Application of cepstrum pre-whitening for the diagnosis of bearing faults under variable speed conditions

Diagnostics of rolling element bearings involves a combination of different techniques of signal enhancing and analysis. The most common procedure presents a first step of order tracking and synchronous averaging, able to remove the undesired components, synchronous with the shaft harmonics, from the signal, and a final step of envelope analysis to obtain the squared envelope spectrum. This indicator has been studied thoroughly, and statistically based criteria have been obtained, in order to identify damaged bearings. The statistical thresholds are valid only if all the deterministic components in the signal have been removed. Unfortunately, in various industrial applications, characterized by heterogeneous vibration sources, the first step of synchronous averaging is not sufficient to eliminate completely the deterministic components and an additional step of pre-whitening is needed before the envelope analysis. Different techniques have been proposed in the past with this aim: The most widely spread are linear prediction filters and spectral kurtosis. Recently, a new technique for pre-whitening has been proposed, based on cepstral analysis: the so-called cepstrum pre-whitening. Owing to its low computational requirements and its simplicity, it seems a good candidate to perform the intermediate pre-whitening step in an automatic damage recognition algorithm. In this paper, the effectiveness of the new technique will be tested on the data measured on a full-scale industrial bearing test-rig, able to reproduce the harsh conditions of operation. A benchmark comparison with the traditional pre-whitening techniques will be made, as a final step for the verification of the potentiality of the cepstrum pre-whitening.

The combination of empirical mode decomposition and minimum entropy deconvolution for roller bearing diagnostics in non-stationary operation

Diagnostics is based on the characterization of mechanical system condition and allows early detection of a possible fault. Signal processing is an approach widely used in diagnostics, since it allows directly characterizing the state of the system. Several types of advanced signal processing techniques have been proposed in the last decades and added to more conventional ones. Seldom, these techniques are able to consider non-stationary operations. Diagnostics of roller bearings is not an exception of this framework. In this paper, a new vibration signal processing tool, able to perform roller bearing diagnostics in whatever working condition and noise level, is developed on the basis of two data-adaptive techniques as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED), coupled by means of the mathematics related to the Hilbert transform. The effectiveness of the new signal processing tool is proven by means of experimental data measured in a test-rig that employs high power industrial size components.

Bearing Fault Diagnostics Using the Spectral Pattern Recognition

In the field of diagnostics of rolling element bearings, the development of sophisticated techniques, such as Spectral Kurtosis and 2nd Order Cyclostationarity, extended the capability of expert users to identify not only the presence, but also the location of the damage in the bearing. Most of the signal-analysis methods, as the ones previously mentioned, result in a spectrum-like diagram that presents line frequencies or peaks in the neighbourhood of some theoretical characteristic frequencies, in case of damage. These frequencies depend only on damage position, bearing geometry and rotational speed. The major improvement in this field would be the development of algorithms with high degree of automation. This paper aims at this important objective, by discussing for the first time how these peaks can draw away from the theoretical expected frequencies as a function of different working conditions, i.e. speed, torque and lubrication. After providing a brief description of the peak-patterns associated with each type of damage, this paper shows the typical magnitudes of the deviations from the theoretical expected frequencies. The last part of the study presents some remarks about increasing the reliability of the automatic algorithm. The research is based on experimental data obtained by using artificially damaged bearings installed in a gearbox.

