Ayan Sadhu

Hybrid Time‐Frequency Blind Source Separation Towards Ambient System Identification of Structures

This article will discuss how ambient system identification in noisy environments, in the presence of low-energy modes or closely-spaced modes, is a challenging task. Conventional blind source separation techniques such as second-order blind identification (SOBI) and Independent Component Analysis (ICA) do not perform satisfactorily under these conditions. Furthermore, structural system identification for flexible structures require the extraction of more modes than the available number of independent sensor measurements. This results in the estimation of a non-square modal matrix that is spatially sparse. To overcome these challenges, methods that integrate blind identification with time-frequency decomposition of signals have been previously presented. The basic idea of these methods is to exploit the resolution and sparsity provided by time-frequency decomposition of signals, while retaining the advantages of second-order source separation methods. These hybrid methods integrate two powerful time-frequency decompositions—wavelet transforms and empirical mode decomposition—into the framework of SOBI. In the first case, the measurements are transformed into the time-frequency domain, followed by the identification using a SOBI-based method in the transformed domain. In the second case, a subset of the operations are performed in the transformed domain, while the remaining procedure is conducted using the traditional SOBI method. A new method to address the under-determined case arising from sparse measurements is proposed. Each of these methods serve to address a particular situation: closely-spaced modes or low-energy modes. The proposed methods are verified by applying them to extract the modal information of an airport control tower structure located in Canada.

Re-tuning tuned mass dampers using ambient vibration measurements

Deterioration, accidental changes in the operating conditions, or incorrect estimates of the structure modal properties lead to de-tuning in tuned mass dampers (TMDs). To restore optimal performance, it is necessary to estimate the modal properties of the system, and re-tune the TMD to its optimal state. The presence of closely spaced modes and a relatively large amount of damping in the dominant modes renders the process of identification difficult. Furthermore, the process of estimating the modal properties of the bare structure using ambient vibration measurements of the structure with the TMD is challenging. In order to overcome these challenges, a novel identification and re-tuning algorithm is proposed. The process of identification consists of empirical mode decomposition to separate the closely spaced modes, followed by the blind identification of the remaining modes. Algorithms for estimating the fundamental frequency and the mode shape of the primary structure necessary for re-tuning the TMD are proposed. Experimental results from the application of the proposed algorithms to identify and re-tune a laboratory structure TMD system are presented.

Decentralized modal identification using sparse blind source separation

Popular ambient vibration-based system identification methods process information collected from a dense array of sensors centrally to yield the modal properties. In such methods, the need for a centralized processing unit capable of satisfying large memory and processing demands is unavoidable. With the advent of wireless smart sensor networks, it is now possible to process information locally at the sensor level, instead. The information at the individual sensor level can then be concatenated to obtain the global structure characteristics. A novel decentralized algorithm based on wavelet transforms to infer global structure mode information using measurements obtained using a small group of sensors at a time is proposed in this paper. The focus of the paper is on algorithmic development, while the actual hardware and software implementation is not pursued here. The problem of identification is cast within the framework of under-determined blind source separation invoking transformations of measurements to the time–frequency domain resulting in a sparse representation. The partial mode shape coefficients so identified are then combined to yield complete modal information. The transformations are undertaken using stationary wavelet packet transform (SWPT), yielding a sparse representation in the wavelet domain. Principal component analysis (PCA) is then performed on the resulting wavelet coefficients, yielding the partial mixing matrix coefficients from a few measurement channels at a time. This process is repeated using measurements obtained from multiple sensor groups, and the results so obtained from each group are concatenated to obtain the global modal characteristics of the structure.

Blind identification of earthquake-excited structures

A new method based on the popular second-order blind identification method, SOBI, is presented to estimate the modal properties of structures under non-stationary earthquake excitations. Since the proposed method is cast within the framework of blind source separation, the issues associated with model-order pre-selection and the use of stability charts in traditional system identification methods are not present. The SOBI method involves the joint diagonalization of multiple covariance matrices of measurements, which is rendered difficult in the presence of non-stationary excitations. This difficulty is overcome in the proposed method by a diagonalization procedure involving a new set of weighted covariance matrices. There are two main contributions in this paper. First, a diagonalization technique that involves the joint-approximate diagonalization of the proposed set of several time-lagged and suitably weighted covariance matrices is developed. Next, a parametric relationship between the key parameters of the proposed method and a suitably chosen non-stationary parameter of the response is developed to aid in the selection of the optimal parameters under non-stationary excitations. In order to demonstrate the results obtained using the proposed method, identification results from the UCLA Factor building using recorded responses from the Parkfield earthquake are utilized.

A novel damage detection algorithm using time-series analysis-based blind source separation

In this paper, a novel damage detection algorithm is developed based on blind source separation in conjunction with time-series analysis. Blind source separation (BSS), is a powerful signal processing tool that is used to identify the modal responses and mode shapes of a vibrating structure using only the knowledge of responses. In the proposed method, BSS is first employed to estimate the modal response using the vibration measurements. Time-series analysis is then performed to characterize the mono-component modal responses and successively the resulting time-series models are utilized for one-step ahead prediction of the modal response. With the occurrence of newer measurements containing the signature of damaged system, a variance-based damage index is used to identify the damage instant. Once the damage instant is identified, the damaged and undamaged modal parameters of the system are estimated in an adaptive fashion. The proposed method solves classical damage detection issues including the identification of damage instant, location as well as the severity of damage. The proposed damage detection algorithm is verified using extensive numerical simulations followed by the full scale study of UCLA Factor building using the measured responses under Parkfield earthquake.

