Non-stationary Loading Research Articles

Diagnostics of bearings in presence of strong operating conditions non-stationarity—A procedure of load-dependent features processing with application to wind turbine bearings

Condition monitoring of bearings used in Wind Turbines (WT) is an important issue. In general, bearings diagnostics is a well recognized field of research; however, it is not the case for machines operating under non-stationary load. In the case of varying load/speed, vibration signal generated by rolling element bearings is affected by operation factors, and makes the diagnosis relatively difficult. These difficulties come from the variation of vibration-based diagnostic features caused mostly by load/speed variation (operation factors), low energy of sought-after features, and low signal-to-noise levels. Analysis of the signal from the main bearing is even more difficult due to a very low rotational speed of the main shaft. In the paper, a novel diagnostic approach is proposed for bearings used in wind turbines. As an input data we use parameters obtained from commercial diagnostic system (peak-to-peak and root mean square (RMS) of vibration acceleration, and generator power that is related to the operating conditions). The received data cover the period of several months.The method presented in the paper was triggered by two case studies, which will be presented here: first when the bearing has been replaced due to its failure and the new one has been installed, second when bearing in good condition has significantly changed its condition. Due to serious variability of the mentioned data, a decision making process on the condition of bearings is difficult. Application of classical statistical pattern recognition techniques for “bad condition” and “good condition” data is not sufficient because the probability distribution/density functions (pdf) of features overlap each other (for example probability distribution/density function of peak-to-peak feature for bad and good conditions). It was found that these data are strongly dependent on operating condition (generator power) variation, and there is a need to remove such dependency by suitable data presentation. To achieve it, load susceptibility characteristics (LSCh) presenting as feature – operating condition space has been used. Presented approach is based on an idea proposed earlier for planetary gearboxes, i.e. to analyse data for bad/good conditions in two dimensional space, feature – load/rotation speed. Here it has been proven experimentally for the first time that there are two types of susceptibility characteristics related to the type of a fault.The novelty of the paper also comes from an extension of previous study that is statistical processing of data (linear regression analysis) in moving window in the long time of a turbine operation is used for feature extraction. It is proposed here to use novel features for long term monitoring. It will be shown that parameters of regression analysis can be used as unvarying, and fault sensitive features for decision making.

Influence of Combined Loading on Microstructure and Properties of Aluminum Alloy 2024-T3

The article gives results of the experimental study of mechanical properties and structure of the fractured specimens of multiphase aluminum-base alloy 2024-T3, which were deformed under the dynamic tension conditions. The study shows that the impact in an elastic region leads to an insignificant non-stationary deformation (i.e., deformation in the impact application process) and an insignificant weakening of the material, whereas in the presence of the appreciable plastic deformation before the impact the non-stationary deformation increases more than by an order of magnitude, and a marked weakening takes place. The effects observed are related to the synergy of structure under non-stationary loading. It was concluded that self-organization of the crystalline structure defects in the form of hydrodynamic flow channels, leading to increase in ductility and weakening, may occur only under the nonlinear (plastic) deformation conditions. In the elastic region, the synergic structure formation is limited only to a change of phase composition of the alloy, which may lead to premature fracture of the material under subsequent static deformation. This makes it impossible to predict durability of the material at a probability of uncontrollable load surges. Statistical examination of structure of the fractured specimens revealed the presence of the relaxation structure in the form of recrystallized grains of different sizes, characterized by the presence of scale invariance (scaling). As shown by the grain size analysis, the process of coarsening of the recrystallized grains under dynamic loading and fracture is controlled by some cooperative process related to the atomic and probably electronic structure of the deformed material.

Reliability Evaluation Based on Different Distributions of Random Load

The reliability models of the components under the nonstationary random load are developed in this paper. Through the definition of the distribution of the random load, it can be seen that the conventional load-strength interference model is suitable for the calculation of the static reliability of the components, which does not reflect the dynamic change in the reliability and cannot be used to evaluate the dynamic reliability. Therefore, by developing an approach to converting the nonstationary random load into the random load whose pdf is the same at each moment when the random load applies, the reliability model based on the longitudinal distribution is derived. Moreover, through the definition of the transverse standard load and the transverse standard load coefficient, the reliability model based on the transverse distribution is derived. When the occurrence of the random load follows the Poisson process, the dynamic reliability models considering the strength degradation are derived. These models take the correlation between the random load and the strength into consideration. The result shows that the dispersion of the initial strength and that of the transverse standard load coefficient have great influences on the reliability and the hazard rate of the components.

