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1

Said Ali El-Quliti, Said Ali El-Quliti. "Economic Scheduling of the Electric Transmission/ Distribution Substations in Jeddah City with Parametric Results." journal of King Abdulaziz University Engineering Sciences 23, no. 1 (2012): 115–36. http://dx.doi.org/10.4197/eng.23-2.7.

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This paper is devoted to economically scheduling the number of electric transmission/ distribution substations for long-term time horizon (2011 – 2020). The schedule aims at minimizing the total costs while maintaining the problem constraints based on a dynamic programming model. There are many parameters affecting the solution of the problem, these parameters are: initial value of the substation building cost, percentage of yearly increase in the substation building cost, percentage of discount for buying more than one substation, and present and future values of the operation cost. The proposed dynamic programming model will provide Saudi Electricity Company (SEC) with a systematic procedure to arrive at the best decision based on the optimal combination of the number of substations to be built in each year during the planning time horizon. It gives also an overview for the sensitivity range of parameter changes for the same optimal solution, and gives other optimal solution ranges for more changes in the parameters.
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MENDES, ALEXANDRE C., and NASSER FARD. "ACCELERATED FAILURE TIME MODELS COMPARISON TO THE PROPORTIONAL HAZARD MODEL FOR TIME-DEPENDENT COVARIATES WITH RECURRING EVENTS." International Journal of Reliability, Quality and Safety Engineering 21, no. 02 (2014): 1450010. http://dx.doi.org/10.1142/s0218539314500107.

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This paper presents an analysis of parametric survival models and compares their applications to time to event data used to validate the approximation for repeated events applying the Proportional Hazard Model (PHM) proposed in Mendes and Fard [Int. J. Reliab., Qual. Saf. Eng.19(6) (2012) 1240004.1–1240004.18]. The subjects studied do not show degrading failures, allowing the comparison between accelerated failure time models with the PHM. Results showed the applicability of the Weibull model and the versatility of the PHM not only to match the results of the parametric model, but also to allow the implementation of time-dependent covariates, resulting in superior model fit and more insightful interpretation for the covariate hazards. The paper contribution is to present the PHM as a simpler, more robust model to determine the acceleration factor for reliability testing when compared to the formidable task of fitting a parametric model for the distribution of failure. The Kaplan–Meier method may provide misleading guidance for covariate significance when time-dependent covariates are applied; however, relevant graphical screening is supplied. Notwithstanding, the PHM provides additional options to treat the repeated observations applying robust covariance correction for lack of heterogeneity in the fixed effects model or adopting the stratified model that absorbs the error using the stratification concept.
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Koźniewski, Edwin, and Marcin Orłowski. "Volume Optimization of Solid Waste Landfill Using Voronoi Diagram Geometry." Open Engineering 9, no. 1 (2019): 307–11. http://dx.doi.org/10.1515/eng-2019-0040.

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AbstractThe loose material, falling freely on the flat area, creates a geometric object similar to the roof. This object, which is in fact an embankment, the authors described and examined in previous works. They stated that the top view of such an object is a flat diagram of Voronoi. In view of the need to enlarge the landfill by combining the existing disjoint embankments, the authors were encouraged to apply the results obtained in practice. They also provided a detailed methodology for creating such embankments. In particular, they used the standard version of AutoCAD software and built a 3D model of the landfill based on solid operations. This parametric approach to design enables the rapid determination of the volume and surface area and fits in the BIM technology of designing engineering objects.
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Dorey, Alfred B., David W. Murray, and J. J. Roger Cheng. "Critical Buckling Strain Equations for Energy Pipelines—A Parametric Study." Journal of Offshore Mechanics and Arctic Engineering 128, no. 3 (2005): 248–55. http://dx.doi.org/10.1115/1.2199561.

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A recent review of available predictive critical buckling strain equations for segments of line pipe has shown that the equations give poor test-to-predicted ratios when validated using the more than 50 full-scale experimental pipeline test results available in the University of Alberta (U of A) database (Dorey, A. B., Murray, D. W., and Cheng, J. J. R., 2000, “An Experimental Comparison of Critical Buckling Strain Criteria,” Proceeding of the International Pipeline Conference, Calgary, Alberta, Oct. 1–5, ASME, New York, pp. 71–77, Paper No. IPC00-0157.). The pipeline specimens in the experimental database were subjected to a combination of axial load, internal pressure, and monotonically increasing curvature with magnitudes representative of those that might be experienced under field operating conditions. Research has been undertaken at the U of A to develop more reliable equations and a database of over 200 experimental and numerical results now exists. The numerical results were generated using a nonlinear finite element analysis (FEA) model that was validated using the experimental database. The FEA model provided a mean test-to-predicted ratio for the peak moment capacity of 1.025 with a coefficient of variation of 0.040 and a mean test-to-predicted ratio for the local critical buckling strain of 0.997 with a coefficient of variation of 0.067 (Dorey, A. B., Murray, D. W., and Cheng, J. J. R., 2005b, “A Comparison of Experimental and FEA Results for Segments of Line Pipe Under Combined Loads,” ASME J. Offshore Mech. Arct. Eng., in press.) for the 162 load cases analyzed. This paper presents the new predictive critical buckling strain equations developed from the U of A database.
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Aljuri, Nikolai, Lutz Freitag, and José G. Venegas. "Modeling expiratory flow from excised tracheal tube laws." Journal of Applied Physiology 87, no. 5 (1999): 1973–80. http://dx.doi.org/10.1152/jappl.1999.87.5.1973.

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Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area ( A tr) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. A tr was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126–147, 1977) for elastic tubes: Ptm = K p[( A tr/ A tr0)− n − 1], where A tr0 is A tr at Ptm = 0 and K p is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.
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6

Afsar, Salah Uddin, Mohammad Rashed Iqbal Faruque, Mohammad Jakir Hossain, Mayeen Uddin Khandaker, Hamid Osman, and Sultan Alamri. "Modified Hexagonal Split Ring Resonator Based on an Epsilon-Negative Metamaterial for Triple-Band Satellite Communication." Micromachines 12, no. 8 (2021): 878. http://dx.doi.org/10.3390/mi12080878.

