Advanced Mission Synthesis Algorithms for Vibration-based Accelerated Life-testing

In the field of vibration qualification testing, with the popular Random Control mode of shakers, the specimen is excited by random vibrations typically set in the form of a Power Spectral Density (PSD). The corresponding signals are stationary and Gaussian, i.e. featuring a normal distribution. Conversely, real-life excitations are frequently non-Gaussian, exhibiting high peaks and/or burst signals and/or deterministic harmonic components. The so-called kurtosis is a parameter often used to statistically describe the occurrence and significance of high peak values in a random process. Since the similarity between test input profiles and real-life excitations is fundamental for qualification test reliability, some methods of kurtosis-control can be implemented to synthesize realistic (non-Gaussian) input signals. Durability tests are performed to check the resistance of a component to vibration-based fatigue damage. A procedure to synthesize test excitations which starts from measured data and preserves both the damage potential and the characteristics of the reference signals is desirable. The Fatigue Damage Spectrum (FDS) is generally used to quantify the fatigue damage potential associated with the excitation. The signal synthesized for accelerated durability tests (i.e. with a limited duration) must feature the same FDS as the reference vibration computed for the component’s expected lifetime. Current standard procedures are efficient in synthesizing signals in the form of a PSD, but prove inaccurate if reference data are non-Gaussian. This work presents novel algorithms for the synthesis of accelerated durability test profiles with prescribed FDS and a non-Gaussian distribution. An experimental campaign is conducted to validate the algorithms, by testing their accuracy, robustness, and practical effectiveness. Moreover, an original procedure is proposed for the estimation of the fatigue damage potential, aiming to minimize the computational time. The research is thus supposed to improve both the effectiveness and the efficiency of excitation profile synthesis for accelerated durability tests.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Kinematic description of the rupture from strong motion data: strategies for a robust inversion

We present a non linear technique to invert strong motion records with the aim of obtaining the final slip and rupture velocity distributions on the fault plane. In this thesis, the ground motion simulation is obtained evaluating the representation integral in the frequency. The Green’s tractions are computed using the discrete wave-number integration technique that provides the full wave-field in a 1D layered propagation medium. The representation integral is computed through a finite elements technique, based on a Delaunay’s triangulation on the fault plane. The rupture velocity is defined on a coarser regular grid and rupture times are computed by integration of the eikonal equation. For the inversion, the slip distribution is parameterized by 2D overlapping Gaussian functions, which can easily relate the spectrum of the possible solutions with the minimum resolvable wavelength, related to source-station distribution and data processing. The inverse problem is solved by a two-step procedure aimed at separating the computation of the rupture velocity from the evaluation of the slip distribution, the latter being a linear problem, when the rupture velocity is fixed. The non-linear step is solved by optimization of an L2 misfit function between synthetic and real seismograms, and solution is searched by the use of the Neighbourhood Algorithm. The conjugate gradient method is used to solve the linear step instead. The developed methodology has been applied to the M7.2, Iwate Nairiku Miyagi, Japan, earthquake. The estimated magnitude seismic moment is 2.6326 dyne∙cm that corresponds to a moment magnitude MW 6.9 while the mean the rupture velocity is 2.0 km/s. A large slip patch extends from the hypocenter to the southern shallow part of the fault plane. A second relatively large slip patch is found in the northern shallow part. Finally, we gave a quantitative estimation of errors associates with the parameters.

Analysis of slip distribution of large earthquakes oriented to tsunamigenesis characterisation

The present thesis focuses on the on-fault slip distribution of large earthquakes in the framework of tsunami hazard assessment and tsunami warning improvement. It is widely known that ruptures on seismic faults are strongly heterogeneous. In the case of tsunamigenic earthquakes, the slip heterogeneity strongly influences the spatial distribution of the largest tsunami effects along the nearest coastlines. Unfortunately, after an earthquake occurs, the so-called finite-fault models (FFM) describing the coseismic on-fault slip pattern becomes available over time scales that are incompatible with early tsunami warning purposes, especially in the near field. Our work aims to characterize the slip heterogeneity in a fast, but still suitable way. Using finite-fault models to build a starting dataset of seismic events, the characteristics of the fault planes are studied with respect to the magnitude. The patterns of the slip distribution on the rupture plane, analysed with a cluster identification algorithm, reveal a preferential single-asperity representation that can be approximated by a two-dimensional Gaussian slip distribution (2D GD). The goodness of the 2D GD model is compared to other distributions used in literature and its ability to represent the slip heterogeneity in the form of the main asperity is proven. The magnitude dependence of the 2D GD parameters is investigated and turns out to be of primary importance from an early warning perspective. The Gaussian model is applied to the 16 September 2015 Illapel, Chile, earthquake and used to compute early tsunami predictions that are satisfactorily compared with the available observations. The fast computation of the 2D GD and its suitability in representing the slip complexity of the seismic source make it a useful tool for the tsunami early warning assessments, especially for what concerns the near field.

A methodological approach for the performance optimization of transient seepage models through inverse analysis

The topic of the Ph.D project focuses on the modelling of the soil-water dynamics inside an instrumented embankment section along Secchia River (Cavezzo (MO)) in the period from 2017 to 2018 and the quantification of the performance of the direct and indirect simulations . The commercial code Hydrus2D by Pc-Progress has been chosen to run the direct simulations. Different soil-hydraulic models have been adopted and compared. The parameters of the different hydraulic models are calibrated using a local optimization method based on the Levenberg - Marquardt algorithm implemented in the Hydrus package. The calibration program is carried out using different types of dataset of observation points, different weighting distributions, different combinations of optimized parameters and different initial sets of parameters. The final goal is an in-depth study of the potentialities and limits of the inverse analysis when applied to a complex geotechnical problem as the case study. The second part of the research focuses on the effects of plant roots and soil-vegetation-atmosphere interaction on the spatial and temporal distribution of pore water pressure in soil. The investigated soil belongs to the West Charlestown Bypass embankment, Newcastle, Australia, that showed in the past years shallow instabilities and the use of long stem planting is intended to stabilize the slope. The chosen plant species is the Malaleuca Styphelioides, native of eastern Australia. The research activity included the design and realization of a specific large scale apparatus for laboratory experiments. Local suction measurements at certain intervals of depth and radial distances from the root bulb are recorded within the vegetated soil mass under controlled boundary conditions. The experiments are then reproduced numerically using the commercial code Hydrus 2D. Laboratory data are used to calibrate the RWU parameters and the parameters of the hydraulic model.

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.