A new fast discrete S-transform for power quality disturbance monitoring

AbstractIn this paper a new fast discrete S-transform (ST) has been proposed for the estimation of power quality (PQ) disturbance signal parameters in an electric power system. The proliferation of non-stationary non-linear loads and various PQ disturbances such as voltage dips, swells, transients, interruptions, voltage flicker, and spikes, etc., necessitate high PQ level in micro and smart grids. The proposed algorithm is based on the generalised Fourier algorithm that combines down sampling and signal cropping to produce a fast discrete ST. The technique is based on Heisenberg’s uncertainty principle, which limits the time-frequency resolution of ST and employs a trade-off between the time resolution and frequency resolution. In ST the window width decreases at higher frequencies with a reduction in frequency resolution and conversely at low frequencies with wider windows. Hence the signal can be down sampled at low frequencies and cropped at high frequencies to result in fewer samples to be evaluated....

A New Fast Discrete S-Transform for Power Quality Disturbance Monitoring

In this paper a new fast discrete S-transform (ST) has been proposed for the estimation of power quality (PQ) disturbance signal parameters in an electric power system. The proliferation of non-stationary non-linear loads and various PQ disturbances such as voltage dips, swells, transients, interruptions, voltage flicker, and spikes, etc., necessitate high PQ level in micro and smart grids. The proposed algorithm is based on the generalised Fourier algorithm that combines down sampling and signal cropping to produce a fast discrete ST. The technique is based on Heisenberg’s uncertainty principle, which limits the time-frequency resolution of ST and employs a trade-off between the time resolution and frequency resolution. In ST the window width decreases at higher frequencies with a reduction in frequency resolution and conversely at low frequencies with wider windows. Hence the signal can be down sampled at low frequencies and cropped at high frequencies to result in fewer samples to be evaluated. The algorithm models the typical time-varying signal and the accompanied distortions due to harmonics and random noise in a manner that will be suitable for real-time PQ indices estimation. Various PQ disturbance waveforms like voltage sag, swell, harmonics and interharmonics, and oscillatory transients are considered for tracking and estimation of PQ indices.

Structural Reliability Sensitivities under Nonstationary Random Vibrations

Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

Wind Turbine Main Bearing Diagnosis - A Proposal of Data Processing and Decision Making Procedure under Non Stationary Load Condition

Condition Monitoring of bearings used in Wind Turbines (WT) is an important issue. In general, bearings diagnostics is well-recognized field; however it is not the case for machines working under non-stationary load. An additional difficulty is that the Main Bearing (MB) discussed here, it is used to support low speed shaft, so dynamic response of MB is not clear as for a high-speed shaft. In the case of varying load/speed a vibration signal acquired from bearings is affected by operation and makes the diagnosis difficult. These difficulties come from the variation of diagnostic features caused mostly by load/speed variation, low energy of sought features and high noise levels. In the paper a novel diagnostic approach is proposed for main rotor bearings used in wind turbines. From a commercial diagnostic system two kind of information have been acquired: peak-to-peak vibration acceleration and generator power that is related to the operating conditions. The received data cover the period of several months, when the bearing has been replaced due to its failure and the new one has been installed. Due to serious variability of the mentioned data, a decision-making regarding the condition of bearings is pretty difficult. Application of classical statistical pattern recognition for data from the period A (bad condition) and the period B (after replacement, good condition) is not sufficient because the probability density functions of features overlap each other (pdf of peak-to-peak feature for bad and good conditions). Proposed approach is based on an idea proposed earlier for planetary gearboxes, i.e. to analyse data for bad/good conditions in two-dimensional space,feature - load. It is shown that the final data presentation is a good basis to the very successful classification of data (i.e. recognition of damaged and undamaged bearings).

Basic propositions of damage mechanics as a basis for justifying the strength and service life of nuclear power systems

The paper addresses the problem of providing a long-term (up to 60 years) strength reliability of engineering facilities operated under developing damage accumulation. Basic propositions of damage mechanics for derivation of coupled equations descriptive of elastoplastic deformation and fatigue damage accumulation in structural elements of nuclear power systems are given as a tool to assess their expended and residual life from actual operation history. The mathematical model is based on macroscopic variables that integrally characterize the mesoscale structural changes of material under deformation and damage accumulation. The degree of bulk isotropic fatigue damaging is estimated using a macroscopic parameter (0 which is an internal state parameter interpreted as the relative volume fraction of defects in a given material zone. The assessment of fatigue damage accumulation in danger zones of nuclear power systems from actual history of their thermal force loading is based on simulation of the main physical stages of damage accumulation: nucleation and development of micro defects and their coalescence into a fatigue macrocrack. The energy approach used to simulate the damage accumulation allows one to take into account the main peculiarities of elastoplastic deformation in danger zones of structural elements of nuclear power systems under complex nonstationary thermomechanical loading: pronounced localization of damage accumulation due to a high load gradient and design- and process-dependent stress concentration; multiaxial stress-strain states; rotation of principal planes of stress and strain tensors; and nonlinear damage accumulation under changes of loading modes.

