Nonlinear Models and Their Applications

This chapter covers multiple regression and links statistical inference to general topics such as lurking variables that arose earlier. Many examples can be used to illustrate multiple regression, but we have found it useful to come to class prepared with a specific example, with computer output (since our students learn to run the regressions on the computer). We have found it is a good strategy to simply use a regression analysis from some published source (e.g., a social science journal) and go through the model and its interpretation with the class, asking students how the regression results would have to differ in order for the study’s conclusions to change. The chapter includes examples that revisit the simple linear model of height and income, involve the class in models of exam scores, and fit a nonlinear model (for more advanced classes) for golf putting.

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Set-membership identifiability of nonlinear models and related parameter estimation properties

International Journal of Applied Mathematics and Computer Science ◽

10.1515/amcs-2016-0057 ◽

2016 ◽

Vol 26 (4) ◽

pp. 803-813 ◽

Cited By ~ 2

Author(s):

Carine Jauberthie ◽

Louise Travé-MassuyèEs ◽

Nathalie Verdière

Keyword(s):

Mathematical Model ◽

Parameter Estimation ◽

Dynamic System ◽

Nonlinear Models ◽

Differential Algebra ◽

Related Parameter ◽

Set Membership ◽

Estimation Problems ◽

The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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Optimization of Sintering Process of Alumina Ceramics Using Response Surface Methodology

Sustainability ◽

10.3390/su13126739 ◽

2021 ◽

Vol 13 (12) ◽

pp. 6739

Author(s):

Darko Landek ◽

Lidija Ćurković ◽

Ivana Gabelica ◽

Mihone Kerolli Mustafa ◽

Irena Žmak

Keyword(s):

Response Surface Methodology ◽

Response Surface ◽

Heating Rate ◽

Sintering Temperature ◽

Nonlinear Models ◽

Slip Casting ◽

Holding Time ◽

Alumina Ceramics ◽

Aqueous Suspensions ◽

Temperature Heating

In this work, alumina (Al2O3) ceramics were prepared using an environmentally friendly slip casting method. To this end, highly concentrated (70 wt.%) aqueous suspensions of alumina (Al2O3) were prepared with different amounts of the ammonium salt of a polycarboxylic acid, Dolapix CE 64, as an electrosteric dispersant. The stability of highly concentrated Al2O3 aqueous suspensions was monitored by viscosity measurements. Green bodies (ceramics before sintering) were obtained by pouring the stable Al2O3 aqueous suspensions into dry porous plaster molds. The obtained Al2O3 ceramic green bodies were sintered in the electric furnace. Analysis of the effect of three sintering parameters (sintering temperature, heating rate and holding time) on the density of alumina ceramics was performed using the response surface methodology (RSM), based on experimental data obtained according to Box–Behnken experimental design, using the software Design-Expert. From the statistical analysis, linear and nonlinear models with added first-order interaction were developed for prediction and optimization of density-dependent variables: sintering temperature, heating rate and holding time.

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