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A triple-band epsilon-negative (ENG) metamaterial based on a split ring resonator (SSR) with a modified hexagonal-shaped metal strip proposed in this study is a new combination of a single slit square resonator and a modified hexagonal-shaped metal strip. The desired unit cell FR-4 (lossy) that was selected as the substrate was 1.6 mm thick. Following the assessment of the unit cell, a high-frequency electromagnetic simulator like the computer simulation technology (CST) microwave studio was applied to assess the S-parameters. The proposed design exhibited resonance at 2.89, 9.42, and 15.16 GHz. The unit cell also demonstrated negative permittivity in the frequency ranges 2.912–3.728 GHz, 9.552–10.144 GHz, and 15.216–17.328 GHz, along with a negative refractive index. An effective medium ratio (EMR) of 11.53 is an indicator of the goodness of the metamaterial unit cell. It is deliberate at the lowermost resonance frequency of 2.89 GHz. Moreover, the simulated results that were validated using HFSS and equivalent circuit model indicated slight variations. The proposed design was finalised based on several parametric studies, including design optimisation, different unit cell sizes, various substrate materials, and different electromagnetic (EM) field propagations. The proposed triple band (S, X, and Ku bands) negative permittivity metamaterial unit cell can be utilised for various wireless applications, such as microwave communication, satellite communication, and long-distance radio communication.
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7

Pascual-marqui, Roberto D., Pedro A. Valdes-sosa, and Alfredo Alvarez-amador. "A Parametric Model for Multichannel EEG Spectra." International Journal of Neuroscience 40, no. 1-2 (1988): 89–99. http://dx.doi.org/10.3109/00207458808985730.

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Blanco-Oliver, A., A. Irimia-Dieguez, M. D. Oliver-Alfonso, and M. J. Vázquez-Cueto. "Hybrid model using logit and nonparametric methods for predicting micro-entity failure." Investment Management and Financial Innovations 13, no. 3 (2016): 35–46. http://dx.doi.org/10.21511/imfi.13(3).2016.03.

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Following the calls from literature on bankruptcy, a parsimonious hybrid bankruptcy model is developed in this paper by combining parametric and non-parametric approaches.To this end, the variables with the highest predictive power to detect bankruptcy are selected using logistic regression (LR). Subsequently, alternative non-parametric methods (Multilayer Perceptron, Rough Set, and Classification-Regression Trees) are applied, in turn, to firms classified as either “bankrupt” or “not bankrupt”. Our findings show that hybrid models, particularly those combining LR and Multilayer Perceptron, offer better accuracy performance and interpretability and converge faster than each method implemented in isolation. Moreover, the authors demonstrate that the introduction of non-financial and macroeconomic variables complement financial ratios for bankruptcy prediction
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Robinson, Andrew P., Stephen E. Lane, and Guillaume Thérien. "Fitting forestry models using generalized additive models: a taper model example." Canadian Journal of Forest Research 41, no. 10 (2011): 1909–16. http://dx.doi.org/10.1139/x11-095.

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Nonparametric and semiparametric modelling methods are commonly applied in many fields. However, such methods have not been widely adopted in forestry, other than the most similar neighbour and nearest neighbor methods. Generalized additive modelling is a flexible semiparametric regression method that is useful when model-based prediction is the main goal and the parametric form of the model is unknown and possibly complex. Routines to fit generalized additive models (GAMs) are now readily available in much statistical software, making them an attractive option for forest modelling. Here, the use of GAMs is demonstrated by the construction of a taper model for six tree species in British Columbia, Canada. We compare the results with an existing flexible parametric taper model. We assess the performance of the models using the 0.632+ bootstrap method according to five key attributes: whole-stem volume, merchantable volume, number of logs, small-end diameter of the first log, and volume of the first log. The results show that the GAMs and the flexible taper function yielded similar accuracy for all attributes and all species.
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10

MARRANGHELLO, G. F., C. PROVIDÊNCIA, and A. M. S. DOS SANTOS. "PARAMETRIC COUPLING MODEL: RECENT ADVANCES." International Journal of Modern Physics D 19, no. 08n10 (2010): 1463–68. http://dx.doi.org/10.1142/s0218271810017470.

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We review the properties of the parametric coupling model and analyze its results when considering neutron star observations and heavy-ion collision experiments, specially those concerning the isospin characteristics of symmetric and asymmetric nuclear matter. By the end of the analysis, we are able to constrain the free parameters to a very small range of acceptable values.
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Shaheed, M. H., and M. O. Tokhi. "Dynamic modelling of a single-link flexible manipulator: parametric and non-parametric approaches." Robotica 20, no. 1 (2002): 93–109. http://dx.doi.org/10.1017/s0263574701003678.

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This paper presents an investigation into the development of parametric and non-parametric approaches for dynamic modelling of a flexible manipulator system. The least mean squares, recursive least squares and genetic algorithms are used to obtain linear parametric models of the system. Moreover, non-parametric models of the system are developed using a non-linear AutoRegressive process with eXogeneous input model structure with multi-layered perceptron and radial basis function neural networks. The system is in each case modelled from the input torque to hub-angle, hub-velocity and end-point acceleration outputs. The models are validated using several validation tests. Finally, a comparative assessment of the approaches used is presented and discussed in terms of accuracy, efficiency and estimation of the vibration modes of the system.
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Dolinsky, Pavol, Imrich Andras, Linus Michaeli, and Jan Saliga. "An ECG signal model based on a parametric description of the characteristic waves." ACTA IMEKO 9, no. 2 (2020): 3. http://dx.doi.org/10.21014/acta_imeko.v9i2.760.

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This article introduces a new electrocardiogram (ECG) signal model based on geometric signal properties. Instead of the artificial functions used in common ECG models, the proposed model is based on the modelling of real ECG signals divided into time segments. Each segment has been modelled using simple geometrical forms. The final ECG signal model is represented by the sequence of parameters of the base functions. Parameter variations allow for the generation of different waveforms for each subsequent heartbeat without mixing up the PQRST waves order. Two basic models utilize slightly modified elementary functions, which are computationally simple. A combination of both models allows for the modelling of irregularities in the consecutive heartbeats of the specific ECG waveforms. Respiratory, noise, and powerline interference can be added in order to make the generated ECG signal more realistic. The model parameters are estimated by differential evolution optimization and a comparison between the modelled ECG and the acquired signal. The proposed models are tested by the database included in the LabVIEW Biomedical Toolkit and ECG records in the MIT-BIH arrhythmia database.
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13

Fajar, Muhammad. "PEMODELAN PARAMETRIK KURVA PERTUMBUHAN EPIDEMI COVID-19 DI INDONESIA." Jurnal Matematika dan Sains 25, no. 2 (2020): 45–48. http://dx.doi.org/10.5614/jms.2020.25.2.4.

