The balanced mode decomposition algorithm for data-driven LPV low-order models of aeroservoelastic systems

A novel approach to reduced-order modeling of high-dimensional systems with time-varying properties is proposed. It combines the problem formulation of the Dynamic Mode Decomposition method with the concept of balanced realization. It is assumed that the only information available on the system comes from input, state, and output trajectories, thus the approach is fully data-driven. The goal is to obtain an input-output low dimensional linear model which approximates the system across its operating range. Time-varying features of the system are retained by means of a Linear Parameter-Varying representation made of a collection of state-consistent linear time-invariant reduced-order models. The algorithm formulation hinges on the idea of replacing the orthogonal projection onto the Proper Orthogonal Decomposition modes, used in Dynamic Mode Decomposition-based approaches, with a balancing oblique projection constructed from data. As a consequence, the input-output information captured in the lower-dimensional representation is increased compared to other projections onto subspaces of same or lower size. Moreover, a parameter-varying projection is possible while also achieving state-consistency. The validity of the proposed approach is demonstrated on a morphing wing for airborne wind energy applications by comparing the performance against two recent algorithms. Analyses account for both prediction accuracy and closed-loop performance in model predictive control applications

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft

Model reduction for LPV systems based on approximate modal decomposition

The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently reduced by parameter varying reduction methods. The decomposition starts with the construction of a modal transformation that separates the modal subsystems. Hierarchical clustering is applied then to collect the dynamically similar modal subsystems into larger groups. The resulting parameter varying subsystems are then independently reduced. This approach substantially differs from most of the previously proposed LPV model reduction techniques, since it performs manipulations on the LPV model itself, instead of on a set of linear time-invariant (LTI) models defined at fixed scheduling parameter values. Therefore the interpolation, which is often a challenging part in reduction techniques, is inherently solved. The applicability of the developed algorithm is thoroughly investigated and demonstrated by numerical case studies

FlexWing-ROM: A matlab framework for data-driven reduced-order modeling of flexible wings

Flexible wings pose a considerable modeling challenge, as they involve highly coupled and nonlinear interactions between the aerodynamic and structural dynamics. In this work, we provide an open source code framework, unifying recent data-driven modeling methods that extend the dynamic mode decomposition with control (DMDc) to model the nonlinear aeroelasticity of flexible wings. Our framework consists of (1) a fully parametrized flexible wing model; (2) a fluid-structure interaction (FSI) solver that couples a detailed finite element model of the wing structure with a 3D unsteady aerodynamic panel method; and (3) three different data-driven reduced-order aeroelastic modeling methods. We demonstrate our framework on two flexible wings and provide tutorials to compare the different data-driven methods. The code is widely applicable and useful for generating accurate and efficient data-driven reduced-order models, and it provides a benchmark for future developments of aeroelastic reduced-order modeling methods

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