON, H. NAJIB, and P. GOURBESVILLE. "Rating curve modelling with Manning's equation to manage instability and improve extrapolation." Hydrological Sciences Journal 45, no. 5 (October 2000): 739–50. http://dx.doi.org/10.1080/02626660009492374.

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Diekmann, Uwe, Alex Miron, and Andreea Trasca. "Hybrid Modeling of Materials Properties for Improved CAE-Simulations." Materials Science Forum 854 (May 2016): 163–66. http://dx.doi.org/10.4028/www.scientific.net/msf.854.163.

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The new MatPlus software supports the multi-dimensional modelling of materials properties using different data sources. Extensive mathematical functions allow curve fitting of data from different sources to any constitutive models and selectively combining models and datapoints along different dimensions. Physically consistent extrapolation of measured data within the complete multi-dimensional parametric space can be achieved. An integrated library of models can be extended by the user and already contains many popular equations like Hensel-Spittel and Zerilli-Armstrong for flow curves.

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Ayeni, B. J. "Parameter Estimation for Hyperbolic Decline Curve." Journal of Energy Resources Technology 111, no. 4 (December 1, 1989): 279–83. http://dx.doi.org/10.1115/1.3231437.

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The problem of estimating the nonlinear parameters associated with the hyperbolic decline curve equation is considered in this paper. Estimation equations are developed to estimate these nonlinear parameters. The condition under which the results can be used to predict future oil productions is examined using actual field data. An approximate linear term is obtained from the nonlinear hyperbolic equation through Taylor’s series expansion, and the optimum parameter values are determined by employing the method of least squares through an iterative process. The estimated parameters are incorporated into the original hyperbolic decline equation to provide realistic forecast function. This method does not require any straight line extrapolation, shifting, correcting and/or adjusting scales in order to estimate future oil and gas predictions. The method has been successfully applied to actual oil production data from a West Cameron Block 33 Field in South Louisiana. The results obtained are provided in Fig. 1.

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Warley, Russ. "Modeling the Pressure Decay Curve of a Capillary Rheometer." Applied Rheology 13, no. 1 (February 1, 2003): 8–13. http://dx.doi.org/10.1515/arh-2003-0001.

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Abstract A mathematical model for the transient pressure response in a capillary rheometer is implemented and validated with experimental data for both a natural rubber compound and a silicone rubber compound. The pressure decay curve after the cessation of motion of the instrument piston is shown to be consistent with the extrapolation of the power law model to shear rates two decades lower than experimentally attainable in the instrument employed. The model is useful for extending the range of the instrument in question by approximating material properties at shear rates lower than attainable in a steady flow experiment.

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Di Baldassarre, Giuliano, and Pierluigi Claps. "A hydraulic study on the applicability of flood rating curves." Hydrology Research 42, no. 1 (February 1, 2011): 10–19. http://dx.doi.org/10.2166/nh.2010.098.

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Several hydrological studies have shown that river discharge records are affected by significant uncertainty. This uncertainty is expected to be very high for river flow data referred to flood events, when the stage–discharge rating curve is extrapolated far beyond the measurement range. This study examines the standard methodologies for the construction and extrapolation of rating curves to extreme flow depths and shows the need of proper approaches to reduce the uncertainty of flood discharge data. To this end, a comprehensive analysis is performed on a 16km reach of the River Po (Italy) where five hydraulic models (HEC-RAS) were built. The results of five topographical surveys conducted during the last 50 years are used as geometric input. The application demonstrates that hydraulically built stage–discharge curves for the five cases differ only for ordinary flows, so that a common rating curve for flood discharges can be derived. This result confirms the validity of statistical approaches to the estimation of the so-called ‘flood rating curve’, a unique stage–discharge curve based on data of contemporaneous annual maxima of stage and discharge values, which appears insensitive to marginal changes in river geometry.

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Zohdy, A. A. R. "A new method for the automatic interpretation of Schlumberger and Wenner sounding curves." GEOPHYSICS 54, no. 2 (February 1989): 245–53. http://dx.doi.org/10.1190/1.1442648.

