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

Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring (SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3 damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes (quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression) and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration measurements.

Operational modal analysis (OMA) is a widely used construction verification and structural health monitoring technique aiming to obtain the modal properties of vibrating civil engineering structures subject to ambient dynamic loads by collecting and processing structural response acceleration signals. Motivated by the need for cost-efficient OMA using wireless sensor networks which acquire and transmit measurements at a lower than the Nyquist rate, a novel OMA approach is put forth to derive modal properties directly from sub-Nyquist sampled (compressed) acceleration measurements from arrays of sensors. This is achieved by adopting sub-Nyquist deterministic non-uniform multi-coset sampling devices and by extending a previously proposed in the literature power spectrum blind sampling method for single-channel spectral estimation of stochastic processes to treat the case of multiple channel cross-spectral estimation. The standard frequency domain decomposition is used to obtain the modal properties from the cross-spectral matrix derived directly from the sub-Nyquist measurements. The applicability and efficiency of the proposed approach is exemplified by retrieving mode shapes of a white-noise excited simply supported steel beam with good accuracy according to the widely used modal assurance criterion using 70% less than the Nyquist rate measurements.

Damage detection and structural health monitoring have always been of great importance to civil engineers and researchers. Vibration-based damage detection has several advantages compared to traditional methods of non-destructive evaluation, such as ground penetrating radar (GPR) or ultrasonic testing, since they give a global response and are feasible for large structures. Damage detection requires a comparison between two systems states, the baseline or “healthy state”, i.e., the initial modal parameters, and the damaged state. In this study, system identification (SI) was carried out on a pedestrian bridge by measuring the dynamic response using six low-cost triaxial accelerometers. These low-cost accelerometers use a micro-electro-mechanical system (MEMS), which is cheaper compared to a piezoelectric sensor. The frequency domain decomposition algorithm, which is an output-only method of modal analysis, was used to obtain the modal properties, i.e., natural frequencies and mode shapes. Three mode shapes and frequencies were found out using system identification and were compared with the finite element model (FEM) of the bridge, developed using the commercial finite element software, Abaqus. A good comparison was found between the FEM and SI results. The frequency difference was nearly 10%, and the modal assurance criterion (MAC) of experimental and analytical mode shapes was greater than 0.80, which proved to be a good comparison despite the small number of accelerometers available and the simplifications and idealizations in FEM.

Behavior of interfaces between soils and reinforcing elements plays a key role in the design and analysis of civil engineering structures, such as reinforced backfills or soil nailed structures. In this paper, we present a new laboratory device, the ring simple shear apparatus, especially designed for studying and measuring friction between sand and reinforcing elements. The principle of the apparatus is to revolve a rigid steel cylinder (modeling the reinforcement) in an annular sample of soil. The results presented herein are obtained with samples of Hostun sand (D50=0.36 mm) or Hostun gravel (D50=3 mm). The cylinder used have smooth or rough surfaces. The results show that the main factors which affect the friction and its mobilization are the nature of the surface, the nature and the density of the soil and the overburden pressure. Results of cyclic test show the degradation of the mobilized friction with the number of cycles.

This paper proposes an application of already established higher-order models and, namely, investigates the free vibration analysis of civil engineering structures subjected to nonstructural masses. The refined one-dimensional theories adopted are based on the Carrera unified formulation (CUF). The stiffness and mass matrices are obtained by means of the principle of virtual displacements in conjunction with the finite element method (FEM). According to CUF, in fact, their formulation is performed in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the axis. In order to account for nonstructural localised masses, the fundamental nucleus of the mass matrix has been opportunely modified. In this work, Lagrange polynomials have been employed in the framework of CUF to develop pure translational displacement-based refined beam models. The models obtained using this approach are referred, in the literature, to as component wise (CW), which allows to model each structural component as a 1D element. The free vibration analysis has been carried out for different cases of nonstructural mass distribution in typical civil buildings. The results obtained are compared with classical Solid/Shell FEM solutions from the commercial code MSC Nastran. The capabilities of the CW models are demonstrated, since this formulation is able to replicate the 3D solid results with enhanced performances in terms of computational efforts. Moreover, the importance of taking into account the correct distribution of the nonstructural masses is shown to be of fundamental importance in vibration analysis of civil buildings.

