Architected frames for elastic wave attenuation: Experimental validation and local tuning via affine transformation

We experimentally demonstrate the capability of architected plates, with a frame-like cellular structure, to inhibit the propagation of elastic flexural waves. By leveraging the octet topology as a unit cell to design the tested prototypes, a broad and easy-to-tune bandgap is experimentally generated. The experimental outcomes are supported by extensive numerical analyses based on 3D solid elements. Drawing from the underlying dynamic properties of the octet cell, we numerically propose a tailorable design with enhanced filtering capabilities. We transform the geometry of the original unit cell by applying a uniaxial scaling factor that, by breaking the in-plane symmetry of the structure, yields independently tuned struts and consequently multiple tunable bandgaps within the same cell. Our findings expand the spectrum of available numerical analyses on the octet lattice, taking it a significant step closer to its physical implementation. The ability of the octet lattice to control the propagation of flexural vibrations is significant within various applications in the mechanical and civil engineering domains, and we note such frame-like designs could lead to advancements in energy harvesting and vibration protection devices (e.g., lightweight and resonance-tunable absorbers)

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This paper assesses numerically the potential of two different spectral estimation approaches supporting non-uniform in time data sampling at sub-Nyquist average rates (i.e., below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks (WSNs) for operational modal analysis (OMA) of civil engineering structures. This consideration relaxes transmission bandwidth constraints in WSNs and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements and structural mode shapes are extracted using the frequency domain decomposition algorithm. The first approach relies on the compressive sensing (CS) theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e., have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling (PSBS) technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion (MAC) is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates (CRs) using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given CR, the performance of the CS-based approach is detrimentally affected by signal sparsity, while the PSBS-based approach achieves MAC>0.96 independently of signal sparsity for CRs as low as 11% the Nyquist rate. It is concluded that the PSBS-based approach reduces effectively data transmission requirements in WSNs for OMA, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity

Measuring sub-mm structural displacements using QDaedalus: a digital clip-on measuring system developed for total stations

The monitoring of rigid structures of modal frequencies greater than 5 Hz and sub-mm displacement is mainly based so far on relative quantities from accelerometers, strain gauges etc. Additionally geodetic techniques such as GPS and Robotic Total Stations (RTS) are constrained by their low accuracy (few mm) and their low sampling rates. In this study the application of QDaedalus is presented, which constitutes a measuring system developed at the Geodesy and Geodynamics Lab, ETH Zurich and consists of a small CCD camera and Total Station, for the monitoring of the oscillations of a rigid structure. In collaboration with the Institute of Structural Engineering of ETH Zurich and EMPA, the QDaedalus system was used for monitoring of the sub-mm displacement of a rigid prototype beam and the estimation of its modal frequencies up to 30 Hz. The results of the QDaedalus data analysis were compared to those of accelerometers and proved to hold sufficient accuracy and suitably supplementing the existing monitoring techniques

A discontinuous unscented kalman filter for non-smooth dynamic problems

For a number of applications, including real/time damage diagnostics as well as control, online methods, i.e., methods which may be implemented on-the-fly, are necessary. Within a system identification context, this implies adoption of filtering algorithms, typically of the Kalman or Bayesian class. For engineered structures, damage or deterioration may often manifest in relation to phenomena such as fracture, plasticity, impact, or friction. Despite the different nature of the previous phenomena, they are described by a common denominator: switching behavior upon occurrence of discrete events. Such events include for example, crack initiation, transitions between elastic and plastic response, or between stick and slide modes. Typically, the state-space equations of such models are non-differentiable at such events, rendering the corresponding systems non-smooth. Identification of non-smooth systems poses greater difficulties than smooth problems of similar computational complexity. Up to a certain extent, this may be attributed to the varying identifiability of such systems, which violates a basic requirement of online Bayesian Identification algorithms, thus affecting their convergence for non-smooth problems. Herein, a treatment to this problem is proposed by the authors, termed the Discontinuous D– modification, where unidentifiable parameters are acknowledged and temporarily excluded from the problem formulation. In this work, the D– modification is illustrated for the case of the Unscented Kalman Filter UKF, resulting in a method termed DUKF, proving superior performance to the conventional, and widely adopted, alternative