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A fast iterative method for the automatic interpretation of Schlumberger and Wenner sounding curves is based on obtaining interpreted depths and resistivities from shifted electrode spacings and adjusted apparent resistivities, respectively. The method is fully automatic. It does not require an initial guess of the number of layers, their thicknesses, or their resistivities; and it does not require extrapolation of incomplete sounding curves. The number of layers in the interpreted model equals the number of digitized points on the sounding curve. The resulting multilayer model is always well‐behaved with no thin layers of unusually high or unusually low resistivities. For noisy data, interpretation is done in two sets of iterations (two passes). Anomalous layers, created because of noise in the first pass, are eliminated in the second pass. Such layers are eliminated by considering the best‐fitting curve from the first pass to be a smoothed version of the observed curve and automatically reinterpreting it (second pass). The application of the method is illustrated by several examples.

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Gilad, Erez, Yael Neumeier, and Chen Dubi. "Dead time corrections on the Feynman-Y curve using the backward extrapolation method." Journal of Nuclear Science and Technology 55, no. 2 (October 31, 2017): 229–37. http://dx.doi.org/10.1080/00223131.2017.1394231.

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Vickers, Adrian. "An Evaluation of Survival Curve Extrapolation Techniques Using Long-Term Observational Cancer Data." Medical Decision Making 39, no. 8 (October 20, 2019): 926–38. http://dx.doi.org/10.1177/0272989x19875950.

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Objectives. Uncertainty in survival prediction beyond trial follow-up is highly influential in cost-effectiveness analyses of oncology products. This research provides an empirical evaluation of the accuracy of alternative methods and recommendations for their implementation. Methods. Mature (15-year) survival data were reconstructed from a published database study for “no treatment,” radiotherapy, surgery plus radiotherapy, and surgery in early stage non–small cell lung cancer in an elderly patient population. Censored data sets were created from these data to simulate immature trial data (for 1- to 10-year follow-up). A second data set with mature (9-year) survival data for no treatment was used to extrapolate the predictions from models fitted to the first data set. Six methodological approaches were used to fit models to the simulated data and extrapolate beyond trial follow-up. Model performance was evaluated by comparing the relative difference in mean survival estimates and the absolute error in the difference in mean survival v. the control with those from the original mature survival data set. Results. Model performance depended on the treatment comparison scenario. All models performed reasonably well when there was a small short-term treatment effect, with the Bayesian model coping better with shorter follow-up times. However, in other scenarios, the most flexible Bayesian model that could be estimated in practice appeared to fit the data less well than the models that used the external data separately. Where there was a large treatment effect (hazard ratio = 0.4), models that used external data separately performed best. Conclusions. Models that directly use mature external data can improve the accuracy of survival predictions. Recommendations on modeling strategies are made for different treatment benefit scenarios.

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Alfassi, Z. B., F. Groppi, M. L. Bonardi, O. Presler, and U. German. "Interpolation and extrapolation of gamma detection efficiency curve as a function of distance." Journal of Radioanalytical and Nuclear Chemistry 268, no. 3 (June 2006): 639–40. http://dx.doi.org/10.1007/s10967-006-0219-1.

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Gupta, Manish Kumar, and Nilamber Kumar Singh. "Post Necking Behaviour and Hardening Characterization of Mild Steel." Solid State Phenomena 319 (June 14, 2021): 7–12. http://dx.doi.org/10.4028/www.scientific.net/ssp.319.7.

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This paper investigates the post necking phenomenon in mild steel using six different hardening laws (Hollomon, Swift, Ludwik, Ghosh, Voce and Hockett-Sherby) by extrapolation method. This is carried out through the finite element simulation on tensile deformation of a mild steel specimen under quasi-static condition. Reference flow curves are obtained analytically and found helpful for the numerical simulation. The material parameters of the above hardening laws are evaluated by curve fitting method based on the pre necking experimental data and their suitability is examined before and after necking.

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Millard, R. K. "Indicator-dilution dispersion models and cardiac output computing methods." American Journal of Physiology-Heart and Circulatory Physiology 272, no. 4 (April 1, 1997): H2004—H2012. http://dx.doi.org/10.1152/ajpheart.1997.272.4.h2004.