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The purpose of this study is to carry out parametric modeling of the COVID-19 epidemic growth curve so that the maximum value of the cumulative COVID-19 case and the time when it reaches that maximum point can be obtained. The data used in this study is the cumulative number of COVID-19 positive confirmed cases originating from www.covid19.go.id. The method used in this study is fitting data with the Logistic and Gompertz models. The results obtained from this study are (1) the Logistic and Gompertz mod-els are very fit in modeling the COVID-19 epidemic growth curve, indicated from the value of R2 (coefficient of determination) which reaches more than 99%, (2) From the Logistics model it is obtained that the estimated amount of the maximum cumulative case at the end of the COVID-19 epidemic is 7,714 positive confirmed cases, achieved in about 82 days (22 May 2020) from 2 March 2020 when the first positive COVID-19 case was announced by the Government. (3) From the Gompertz model, it is ob-tained that the estimated maximum cumulative case at the end of the COVID-19 epidemic is 33,975 positive confirmed cases, achieved in about 152 days (30 July 2020) from 2 March 2020 when the first positive COVID-19 case was announced by the Government. From this finding, the results of this study can be used as input to the Government to take steps in controlling the spread of COVID-19
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Zohra, Benamara Fatima, Belabed Lazhar, and Rouaiguia Ammar. "Proposed Improvements To Analytical Models of Anchored Retaining Walls." Environmental and Engineering Geoscience 25, no. 2 (2019): 115–26. http://dx.doi.org/10.2113/eeg-2078.

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ABSTRACT Anchored retaining walls are restraining walls constructed using anchors to achieve the highest stiffness possible within economic considerations. Anchor length estimation has an important role in the study of the stability of anchored retaining walls. The purpose of this study was to investigate the anchor length using different proposed failure models and Kranz's classic model. In addition, several parametric studies were conducted to find reliable results in the stability analysis of retaining anchored walls with the aim of obtaining stable and shorter anchor lengths. A numerical study was carried out using Geo4 and Plaxis 8.6 software on the same standard profile as analytically studied so as to validate the proposed mechanical models. The failure models proposed in this work are shown to be a useful tool for obtaining stable and shorter anchor lengths for anchored retaining walls.
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Et.al, Md Azman Shahadan. "Bayesian Hierarchical Growth Model for Experimental Data on the Effectiveness of an Incentive-Based Weight Reduction Method." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 1036–47. http://dx.doi.org/10.17762/turcomat.v12i3.840.

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The objective of this current research is to model the experimental data on the effectiveness of an incentive-based weight reduction method by using Bayesian hierarchical growth models. Three Bayesian hierarchical growth models are proposed, namely parametric Bayesian hierarchical growth model with correlated intercept and slope random effects model, parametric Bayesian hierarchical growth model with no correlated intercept and slope random effects model and semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The data is obtained from forty eight (48) students who had participated in an experiment on weight reduction method. The students were divided equally into two groups: single and pair groups. The experiment was carried out over the period of three months with a weight reading session for every two weeks. At the end of the study, we had six repeated measures of each student’s weight in kg and some measures of covariates and factors. Our results showed that the best model for the above data based on the Bayesian fit indexes and the models’ flexibility is the semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model. The results of the semi-parametric model showed that the ‘growth’ or reduction rates of the weight reduction experiment relate to the students’ gender, height in cm, experimental group (single or pair) and time in term of weeks.
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He, Li Lun, Xi Bin Wang, Zhi Bing Liu, Ming Chen, and Zong Wei Xu. "Mathematical Modeling and Parametric Design of Taper End Mills." Advanced Materials Research 797 (September 2013): 574–78. http://dx.doi.org/10.4028/www.scientific.net/amr.797.574.

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The mathematical modeling of the cutting tools is an important aspect for the design and manufacturing engineers from the viewpoint of shape realization. Taper mill is composed of side and end edges. In order to make each patch closely combined, the groove section is designed by considering the relation among tapered radius, groove depth and radius of inner land. Through translation and rotation of shape curve, the side flute and end flute model can be established. These models can be rendered in three dimensional software according to parametric design of taper end mills. And this methodology can be easily extended to design, manufacture other tools.
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Arize, Augustine C., Charles J. Berendt, Giuliana Campanelli Andreopoulos, Ioannis N. Kallianiotis, and John Malindretos. "Foreign Currency Forecasts: A Combination Analysis." International Journal of Financial Research 8, no. 2 (2017): 194. http://dx.doi.org/10.5430/ijfr.v8n2p194.

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This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better model is equation (34), but none of them gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.
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Xu, Wei, and Ingo Neumann. "Finite Element Analysis based on A Parametric Model by Approximating Point Clouds." Remote Sensing 12, no. 3 (2020): 518. http://dx.doi.org/10.3390/rs12030518.

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Simplified models are widely applied in finite element computations regarding mechanical and structural problems. However, the simplified model sometimes causes many deviations in the finite element analysis (FEA) of structures, especially in the non-designed structures which have undergone unknowable deformation features. Hence, a novel FEA methodology based on the parametric model by approximating three-dimensional (3D) feature data is proposed to solve this problem in the present manuscript. Many significant and effective technologies have been developed to detect 3D feature information accurately, e.g., terrestrial laser scanning (TLS), digital photogrammetry, and radar technology. In this manuscript, the parametric FEA model combines 3D point clouds from TLS and the parametric surface approximation method to generate 3D surfaces and models accurately. TLS is a popular measurement method for reliable 3D point clouds acquisition and monitoring deformations of structures with high accuracy and precision. The B-spline method is applied to approximate the measured point clouds data automatically and generate a parametric description of the structure accurately. The final target is to reduce the effects of the model description and deviations of the FEA. Both static and dynamic computations regarding a composite structure are carried out by comparing the parametric and general simplified models. The comparison of the deformation and equivalent stress of future behaviors are reflected by different models. Results indicate that the parametric model based on the TLS data is superior in the finite element computation. Therefore, it is of great significance to apply the parametric model in the FEA to compute and predict the future behavior of the structures with unknowable deformations in engineering accurately.
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Kazemzadeh, R., W. John, J. Wellmann, U. B. Bala, and A. Thiede. "Advanced parametrical modelling of 24 GHz radar sensor IC packaging components." Advances in Radio Science 9 (August 1, 2011): 383–89. http://dx.doi.org/10.5194/ars-9-383-2011.

