Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter estimation

A new control scheme has been presented in this thesis. Based on the NonLinear Geometric Approach, the proposed Active Control System represents a new way to see the reconfigurable controllers for aerospace applications. The presence of the Diagnosis module (providing the estimation of generic signals which, based on the case, can be faults, disturbances or system parameters), mean feature of the depicted Active Control System, is a characteristic shared by three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric Approach (NLGA) has been accurately investigated and than improved to extend its applicability to more complex models. The standard NLGA procedure has been modified to take account of feasible and estimable sets of unknown signals. Furthermore the application of the Singular Perturbations approximation has led to the solution of Detection and Isolation problems in scenarios too complex to be solved by the standard NLGA. Also the estimation process has been improved, where multiple redundant measuremtent are available, by the introduction of a new algorithm, here called "Least Squares - Sliding Mode". It guarantees optimality, in the sense of the least squares, and finite estimation time, in the sense of the sliding mode. The Active Control System concept has been formalized in two controller: a nonlinear backstepping controller and a nonlinear composite controller. Particularly interesting is the integration, in the controller design, of the estimations coming from the Diagnosis module. Stability proofs are provided for both the control schemes. Finally, different applications in aerospace have been provided to show the applicability and the effectiveness of the proposed NLGA-based Active Control System.

Modelling biogeochemical cycles in forest ecosystems: a Bayesian approach

Forest models are tools for explaining and predicting the dynamics of forest ecosystems. They simulate forest behavior by integrating information on the underlying processes in trees, soil and atmosphere. Bayesian calibration is the application of probability theory to parameter estimation. It is a method, applicable to all models, that quantifies output uncertainty and identifies key parameters and variables. This study aims at testing the Bayesian procedure for calibration to different types of forest models, to evaluate their performances and the uncertainties associated with them. In particular,we aimed at 1) applying a Bayesian framework to calibrate forest models and test their performances in different biomes and different environmental conditions, 2) identifying and solve structure-related issues in simple models, and 3) identifying the advantages of additional information made available when calibrating forest models with a Bayesian approach. We applied the Bayesian framework to calibrate the Prelued model on eight Italian eddy-covariance sites in Chapter 2. The ability of Prelued to reproduce the estimated Gross Primary Productivity (GPP) was tested over contrasting natural vegetation types that represented a wide range of climatic and environmental conditions. The issues related to Prelued's multiplicative structure were the main topic of Chapter 3: several different MCMC-based procedures were applied within a Bayesian framework to calibrate the model, and their performances were compared. A more complex model was applied in Chapter 4, focusing on the application of the physiology-based model HYDRALL to the forest ecosystem of Lavarone (IT) to evaluate the importance of additional information in the calibration procedure and their impact on model performances, model uncertainties, and parameter estimation. Overall, the Bayesian technique proved to be an excellent and versatile tool to successfully calibrate forest models of different structure and complexity, on different kind and number of variables and with a different number of parameters involved.

Novel methods of state estimation and parameter identification for high-performance motorcycles

This research activity aims at providing a reliable estimation of particular state variables or parameters concerning the dynamics and performance optimization of a MotoGP-class motorcycle, integrating the classical model-based approach with new methodologies involving artificial intelligence. The first topic of the research focuses on the estimation of the thermal behavior of the MotoGP carbon braking system. Numerical tools are developed to assess the instantaneous surface temperature distribution in the motorcycle's front brake discs. Within this application other important brake parameters are identified using Kalman filters, such as the disc convection coefficient and the power distribution in the disc-pads contact region. Subsequently, a physical model of the brake is built to estimate the instantaneous braking torque. However, the results obtained with this approach are highly limited by the knowledge of the friction coefficient (μ) between the disc rotor and the pads. Since the value of μ is a highly nonlinear function of many variables (namely temperature, pressure and angular velocity of the disc), an analytical model for the friction coefficient estimation appears impractical to establish. To overcome this challenge, an innovative hybrid solution is implemented, combining the benefit of artificial intelligence (AI) with classical model-based approach. Indeed, the disc temperature estimated through the thermal model previously implemented is processed by a machine learning algorithm that outputs the actual value of the friction coefficient thus improving the braking torque computation performed by the physical model of the brake. Finally, the last topic of this research activity regards the development of an AI algorithm to estimate the current sideslip angle of the motorcycle's front tire. While a single-track motorcycle kinematic model and IMU accelerometer signals theoretically enable sideslip calculation, the presence of accelerometer noise leads to a significant drift over time. To address this issue, a long short-term memory (LSTM) network is implemented.

Ground penetrating radar early-time technique for soil electromagnetic parameters estimation

In recent years, thanks to the technological advances, electromagnetic methods for non-invasive shallow subsurface characterization have been increasingly used in many areas of environmental and geoscience applications. Among all the geophysical electromagnetic methods, the Ground Penetrating Radar (GPR) has received unprecedented attention over the last few decades due to its capability to obtain, spatially and temporally, high-resolution electromagnetic parameter information thanks to its versatility, its handling, its non-invasive nature, its high resolving power, and its fast implementation. The main focus of this thesis is to perform a dielectric site characterization in an efficient and accurate way studying in-depth a physical phenomenon behind a recent developed GPR approach, the so-called early-time technique, which infers the electrical properties of the soil in the proximity of the antennas. In particular, the early-time approach is based on the amplitude analysis of the early-time portion of the GPR waveform using a fixed-offset ground-coupled antenna configuration where the separation between the transmitting and receiving antenna is on the order of the dominant pulse-wavelength. Amplitude information can be extracted from the early-time signal through complex trace analysis, computing the instantaneous-amplitude attributes over a selected time-duration of the early-time signal. Basically, if the acquired GPR signals are considered to represent the real part of a complex trace, and the imaginary part is the quadrature component obtained by applying a Hilbert transform to the GPR trace, the amplitude envelope is the absolute value of the resulting complex trace (also known as the instantaneous-amplitude). Analysing laboratory information, numerical simulations and natural field conditions, and summarising the overall results embodied in this thesis, it is possible to suggest the early-time GPR technique as an effective method to estimate physical properties of the soil in a fast and non-invasive way.