Damage detection in cable structures using vibration characteristics

Cable structures find many applications such as in power transmission, in anchors and especially in bridges. They serve as major load bearing elements in suspension bridges, which are capable of spanning long distances. All bridges, including suspension bridges, are designed to have long service lives. However, during this long life, they become vulnerable to damage due to changes in loadings, deterioration with age and random action such as impacts. The main cables are more vulnerable to corrosion and fatigue, compared to the other bridge components, and consequently reduces the serviceability and ultimate capacity of the bridge. Detecting and locating such damage at the earliest stage is challenging in the current structural health monitoring (SHM) systems of long span suspension bridges. Damage or deterioration of a structure alters its stiffness, mass and damping properties which in turn modify its vibration characteristics. This phenomenon can therefore be used to detect damage in a structure. The modal flexibility, which depends on the vibration characteristics of a structure, has been identified as a successful damage indicator in beam and plate elements, trusses and simple structures in reinforced concrete and steel. Successful application of the modal flexibility phenomenon to detect and locate the damage in suspension bridge main cables has received limited attention in recent research work. This paper, therefore examines the potential of the modal flexibility based Damage Index (DI) for detecting and locating damage in the main cable of a suspension bridge under four different damage scenarios. Towards this end, a numerical model of a suspension bridge cable was developed to extract the modal parameters at both damaged and undamaged states. Damage scenarios considered in this study with varied location and severity were simulated by changing stiffness at particular locations of the cable model. Results confirm that the DI has the potential to successfully detect and locate damage in suspension bridge main cables. This simple method can therefore enable bridge engineers and managers to detect and locate damage in suspension bridges at an early stage, minimize expensive retrofitting and prevent bridge collapse.

Review of the fire performance of LSF walls

Load bearing LSF walls are commonly made of cold-formed steel frames, gypsum plasterboards and insulation, and their fire performance is an important aspect of design. Many experimental and numerical studies have been conducted on the fire performance of LSF walls at the Queensland University of Technology (QUT). These studies have shown that increasing the number or thickness or quality of gypsum plasterboards has improved the fire resistance ratings (FRR) of LSF walls while the use of cavity insulation has reduced their FRR. Therefore new LSF wall systems with external insulation sandwiched between two layers of plasterboards were proposed, which provided higher FRR than cavity insulated walls. There are also other parameters that can improve the fire performance of LSF walls such as the steel type, stud geometry and depth, type of screw fasteners used, joints in the plasterboard and the plasterboard fall off time. This paper presents a review of the fire performance of LSF walls as a function of these parameters based on our research at QUT. Their effects on both the thermal and structural performance of LSF walls are discussed in detail and suitable improvements are recommended, for example, improved plasterboard joint types.

Experimental study on the fire performance of superior LSF wall systems

Load bearing Light Gauge Steel Frame (LSF) walls are commonly made of conventional lipped channel sections and gypsum plasterboards. Recently, innovative steel sections such as hollow flange channel sections have been proposed as studs in LSF wall frames with a view to improve their fire resistance ratings. A series of full scale fire tests was then undertaken to investigate the fire performance of the new LSF wall systems under standard fire conditions. Test wall frames made of hollow flange section studs were lined with fire resistant gypsum plasterboards on both sides, and were subjected to increasing temperatures as given by the standard fire curve on one side. Both uninsulated and cavity insulated walls were tested with varying load ratios from 0.2 to 0.6. This paper presents the details of this experimental study on the fire performance of LSF walls and the results. Test results showed that the walls made of the new hollow flange channel section studs have a superior fire performance in comparison to that of lipped channel section stud walls. They also showed that the fire performance of cavity insulated walls was inferior to that of uninsulated walls. The reasons for this fire behaviour are described in this paper.

A simulation-based large deflection and inelastic analysis of steel frames under fire

This paper presents an accurate and robust geometric and material nonlinear formulation to predict structural behaviour of unprotected steel members at elevated temperatures. A fire analysis including large displacement effects for frame structures is presented. This finite element formulation of beam-column elements is based on the plastic hinge approach to model the elasto-plastic strain-hardening material behaviour. The Newton-Raphson method allowing for the thermal-time dependent effect was employed for the solution of the non-linear governing equations for large deflection in thermal history. A combined incremental and total formulation for determining member resistance is employed in this nonlinear solution procedure for the efficient modeling of nonlinear effects. Degradation of material strength with increasing temperature is simulated by a set of temperature-stress-strain curves according to both ECCS and BS5950 Part 8, which implicitly allows for creep deformation. The effects of uniform or non-uniform temperature distribution over the section of the structural steel member are also considered. Several numerical and experimental verifications are presented.

