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The response of single SnO2 nanowire gas sensors with different diameters between 20 and 140 nm are evaluated by calculating the nanowire conductivity as a function of the surface charge density. The procedure involves the numerical solution of the Poisson-Boltzmann equation for the electrostatic potential in cylindrical geometry in order to model the depletion region and band bending at the SnO2 nanowire surface. In the model we take into account varying surface charge densities σ and bulk electron concentrations n0 to calculate the electrical conductivity. Considering the fact that the surface charge density depends on the nanowire surface interactions with ambient gas, the model allows us to simulate the sensor response when the nanowire is employed as gas sensing component. We report a saturation in depletion length λ versus surface charge density σ which is the principal reason for limiting the sensor responses. The results also show that the conductivity is decreasing by increasing surface charge density, the smaller the nanowire diameter the steeper the decrease. As a result the nanowire response is proportional to 1/d where d is the nanowire diameter. Furthermore, we argue about the validity of the modeling results and their relevance to experimental findings on SnO2 nanowire based gas sensors reported in literature.

Hybrid semiparametric models integrate physics-based (“white-box”, parametric) and data-driven (“black-box”, non-parametric) submodels. Black-box models are often implemented using artificial neural networks (ANNs). In this work, we investigate the fitness of symbolic regression (SR) for black-box modelling. The main advantage of this approach is that a trained hybrid model can be expressed in closed form as an algebraic equation. We examine and test the idea on a simple example, namely the v-shape bending of a metal sheet, where an analytical solution for the stamping force is readily available. We explore unconstrained and hybrid symbolic regression modelling to show that hybrid SR models, where the regression tree is partly fixed according to a-priori knowledge, perform much better than purely data-driven SR models based on unconstrained regression trees. Furthermore, the generation of algebraic equations by this method is much more repeatable, which makes the approach applicable to process knowledge discovery.

A simple hybrid model, integrating observation (black-box) and physical knowledge (white-box), is employed to model an induction heating process. A neural network is used to estimate the unknown physical process parameter in the physical model. Most relevant to induction hardening is the temperature evolution in a layer under the surface of a sample, in our case a cylindrical sample. We show that with a hybrid model, in which a simple ordinary differential equation describes the heating rate, the experimental data can be approximated better than using a black-box only. The hybrid model extrapolates better and it is easier to interpret. The hybrid model can be used as a prediction tool to operate and optimize induction heating processes.