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The general theory of indicator-dilution methods provides a basis for computing improved cardiac output estimates. Interpretation is via indicator-dispersion modeling with Brownian motion of drifting particles. Detected curves indicate the distribution of passage times from the injection site: the local density random walk (LDRW) function of a Wiener process. Fitting the LDRW to 70 dye curves by nonlinear regression for examples, I show how all possible undistorted curves can, in principle, be simulated. I show via semilogarithmic plots that conventional exponential decay constructs systematically underestimate cardiac output by up to 8%. To help reconcile the predictions of LDRW-fitted dilution curves and contemporary practice, I show how curve-shape asymmetry (skewness) dramatically affects the enclosed areas. Mean transit times may overestimate blood volumes by 15-100% in very skewed thermodilution curves if the dispersion effects are overlooked. Triangle constructions, which accounted for hundreds of experimental findings, also have theoretical explanations. Curve-fitting methods reduce the extrapolation biases inherent in many computers and in any respiration-induced artifacts. Compatibility of cardiac output predictions from various dilution methods and modules becomes feasible.

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31

Liu, Ying, Ming Yue Zhai, Li Peng Lu, and Yong Xiao Liu. "An Improved Method for Short-Term Power Load Forecasting Based on Fractal Extrapolation." Applied Mechanics and Materials 229-231 (November 2012): 1077–80. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.1077.

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Load forecasting based on fractal extrapolation is a very important method. However, traditional methods exists several disadvantages such as vertical scale factor difficult to calculate, low-precision, difficult to use. Therefore, a method is proposed combined with self-similarity theory and fractal extrapolation theory to solve the above problems. In this paper, the self-similarity of electrical load historical data is analyzed using multi-resolution wavelet firstly. Then use the Hurst parameter values to calculate vertical scaling factors based on the values of Hurst parameter and the other four parameters of Iterative Function Systems (IFS) affine transformation. At last the electrical load forecasting curve was generated by the iterations system. Considering the actual practical application, the algorithm was used to forecast electrical load based on fractal extrapolation. The computer simulation resulted that this algorithm has advantages of high-precision, less-sample demands, less-interpolation points and easy to use.

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LOPEZ, S., and E. OTRANTO. "EVALUATION OF THE FOLD LINE BY ASYMPTOTIC EXTRAPOLATION FOR STRUCTURAL ANALYSIS." International Journal of Structural Stability and Dynamics 04, no. 02 (June 2004): 147–70. http://dx.doi.org/10.1142/s0219455404001161.

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A technique for imperfection sensitivity analysis with reference to the geometrically nonlinear analysis of structures is presented. The paper discusses how detailed information on structural behavior can be obtained with less computational cost. The imperfection sensitivity analysis of structures is carried out by detecting the critical states on the equilibrium path relating to the various imperfections. In fact we can investigate the behavior of imperfect structures without considering the imperfect equilibrium curve. In this work we obtained the fold line, the one-dimensional equilibrium subset of limit points relating to different values of imperfection, by asymptotic extrapolation from a known singular point. The evaluation of this singular point on the perfect equilibrium curve is carried out by a path-following algorithm. A procedure that overcomes the ill-conditioning of the systems defined in the critical points is described. This proves to be highly advantageous in terms of computational cost in comparison with classical methods of analysis. The paper investigates the behavior of cylindrical shell. In particular the sensitivity analysis for load imperfections is carried out. The asymptotic extrapolation algorithm is also compared with continuation methods for the analysis of imperfect cylindrical shell.

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Domeneghetti, A., A. Castellarin, and A. Brath. "Assessing rating-curve uncertainty and its effects on hydraulic model calibration." Hydrology and Earth System Sciences 16, no. 4 (April 11, 2012): 1191–202. http://dx.doi.org/10.5194/hess-16-1191-2012.

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Abstract. This study considers the overall uncertainty affecting river flow measurements and proposes a framework for analysing the uncertainty of rating-curves and its effects on the calibration of numerical hydraulic models. The uncertainty associated with rating-curves is often considered negligible relative to other approximations affecting hydraulic studies, even though recent studies point out that rating-curves uncertainty may be significant. This study refers to a ~240 km reach of River Po and simulates ten different historical flood events by means of a quasi-twodimensional (quasi-2-D) hydraulic model in order to generate 50 synthetic measurement campaigns (5 campaigns per event) at the gauged cross-section of interest (i.e. Cremona streamgauge). For each synthetic campaign, two different procedures for rating-curve estimation are applied after corrupting simulated discharges according to the indications reported in the literature on accuracy of discharge measurements, and the uncertainty associated with each procedure is then quantified. To investigate the propagation of rating-curve uncertainty on the calibration of Manning's roughness coefficients further model simulations are run downstream Cremona's cross-section. Results highlight the significant role of extrapolation errors and how rating-curve uncertainty may be responsible for estimating unrealistic roughness coefficients. Finally, the uncertainty of these coefficients is analysed and discussed relative to the variability of Manning's coefficient reported in the literature for large natural streams.

