Matteo Strozzi

This study investigates the application of Detectivity, a composite metric derived from Hjorth’s parameters, for the condition monitoring of wind turbines. These parameters were originally introduced to describe the morphology of biomedical signals, and they consist of three scalar descriptors: Activity, Mobility, and Complexity, capturing, respectively, signal variance, frequency content, and waveform shape. Detectivity, proposed in a previous work by the authors as a condensation of Hjorth’s parameters, can be interpreted as the total gain in these parameters with respect to a reference condition corresponding to a healthy component. The analysis is conducted on two distinct datasets. The first, publicly available from the Luleå University website, contains vibration data from six wind turbines in a Swedish wind farm, one of which is affected by a bearing fault. A robust methodology was developed to manage the strong variability in rotational speed. The second dataset includes vibration signals from a 2 MW commercial turbine, acquired over 50 consecutive days during which an inner race fault progressively developed. The use of the Detectivity cumulant proved particularly effective: in the first case, it clearly identified the faulty machine; in the second, it enabled the detection of the time at which the probable onset of the fault occurred.

This paper introduces a comprehensive and publicly accessible data set from an experimental study on an independent cart system powered by linear motors. The primary objective is to advance research in machine health monitoring, predictive maintenance, and stochastic modeling by providing the first data set of its kind. Vibration signals were collected using sensors placed along the track, alongside key system variables such as cart position, following error, speed, and set current. Experiments were conducted under a wide range of operating conditions, including different fault types, fault severities, cart speeds, and fault orientations, for both single-cart and multi-cart configurations. The data set captures the relationship between vibration signatures, system variables, and fault characteristics across diverse speed profiles. The data set includes inner race (IR) and outer race (OR) faults in both the top and bottom bearings, with fault severities of 0.25 mm, 0.5 mm, 1.0 mm, and 1.5 mm in width. Eight different types of experiments were performed, classified based on the number of carts used, the section of the guide rail traversed, and the type of movement exhibited. Each experiment was conducted at two distinct nominal speeds of 1000 mm/s and 2000 mm/s, with acquisition durations ranging from 30 s to 2 min. Many experiments included multiple realizations to ensure statistical reliability. Data were recorded at a sampling frequency of 50 kHz with a resolution of 24 bits. For single-cart experiments, 5 system variables were captured, while for three-cart experiments, 15 system variables were recorded along with nine vibration channels. The total data set is approximately 400 GB, offering an extensive resource for data-driven research. Independent cart systems present unique challenges such as non-synchronous operation, speed reversals, and modularity, with each cart containing multiple bearings. In industrial applications where hundreds of carts may operate simultaneously, monitoring a large number of bearings becomes highly complex, making fault identification and localization particularly difficult. Unlike conventional rotary systems, where bearings are fixed around a rotating shaft, independent cart systems involve bearings that both rotate and translate along the track. This fundamental difference makes existing data sets and methodologies inadequate, emphasizing the need for specialized research. By addressing this gap, this work provides a critical resource for benchmarking and developing novel algorithms for fault diagnosis, signal processing, and machine learning in industrial transport applications. The outcomes of this study lay the foundation for future research in the condition monitoring of linear motor-driven transport systems.

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

In this paper, a novel nonlocal strain gradient anisotropic elastic shell model is developed to analyse the vibrations of simply supported single‒walled carbon nanotubes (SWCNTs). Sanders‒Koiter shell theory is used to obtain the strain‒displacement relationships. Eringen nonlocal elasticity theory and Mindlin strain gradient theory are adopted to derive the constitutive equations, where the anisotropic elastic constants are expressed via Chang molecular mechanics model. The complex variable method is used to analytically solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model is validated via comparisons with the results of molecular dynamics simulations reported in the literature. Then, the effect of nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers is analysed. From the numerical simulations it is obtained that the natural frequencies decrease with increasing nonlocal parameter, while they increase with increasing material parameter. Moreover, the decrease of natural frequencies with increasing SWCNT radius is exponential as the material parameter increases, while it is linear as the nonlocal parameter increases. Finally, as the number of waves increases, the natural frequencies linearly vary with increasing nonlocal parameter, while they exponentially increase with increasing material parameter.

In this paper, a comparison of signal analysis techniques for the diagnostics of rolling element bearings is carried out. Specifically, the comparison is performed in terms of fault detection, diagnosis and prognosis techniques with regards to the first rolling element bearing dataset released by NASA IMS Center in 2014. As for fault detection, it is obtained that RMS value, Kurtosis and Detectivity, as statistical parameters, are able to properly detect the arising of the fault on the defective bearings. Then, several signal processing techniques, such as deterministic/random signal separation, time-frequency and cyclostationary analyses are applied to perform fault diagnosis. Among these techniques, it is found that the combination of Cepstrum Pre-Whitening and Squared Envelope Spectrum, and Improved Envelope Spectrum, allow the faults to be correctly identified on specific bearing components. Finally, the Correlation, Monotonicity and Robustness of the previous statistical parameters are computed to identify the most accurate tools for bearing fault prognosis.

In the present paper, a comparison is conducted between three classical shell theories as applied to the linear vibrations of single-walled carbon nanotubes (SWCNTs); specifically, the evaluation of the natural frequencies is conducted via Donnell, Sanders, and Flügge shell theories. The actual discrete SWCNT is modelled by means of a continuous homogeneous cylindrical shell considering equivalent thickness and surface density. In order to take into account the intrinsic chirality of carbon nanotubes (CNTs), a molecular based anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and a complex method is applied to solve the equations of motion and to obtain the natural frequencies. Comparisons with the results of molecular dynamics simulations available in literature are performed to check the accuracy of the three different shell theories, where the Flügge shell theory is found to be the most accurate. Then, a parametric analysis evaluating the effect of diameter, aspect ratio, and number of waves along the longitudinal and circumferential directions on the natural frequencies of SWCNTs is performed in the framework of the three different shell theories. Assuming the results of the Flügge shell theory as reference, it is obtained that the Donnell shell theory is not accurate for relatively low longitudinal and circumferential wavenumbers, for relatively low diameters, and for relatively high aspect ratios. On the other hand, it is found that the Sanders shell theory is very accurate for all the considered geometries and wavenumbers, and therefore, it can be correctly adopted instead of the more complex Flügge shell theory for the vibration modelling of SWCNTs.

Condition monitoring is today a crucial and unavoidable practice related to the use of widespread mechanical components as rolling element bearings. Despite the diffusion of new data-driven techniques to analyze vibrational signals and detect the state of health of the system, mathematical tools, deriving more or less directly from the Fourier transform and defined either on the time or the frequency domain or on a combination of them (i.e. signal-based techniques), remain still essential and irreplaceable in the light of the deep and detailed information they provide. In this paper the diagnostic efficacy of an ample spectrum of these methods is investigated, applying them to study faults occurrence in the first bearing dataset released by NASA IMS Center. Thanks to their analytical definition, which is formulated taking into consideration to some extent the mathematical nature of the signal, faults signatures can be clearly identified and their temporal development can be fully traced, confirming their ability as powerful means to constantly monitor the state of a system even in real-time applications.