Conference Agenda

Structures exhibiting nonlinear dynamic behavior present significant challenges for damage detection, especially when limited experimental data are available. This work proposes a novel hybrid strategy, Co-GP–NARX, that combines the multi-fidelity regression capability of co-kriging, used to merge high- and low-fidelity datasets, with the nonlinear system modeling of Gaussian Process NARX (GP-NARX) models. In this framework, the expensive (high-fidelity) data correspond to experimental vibration measurements of a clamped-free beam with magnetic interaction at its free end, serving as a benchmark for nonlinear vibration analysis. The cheap (low-fidelity) data are obtained from a numerical Duffing oscillator, developed to emulate the nonlinear behavior observed experimentally and to extend the response to higher excitation amplitudes not available in the experiments. By integrating these two data sources, the Co-GP-NARX model aims to enhance the model’s predictive capability under unseen excitation levels or loading conditions. The validation scenario simulates an unexpected excitation event: models are trained on intermediate amplitude levels and tested at higher amplitudes to assess their ability to distinguish between healthy and damaged states. Results show that the conventional GP-NARX tends to misclassify high-amplitude healthy conditions as damaged, increasing false-positive rates. In contrast, the proposed Co-GP-NARX significantly reduces these false positives by leveraging complementary information from the numerical data. The proposed strategy shows promise as a cost-effective and accurate framework for nonlinear damage detection using hybrid experimental–numerical datasets.

As sensor data is collected over time, the data points form a time series, where each point is influenced by its past to some extent. Many models to describe the time series rely on fixed coefficients. As a result, the influence of the past is always the same. However, reality tells a different story. There would be no need for weather forecasts if temperatures followed a determined series. Moreover, man-made phenomena like traffic varies over time. Weekends and workdays, holidays and school vacations, they all have an influence on the volume of traffic and are not entirely predetermined. Varying the regression coefficient by adding a random effect to it provides a solution to this issue. A popular model for that is the so-called Random Coefficient Autoregressive Model by Nicholls and Quinn (1982). Inspired by financial mathematics, we show how to determine the model coefficients for an engineering equivalent of log-returns via the quasi-maximum-likelihood method proposed by Aue et al. (2006) using the example of a crack width on a concrete bridge in Bochum, Germany. The data was collected during the project SFB 823, B5 of the German Research Foundation with the help of inductive displacement sensors. Since the bridge was fully operating during the monitoring, environmental factors such as temperature, humidity and wind as well as operational factors like traffic influenced the cracks. Sensor-induced variability can already be successfully subtracted out as shown by Heinrich et al. (2021), leaving us to deal with uncertainty coming from outside. The quasi-maximum-likelihood method relies on minimal assumptions regarding the noise process, making it suitable for a broad spectrum of applications. Additionally, we simulate alternative paths of the time series formed by the crack width based on the estimated parameters to illustrate their validity. These simulations, in turn, serve as a starting point for further evaluation and prediction using risk measures also known from finance. They are applied solely to the time series without the need to incorporate influential factors explicitly. All in all, this approach allows us to take influences into account without having to know the exact nature or characteristics of these influences beforehand.

Contemporary industrial processes typically operate with time-varying statistical properties. Specifically, these processes exhibit fluctuating mean, variance, and covariance values. Such variation leads to the emergence of nonstationary characteristics in these processes. These rapidly changing statistical properties result in process variables displaying unexpected patterns that fall outside the assumptions underlying classical monitoring methods. This major difference is particularly problematic when working with nonstationary data that has varying levels of integration (which means how many times a series needs to be differenced to become stationary, noted as I(d), where d can be 0, 1, or 2) in the process variables, making standard methods much less useful.

To address this challenge, an individual model of an intricate nonstationary time series using cointegration is proposed. Cointegration, a technique that can address non-stationarity. However, it demands that the variables under investigation share at least a common trend and the same integration order. The approach begins by classifying variables according to their order of integration using the Augmented Dickey-Fuller (ADF) test and subsequently identifies long-run equilibrium relationships among these variables within each group. By capturing the inherent cointegration structure, it becomes possible to develop more robust monitoring statistics that are sensitive to process deviations, even in the presence of complex, nonstationary behaviours.

The proposed approach has been validated through a numerical simulation by generating the synthetic time series data with various fault conditions. Overall, the findings and comparisons with two well-established techniques, principal component analysis (PCA) and dynamic principal component analysis (DPCA), demonstrate that the proposed approach provides superior monitoring performance, particularly for variables characterised by a higher order of integration.