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Domeneghetti, A., A. Castellarin, and A. Brath. "Assessing rating-curve uncertainty and its effects on hydraulic model calibration." Hydrology and Earth System Sciences Discussions 8, no. 6 (December 5, 2011): 10501–33. http://dx.doi.org/10.5194/hessd-8-10501-2011.

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Abstract. This study considers the overall uncertainty affecting river flow measurements and proposes a framework for analysing the uncertainty of rating-curves and its effects on the calibration of numerical hydraulic models. The uncertainty associated with rating-curves is often considered negligible relative to other approximations affecting hydraulic studies, even though recent studies point out that rating-curves uncertainty may be significant. This study refers to a ∼240 km reach of River Po and simulates ten different historical flood events by means of a quasi-twodimensional (quasi-2-D) hydraulic model in order to generate 50 synthetic measurement campaigns (5 campaigns per event) at the gauged cross-section of interest (i.e. Cremona streamgauge). For each synthetic campaign, two different procedures for rating-curve estimation are applied after corrupting simulated discharges according to the indications reported in the literature on accuracy of discharge measurements, and the uncertainty associated with each procedure is then quantified. To investigate the propagation of rating-curve uncertainty on the calibration of Manning's roughness coefficients further model simulations are run downstream Cremona's cross-section. Results highlight the significant role of extrapolation errors and how rating-curve uncertainty may be responsible for estimating unrealistic roughness coefficients. Finally, the uncertainty of these coefficients is analysed and discussed relative to the variability of Manning's coefficient reported in the literature for large natural streams.

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Vickers, AD, and E. Hawe. "PRM159 - AN EVALUATION OF SURVIVAL CURVE EXTRAPOLATION TECHNIQUES USING LONG-TERM OBSERVATIONAL CANCER DATA." Value in Health 21 (October 2018): S383. http://dx.doi.org/10.1016/j.jval.2018.09.2279.

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36

Sleivert, Gordon, and Laurel Traegar Mackinnon. "The validation of backward extrapolation of submaximal oxygen consumption from the oxygen recovery curve." European Journal of Applied Physiology and Occupational Physiology 63, no. 2 (August 1991): 135–39. http://dx.doi.org/10.1007/bf00235183.

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37

Xu, Yan, Baojian Wu, Xinrui Jiang, Haomiao Guo, and Feng Wen. "Experimental Measurement of Absorption Coefficients for Effective Erbium-Doping Concentration to Optimize Few-Mode Erbium-Doped Fiber Amplifiers with Low Differential Mode Gain." Photonics 8, no. 6 (May 25, 2021): 185. http://dx.doi.org/10.3390/photonics8060185.

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According to the analytical expression for modal gain of few-mode erbium-doped fiber amplifiers (FM-EDFAs), we propose a method of measuring the absorption loss coefficients of few-mode signals in few-mode erbium-doped fibers (FM-EDFs) by extrapolating the mode–gain curve dependent on the average population inversion. The absorption loss coefficient of an FM-EDF was measured in our experimental platform and used to estimate the effective erbium-ion doping concentration. The feasibility of the extrapolation method was verified by simulation and comparison with the transmission method. Furthermore, the FM-EDFAs with high modal gain and low differential mode gain (DMG) could be optimized by adjusting the FM-EDF’s length and pump power. The analysis process presented here is very useful for the efficient design of FM-EDFAs from a practical point of view.

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Cigizoglu, Hikmet Kerem. "A Method Based on Taking the Average of Probabilities to Compute the Flow Duration Curve." Hydrology Research 31, no. 3 (June 1, 2000): 187–206. http://dx.doi.org/10.2166/nh.2000.0012.

