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Structures such as fuselage, blade and wing in aeronautical and astronautical engineering are often subjected to cyclic loads in their service life, which in turn causes breathing cracks in these structures. To provide much more precise position of breathing cracks in structures and avoid structure failure, a local vibration-based approach using transmissibility function-based features is proposed and verified in this study. In the new method, nonlinear dynamic behaviour of cracked structures is simulated by a chain-type multiple-degree-of-freedom (MDOF) model, in which breathing cracks are represented as related nonlinear connections between masses. By modifying local structural physical parameters (mass, stiffness or damping coefficient), transmissibility function-based features are derived from cracked structures only and corresponding damage indicator is calculated for fault localization. Based on results of simulations on the chain-type model with breathing cracks, the effectiveness and practicability of damage indicator and method are verified and demonstrated. Moreover, merits, drawbacks and further development of this method are summarized and discussed.

The beam-like structures commonly exist in engineering systems and there are many critical issues relevant to fault diagnosis of those structures. Noticeably, among all other existing methods, transmissibility function-based diagnostic methods, providing much more sensitive damage indexes, are frequently applied and extensively studied, and it is thus meaningful to have a thorough review on most recent advance and related technical difficulties. This paper is, therefore, to present a comprehensive review on this topic for those engineering-oriented beam-like structures, focusing on fundamental theory, critical fault properties and potential applications, respectively. According to different transmissibility function-based features, existing methods are classified into several categories, i.e. general linear transmissibility function, general nonlinear transmissibility function, generalized frequency response function and the second-order output spectrum. With a chain-type multi-degree-of-freedom model with additional connections used for analysing dynamics of beam-like engineering structures, essential topics of these methods including types of transmissibility functions, damage indexes and procedures are discussed in detail. Moreover, the effectiveness, merits and demerits are illustrated by the numerical and experimental results, respectively. It should be noted that some methods discussed here can be readily extended and applied to diagnosis of other plate-like and rotor-like, etc., engineering structures. Apart from fault detection and localization, more sensitive transmissibility function-based damage indicators providing severity and residual life of damaged structures would be further development topics in this area.

Complex grid-like structures such as steel truss bridges and steel truss roofs commonly exist in civil engineering applications. Since these structures are usually subject to dynamic operational forces, faults like chemical corrosion, fatigue crack, and bolt loosening arise, and seriously affect structural health. To consider some issues in existing frequency domain fault evaluation methods like applicability for complex structures, requirement of baseline data, neglect of nonlinear boundaries, and localization of local faults, a novel method using nonlinear vibration features and Euclidean distance measurement is presented in this paper. Firstly, complex grid-like structures are decomposed into a series of simple T-type substructures according to structural characteristics and load paths. Secondly, related T-type multi-degree-of-freedom model is built by simulating potential faults and nonlinear boundaries as related nonlinear damper-spring connections. Thirdly, exciting the model and extracting output responses only, novel and local fault features, which are functions of structural properties, nonlinear fault-induced loads and transmissibility functions, are defined. Then, utilizing defined features from the local substructure to be evaluated only, a novel fault index is defined with Euclidean distance measurement. Finally, corresponding evaluation method is developed, and its effectiveness and applicability are demonstrated by comparative studies on a lab bolted grid-like structure.

Bolt-loosening faults frequently exist in industrial engineering structures since these bolted structures are often subjected to vibrations or the like in their service process. In this paper, a novel method based on the second-order output spectrum (SOOS) is proposed to detect potential bolt-loosening faults in a complex satellite-like structure. In this method, a general multi-degree-of-freedom (MDOF) model simulating bolt-loosening faults induced non-linearities and inherent boundary or material non-linearities by non-linear forces is built to describe the non-linear behaviour of the structure, and then a local damage indicator is derived for bolt-loosening fault detection through a local tuning approach (LTA) which tunes local structural properties. Results of experimental cases demonstrate that the state of bolted joint in the satellite-like structure with inherent non-linearities can be estimated by this novel SOOS based method effectively and reliably.