A cyclic simulation approach for the generation of the non-stationary load histories of engineering vehicles

The present paper focuses on the simulation of the non-stationary load histories of engineering vehicles for fatigue tests. For the first time, the characteristics of the service loads experienced by engineering vehicles are described. Then rainflow data-reduction contributing to reduce the testing time and extrapolation of each operating section to generate the unavailable extreme loads in a limit test are carried out. Finally, based on the simulated load history of each operating section using Markov chain Monte Carlo method (MCMC) and the corresponding simulation length generated by the Monte Carlo method, a cyclic simulation approach is proposed to generate non-stationary load histories, by which the cyclic characteristic can be reconstructed well. The results of comparison between the observed and simulated load histories show good agreement.

Response Spectral Characteristics and Reliabilities of Linear Structures to Both Intensity and Frequency Content Time-Varying Earthquake Loads

AbstractA numerical method for estimating the useful spectral characteristics of responses of classically damped linear elastic structures to the Yeh-Wen model of fully nonstationary random earthquake loads is developed. The derivation of the method is carried out in three steps. First, the stationary Gaussian white noise process in the space of a frequency modulation function is transformed to the uniformly modulated Gaussian white noise process in the time space. Second, the numerical computation procedure for the unit impulse response functions in the time domain of the Clough-Penzien filters modified in the space of a frequency modulation function is proposed. Finally, the numerical solutions for the useful spectral characteristics of responses of linear structures to the Yeh-Wen model are given, from which the first-passage reliability problem can be solved by using Vanmarcke’s approximation. Numerical investigation of a simple oscillator shows the effect of the frequency modulation functions on the ...

Stochastic model of nonisothermal creep and long-term strength of materials

A stochastic model of nonisothermal creep and long-term strength of metallic materials is proposed. Experimental data on the creep of the ZhS6KP alloy at temperatures equal to 900, 950, and 1000°C are stochastically analyzed. These experimental data are used to substantiate the hypotheses applied in constructing the model. The stochastic model is checked for adequacy to the experimental data on the creep of the ZhS6KP alloy under stationary and nonstationary loading conditions. It is shown that the calculated and experimental data are in satisfactory agreement.

Influence of the boundary conditions on the stress state of a flexible cylindrical shell of variable stiffness in a magnetic field

The effect of the boundary conditions on the stress state of a circular cylindrical shell of variable thickness (stiffness) is analyzed using a geometrically nonlinear problem statement. The cylindrical shell is subject to a magnetic field, external electric current, and nonstationary mechanical load. Numerical results are presented and analyzed

Thin Film Exfoliation in the Zone of Trapped Elastic Wave Localization

AbstractIn modern constructions, thin‐layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical mechanical properties, which leads to the destruction or detachment of the cover. The impact of static or shock loads on the emergence and development of delamination in multilayer constructions has been studied fairly well, but much less is known about destructions of this type under nonstationary (vibrational) loads. The interest in the latter is caused by the fact that even small variable actions may cause the localization of oscillations in a neighborhood of inhomogeneities (such as inclusions, defects, construction elements, etc.) [1] (and lead to the emergence and growth of defects, which strongly affects the reliability and functionality of the whole construction. The possibility of the localization of oscillations near initial delamination and the impact of localization on the growth of the delamination are studied and a model for analyzing conditions under which a detachment zone grows or ceases to grow is suggested. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fatigue Crack Growth Simulation in Railway Axles

In order to carry out the railway axle design according to the “Damage Tolerance” philosophy, reliable crack-growth models for these kind of components are necessary. Indeed, damage tolerance principles have received more and more attention from railway technical community, thanks to its ambitious task concerning the inspection intervals prevision of railway components subjected to non-stationary loading conditions. In this paper, a simple routine is exposed that is able to calculate the characteristic parameters of the Linear Elastic Fracture Mechanics (LEFM) for a generic cracked mechanical component. Such parameters are then used in a two parameters propagation law to estimate the necessary time for a crack to become critical.