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection

In wireless sensor networks (WSNs), sensor data are usually corrupted by the noise. Meanwhile, it is inevitable to face the problems of node energy in WSNs. For both of these questions, this paper proposes a data gathering method via compressed sensing combined with cross validation. In the proposed method, data gathering via CS can save and balance energy consumption of sensor nodes due to the features of CS, and CV technique is used to judge whether stable reconstruction have been obtained. This method is essentially an adaptive intelligent method. Unlike the existing methods, the proposed method does not need the knowledge of signal sparsity, noise information and/or regularization parameter while those knowledge is expensive to acquire, especially in adaptive systems. That is to say, the method proposed in this paper is not sensitive to signal sparsity, noise, regularization parameters and/or other information when it is used for WSNs data collection for noise case, but the existing methods rely heavily on the prior information. Experimental results show that the proposed data gathering method can obtain stable reconstruction results for noisy WSNs in the case of unknown signal sparsity, noise and/or regularization parameters.

Correlation of modal data using the Modal Assurance Criterion (MAC) is difficult under the best of circumstances. This is especially true for very small structures such as turbine blades. Considering the typical geometric variation in overall blade geometry, the sensitivity of point location geometric variation can have a detrimental effect on the stated mode correlation using MAC. However, visual interpretation can indicate very similar shapes whereas MAC using detailed discrete points for a large number of points typically obtained from optical measuring systems may not yield suitable MAC values.Recently, imaging techniques have been proven to be useful in correlating mode shapes of structures. The imaging techniques used here, specifically Zernike Polynomials (ZPs) and Zernike Moment Descriptors (ZMDs), are utilized as a mechanism to decompose modal vectors of structures that have geometric point locations that do not all accurately align with each other followed by correlating the ZMDs with a traditional MAC. Several cases are shown with analytical models to show the usefulness of the approach as well as with actual data obtained from small turbine blades tested using laser holography techniques.

Conventional imaging sensors often reach their limits in terms of resolution and dynamic range. In addition, conventional imaging in invisible wavelengths is relatively more expensive and complicated. As an alternative, single-pixel cameras allow reduction of cost and complexity that would be otherwise required in a conventional multi-nixel camera. In terms of digital imaging, Nyquist-Shannon theorem states that to stably recover an image without introducing perceptible errors, the number of measurements and the number of image pixels are required to be at least the same. As the number of image pixels is ever increasing, increasing the number of measurements to fulfill Nyquist-Shannon theorem's requirements has become increasingly challenging. Since in many cases increasing the number of measurements means that the cost and time required are increasing accordingly as well. Therefore a mean to recover images from a number of measurements less than the number of pixels (sub-Nyquist measurements) is needed. The objective of this paper is to present and compare single-pixel imaging via compressive sensing/sampling (CS) and spatially-variant resolution (SVR) single-pixel imaging. Both methods are capable of recovering images stably from sub-Nyquist measurements. The measurements and reconstructions of images were done in simulations. SVR single-pixel imaging reduces the number of measurement by sacrificing the resolution of the peripheral regions. This realizes the programmable imaging concept where multi-resolution can be adaptively applied to optimize the balance between image quality and number of measurement. This could benefit some imaging applications where a target in the region of interest (the fovea) is prioritized over the rest of the region (such as the background).

To improve the transmission performance of communication networks and reduce the bit error rate, it is necessary to design the transmission channel equalization in communication networks. A link equalization algorithm based on matched filter autocorrelation detection is proposed for wireless sensor networks. According to the characteristics of inter-symbol interference (ISI) of multipath components in wireless sensor network (WSN), the channel model is constructed, and the communication signal of multipath wireless sensor network is recomposed by autocorrelation matched filter detection technology. The time-frequency flipping characteristic of the output signals of each wireless sensor network is used to suppress the inter-symbol interference, the adaptive modulation of the signal at the data receiving end of the wireless sensor network is realized, and the focusing gain of the wireless sensor network link is obtained by using the spread spectrum coding modulation method. The modulated signal is sampled at Nyquist frequency, so that the spread spectrum coding characteristic information is extended simultaneously in time domain and frequency domain, and channel equalization is realized. The simulation results show that the proposed algorithm can effectively suppress inter-symbol interference, increase signal output gain, optimize communication network transmission and reduce the bit error rate, the communication quality is improved.