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In this study a method based on taking the average of the probabilities is presented to obtain flow duration curve. In this method the exceedance probability for each flow value is computed repeatedly for all time periods within a year. The final representing exceedance is just simply the average of all these probabilities. The applicability of the method to daily mean flows is tested assuming various marginal probability distributions like normal, Pearson type III, log-Pearson type III, 2-parameter lognormal and 3-parameter lognormal distributions. It is seen that the observed flow duration curves were quite well approximated by the 2-parameter lognormal average of probabilities curves. In that case the method requires the computation of the daily mean and standard deviation values of the observed flow data. The method curve enables extrapolation of the available data providing the exceedance probabilities for the flows higher than the observed maximum flow. The method is applied to the missing data and ungauged site problems and the results are quite satisfactory.

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Ardekani, MohammadAli, VahidReza Nafisi, and Foad Farhani. "Extrapolation of calibration curve of hot-wire spirometer using a novel neural network based approach." Journal of Medical Signals & Sensors 2, no. 4 (2012): 185. http://dx.doi.org/10.4103/2228-7477.110317.

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Sweeney, H. L., and M. J. Kushmerick. "Myosin phosphorylation in permeabilized rabbit psoas fibers." American Journal of Physiology-Cell Physiology 249, no. 3 (September 1, 1985): C362—C365. http://dx.doi.org/10.1152/ajpcell.1985.249.3.c362.

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The 18,000-Da myosin light chains in segments of rabbit psoas fibers were stably phosphorylated to assess the mechanical effects of this modification. Before and after phosphorylation of the same fiber, the maximal shortening velocity (Vmax) was measured at 12 degrees C by a quick-release slack test and by extrapolation to Vmax of hyperbolic force-velocity curves from isotonic releases. The experiments were performed at saturating concentrations of Ca2+, as determined from isometric force-pCa curves, under conditions in which the pH and ATP-ADP ratio were buffered. No effect of phosphorylation on isometric force, Vmax, or the shape of the force-velocity curve was detected under conditions of maximal calcium activation. Thus we find no mechanical evidence for a modulation by light chain phosphorylation of actomyosin interaction in these fiber segments.

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Chao, Zhiqiang, Fei Wang, Chuanqing Zhang, Huaying Li, and Feng Wang. "Research on the Algorithm of Measurement Path Planning for Inner Wall of Air-Intake Pipe Based on Spraying Robot System." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 09 (February 16, 2017): 1759018. http://dx.doi.org/10.1142/s0218001417590182.

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To solve the problems with spraying over the inner wall of air-intake pipe, this paper introduces an algorithm of measurement path planning based on the spraying robot system and the laser displacement sensor technology. Scanning measurement path planning is the premise and basis of model construction and spray. Traditional methods, such as arc length extrapolation and polynomial are applicable only for the measurement of a plane curve with finite maximum curvature. Drawing references from existing method, this paper focuses on the pre-scanning measurement method for different types of cross-section curves. Algorithm simulation and model reconstruction show that this study solves the problem of collision avoidance for scanning measurement of the inner wall of air-intake pipe.

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Jakóbczak, Dariusz. "Probabilistic Nodes Combination." International Journal of Organizational and Collective Intelligence 3, no. 3 (July 2012): 22–35. http://dx.doi.org/10.4018/ijoci.2012070102.

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Proposed method, called by author Probabilistic Nodes Combination (PNC), is such a method. This novel PNC method is introduced in the case of Hurwitz- Radon Matrices (MHR). MHR method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is modeled and interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

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Roze, Stéphane, Nicolas Bertrand, Lauriane Eberst, and Isabelle Borget. "Projecting overall survival data for health-economic models in oncology: Do maturity levels impact uncertainty?" Journal of Clinical Oncology 37, no. 15_suppl (May 20, 2019): e18350-e18350. http://dx.doi.org/10.1200/jco.2019.37.15_suppl.e18350.