Study on the Distributed and Non-Stationary Dynamic Load Being Transformed into Several Equivalent Centralized Loads for Aerocraft

Missiles always undergo non-stationary and continuously distributed load. However, only some centralized loads can be adopted in the ground for their vibration experiments. In this paper, the theoretical analysis and numerical simulation computations programs are established for the distributed and non-stationary airdynamic load being translated into several equivalent centralized loads for high-speed missile. The researches showed that, under the equivalent rule of structural modal responses, the average responses error in both domains time and frequency is within 1.5dB, so it is possible to provide a feasible method for the vibration test on the ground for missile structures.

Effect of the tangential components of magnetic-flux density on the stress state of a flexible circular cylinder with variable stiffness

The effect of the tangential components of magnetic-flux density on the stress state of a circular cylindrical shell of variable stiffness is studied following a geometrically nonlinear problem statement. The cylindrical shell is subject to extraneous electric current and nonstationary mechanical loading

Damage accumulation in specimens with edge crack in the prefracture region under nonstationary few-cycle loading

We present the results of experimental studies of strain and fracture of the aluminum alloy D16-T and titanium alloy VT5-1 under nonstationary few-cycle loading by a symmetric three-point bending and consider several loading conditions under which the load is gradually increased or decreased. The parameter determining the damage accumulation process is found. Special attention is paid to the distinction between the damage accumulation mechanisms in titanium and aluminum alloys. It is shown that, as a rule, the damage accumulation is of nonlinear character and significantly depends on the type of the stepwise variation in the load (increase or decrease). In experiments, we also succeeded in relating the characteristic point on the “deflection-force” graph in the case of single loading to a similar point on the graph constructed for a few-cycle loading, which permits predicting the structure survivability in a few-cycle loading from a single loading.

Numerical simulation of deformation of three-layered plates under short-term nonstationary loads

The algorithm for solving problems of stress-deformed state calculation of three-layered finite deflection plates being hinge-supported and rigidly fixed along a contour, which simulates plates of certain motor vehicles, under short-term dynamic loads of various types is implemented. The effect of pulse-load shape and geometry and stiffness parameters on plate deformation is analyzed.

Probability Density Evolution Method for Seismic Reliability Evaluation of Structural Systems

A structural system reliability evaluation approach based on the idea of equivalent extreme-value event and the probability density evolution method is presented. Using the idea of equivalent extreme-value event, for a compound random event as combination of a set of random events, an equivalent extreme-value event could be constructed. So, this makes it possible to transform computation of the probability of the compound random event to a one-dimensional integration of the probability density function of the equivalent extreme-value random variable. In conjunction with the probability density evolution method, which is capable of evaluating the extreme-value distribution of a set of random variables or stochastic processes, the structural system reliability could be evaluated through computing the probability of the equivalent extreme-value event. The proposed approach is discussed in detail on how to construct the equivalent extreme-value event and then implement the procedure numerically. On the other hand, based on the orthogonal expansion method, the stochastic process of earthquake ground motion can be represented as a linear combination of deterministic functions modulated by a set of mutually independent random variables. Combining the above methods, the reliability of structures under earthquake excitations could be successfully evaluated. An example, of which deals with a linear frame structure subjected to non-stationary seismic loading, is illustrated to validate the proposed method.

Challenges for forecasting based on accelerating rates of earthquakes at volcanoes and laboratory analogues

SUMMARY ‘Mean-field’ models have been proposed as falsifiable hypotheses for the acceleration in earthquake rate and other geophysical parameters prior to laboratory rock failure and volcanic eruptions. Importantly, such models may permit forecasting failure or eruption time. However, inexistingretrospectiveanalysesitiscommontofindexamplesofinappropriatetechniquesfor fittingthesemodelstodata.Herewetestthetwomaincompetinghypotheses—exponentialand power-law acceleration—using maximum likelihood techniques and an information criterion for model choice, based on a Poisson process with variable rate. For examples from the laboratory and Mt Etna, the power law is clearly the best model, both in terms of the fit and the resulting error structure, which is consistent with the Poisson approximation. For examples from Kilauea and Mauna Loa the results are less clear-cut and the confidence interval underestimates the number of outliers. Deviations from the models most likely reflect local interactions and/or non-stationary loading processes not captured by the mean-field approach. In addition, we use simulations to demonstrate an inherent problem with model preference, in that a power-law model will only be preferred if failure or eruption occurs close to the singularity. Although mean-field models may well provide valuable insight into the physical process responsible for precursory accelerations in earthquake rate, our findings highlight major difficulties that must be overcome to use such models for forecasting.