Modal analysis based structural health monitoring (SHM) is required now more than ever due to many factors such as aging infrastructure, loading incidents likely earthquakes, over loading etc. Although the continuous monitoring of structures is a full-fledged commercial sector, its high cost makes it infeasible for large structures as the number of sensors required is large. Accelerometers, widely used as sensors in SHM, in addition to high cost, possess some other challenges such as damage vulnerability in environmental and operational conditions. In this research, low cost lead-zirconate-zitanate (PZT) sensors are proposed as replacement of costly and fragile accelerometers as sensors for SHM. PZT patches, which cost less than one-tenth of the accelerometers, can also be embedded in the reinforced concrete structures to protect from the harsh operational conditions. In this paper, PZT patches are studied by technique of experimental modal analysis (EMA) on a steel beam specimen and the results are compared with the traditionally used accelerometers. Single input single output (SISO) approach is adopted for EMA of the rectangular steel beam. PZT sensors are able to capture modal data in terms of natural frequencies and mode shapes in good agreement with accelerometer. The fundamental natural frequency of the beam is obtained with the error of less than 1 % as compared to the accelerometer. The signal to noise ratio is of same order as accelerometer. The strain mode shape from the PZT sensors is well correlated to displacement mode shapes from the accelerometer by a modal assurance criteria (MAC) values greater than 0.9 for observed experimentally.

In this paper, we propose to apply the discrete cosine transform (DCT) and the compressive sampling (CS) techniques to audio signal compression. Using spectral analysis and the properties of the DCT, we can treat audio signals as sparse signals in the frequency domain. This is especially true for sounds representing tones. Thus, we propose the use of DCT as a preprocessor in order to sparsely represent a signal in the frequency domain, combined with CS to obtain an efficient representation of the signals. We show that the subsequent application of CS represents our signals with less information than the well-known sampling theorem.

A method is presented for processing multi-channel seismic data that recovers, simultaneously and unambiguously, signal frequencies above and below the temporal Nyquist of the input data, By exploiting signal stationarity and redundancy, I show that the sample interval of a single input channel does not uniquely determine the maximum recoverable frequency. The method is tested using normal moveout (NMO) and stack on synthetic model data. Frequencies of 10 to 225 Hz are recovered from input data sampled at 4 ms. I then apply the method to real data. The results demonstrate that antialias strategies based on the one-dimensional Shannon-Whittaker sampling theorem (l) impose an unnecessary limit on the ability to recover high frequencies and maximize signal resolution. The method is applicable wherever the trajectory of the signal to be imaged irregularly intersects the sampling grid. It is appropriate for resolving both temporal and spatial aliasing concerns. Introduction Since the inception of digital signal processing, concerns about signal aliasing have played a major role in determining useable signal bandwidth and the cost of obtaining that bandwidth. For example, the authors of a 1991 article in The Leading Edge observed that "..the major use of Nyquist's work in geophysics is the elimination of alias frequencies on digitally recorded seismic data. The Nyquist frequency is the highest frequency that can be obtained for a given sampling interval." (2). Such concerns have led the seismic industry to systematically restrict potential signal frequencies to below the Nyquist frequency by the application of antialiasing filters based on the Whittaker-Shannon sampling theorem. This paper describes a simple methodology for the recovery of signal components in excess of the Nyquist limit predicted by the one-dimensional Whittaker-Shannon sampling theorem. With this method, an optimum balance of image bandwidth and signal-to-noise ratio may be achieved by simple processing parameter choices. The methodology is applicable whenever the signal trajectory is irregularly intersected by a sampling grid of two or more dimensions. Aliasing It is generally accepted that the digital sampling interval and the upper limit of the recoverable signal spectrum are inexorably linked. Authors usually cite the one-dimensional Whittaker-Shannon sampling theorem which states that the maximum recoverable frequency (? Nyq) in an evenly-sampled function is given by:(mathematical equation)(available in full paper) where ?t is the sampling interval (in seconds). Frequencies in the input function prior to sampling, which are in excess of this Nyquist frequency, are, if not removed prior to sampling, said to be aliased (or folded) in the sampled output. Aliasing is generally understood to mean that those frequencies above ? Nyq are irretrievably lost due to being "mixed" with those below ? Nyq. Commonly, aliasing has been dealt with by one or both of two methods: Alias reduction method #1 Antialias filtering is almost always used to significantly reduce contamination by aliased frequencies whenever analog data are sampled (e.g., during field recording) or whenever the sampling interval is increased. While usually successful in preventing anticipated aliasing problems, this filtering can result in a loss of valuable signal both above and below ? Nyq. Also, additional equipment and/or processing costs are usually incurred.

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.