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Abstract. This paper deals with the development of an advanced parametrical modelling concept for packaging components of a 24 GHz radar sensor IC used in automotive driver assistance systems. For fast and efficient design of packages for system-in-package modules (SiP), a simplified model for the description of parasitic electromagnetic effects within the package is desirable, as 3-D field computation becomes inefficient due to the high density of conductive elements of the various signal paths in the package. By using lumped element models for the characterization of the conductive components, a fast indication of the design's signal-quality can be gained, but so far does not offer enough flexibility to cover the whole range of geometric arrangements of signal paths in a contemporary package. This work pursues to meet the challenge of developing a flexible and fast package modelling concept by defining parametric lumped-element models for all basic signal path components, e.g. bond wires, vias, strip lines, bumps and balls.
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Arize, Augustine C., Charles J. Berendt, Giuliana Campanelli Andreopoulos, Ioannis N. Kallianiotis, and John Malindretos. "Foreign Currency Prognostication: Diverse Tests for Germany." International Journal of Financial Research 8, no. 3 (2017): 111. http://dx.doi.org/10.5430/ijfr.v8n3p111.

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This paper uses a large variety of different models and examines the predictive performance of these exchange rate models by applying parametric and non-parametric techniques. For forecasting, we will choose that predictor with the smallest root mean square forecast error (RMSE). The results show that the better models are in equations (3), (10), (17), and (18), although none gives a perfect forecast. At the end, error correction versions of the models will be fit so that plausible long-run elasticities can be imposed on the fundamental variables of each model.
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Beirlant, J., G. Matthys, and G. Dierckx. "Heavy-Tailed Distributions and Rating." ASTIN Bulletin 31, no. 1 (2001): 37–58. http://dx.doi.org/10.2143/ast.31.1.993.

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AbstractIn this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.
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Vitković, Nikola, Jelena Mitić, Miodrag Manić, et al. "The Parametric Model of the Human Mandible Coronoid Process Created by Method of Anatomical Features." Computational and Mathematical Methods in Medicine 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/574132.

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Geometrically accurate and anatomically correct 3D models of the human bones are of great importance for medical research and practice in orthopedics and surgery. These geometrical models can be created by the use of techniques which can be based on input geometrical data acquired from volumetric methods of scanning (e.g., Computed Tomography (CT)) or on the 2D images (e.g., X-ray). Geometrical models of human bones created in such way can be applied for education of medical practitioners, preoperative planning, etc. In cases when geometrical data about the human bone is incomplete (e.g., fractures), it may be necessary to create its complete geometrical model. The possible solution for this problem is the application of parametric models. The geometry of these models can be changed and adapted to the specific patient based on the values of parameters acquired from medical images (e.g., X-ray). In this paper, Method of Anatomical Features (MAF) which enables creation of geometrically precise and anatomically accurate geometrical models of the human bones is implemented for the creation of the parametric model of the Human Mandible Coronoid Process (HMCP). The obtained results about geometrical accuracy of the model are quite satisfactory, as it is stated by the medical practitioners and confirmed in the literature.
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Wang, Aaron J. "Numerical studies on the structural behaviour of composite end-plate connections." Canadian Journal of Civil Engineering 37, no. 6 (2010): 907–21. http://dx.doi.org/10.1139/l10-045.

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A three-dimensional (3-D) finite element model is established to predict the structural behaviour of composite end-plate connections with full incorporation of material and geometrical nonlinearities. A two-dimensional (2-D) finite element model is also proposed as a tool for a comprehensive parametric study, analysis, and design. The accuracy of both the models is verified by comparing the numerical results with those from tests and a design model. Various important structural behaviours of composite end-plate connection are also studied through the numerical and analytical simulations. These models are regarded as effective tools for conducting performance-based design of composite connections and semi-continuous beams with reasonable consideration of nonlinear deformation characteristics of both tensile reinforcements and shear connectors.
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Skorniakov, Viktor, Antanas Mainelis, Petras Navickas, Germanas Marinskis, and Albinas Stankus. "On the P-wave model of a single electrocardiogram lead." Seminars in Cardiovascular Medicine 27, no. 1 (2021): 1–11. http://dx.doi.org/10.2478/semcard-2021-0001.

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Summary We describe a parametric model for the P-wave of a single electrocardiogram (ECG) lead trajectory. Though previously met in the bioengineering literature, the model was not treated in a complete parametric fashion. The paper fills the gap by making use of both frequentist and Bayesian approaches. Supporting real data example is provided. Further potential applications are also discussed.
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Бейн, Дмитрий, Dmitriy Beyn, Михаил Булычев, and Mikhail Bulychev. "Condensed algorithm structural and parametric optimization of end walls of freight cars." Bulletin of Bryansk state technical university 2014, no. 1 (2014): 4–11. http://dx.doi.org/10.12737/23365.

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Proposed condensed algorithm structural and parametric optimization of end walls of freight cars. An example of optimization of end wall gondola model 12-119 according to the algorithm proposed. Shows the effectiveness of the proposed algorithm is compared with the results of the separately undertaken parametric optimization.
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Salem, Osama (Sam). "Parametric study on load ratio effect on the flexural bending behaviour of axially-restrained HSS steel beams subjected to fire." Journal of Structural Fire Engineering 9, no. 4 (2018): 342–60. http://dx.doi.org/10.1108/jsfe-10-2017-0042.

