Rainfall spatial predictions: a two-part model and its assessment

Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software. Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.

Vibration as a method for muscular stimulation

Human reactions to vibration have been extensively investigated in the past. Vibration, as well as whole-body vibration (WBV), has been commonly considered as an occupational hazard for its detrimental effects on human condition and comfort. Although long term exposure to vibrations may produce undesirable side-effects, a great part of the literature is dedicated to the positive effects of WBV when used as method for muscular stimulation and as an exercise intervention. Whole body vibration training (WBVT) aims to mechanically activate muscles by eliciting neuromuscular activity (muscle reflexes) via the use of vibrations delivered to the whole body. The most mentioned mechanism to explain the neuromuscular outcomes of vibration is the elicited neuromuscular activation. Local tendon vibrations induce activity of the muscle spindle Ia fibers, mediated by monosynaptic and polysynaptic pathways: a reflex muscle contraction known as the Tonic Vibration Reflex (TVR) arises in response to such vibratory stimulus. In WBVT mechanical vibrations, in a range from 10 to 80 Hz and peak to peak displacements from 1 to 10 mm, are usually transmitted to the patient body by the use of oscillating platforms. Vibrations are then transferred from the platform to a specific muscle group through the subject body. To customize WBV treatments, surface electromyography (SEMG) signals are often used to reveal the best stimulation frequency for each subject. Use of SEMG concise parameters, such as root mean square values of the recordings, is also a common practice; frequently a preliminary session can take place in order to discover the more appropriate stimulation frequency. Soft tissues act as wobbling masses vibrating in a damped manner in response to mechanical excitation; Muscle Tuning hypothesis suggest that neuromuscular system works to damp the soft tissue oscillation that occurs in response to vibrations; muscles alters their activity to dampen the vibrations, preventing any resonance phenomenon. Muscle response to vibration is however a complex phenomenon as it depends on different parameters, like muscle-tension, muscle or segment-stiffness, amplitude and frequency of the mechanical vibration. Additionally, while in the TVR study the applied vibratory stimulus and the muscle conditions are completely characterised (a known vibration source is applied directly to a stretched/shortened muscle or tendon), in WBV study only the stimulus applied to a distal part of the body is known. Moreover, mechanical response changes in relation to the posture. The transmissibility of vibratory stimulus along the body segment strongly depends on the position held by the subject. The aim of this work was the investigation on the effects that the use of vibrations, in particular the effects of whole body vibrations, may have on muscular activity. A new approach to discover the more appropriate stimulus frequency, by the use of accelerometers, was also explored. Different subjects, not affected by any known neurological or musculoskeletal disorders, were voluntarily involved in the study and gave their informed, written consent to participate. The device used to deliver vibration to the subjects was a vibrating platform. Vibrations impressed by the platform were exclusively vertical; platform displacement was sinusoidal with an intensity (peak-to-peak displacement) set to 1.2 mm and with a frequency ranging from 10 to 80 Hz. All the subjects familiarized with the device and the proper positioning. Two different posture were explored in this study: position 1 - hack squat; position 2 - subject standing on toes with heels raised. SEMG signals from the Rectus Femoris (RF), Vastus Lateralis (VL) and Vastus medialis (VM) were recorded. SEMG signals were amplified using a multi-channel, isolated biomedical signal amplifier The gain was set to 1000 V/V and a band pass filter (-3dB frequency 10 - 500 Hz) was applied; no notch filters were used to suppress line interference. Tiny and lightweight (less than 10 g) three-axial MEMS accelerometers (Freescale semiconductors) were used to measure accelerations of onto patient’s skin, at EMG electrodes level. Accelerations signals provided information related to individuals’ RF, Biceps Femoris (BF) and Gastrocnemius Lateralis (GL) muscle belly oscillation; they were pre-processed in order to exclude influence of gravity. As demonstrated by our results, vibrations generate peculiar, not negligible motion artifact on skin electrodes. Artifact amplitude is generally unpredictable; it appeared in all the quadriceps muscles analysed, but in different amounts. Artifact harmonics extend throughout the EMG spectrum, making classic high-pass filters ineffective; however, their contribution was easy to filter out from the raw EMG signal with a series of sharp notch filters centred at the vibration frequency and its superior harmonics (1.5 Hz wide). However, use of these simple filters prevents the revelation of EMG power potential variation in the mentioned filtered bands. Moreover our experience suggests that the possibility of reducing motion artefact, by using particular electrodes and by accurately preparing the subject’s skin, is not easily viable; even though some small improvements were obtained, it was not possible to substantially decrease the artifact. Anyway, getting rid of those artifacts lead to some true EMG signal loss. Nevertheless, our preliminary results suggest that the use of notch filters at vibration frequency and its harmonics is suitable for motion artifacts filtering. In RF SEMG recordings during vibratory stimulation only a little EMG power increment should be contained in the mentioned filtered bands due to synchronous electromyographic activity of the muscle. Moreover, it is better to remove the artifact that, in our experience, was found to be more than 40% of the total signal power. In summary, many variables have to be taken into account: in addition to amplitude, frequency and duration of vibration treatment, other fundamental variables were found to be subject anatomy, individual physiological condition and subject’s positioning on the platform. Studies on WBV treatments that include surface EMG analysis to asses muscular activity during vibratory stimulation should take into account the presence of motion artifacts. Appropriate filtering of artifacts, to reveal the actual effect on muscle contraction elicited by vibration stimulus, is mandatory. However as a result of our preliminary study, a simple multi-band notch filtering may help to reduce randomness of the results. Muscle tuning hypothesis seemed to be confirmed. Our results suggested that the effects of WBV are linked to the actual muscle motion (displacement). The greater was the muscle belly displacement the higher was found the muscle activity. The maximum muscle activity has been found in correspondence with the local mechanical resonance, suggesting a more effective stimulation at the specific system resonance frequency. Holding the hypothesis that muscle activation is proportional to muscle displacement, treatment optimization could be obtained by simply monitoring local acceleration (resonance). However, our study revealed some short term effects of vibratory stimulus; prolonged studies should be assembled in order to consider the long term effectiveness of these results. Since local stimulus depends on the kinematic chain involved, WBV muscle stimulation has to take into account the transmissibility of the stimulus along the body segment in order to ensure that vibratory stimulation effectively reaches the target muscle. Combination of local resonance and muscle response should also be further investigated to prevent hazards to individuals undergoing WBV treatments.