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e18350 Background: A lifetime horizon is recommended for health-economic evaluation of anticancer drugs. If overall survival (OS) data is immature, extrapolation of the Kaplan-Meier (KM) curve using distributions is done to obtain long-term data. Depending on OS maturity, the distribution chosen may impact estimation of life expectancy (LE) and of life years gained (LYG) between treatments. This study aimed to estimate the error (on LE and LYG) induced by the choice of extrapolation distributions, for 2 levels of OS maturity (30% and 50%), as compared to LE and LYG at full maturity. Methods: Fifteen phase 3 trials published between 2013 and 2017 containing OS KM curves were selected if maturity > 70% (Full). To test 2 maturity levels, each KM curve was truncated at 30% and 50%. A 3-step process was performed: 1) KM was digitalized, 2) individual patient-data was reproduced using the Guyot algorithm, and 3) 5 parametric survival distributions were fit using the R-Survival package. For each study, the process was done for each treatment arm and each of the 3 maturity levels on the same time horizon, equal to the maximum follow-up of the study. For each curve, the best distribution was chosen by a board of 2 oncologists and 2 health-economists, based on visual inspection, Akaike/Bayesian Information criteria and external validity. Results: Based on the board review of the 90 KM curves, main chosen distributions were Weibull (33%), Log-logistic (32%) and Log-normal (27%). As compared to LE at full maturity, LE was overestimated in 23% and 40% at 30% and 50% maturity, respectively. Mean absolute error was 0.88 at 30% maturity, and decreased to 2.12 at 50% maturity, i.e. estimation was 2.4 times better from 30% to 50% maturity. On average, at 30% maturity versus full, mean percentage of error in LYG was 126.4% and 62.4% at 50% maturity versus full. Conclusions: The use of immature OS data increases the risk of error when projecting long-term LE. Even marginal gains in OS maturity can be translated in more accurate estimations and guide health-economist in developing models.

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Zhou, Guang-Dong, Ting-Hua Yi, Tai-Yong Zhu, and Huan Zhang. "A Whole-Range S–N Curve for Fatigue Assessment of Steel Orthotropic Bridge Decks." International Journal of Structural Stability and Dynamics 18, no. 08 (August 2018): 1840010. http://dx.doi.org/10.1142/s0219455418400102.

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The fatigue assessment of orthotropic bridge decks under routine traffic loading is a significant task to ensure the serviceability and safety of steel bridges. The sequential law computes fatigue damages using whole-range [Formula: see text]–[Formula: see text] curves and sequential stress histories and has been proven to provide more realistic results than Miner’s rule under variable amplitude loading. In this paper, a whole-range [Formula: see text]–[Formula: see text] curve covering the very low-cycle region, the low-cycle region, the finite life region, the high-cycle region, and the very high-cycle region is proposed for the sequential law to evaluate the fatigue performance of steel orthotropic bridge decks. The mathematical model of the whole-range [Formula: see text]–[Formula: see text] curve is first deduced based on the partially known [Formula: see text]–[Formula: see text] curve recommended in steel bridge design codes. The properties of the whole-range [Formula: see text]–[Formula: see text] curve are then explained from the geometrical point of view in the double logarithm coordinates system. Finally, rib-to-deck joints in steel orthotropic bridge decks are used as a case study. Fatigue test data are used to validate the proposed model. The whole-range [Formula: see text]–[Formula: see text] curve, with a 97.5% survival limit, is established for fatigue assessment of rib-to-deck joints in real bridges. The results show that the proposed whole-range [Formula: see text]–[Formula: see text] curve allows a good fit of experimental data and excellent agreement with code [Formula: see text]–[Formula: see text] curves in the finite life region and provides an effective extrapolation from the finite life region to the whole range of cycle numbers.

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Gerritse, RG. "Effect of reaction-rate on leaching of phosphate through sandy soils of Western-Australia." Soil Research 33, no. 1 (1995): 211. http://dx.doi.org/10.1071/sr9950211.

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The effect of reaction rate on the mobility of phosphate in soils was measured from breakthrough curves in the leachate from small columns of soil, following step increases in the input concentration of phosphate. Average mobilities of phosphate in columns of soil, following a step increase in the input concentration, decrease with decreasing rate of flow and with increasing distance travelled and appear to be linearly correlated on a log-log scale with both flow rate and distance travelled. An empirical equation, describing these relationships, fits data from leaching experiments at flow rates between 30 and 600 cm/day in columns of soil ~10-30 cm in length. Two coefficients are required and are obtained by curve fitting breakthrough curves, calculated with a numerical computer simulation model, to experimental breakthrough curves. The fitted equation enables extrapolation to flow rates and distances travelled that are more relevant to a field situation.

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Renhart, Werner, Oszkár Bíró, Christian Magele, Kurt Preis, and Alexander Rabel. "Inrush current computations using an optimised analytical hysteresis model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (September 4, 2017): 1568–76. http://dx.doi.org/10.1108/compel-03-2017-0117.