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Purpose In fire condition, the limiting temperature of a restrained steel beam depends on a few parameters, e.g. temperature distributions along and across the beam, beam’s load ratio and span length. The purpose of this study is to investigate the structural fire behaviour of axially restrained steel beams under different beam’s load ratios, taking into consideration the effect of the beam’s end connections configuration. Design/methodology/approach A three-dimensional finite element (FE) computer model has been developed to simulate the structural fire behaviour of axially restrained steel beams and their end connections. After successfully validating the developed model against the outcomes of the available large-size fire resistance experiments, the FE model has been used in a parametric study to investigate the beam’s load ratio effect on the behaviour of the axially restrained steel beams and their end connections. Findings The parametric study showed that increasing the beam loading level significantly increased the beam deflections at elevated temperatures; where, increasing the beam’s load ratio from 0.5 to 0.9 reduced the beam fire resistance by about 100 s. In contrast, decreasing the beam’s load ratio from 0.5 to 0.3 allowed the beam to easily achieve a 30-min fire resistance rating with no fire protection applied. Originality/value Experimental parametric studies are difficult to control in a laboratory setting and are also expensive and time consuming. Therefore, the reasonable accuracy of the validated FE model in reproducing the experimental fire behaviour of steel beams and their end connections makes it a very useful tool for both numerical and analytical studies.
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Wissel, Tobias, and Ramaswamy Palaniappan. "Considerations on Strategies to Improve EOG Signal Analysis." International Journal of Artificial Life Research 2, no. 3 (2011): 6–21. http://dx.doi.org/10.4018/jalr.2011070102.

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Electrooculogram (EOG) signals have been used in designing Human-Computer Interfaces, though not as popularly as electroencephalogram (EEG) or electromyogram (EMG) signals. This paper explores several strategies for improving the analysis of EOG signals. This article explores its utilization for the extraction of features from EOG signals compared with parametric, frequency-based approach using an autoregressive (AR) model as well as template matching as a time based method. The results indicate that parametric AR modeling using the Burg method, which does not retain the phase information, gives poor class separation. Conversely, the projection on the approximation space of the fourth level of Haar wavelet decomposition yields feature sets that enhance the class separation. Furthermore, for this method the number of dimensions in the feature space is much reduced as compared to template matching, which makes it much more efficient in terms of computation. This paper also reports on an example application utilizing wavelet decomposition and the Linear Discriminant Analysis (LDA) for classification, which was implemented and evaluated successfully. In this application, a virtual keyboard acts as the front-end for user interactions.
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Terry, William, Hongmei Zhang, Arnab Maity, Hasan Arshad, and Wilfried Karmaus. "Unified variable selection in semi-parametric models." Statistical Methods in Medical Research 26, no. 6 (2015): 2821–31. http://dx.doi.org/10.1177/0962280215610928.

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We propose a Bayesian variable selection method in semi-parametric models with applications to genetic and epigenetic data (e.g., single nucleotide polymorphisms and DNA methylation, respectively). The data are individually standardized to reduce heterogeneity and facilitate simultaneous selection of categorical (single nucleotide polymorphisms) and continuous (DNA methylation) variables. The Gaussian reproducing kernel is applied to the transformed data to evaluate joint effect of the variables, which may include complex interactions between, e.g., single nucleotide polymorphisms and DNA methylation. Indicator variables are introduced to the model for the purpose of variable selection. The method is demonstrated and evaluated using simulations under different scenarios. We apply the method to identify informative DNA methylation sites and single nucleotide polymorphisms in a set of genes based on their joint effect on allergic sensitization. The selected single nucleotide polymorphisms and methylation sites have the potential to serve as early markers for allergy prediction, and consequently benefit medical and clinical research to prevent allergy before its manifestation.
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Alves de Oliveira, Vinicius, Marie Chabert, Thomas Oberlin, et al. "Reduced-Complexity End-to-End Variational Autoencoder for on Board Satellite Image Compression." Remote Sensing 13, no. 3 (2021): 447. http://dx.doi.org/10.3390/rs13030447.

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Recently, convolutional neural networks have been successfully applied to lossy image compression. End-to-end optimized autoencoders, possibly variational, are able to dramatically outperform traditional transform coding schemes in terms of rate-distortion trade-off; however, this is at the cost of a higher computational complexity. An intensive training step on huge databases allows autoencoders to learn jointly the image representation and its probability distribution, possibly using a non-parametric density model or a hyperprior auxiliary autoencoder to eliminate the need for prior knowledge. However, in the context of on board satellite compression, time and memory complexities are submitted to strong constraints. The aim of this paper is to design a complexity-reduced variational autoencoder in order to meet these constraints while maintaining the performance. Apart from a network dimension reduction that systematically targets each parameter of the analysis and synthesis transforms, we propose a simplified entropy model that preserves the adaptability to the input image. Indeed, a statistical analysis performed on satellite images shows that the Laplacian distribution fits most features of their representation. A complex non parametric distribution fitting or a cumbersome hyperprior auxiliary autoencoder can thus be replaced by a simple parametric estimation. The proposed complexity-reduced autoencoder outperforms the Consultative Committee for Space Data Systems standard (CCSDS 122.0-B) while maintaining a competitive performance, in terms of rate-distortion trade-off, in comparison with the state-of-the-art learned image compression schemes.
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NI, HE, and HUJUN YIN. "SELF-ORGANISING MIXTURE AUTOREGRESSIVE MODEL FOR NON-STATIONARY TIME SERIES MODELLING." International Journal of Neural Systems 18, no. 06 (2008): 469–80. http://dx.doi.org/10.1142/s0129065708001737.

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Modelling non-stationary time series has been a difficult task for both parametric and nonparametric methods. One promising solution is to combine the flexibility of nonparametric models with the simplicity of parametric models. In this paper, the self-organising mixture autoregressive (SOMAR) network is adopted as a such mixture model. It breaks time series into underlying segments and at the same time fits local linear regressive models to the clusters of segments. In such a way, a global non-stationary time series is represented by a dynamic set of local linear regressive models. Neural gas is used for a more flexible structure of the mixture model. Furthermore, a new similarity measure has been introduced in the self-organising network to better quantify the similarity of time series segments. The network can be used naturally in modelling and forecasting non-stationary time series. Experiments on artificial, benchmark time series (e.g. Mackey-Glass) and real-world data (e.g. numbers of sunspots and Forex rates) are presented and the results show that the proposed SOMAR network is effective and superior to other similar approaches.
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Fan, Meng Chao, Xian Li Liu, Wei Ji, Dian Ge Zuo, and Ming Yang Wu. "Cutting Edge Mathematical Model for Ellipsoidal End Mill." Materials Science Forum 800-801 (July 2014): 495–500. http://dx.doi.org/10.4028/www.scientific.net/msf.800-801.495.