In this paper, the application of properties of the second-order output spectrum (SOOS) for nonlinear fault localization in ring type structures is studied. A more general ring type multiple-degree-of-freedom model, which regards nonlinear faults (bolt loosening or fatigue crack) and inherent material or boundary nonlinearities as nonlinear restoring forces, is utilized to describe the nonlinear behavior of ring type structures. Through harmonic excitation analysis and a novel local tuning approach, properties of the SOOS of nonlinear ring type structures are analyzed and clearly demonstrated with examples. Based on these properties, a novel SOOS-based method with a local damage index is proposed for nonlinear fault localization. The effectiveness and feasibility of this novel method are validated with multiple bolt loosening fault localization on a satellite-like structure in experiments and are further illustrated through comparisons with several existing methods.

Fault diagnosis of shaft cracks plays an important role for the safety and reliability of rotating machineries such as aero-engine, turbopump, wind power generator and internal combustion turbine in modern industrial applications. In this paper, a novel method for diagnosing shaft cracks of rotating machineries based on nonlinear transmissibility function is proposed. In the new method, a nonlinear dynamic model is built to describe the nonlinear behavior of a simply supported rotor with breathing cracks and nonlinear supports (nonlinear bearing damping and stiffness coefficients). Damage features for benchmark and cracked structures are derived respectively, and damage indicator for crack diagnosis is defined as the relative change between damage features. Through two numerical studies simulated by the Matlab software, procedures of proposed method are demonstrated and method’s effectiveness and availability are verified. In the future study, the proposed nonlinear transmissibility function-based crack diagnosis method could be extended and applied for other faults in rotating machineries like unbalance, misalignment, stator-to-rotor rub and support structure looseness and so forth.

Because of some advantages such as low cost, detachability and reusability, bolted joints are widely applied in various open beam-like engineering structures like steel beams and train rails and closed ring-type engineering structures like steel frames and oil pipelines to keep different structural components together. However, bolted engineering structures often encounter vibration-induced joint faults like self-loosening, crack, leakage and corrosion since they are generally subjected to external dynamic loads caused by vibration environments. Joint damages would seriously affect structures’ reliability and durability, and increase maintenance costs. Therefore, fault detection of bolted engineering structures is very important and necessary. For beam-like and ring-type engineering structures with single excitation and multiple damaged bolted joints, various methods monitoring changes in nonlinear structural features have been developed. To avoid the use of structural features from benchmark structures for reference during the derivation of damage indicators, a novel vibration-based fault detection approach utilizing features from damaged structures only is proposed in this study. In the new method, the dynamic model of bolted engineering structures is simplified as a general MDOF model with nonlinear elements simulating nonlinear bolt loosening faults. By changing the value of related mass, three similar equations from the damaged structure are used to form one matrix, and then the singularity of matrix is used to detect the existence and position of faults. Results from simulations on the beam-like and ring-type models with multiple damages demonstrate that the proposed approach could be an effective tool to estimate the state of bolted engineering structures.

This article presents a novel second-order output spectrum–based method for detecting and localizing multiple bolt loosening faults in complex structures with a sensor chain. This new method is developed based on a recently developed nth-order output spectrum estimation algorithm using only proper data obtained from a chain of sensors. The properties of the second-order output spectrum transmissibility of the sensor chain along physical structures with bolts are studied systematically. In the new method, the noise effect on accuracy of the estimation of fault indicators is investigated as well. The new method also considers more general nonlinear restoring forces not only due to faults but also due to inherent nonlinearity in structure when deriving the properties of the second-order output spectrum transmissibility. Extensive simulation and experimental results demonstrate that the second-order output spectrum of the studied structure can be estimated efficiently, and the second-order output spectrum transmissibility can be used as an effective and reliable damage indicator for the detection and localization of multiple bolt loosening faults in complex bolted structures.

A novel nonlinear second-order output spectrum (SOOS) approach for feature characterization and fault detection and location of bolt loosening in a satellite-like structure is proposed in this study using a simple sensor chain. The new method is developed based on a recently developed nonlinear decomposition method using the data measured from a chain of sensors for feature abstraction, together with the properties of transfer ratios of the SOOS of a multi-degree-of-freedom system with nonlinear components developed in this study. The new method is compared with other related vibration-based methods and validated with real experimental results. It is shown that the nonlinear SOOS of the satellite-like structure subject to a harmonic vibration excitation can be calculated efficiently, and it can be effectively and conveniently used as the fault indicator for detection and location of the bolt loosening problem of different severity in this complex structure.

