scholarly journals maxsmooth: Derivative Constrained Function Fitting

2020 ◽  
Vol 5 (54) ◽  
pp. 2596
Author(s):  
Harry Bevins
Keyword(s):  
Function Fitting ◽  
Constrained Function

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

A novel algorithm for acoustic above ground marking based on function fitting

Measurement ◽  
2013 ◽  
Vol 46 (8) ◽  
pp. 2341-2347 ◽  
Author(s):  
Yibo Li ◽  
Dian Wang ◽  
Liying Sun
Keyword(s):  
Function Fitting ◽  
Novel Algorithm

Experimental Study on Fracture Toughness of Q460C the High-Strength Construction Steel at Low Temperature

2011 ◽  
Vol 71-78 ◽  
pp. 890-897 ◽  
Author(s):  
Yuan Qing Wang ◽  
Yun Lin ◽  
Yan Nian Zhang ◽  
Yong Jiu Shi
Keyword(s):  
Low Temperature ◽  
High Strength ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Three Point Bending ◽  
Function Fitting ◽  
Ductile Brittle Transition Temperature ◽  
Boltzmann Function ◽  
Fracture Appearance ◽  
Crack Tip Opening

Three point bending tests were carried out on 14mm-thick Q460C the high-strength structural steel at low temperature, and scanning electronic microscope of the fracture appearance was analyzed. The results showed that the obvious feature of brittle mechanism was shown on the three point bending specimen fracture whose testing took place at -40°C. And the crack tip opening displacement value of Q460C steel, which was less than that of Q235 steel, Q345 steel and Q390 steel at low temperature, tended to decrease with respect to the temperature reduction. Moreover, a Boltzmann function fitting analysis was applied to the experimental data, and the ductile-brittle transition temperature and the changing regularity were obtained.

scholarly journals Flux control coefficients determined by inhibitor titration: the design and analysis of experiments to minimize errors

1993 ◽  
Vol 296 (2) ◽  
pp. 423-433 ◽  
Author(s):  
J R Small
Keyword(s):  
Random Errors ◽  
Flux Control ◽  
Graph Method ◽  
Function Fitting ◽  
Fitting Method ◽  
Simple Extrapolation ◽  
Experimental Errors ◽  
Flux Control Coefficients ◽  
Fitted Function ◽  
Control Coefficients

This paper is a study into the effects of experimental error on the estimated values of flux control coefficients obtained using specific inhibitors. Two possible techniques for analysing the experimental data are compared: a simple extrapolation method (the so-called graph method) and a non-linear function fitting method. For these techniques, the sources of systematic errors are identified and the effects of systematic and random errors are quantified, using both statistical analysis and numerical computation. It is shown that the graph method is very sensitive to random errors and, under all conditions studied, that the fitting method, even under conditions where the assumptions underlying the fitted function do not hold, outperformed the graph method. Possible ways of designing experiments to minimize the effects of experimental errors are analysed and discussed.

Highway Tunnel Lighting Research Based on Mesopic Vision

2011 ◽  
Vol 71-78 ◽  
pp. 4061-4064
Author(s):  
Yong Yang ◽  
Chuan Zheng Zhu ◽  
Lei Wang
Keyword(s):  
Reaction Time ◽  
Design Method ◽  
B Value ◽  
Light Sources ◽  
White Led ◽  
Mesopic Vision ◽  
Highway Tunnel ◽  
Function Fitting ◽  
Sodium Lamp ◽  
High Pressure Sodium Lamp

The white LED and high-pressure sodium lamp (HPS) are used to simulate highway tunnel lighting under different background brightness (abbreviated as B) conditions, from a series of reaction time tests, the result shows that white LED can provide shorter reaction time for observers compared with HPS, further research suggests under the mesopic vision, different kinds of light sources maybe have unlike brightness, although which is identical under the photopic vision. From the luminous spectrum test and mesopic vision spectral luminous efficiency function fitting calculation, the mesopic equivalent brightness can be determined with certain light source and B value. This conclusion would provide a more accurate and lower energy consumption lighting design method for highway tunnel.

Composite Laminate Stiffnesses and Their Sensitivities

1994 ◽  
Author(s):  
Bodo Geier ◽  
Rolf Zimmermann
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Composite Laminate ◽  
Shear Stiffness ◽  
Efficient Algorithms ◽  
Search Procedure ◽  
Object Function ◽  
Stiffness Matrices ◽  
Derivatives Of ◽  
Constrained Function

Abstract The great number of possible stacking orders to form laminates suggests to apply optimization, more frequently than usual, in the design of structures made of composite materials. One of the columns upon which optimization of structures is built is the mathematical search procedure for locating a minimum (or maximum) of a constrained function. Efficient algorithms will require the evaluation of derivatives of the object function as well as of the constraints. In that context the sensitivities of laminate stiffness matrices may be required. In order to meet such a requirement the derivatives with respect to both ply thicknesses and ply angles, of laminate stiffnesses, including transverse shear stiffness, will be presented in this report.

A Method to Compare Heterogeneous Types of Bone and Cartilage Meshes

2021 ◽  
Author(s):  
Nynke B. Rooks ◽  
Marco T. Y. Schneider ◽  
Ahmet Erdemir ◽  
Jason P. Halloran ◽  
Peter J. Laz ◽  
...  
Keyword(s):  
Knee Joint ◽  
Subchondral Bone ◽  
Joint Modeling ◽  
Bone Morphology ◽  
Research Teams ◽  
Mesh Topology ◽  
Function Fitting ◽  
The Mean ◽  
Nodal Density ◽  
And Cartilage

Abstract Accurately capturing the bone and cartilage morphology and generating a mesh remains a critical step in the workflow of computational knee joint modeling. Currently there is no standardized method to compare meshes of different element types and nodal densities, making comparisons across research teams a significant challenge. The aim of this paper is to describe a method to quantify differences in knee joint bone and cartilages meshes, independent of bone and cartilage mesh topology. Bone mesh-to-mesh distances, subchondral bone boundaries and cartilage thicknesses from meshes of any type of mesh are obtained using a series of steps involving registration, resampling, and radial basis function fitting after which the comparisons are performed. Subchondral bone boundaries and cartilage thicknesses are calculated and visualized in a common frame of reference for comparison. The established method is applied to models developed by five modeling teams. Our approach to obtain bone mesh-to-mesh distances decreased the divergence seen in selecting a reference mesh (i.e. comparing mesh A-to-B vs. mesh B-to-A). In general the bone morphology was similar across teams. The cartilage thicknesses for all models were calculated and the mean absolute cartilage thickness difference was presented, the articulating areas had the best agreement across teams. The teams showed disagreement on the subchondral bone boundaries. The method presented in this paper allows for objective comparisons of bone and cartilage geometry that is agnostic to mesh type and nodal density.

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