Advanced signal and receiver design for next generation OFDM systems

This thesis deal with the design of advanced OFDM systems. Both waveform and receiver design have been treated. The main scope of the Thesis is to study, create, and propose, ideas and novel design solutions able to cope with the weaknesses and crucial aspects of modern OFDM systems. Starting from the the transmitter side, the problem represented by low resilience to non-linear distortion has been assessed. A novel technique that considerably reduces the Peak-to-Average Power Ratio (PAPR) yielding a quasi constant signal envelope in the time domain (PAPR close to 1 dB) has been proposed.The proposed technique, named Rotation Invariant Subcarrier Mapping (RISM),is a novel scheme for subcarriers data mapping,where the symbols belonging to the modulation alphabet are not anchored, but maintain some degrees of freedom. In other words, a bit tuple is not mapped on a single point, rather it is mapped onto a geometrical locus, which is totally or partially rotation invariant. The final positions of the transmitted complex symbols are chosen by an iterative optimization process in order to minimize the PAPR of the resulting OFDM symbol. Numerical results confirm that RISM makes OFDM usable even in severe non-linear channels. Another well known problem which has been tackled is the vulnerability to synchronization errors. Indeed in OFDM system an accurate recovery of carrier frequency and symbol timing is crucial for the proper demodulation of the received packets. In general, timing and frequency synchronization is performed in two separate phases called PRE-FFT and POST-FFT synchronization. Regarding the PRE-FFT phase, a novel joint symbol timing and carrier frequency synchronization algorithm has been presented. The proposed algorithm is characterized by a very low hardware complexity, and, at the same time, it guarantees very good performance in in both AWGN and multipath channels. Regarding the POST-FFT phase, a novel approach for both pilot structure and receiver design has been presented. In particular, a novel pilot pattern has been introduced in order to minimize the occurrence of overlaps between two pattern shifted replicas. This allows to replace conventional pilots with nulls in the frequency domain, introducing the so called Silent Pilots. As a result, the optimal receiver turns out to be very robust against severe Rayleigh fading multipath and characterized by low complexity. Performance of this approach has been analytically and numerically evaluated. Comparing the proposed approach with state of the art alternatives, in both AWGN and multipath fading channels, considerable performance improvements have been obtained. The crucial problem of channel estimation has been thoroughly investigated, with particular emphasis on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSSs). In this contest our contribution is twofold, from the theoretical side, we derived lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy,from the receiver design we proposed novel MSS selection strategies which have been shown to approach these MSE lower bounds, and outperformed the state-of-the-art alternatives. Finally, the possibility of using of Single Carrier Frequency Division Multiple Access (SC-FDMA) in the Broadband Satellite Return Channel has been assessed. Notably, SC-FDMA is able to improve the physical layer spectral efficiency with respect to single carrier systems, which have been used so far in the Return Channel Satellite (RCS) standards. However, it requires a strict synchronization and it is also sensitive to phase noise of local radio frequency oscillators. For this reason, an effective pilot tone arrangement within the SC-FDMA frame, and a novel Joint Multi-User (JMU) estimation method for the SC-FDMA, has been proposed. As shown by numerical results, the proposed scheme manages to satisfy strict synchronization requirements and to guarantee a proper demodulation of the received signal.