Blade Tip Timing (BTT) is a non-contact measurement technique widely used for monitoring turbine engines used in aerospace propulsion and power generation systems. The method is based on recording the Time of Arrival (TOA) of each blade tip as it passes fixed probes installed on the engine casing, which is used to retrieve blade tip vibration amplitudes under real operating conditions [1–3]. The knowledge of the vibration level is crucial for identifying potential anomalies, enabling predictive structural monitoring of rotating components.

Currently, Blade Tip Timing Measurement Systems (BTTMS) are commonly used during the design phase to help prevent blade failure, but the lack of recognized standards and procedures for their calibration still limits the use of this technique in formal qualification and certification of turbines, where a rigorous uncertainty quantification is required. Bridging this gap would provide the aeronautical and energy industries with a valuable tool for low and high speed turbomachinery certification and continuous monitoring.

This work presents the progress of a research project, financed by the Italian Ministry of University and Research (MUR) and now approaching its conclusion, aimed at developing a BTT uncertainty evaluation model [4] and realizing an experimental bench integrating high-accuracy reference methods for calibrating BTTMS.

As measurements on actual turbomachinery rotors are affected by the stochastic nature of blade vibrations, a direct calibration method based on the blade tip TOA would be inherently limited by the intrinsic uncertainty on the reference signal. For this reason, the distinctive feature of the project is the design of the experimental bench based on an inverse kinematics concept. In this approach, the TOA of rigid reference blades, simulated by a marker following a purely circular trajectory around the rotor axis, is measured by a sensor subjected to a vibratory motion with controlled frequency and amplitude. This configuration allows to decouple the structural dynamics of the blade from the sensor response, avoiding the stochastic vibration phenomenon and therefore reducing the calibration uncertainty.

The calibration bench consists of two independently engineered subsystems: a rotary unit, responsible for generating purely rotational motion with minimized undesired vibrations, and a vibratory unit, designed to impose a controlled oscillatory motion on the sensor under test. The system was experimentally characterized to evaluate the rotor angular velocity stability and the sensor vibration accuracy, fundamental to minimize the calibration uncertainty, and to investigate eventual additional uncertainty sources.

This research project represents the first traceable uncertainty quantification of BTTMS against reference instrumentation and can be intended as an enabling step towards robust turbomachinery BTT based SHM frameworks. Project outcomes are also expected to support the development of hydrogen powered turbine engines, in line with the European Green Deal’s targets. Notably, in 2020, Snam and Baker Hughes successfully tested a hydrogen fueled turbine in Florence, with the involvement of researchers from this project.

Bolted joints are essential components in many industrial structures, yet they remain prone to loosening and therefore require periodic inspections. Direct inspections are costly and intrusive, making indirect detection an important challenge, especially in the presence of variability and nonlinear effects. This work presents a probabilistic damage detection strategy that operates directly on raw frequency response data, avoiding the need for handcrafted features. The structure investigated is the Orion beam, a benchmark proposed for assessing damage detection methodologies in the presence of loosening of tightening torque. A Gaussian Process Regression model is first trained on transmissibility functions to build a baseline representation in the frequency domain, from which a GPR-based damage index is derived to identify deviations associated with loosening. Sensitivity to loosening is enhanced through a Global Sensitivity Analysis using Sobol indices, which identifies frequency regions most affected by the damage and improves detection robustness. Figure 1 illustrates the damage index obtained utilizing the GPR-based, which indicates the capacity of the methodology to detect damages in the presence of data variability. The approach is further extended to a three-dimensional formulation that accounts for the evolution of nonlinear behaviour with increasing excitation levels, enabling the distinction between regime changes and actual loosening effects. The results indicate that the proposed framework provides a clear and reliable means to detect bolt loosening while limiting false indications in the presence of data variability.

Damage diagnosis is a central task in Structural Health Monitoring (SHM), involving the detection and localization of damage from measured data. This study develops a sensitivity-based approach for structural damage localization using vibration measurements with a Kalman-based residual. Measurement data from the current state are processed using a Kalman filter constructed from the reference-state model. Damage induces a change in the mean of the residual, which is related to variations in physical structural parameters through a first-order perturbation analysis involving sensitivities with respect to structural parameters from a finite element (FE) model. Damage localization is then formulated as a statistical hypothesis testing problem for the individual structural parameters.

Previous formulations relied on the full FE model for the Kalman filter, limiting applicability to realistic SHM problems. The present work instead considers a modally truncated formulation, which can moreover be identified directly from reference-state vibration measurements. This enables the Kalman filter to be constructed from experimentally identified modal parameters rather than FE model-based quantities. The approach is validated numerically on a truss structure.