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In this paper, a new kind of ellipsoid end mill is proposed in order to improve the quality and efficiency in machining the sculptured surface. An integral ellipsoid end mill parameter optimization system architecture is developed to make the parametric design automatically and efficiently. Then, the mathematical model of continuous blade curve with constant helix angle and normal helix cutting edge of ellipsoid end mill is presented, as well as the cutting edge on the cylinder of cylindrical ellipsoid end mill. And then, all curves are simulated based on MATLAB software. Finally, the ellipsoid end mill is manufactured using a SAACKE UWIF CNC grinding machine to verify the feasibility of ellipsoid end mill.
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Brotherstone, S., I. M. S. White, and K. Meyer. "Genetic modelling of daily milk yield using orthogonal polynomials and parametric curves." Animal Science 70, no. 3 (2000): 407–15. http://dx.doi.org/10.1017/s1357729800051754.

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AbstractRandom regression models have been advocated for the analysis of test day records in dairy cattle. The effectiveness of a random regression analysis depends on the function used to model the data. To investigate functions suitable for the analysis of daily milk yield, test day milk yields of 7860 first lactation Holstein Friesian cows were analysed using random regression models involving three types of curves. Each analysis fitted the same curve to model overall trends through a fixed regression and random deviations due to animals. Curves included orthogonal polynomials, fitted to order 3 (quadratic), 4 (cubic) and 5 (quartic), respectively, a three-parameter parametric curve and a five-parameter parametric curve. Sets of random regression coefficients were fitted to model both animals’ genetic effects and permanent environmental effects. Temporary measurement errors were assumed independently but heterogeneously distributed, and assigned to one of 12 classes. Results showed that the measurement error variances were generally lowest around peak lactation, and higher at the beginning and end of lactation. Parametric curves yielded the highest likelihoods, but produced negative genetic associations between yield in early lactation and later lactation yields, while positive genetic correlations across the entire lactation were estimated with all models involving orthogonal polynomials. The fit of models using orthogonal polynomials to model test day yield was improved by including higher order fixed regressions.
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Pratikto, Fransiscus Rian. "Prediksi Akhir Pandemi COVID-19 di Indonesia dengan Simulasi Berbasis Model Pertumbuhan Parametrik." Jurnal Rekayasa Sistem Industri 9, no. 2 (2020): 63–68. http://dx.doi.org/10.26593/jrsi.v9i2.4018.63-68.

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This research aims to predict the end of the COVID-19 pandemic in Indonesia based on parametric growth models. The models are chosen by considering their fitness with the data of Taiwan which is believed to have passed over the peak of the pandemic and have gone through all phases in the growth curves. The models are parameterized using the nonlinear least squares method. The deviation and confidence interval of each parameter is estimated using the k-fold cross-validation and the bootstrap techniques. Using the total cases per million population data from March 2 to June 18, 2020, it was found that two growth models fit the data, i.e. logistic and modified Gompertz, where the latter performs better. Using the information about the deviation of each model parameter, a simulation model is developed to predict the time at which the total cases curve starts to flatten, which is an indication of the end of the pandemic. It was found with 95% confidence level that based on the modified Gompertz model the pandemic will end somewhere between March 9 – September 7, 2021 with total cases per million of 206 - 555. Meanwhile, based on the logistic growth model, the end of the pandemic is between August 28 – September 23, 2020 with total cases per million of 180 - 375. This model can be extended by making comparative scenario with Taiwan based on measures that represent the quality of the pandemic mitigation such as test ratio and the intensity of social restriction.
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Matusikova, Anna, Petra Rozehnalova, František Girgle, Vojtěch Kostiha, and Petr Štěpánek. "An Engineering Heat and Mass Transport Model Utilized for Concrete at Fire." Key Engineering Materials 738 (June 2017): 58–68. http://dx.doi.org/10.4028/www.scientific.net/kem.738.58.

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Mathematical models which can sufficiently describe processes proceeding in concrete during fire play an important role when assessing a load bearing capacity of concrete structures. In this paper a coupled heat and mass transport model based on principles of conservation of mass and energy is presented. A 2D computational solver using FEM was created to find three unknowns – a temperature, an amount of free water and a magnitude of pore pressure in concrete cross section during rapid heating. These variables, mutually connected through state equation, are necessary not only for determination the load bearing capacity of concrete element but also for prediction of concrete spalling. A parametric study of numerical results influenced by material properties of concrete (e.g. permeability, thermal conductivity) and initial conditions (e.g. relative humidity, temperature) is introduced and discussed in the end.
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35

Böhning, Dankmar. "Empirical Bayes estimators and non-parametric mixture models for space and time-space disease mapping and surveillance." Environmetrics 14, no. 5 (2003): 431–51. http://dx.doi.org/10.1002/env.598.

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36

Li, Yong Bing, Xin Min Lai, and Guan Long Chen. "The Influence of Interfacial Thermal Contact Conductance on Resistance Spot Weld Nugget Formation." Advanced Materials Research 97-101 (March 2010): 3239–42. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3239.

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Resistance spot welding process is strongly related to interfacial contact behaviors. The effects of thermal contact is rarely investigated so far and generally ignored in numerical models. In this work, a parametric FE model, which considers the variation of the surface roughness of the electrodes and workpieces, has been developed to investigate the effects of thermal contact on weld nugget formation. With the parametric model, four cases, e.g. ideal smooth surface, minimal roughness surface and maximum roughness surface for steel sheets and electrodes of as-received condition, and highly rough electrode surface, are investigated. Researches show that when the surface roughness of the electrodes exceeds some limit, the thermal contact conductance will substantially affect the weld nugget formation, therefore, must be considered in numerical models to precisely predict welding process.
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37

Han, Lei, Xuefeng Cheng, Lei Jiang, Rong Li, Guofu Ding, and Shengfeng Qin. "Research on parametric modeling and grinding methods of bottom edge of toroid-shaped end-milling cutter." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 233, no. 1 (2017): 31–43. http://dx.doi.org/10.1177/0954405417717547.

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For a toroid-shaped end-milling cutter to have multi-structure features of tooth offset center and introversion of bottom edge, this article proposes a generalized parametric modeling method of the bottom edge, including a straight edge segment and a circular arc edge segment. And based on the parametric model, this article also deduces the corresponding tool path for grinding of the bottom edge’s rake and flank faces. The parametric modeling method is based on the geometric analytic equations while the grinding method is driven by the proposed parametric model and the parameters of rake and flank faces. The two methods can be applied to a bottom edge of a cutter with multi-structure features to guarantee G1 continuity at the two joints for connecting a circular arc edge with a straight edge and a conical helix edge, respectively. In order to verify the accuracy of proposed methods, experiments were carried out. The modeling and grinding experimental results verified the accuracy and utility of the methods.
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38

Huizenga, H. M., J. C. de Munck, L. J. Waldorp, and R. P. P. P. Grasman. "Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model." IEEE Transactions on Biomedical Engineering 49, no. 6 (2002): 533–39. http://dx.doi.org/10.1109/tbme.2002.1001967.