Nonlinear pre-fire and post-fire analysis of steel frames

A numerical procedure based on the plastic hinge concept for study of the structural behaviour of steel framed structures exposed to fire is described. Most previous research on fire analysis considered the structural performance due to rising temperature. When strain reversal occurs during the cooling phase, the stress–strain curve is different. The plastic deformation is incorporated into the stress–strain curve to model the strain reversal effect in which unloading under elastic behaviour is allowed. This unloading response is traced by the incremental–iterative Newton–Raphson method. The mechanical properties of the steel member in the present fire analysis follows both Eurocode 3 Part 1.2 and BS5950 Part 8, which implicitly allow for thermal creep deformation. This paper presents an efficient fire analysis procedure for predicting thermal and cooling effects on an isolated element and a multi-storey frame. Several numerical and experimental examples related to structural behaviour in cooling phase are studied and compared with results obtained by other researchers. The proposed method is effective in the fire safety design and analysis of a building in a real fire scenario. The scope of investigation is of great significance since a large number of rescuers would normally enter a fire site as soon as the fire is extinguished and during the cooling phase, so a structural collapse can be catastrophic.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Direct second-order elastic analysis for steel frame design

The traditional structural design procedure, especially for the large-scale and complex structures, is time consuming and inefficient. This is due primarily to the fact that the traditional design takes the second-order effects indirectly by virtue of design specifications for every member instead of system analysis for a whole structure. Consequently, the complicated and tedious design procedures are inevitably necessary to consider the second-order effects for the member level in design specification. They are twofold in general: 1) Flexural buckling due to P-d effect, i.e. effective length. 2) Sway effect due to P-D effect, i.e. magnification factor. In this study, a new system design concept based on the second-order elastic analysis is presented, in which the second-order effects are taken into account directly in the system analysis, and also to avoid the tedious member-by-member stability check. The plastic design on the basis of this integrated method of direct approach is ignored in this paper for simplicity and clarity, as the only emphasis is placed on the difference between the second-order elastic limit-state design and present system design approach. A practical design example, a 57m-span dome steel skylight structure, is used to demonstrate the efficiency and effectiveness of the proposed approach. This skylight structure is also designed by the traditional design approach BS5950-2000 for comparison on which the emphasis of aforementioned P-d and P-D effects is placed.

On the advanced analysis of steel frames allowing for flexural, local and lateral-torsional buckling

Detailed procedure for second-order analysis has been coded in the newest Eurocode 3 and the Hong Kong steel code (2005). The effective length method has been noted to be inapplicable to analysis of shallow domes of imperfect members exhibiting snap-through buckling, to portals with leaning columns and others. On the other hand, the advanced analysis is not limited to buckling design of these structures. This paper demonstrates its application to the design of a simple plane sway portal and a three diminsional non-sway steel building. The results by the advanced analysis and the first-order linear analysis are compared and the technique for practical second-order analysis steel structures is described. It is observed that the use of a straight element by itself cannot model the buckling resistance of columns governed by different buckling curves for hot-rolled and cold-formed sections of various shapes like I, H, hollow etc. Also the curvature of the conventional cubic Hermite element is not varied by the external axial force and thus it cannot simulate the response of a buckling column. Thus its use for second-order analysis is basically unacceptable. A technique for additional checking of beams undergoing lateral-torsional buckling is also suggested making the advanced analysis a complete design tool for conventional steel frames.

Performance-based structural fire design of steel frames using conventional computer software

Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.

Bond performance of CFRP strengthened steel members subjected to axial compression

This paper focuses on the use of externally bonded Carbon Fiber Reinforced Polymer (CFRP) materials to strengthen steel plates subjected to compression. A fully slender steel section was selected in this test programme. CFRP strengthened steel plates and non strengthened plates were tested to fail under compressive load. The middle part of the strut was strengthened using CFRP sheet. The length of the strengthened zone was varied. Eight specimens were tested in this test programme. The test results showed a significant strength gain of 47% and delaying of lateral torsional buckling failure mode of strengthened members. This study confirms that there is great potential to increase the short term performance of CFRP strengthened steel structure under axial compression.