A discontinuous extended kalman filter for non-smooth dynamic problems

Problems that result into locally non-differentiable and hence non-smooth state-space equations are often encountered in engineering. Examples include problems involving material laws pertaining to plasticity, impact and highly non-linear phenomena. Estimating the parameters of such systems poses a challenge, particularly since the majority of system identification algorithms are formulated on the basis of smooth systems under the assumption of observability, identifiability and time invariance. For a smooth system, an observable state remains observable throughout the system evolution with the exception of few selected realizations of the state vector. However, for a non-smooth system the observable set of states and parameters may vary during the evolution of the system throughout a dynamic analysis. This may cause standard identification (ID) methods, such as the Extended Kalman Filter, to temporarily diverge and ultimately fail in accurately identifying the parameters of the system. In this work, the influence of observability of non-smooth systems to the performance of the Extended and Unscented Kalman Filters is discussed and a novel algorithm particularly suited for this purpose, termed the Discontinuous Extended Kalman Filter (DEKF), is proposed

A Discontinuous class of filtering methods for the identification of non-smooth dynamical systems

Engineering problems often arise in relation to phenomena such as plasticity, friction or impact. A common factor in these aforementioned cases lies in that the behavior of the system may vary substantially depending on the realization of its states. Mathematically, this can be attributed to the fact that for the corresponding models the corresponding state-space equations of the system or their derivatives are discontinuous. This discontinuity in turn affects the observability and identifiability properties of such systems, which is a major topic within the context of system identification and structural health monitoring. A notable effect lies in response intervals during which one or more parameters of the system may be unidentifiable, i.e., their value may not be inferred on the basis of the measured signals regardless of the efficiency of the identification algorithm used, while the same parameters may become identifiable in a subsequent time window. As a direct consequence, online system identification algorithms, such as the popularly employed Kalman filter methods, are also affected by the discontinuous nature of the system. In this work, the authors introduce an enhancement to the widely adopted Extended Kalman Filter in order to account for dynamic systems comprising discontinuous governing equations. The corresponding effect on the observability and identifiability properties of the systems will further be assessed. This enhanced variant is in this work referred to as the Discontinuous Extended Kalman Filter. An illustrative example is offered for demonstrating the robustness of the Discontinuous Extended Kalman Filter for physical problems involving discontinuous behavior

A Discontinuous class of filtering methods for the identification of non-smooth dynamical systems

Engineering problems often arise in relation to phenomena such as plasticity, friction or impact. A common factor in these aforementioned cases lies in that the behavior of the system may vary substantially depending on the realization of its states. Mathematically, this can be attributed to the fact that for the corresponding models the corresponding state-space equations of the system or their derivatives are discontinuous. This discontinuity in turn affects the observability and identifiability properties of such systems, which is a major topic within the context of system identification and structural health monitoring. A notable effect lies in response intervals during which one or more parameters of the system may be unidentifiable, i.e., their value may not be inferred on the basis of the measured signals regardless of the efficiency of the identification algorithm used, while the same parameters may become identifiable in a subsequent time window. As a direct consequence, online system identification algorithms, such as the popularly employed Kalman filter methods, are also affected by the discontinuous nature of the system. In this work, the authors introduce an enhancement to the widely adopted Extended Kalman Filter in order to account for dynamic systems comprising discontinuous governing equations. The corresponding effect on the observability and identifiability properties of the systems will further be assessed. This enhanced variant is in this work referred to as the Discontinuous Extended Kalman Filter. An illustrative example is offered for demonstrating the robustness of the Discontinuous Extended Kalman Filter for physical problems involving discontinuous behavior