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39

Kim, Kun Ho, Ting Zhang, and Wei Biao Wu. "PARAMETRIC SPECIFICATION TEST FOR NONLINEAR AUTOREGRESSIVE MODELS." Econometric Theory 31, no. 5 (2014): 1078–101. http://dx.doi.org/10.1017/s0266466614000681.

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The paper considers testing parametric assumptions on the conditional mean and variance functions for nonlinear autoregressive models. To this end, we compare the kernel density estimate of the marginal density of the process with a convolution-type density estimate. It is shown that, interestingly, the latter estimate has a parametric $\left( {\sqrt n } \right)$ rate of convergence, thus substantially improving the classical kernel density estimates whose rates of convergence are much inferior. Our results are confirmed by a simulation study for threshold autoregressive processes and autoregressive conditional heteroskedastic processes.
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40

Luo, Liang, Maohua Du, Jian Yuan, Jun Shi, Suhui Yu, and Yi Zhang. "Parametric Analysis and Stiffness Investigation of Extended End-Plate Connection." Materials 13, no. 22 (2020): 5133. http://dx.doi.org/10.3390/ma13225133.

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Extended end-plate (EP) bolted connections are widely used in steel structures as moment-resisting connections. Most of these connections are semi-rigid or in other words flexible. The paper aims to study the behavior of such connections under the effect of column top-side cyclic loading using the finite element (FE) method. For semi-rigid connections, it is very vital to determine the moment-rotation relationship as well as the connection stiffness. These beam-column connections have been parametrically studied, the effect of joint type, shear forces, diameter of bolt, thickness of end-plate, and end-plate style were studied. Parametric studies show that the panel zone shear force is the key factor and has a significant effect on the connection stiffness. Finally, based on the component method, the stiffness of the bending component is improved, and the initial stiffness calculation model of the connection under column top-side cyclic loadings is established. The results show that the calculation model is in good agreement with the finite element analyses, and this proves that the calculation model proposed in this study could act as a reference method.
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MEKKI, Reem Yousif, Mohamed Hassan MUDAWI, Manahil Saidahmed MUSTAFA, Altaiyb Omer Ahmed MOHMMED, Ahmed Bakheet Abd ALLA, and Abdel Rahman AHMED. "Parametric Survival Models of Hemodialysis Patients in Relation with Patient-Related Factors." Medicina Moderna - Modern Medicine 27, no. 4 (2020): 295–304. http://dx.doi.org/10.31689/rmm.2020.27.4.295.

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Background: Survival analysis refers to analyzing of statistical data for which the outcome variable of interest is time until an event occurs. This research aimed at comparing different models of parametric Proportional Hazards (PH) models (Weibull, exponential, Gompertz) in patients with hemodialysis to determine the best model for assessing the survival of patient. Study consists of 325 hemodialysis patients who referred to public hospitals in Khartoum state in the period from December 2005 to December 2015. Data was used to estimate the survival function with view to identify risk factors influencing among end-stage renal disease (ESRD) population. Based on the Cox-Snell Residuals and AIC, BIC, and Gompertz (PH) model is an efficient model than other when the values of (AIC=662.21), (BIC=703.83) and (R2=0.211) where maintained Study assessed that the variables dealing with univariate models were significant but had a significant effect on hemodialysis survival. The Gompertz model had the smallest AIC and BIC value; therefore; it was selected as the most appropriate model. In multivariable analysis, the BIC had the lowest value and the highest value in each analysis. The study assessed that diabetes mellitus and hypertension, regular, and hospital, had a. significant effect.
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42

Castro e Costa, Eduardo, Joaquim Jorge, Aaron D. Knochel, and José Pinto Duarte. "Enabling parametric design space exploration by non-designers." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 34, no. 2 (2020): 160–75. http://dx.doi.org/10.1017/s0890060420000177.

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AbstractIn mass customization, software configurators enable novice end-users to design customized products and services according to their needs and preferences. However, traditional configurators hardly provide an engaging experience while avoiding the burden of choice. We propose a Design Participation Model to facilitate navigating the design space, based on two modules. Modeler enables designers to create customizable designs as parametric models, and Navigator subsequently permits novice end-users to explore these designs. While most parametric designs support direct manipulation of low-level features, we propose interpolation features to give customers more flexibility. In this paper, we focus on the implementation of such interpolation features into Navigator and its user interface. To assess our approach, we designed and performed user experiments to test and compare Modeler and Navigator, thus providing insights for further developments of our approach. Our results suggest that barycentric interpolation between qualitative parameters provides a more easily understandable interface that empowers novice customers to explore the design space expeditiously.
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Li, Rong, Xue Feng Chen, Guo Fu Ding, Jian Jun Liu, and Xiao Bo Jin. "Development of an Integrated System of Geometric Modeling and Machining Simulation of End Mill." Applied Mechanics and Materials 120 (October 2011): 74–80. http://dx.doi.org/10.4028/www.scientific.net/amm.120.74.

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An integrated system of geometric modeling and machining simulation of end mills is presented for supporting end mill’s cutting analysis, structural optimization and digital manufacturing. In order to obtain accurate structural models, the main elements and detail features of end mills are modeled precisely, based on modular design and parametric design methodology. Through integrates 2D tool path and 3D virtual machining simulation seamlessly, a comprehensive simulation platform is constructed. To ensure the accuracy of manufacturing simulation model, the machining simulation model is compared to ideal design model. The results verify the correctness and rationality of the geometric modeling and machining simulation. NC codes generated by machining simulation can be output to tool grinder, supporting digital manufacturing of end mills.
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44

Bahaz, A., S. Amara, J. P. Jaspart, and J. F. Demonceau. "Analysis of the Behaviour of Semi Rigid Steel End Plate Connections." MATEC Web of Conferences 149 (2018): 02058. http://dx.doi.org/10.1051/matecconf/201814902058.

