Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Damage localization in data-driven vibration-based structural health monitoring using linear quadratic estimation theory

Vibration-based Structural Health Monitoring (SHM) is classically approached from two different directions; both involve the acquisition and processing of vibration signals. The first and most popular strategy, which is also followed in the present thesis, relies entirely on the measurements. In contrast, the second approach employs physical models such as finite element (FE) models that are designed based on mechanical principles. In times in which the real-time processing of digital twins for engineering structures becomes more and more realistic, model-based approaches for vibration-based SHM receive increasing attention. Data-driven strategies are still primarily used in vibration-based SHM, and they will remain appealing in situations where precise physical modeling appears cumbersome. Hence, the need for efficient, robust, and reliable data-driven techniques concerning all stages and hurdles of SHM that can prove themselves in practice will never vanish. In this regard, after over 25 years of research, the number of real-life validation studies is still surprisingly low. As for all SHM strategies, the difficulty concerning damage analysis increases with higher levels of realization. Beginning with the goal of detecting damage, SHM finally seeks to predict the remaining lifetime of a structure. The intermediate steps comprise the localization, classification, and assessment of damage. Without the existence of adequately calibrated physics-based models, the successful implementation of methods tackling the objectives beyond damage localization in an unsupervised data-driven scheme is questionable. The term ‘unsupervised’ refers to the fact that knowledge about the manifestation of damage is not available. Especially in civil engineering, this situation pertains in general and is considered in the present thesis. In data-driven SHM, where the area of structural alterations is narrowed down to adjacent sensors, damage localization suffers from the coarse spatial resolution of parsimonious data acquisition systems. Classical modal approaches that hold potential for damage localization require a dense sensor network or significant damage. Originating from the field of fault detection and isolation, estimator- and filter-based methods have proven to be applicable for damage identification of mechanical and civil engineering structures. Notably, they feature an enormous sensitivity towards structural changes when properly designed. Although it remains advantageous for the sake of precise damage localization, these tools such as Kalman or H-infinity filters do not exhibit the inherent demand for a dense sensor network. Consequently, they promise to be viable techniques for the application in vibration-based SHM. A central challenge of this discipline is the discrimination between the natural variability of the structure’s dynamics and the one caused by damage. The former results from varying environmental and operational conditions (EOCs). Especially highly sensitive methods for damage identification are affected by these natural changes, and thus, rely on an efficient data normalization strategy, which can prove itself in practice. In light of these challenges, this thesis provides a real-life validation for the application of quadratic estimators in data-driven vibration-based SHM. To this end, an elaborate technique for estimator-based damage localization is adapted and included in an SHM framework comprising the necessary steps of data normalization and statistical testing. The damage analysis methodology was originally designed for H-infinity filters, which seem well-suited for use in SHM, as they do not assume specific properties of the excitation acting on the structure nor of the involved disturbances. However, previous studies have shown that, in some cases, the filter performance required to achieve high levels of sensitivity towards localized damage cannot be obtained. This issue can be circumvented by employing well-tuned Kalman filters. Therefore, a novel approach for noise covariance estimation is established at first. The associated estimation scheme constitutes a parametric extension of the popular autocovariance least-squares (ALS) technique. The effectiveness of this estimation technique in the context of Kalman filter-based damage localization is studied first using simulations and laboratory experiments. The second part is dedicated to the problem of handling EOCs. This body of work proposes an identification scheme for linear parameter-varying systems based on the interpolation of linear time-invariant systems for different operating points. A simulation study demonstrates the applicability for the purpose of data normalization. Finally, real-life validation of the proposed methods for SHM is conducted. Therefore, a steel lattice mast located outdoors functions as the test object. It is naturally affected by ambient sources of excitation, variability, and uncertainty. The mast, explicitly designed for this validation purpose, is equipped with reversible damage mechanisms that may be activated or removed to reduce the stiffness at multiple locations of the structure. The investigations conducted in this part of the thesis demonstrate proper damage detection of all considered damages as well as localization for the highest degree of severity. These promising results suggest the applicability of the presented methods for Kalman filter tuning, damage localization, and data-normalization in the context of vibration-based SHM