This paper presents a novel second-order output spectrum (SOOS) based method with a local tuning approach (LTA) for the precise localization of multiple bolt-loosening faults in complex structures with a simple sensor chain. The development of this new method is based on a recently developed virtual beam-like structure (VBLS) concept and the nth-order output spectrum estimation (nth-OSE) algorithm using only properly measured data. In this new method, a more general multi-degree-of-freedom (MDOF) model with general nonlinear restoring forces, caused by not only faults but also inherently existing material or boundary nonlinearities in structures, is considered, and a special local tuning mechanism is intentionally proposed to derive the novel SOOS based damage indicator. Results of numerical and experimental studies demonstrate that this novel SOOS based local tuning method can give more accurate, sensitive and reliable information about fault positions, and then can be used effectively and reliably for the precise localization of multiple bolt-loosening faults in complex structures even with inherent material or boundary nonlinearities. The results of this study would present a totally new insight into initial structural fault detection by employing sensitive nonlinear features from a systematic frequency domain approach.

In order to diagnose potential serious and initial damages (loose bolts or fatigue cracks) in industrial structures more precisely, a systematic second-order output spectrum (SOOS) based method with a local tuning approach (LTA) is proposed in this article. In the novel method, structures with faults, material nonlinearities and nonlinear boundary conditions are represented by the Volterra series, and then a general ring type multi-degree-of-freedom (MDOF) model simulating nonlinearities as nonlinear restoring forces is built to describe the structures’ behavior. With defined nonlinear fault features, two local damage indicators based on the SOOS and LTA are derived for diagnosing serious and initial faults in sequence. Results of experiments on a satellite-like structure with loose bolts show that the systematic SOOS based method can identify serious and initial bolt loosening faults more accurately. Thus, it can be more applicable for fault diagnosis in complex structures in practice.

This paper presents a novel second-order output spectrum (SOOS) based method to diagnose multiple bolt loosening faults in structures with a sensor chain. This new method is based on a recently-developed nth-order output spectrum estimation (nth-OSE) algorithm using only proper input-output data measured from a chain of sensors. The properties of the SOOS transmissibility of the sensor chain along physical structures are studied systematically. In the new method, the noise effect on accuracy of the estimation of fault indicators is investigated as well. The new method also considers more general nonlinear restoring forces not only due to faults but also caused by inherent nonlinearity in structure when deriving the properties of the SOOS transmissibility. Extensive simulation results demonstrate that the SOOS of the studied structure can be estimated efficiently, and the SOOS transmissibility can be used as an effective and reliable damage indicator for the detection and location of multiple bolt loosening faults in structures.

Nonlinearity detection and characterization for crack-/damage-related fault evaluation/detection is a hot engineering topic. This study investigates a novel and systematic nonlinear decomposition and regulation method for nonlinearity characterization. It is shown that, using the proposed output decomposition and regulation, the even-order nonlinearity and crack-incurred nonlinearity (not a simple even-order nonlinearity although at its initial stage) can all be effectively evaluated by the magnitude of the second-order harmonic response, and the latter is a linear function of the crack severity and can be accurately estimated with the proposed method. Theoretical analysis, example studies, finite element modeling, and experiment validation are provided to demonstrate the advantages and effectiveness of the proposed method in characterizing nonlinear dynamics incurred by initial crack or damage. The theory and methods of this study would provide a useful and alternative frequency-domain approach for nonlinear signal processing in crack/damage evaluation, nonlinearity detection and characterization, and can benefit a broad spectrum of engineering practice.

This study presents the analysis and design of a novel sensor system for measuring the absolute vibration displacement of moving platforms based on the concept of quasi-zero-stiffness (QZS). The sensor system is constructed using positive- and negative-stiffness springs, which make it possible to achieve an equivalent QZS and consequently to create a broadband vibration-free point for absolute vibration displacement measurement in moving platforms. Theoretical analysis is conducted for the analysis and design of the influence of structure parameters on system measurement performance. A prototype is designed which can avoid the drawback of instability in existing QZS systems with negative stiffness, and corresponding data-processing software is developed to fulfill time domain measurements. Both the simulation and experimental results verify the effectiveness of this novel sensor system.