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The analysis of steel-framed building structures with full strength beam to column joints is quite standard nowadays. Buildings utilizing such framing systems are widely used in design practice. However, there is a growing recognition of significant benefits in designing joints as partial strength/semi-rigid. The design of joints within this partial strength/semi-rigid approach is becoming more and more popular. This requires the knowledge of the full nonlinear moment-rotation behaviour of the joint, which is also a design parameter. The rotational behaviour of steel semi rigid connections can be studied using the finite element method for the following three reasons: i) such models are inexpensive; ii) they allow the understanding of local effects, which are difficult to measure accurately physically, and iii) they can be used to generate extensive parametric studies. This paper presents a three-dimensional finite element model using ABAQUS software in order to identify the effect of different parameters on the behaviour of semi rigid steel beam to column end plate connections. Contact and sliding between different elements, bolt pretension and geometric and material non-linearity are included in this model. A parametric study is conducted using a model of two end-plate configurations: flush and extended end plates. The studied parameters were as follows: bolts type, end plate thickness and column web stiffener. Then, the model was calibrated and validated with experimental results taken from the literature and with the model proposed by Eurocode3. The procedure for determining the moment–rotation curve using finite element analysis is also given together with a brief explanation of how the design moment resistance and the initial rotational stiffness of the joint are obtained.
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45

Kokhno, P. "Models of the parametric range of competitive products." Obshchestvo i ekonomika, no. 8 (2021): 88. http://dx.doi.org/10.31857/s020736760016142-5.

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In the article an economic and mathematical model is developed for creating a parametric range of competitive military products and dual-use products, since when determining its competitiveness, it is necessary to give it a quantitative assessment. It is proposed to classify new products into two groups, according to their purpose: the first group includes products designed to meet the new needs of society; the second group includes products intended to replace obsolete products. At the same time, the methodology for calculating the set of parameters (tactical and technical characteristics) of a new product is proposed for use in the context of applying the end-to-end planning principle in the "science - production" cycle. The process of updating the range of competitive products, mass-produced for five years, is visually (graphically) represented. In addition, mathematical dependencies have been developed to optimize the cost of an updated sample at the stage of its development, that is, when technical and design capabilities are evaluated for subsequent modernization.
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46

Ugur, Emre, and Hakan Girgin. "Compliant Parametric Dynamic Movement Primitives." Robotica 38, no. 3 (2019): 457–74. http://dx.doi.org/10.1017/s026357471900078x.

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SummaryIn this paper, we propose and implement an advanced manipulation framework that enables parametric learning of complex action trajectories along with their haptic feedback profiles. Our framework extends Dynamic Movement Primitives (DMPs) method with a new parametric nonlinear shaping function and a novel force-feedback coupling term. The nonlinear trajectories of the action control variables and the haptic feedback trajectories measured during execution are encoded with parametric temporal probabilistic models, namely parametric hidden Markov models (PHMMs). PHMMs enable autonomous segmentation of a taught skill based on the statistical information extracted from multiple demonstrations, and learning the relations between the model parameters and the properties extracted from the environment. Hidden states with high-variances in observation probabilities are interpreted as parts of the skill that could not be reliably learned and autonomously executed due to possibly uncertain or missing information about the environment. In those parts, our proposed force-feedback coupling term, which computes the deviation of the actual force feedback from the one predicted by the force-feedback PHMM, acts as a compliance term, enabling a human to scaffold the ongoing movement trajectory to accomplish the task. Our method is verified in a number of tasks including a real pick and place task that involves obstacles of different heights. Our robot, Baxter, successfully learned to generate the trajectory taking into the heights of the obstacles, move its end effector stiffly (and accurately) along the generated trajectory while passing through apertures, and allow human–robot collaboration in the autonomously detected segments of the motion, for example, when the gripper picks up the object whose position is not provided to the robot.
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Warton, David I. "Many zeros does not mean zero inflation: comparing the goodness-of-fit of parametric models to multivariate abundance data." Environmetrics 16, no. 3 (2005): 275–89. http://dx.doi.org/10.1002/env.702.

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Zhang, Li-Na, Feng-Chen Li, Xiao-Yong Wang, and Peng-Fei Cui. "Theoretical and Numerical Analysis of 1 : 1 Main Parametric Resonance of Stayed Cable Considering Cable-Beam Coupling." Advances in Materials Science and Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/6948081.

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For the 1 : 1 main parametric resonances problems of cable-bridge coupling vibration, a main parametric resonances model considering cable-beam coupling is developed and dimensionless parametric resonances differential equations are derived. The main parametric resonances characteristics are discussed by means of multiscale approximation solution methods. Using an actual cable of cable-stayed bridge project for research object, numerical simulation analysis under a variety of conditions is illustrated. The results show that when the coupling system causes 1 : 1 parametric resonance, nonlinear main parametric resonances in response are unrelated to initial displacement of the cable, but with the increase of deck beam end vertical initial displacement increases, accompanied with a considerable “beat” vibration. When the vertical initial displacement of deck beam end is 10−6 m order of magnitude or even smaller, “beat” vibration phenomenon of cable and beam appears. Displacement amplitude of the cable is small and considerable amplitude vibration may not occur at this time, only making a slight stable “beat” vibration in the vicinity of the equilibrium position, which is different from 2 : 1 parametric resonance condition of cable-bridge coupling system. Therefore, it is necessary to limit the initial displacement excitation amplitude of beam end and prevent the occurrence of amplitude main parametric excitation resonances.
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Dado, Mohammad H. "Variable parametric pseudo-rigid-body model for large-deflection beams with end loads." International Journal of Non-Linear Mechanics 36, no. 7 (2001): 1123–33. http://dx.doi.org/10.1016/s0020-7462(00)00076-7.

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He, Li Lun, Zhi Bing Liu, Xi Bin Wang, and Wei Wei Lv. "Parametric Design of Tapered End Mills with Variable Pitch for Improving Stability." Applied Mechanics and Materials 599-601 (August 2014): 381–84. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.381.

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For the problems about design and manufacture of the variable pitch tapered end mills, this study proposes a three-dimensional parametric design method of variable pitch mill. Firstly the equation of calculating the optimal angle between the pitch was presented .Considering existing different patches between two cutting edges, helix edge curve and cross-section groove model of tapered end mill were established .Secondly, mathematical expression of ball end teeth for tapered mill was derived, and all points data of tapered mill surface can be determined by established model. Through the graphical representation, the points set are translated into a solid model.
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