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Purpose The purpose of this paper is the modelling and estimation of inrush currents while energising power devices under no load conditions. An analytical representation of the nonlinear B-H curve serves for considering the hysteresis behaviour in the numerical model. Design/methodology/approach The model is implemented into a standard finite element formulation to compute transient problems. Findings Inrush currents behave like faults in power distribution facilities. Its prior estimation helps to distinguish between operating conditions and faults. Research limitations/implications The magnetic cores may become extremely magnetised. At such high material saturations, the material characteristics are not measurable accurately. Hence, the results depend on the extrapolation of the B-H curves. Originality/value The use of first-order reversal curves within the major hysteresis loops helps in a convenient way to estimate peak and shape of the inrush currents.

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Dottori, F., M. L. V. Martina, and E. Todini. "A dynamic rating curve approach to indirect discharge measurement." Hydrology and Earth System Sciences Discussions 6, no. 1 (February 23, 2009): 859–96. http://dx.doi.org/10.5194/hessd-6-859-2009.

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Abstract. The operational measurement of discharge in medium and large rivers is mostly based on indirect approaches by converting water stages into discharge on the basis of steady-flow rating curves. Unfortunately, under unsteady flow conditions, this approach does not guarantee accurate estimation of the discharge due, on the one hand, to the underlying steady state assumptions and, on the other hand, to the required extrapolation of the rating curve beyond the range of actual measurements used for its derivation. Historically, several formulas were proposed to correct the steady-state discharge value and to approximate the unsteady-flow stage-discharge relationship on the basis of water level measurements taken at a single cross section, where a steady state rating curve is available. However, most of them are either over-simplified or based on approximations that prevented their generalisation. Moreover all the mentioned formulas have been rarely tested on cases where their use becomes essential, namely under unsteady-flow conditions characterised by wide loop rating curves. In the present work, a new approach, based on simultaneous stage measurements at two adjacent cross sections, is introduced and compared to the approaches described in the literature. The comparison has been carried out on channels with constant or spatially variable geometry under a wide range of flood wave and river bed slope conditions. The results clearly show the improvement in the discharge estimation and the reduction of estimation errors obtainable using the proposed approach.

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Bhatnagar, R. M. "Noise reduction in linear variable differential transformer data of recoil motion measurement by numerical methods." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 2 (February 1, 2006): 159–66. http://dx.doi.org/10.1243/09544062jmes140.

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The measurement of recoil distance versus time by various methods such as the recoil potentiometer, photo electric transducer, slide wire, accelerometer, revolving drum system, and linear variable differential transformer (LVDT) has been used for gross muzzle brake efficiency measurements and recoil system performance evaluation by the calculation of recoil velocities. For a long recoil-length gun system, a combination of recoil potentiometer and LVDT is used extensively. In order to dispense with the use of recoil potentiometer in the above combination, the article proposes the use of the least-square-fit-based Richardson's extrapolation method and mean square velocity calculation for the accurate determination of free recoil velocity. The mean square velocity calculation is based on Parseval's theorem. The proposed method is based on the comparative evaluation of second- and third-order finite difference method, Richardson's fourth-order method, and the least-square-fit-based Richardson's extrapolation. The least-square-fit-based Richardson's extrapolation gives the lowest value of residual entropy. This is because the maximum likelihood estimators for Gauss probability distribution function and least-square estimators for the coefficients of polynomial representing recoil velocity time curve are coincident. The results of each of the four methods combined with the mean square velocity method were compared, and the least-square-fit-based Richardson's extrapolation was found to be accurate and consistent. The method can be used even when low pass filter is included in the LVDT circuit for stand-alone use.

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Abdallah, Z., K. Perkins, and S. Williams. "Advances in the Wilshire extrapolation technique—Full creep curve representation for the aerospace alloy Titanium 834." Materials Science and Engineering: A 550 (July 2012): 176–82. http://dx.doi.org/10.1016/j.msea.2012.04.054.

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Kim, Woo-Gon, Jae-Young Park, Seon-Jin Kim, Eung-Seon Kim, and Jinsung Jang. "Improvement of long-term creep life extrapolation using a new master curve for Grade 91 steel." Journal of Mechanical Science and Technology 32, no. 9 (September 2018): 4165–72. http://dx.doi.org/10.1007/s12206-018-0814-4.

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Journal articles on the topic 'Curve extrapolation'

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