Towards damage detection using blind source separation integrated with time-varying auto-regressive modeling

In the last few decades, structural health monitoring (SHM) has been an indispensable subject in the field of vibration engineering. With the aid of modern sensing technology, SHM has garnered significant attention towards diagnosis and risk management of large-scale civil structures and mechanical systems. In SHM, system identification is one of major building blocks through which unknown system parameters are extracted from vibration data of the structures. Such system information is then utilized to detect the damage instant, and its severity to rehabilitate and prolong the existing health of the structures. In recent years, blind source separation (BSS) algorithm has become one of the newly emerging advanced signal processing techniques for output-only system identification of civil structures. In this paper, a novel damage detection technique is proposed by integrating BSS with the time-varying auto-regressive modeling to identify the instant and severity of damage. The proposed method is validated using a suite of numerical studies and experimental models followed by a full-scale structure.

Blind source separation towards decentralized modal identification using compressive sampling

Wireless sensing technology has gained significant attention in the field of structural health monitoring (SHM). Various decentralized modal identification methods have been developed employing wireless sensors. However, one of themajor bottlenecks - especially dealing with long-term SHM - is the large volume of transmitted data. To overcome this problem, we present compressed sensing as a data reduction preprocessing tool within the framework of blind source separation. The results of source separation are ultimately used for modal identification of linear structures under ambient vibrations. When used together with sparsifying time-frequency decompositions, we show that accurate modal identification results are possible with high compression ratios. The main novelty in the method proposed here is in the application of compressive sensing for decentralized modal identification of civil structures.

Fault detection of gearboxes using synchro-squeezing transform

This paper presents a novel fault detection method for gearbox vibration signatures using the synchro-squeezing transform (SST). Premised upon the concept of time-frequency (TF) reassignment, the SST provides a sharp representation of signals in the TF plane compared to many popular TF methods. Additionally, it can also extract the individual components, called intrinsic mode functions or IMFs, of a nonstationary multi-component signal, akin to empirical mode decomposition. The rich mathematical structure based on the continuous wavelet transform makes synchro-squeezing a promising candidate for gearbox diagnosis, as such signals are frequently constituted out of multiple amplitude and frequency modulated signals embedded in noise. This work utilizes the decomposing power of the SST to extract the IMFs from gearbox signals, followed by the application of both condition indicators and fault detection to gearbox vibration data. For robust detection of faults in gear-motors, a fault detection technique based on time-varying auto-regressive coefficients of IMFs as features is utilized. The sequential Karhunen–Loeve transform is employed on the condition indicators to select the appropriate window sizes on which the SST can be applied. This approach promises improved fault detection capability compared to applying condition indicators directly to the raw data. Laboratory experimental data obtained from a drivetrain diagnostics simulator and seeded fault tests from a helicopter gearbox provide test beds to demonstrate the robustness of the proposed algorithm.

Fatigue Testing and Structural Health Monitoring of Retrofitted Web Stiffeners on Steel Highway Bridges

Numerous steel highway bridges, still in use today, were built during the construction boom between the late 1950s and the late 1970s. Fatigue cracking can be considered a main source of deterioration for these bridges. The largest category of observed fatigue cracks is caused by out-of-plane distortion. The most susceptible locations are those at which transverse structural components (such as diaphragms or cross frames) are framed into longitudinal girders through web stiffeners that are not attached to the flanges. In the current study, a web stiffener detail is fatigue tested under different cyclic loading conditions. As-welded specimens are tested, along with specimens retrofitted by grinding and rewelding, needle peening, or the adhesive bonding of fiber-reinforced polymer attachments. Direct strain and deflection measurements are compared with finite element analysis predictions, and local (hot-spot) stresses are compared with hot-spot stress design curves. A time series–based method for damage detection is also explored for the prediction of fatigue crack depth with strain data. The method is validated through the use of small- and large-scale specimen strain data. It is found that damage measures based on strains in the vicinity of the critical hot spot are closely correlated with the true crack depth.

Blind Source Separation of Convolutive Mixtures towards Modal Identification

Blind source separation (BSS) based signal processing techniques have shown significant promise for ambient modal identification of structural and mechanical systems. Many of these methods operate on the assumption that the underlying sources are mixed instantaneously, known as the instantaneous mixing model. If the data contains time synchronization (TS) errors, such as offsets and drifts commonly associated with wireless sensor networks, the equations of motion cannot be reduced to the instantaneous form in the time domain, and must be treated as convolutive mixtures. While other avenues such as time-synchronization protocols exist in the literature to address TS issues, an alternate algorithmic solution within the modal identification framework is presented here. In the proposed method, the convolutive mixtures of measurements are first transformed into instantaneous mixtures in the frequency domain, and then the complex BSS method is employed to separate the independent sources in the transformed domain. Finally, inverse Fourier transform is employed to transform the sources back into the time domain. The application of this algorithm is demonstrated using simulation examples.