Random Loading Conditions Research Articles

Method for assessing the durability of structures under stationary and non-stationary random loading using variational mode decomposition (VMD)

In the era of digital transformation, most devices are equipped with a variety of sensors, which provide information to be used in developing intelligent models for predicting the fatigue life. The development of digital models of real objects for fatigue life estimation faces the lack of algorithms for performing such an estimation. The problem arises in the adaptive and automatic analysis of signals from real sensors installed on the object and their subsequent processing to estimate the fatigue life of the object. We propose a new method for assessing the fatigue life of structures based on application of the adaptive method of variational mode decomposition to signals gained from sensors, including non-stationary ones. Variational mode decomposition involves decomposition of an initial complex random process into simpler random processes (modes) that are stationary and narrowband. An original method of summarizing damage resulted from the action of the modes obtained as a result of the decomposition is used. The developed method can be used as an algorithmic support for the generation of digital doubles of the residual lifetimes of natural products. The proposed method is compared with the «rainflow» method in the time domain. Different realizations of random stationary and non-stationary signals with different bandwidths are compared numerically. In addition, the traditional frequency methods of Dirlik and Benasciutti have been compared with the «rainflow» method. The analysis showed good results for the proposed method, i.e., the error was smaller compared to traditional frequency methods, especially for non-stationary processes.

Random thermal-vibration mechanisms of sandwich ventral fin-type plate-shell systems with porous functionally graded core

The stochastic thermal-vibration mechanisms within a sandwich ventral fin-type plate-shell system, featuring a porous functionally graded (FG) core, are exhaustively analyzed under various random loading conditions employing an innovative node-based, meshless computational approach. The studied structure is decoupled into several plates and open cylindrical panel according to the geometric characteristics, and the mechanical relationships at the structural boundaries or connection interfaces are equivalently simulated by using penalty parameters. Following the general Hamilton's principle, the meshless approach combined with the first-order shear deformation theory (FSDT) incorporating thermal effects is employed to derive the vibration equations of the sandwich ventral fin-type plate-shell systems. Also, the pseudo excitation method (PEM) is introduced to calculate stationary and nonstationary random responses. In order to verify the accuracy of the meshless algorithm in this study, the convergence and correctness are studied comprehensively. And then, the effects of some parameters such as temperature variation, porosity parameters, power-law index and random excitations on the thermal vibration characteristics of the sandwich ventral fin-type plate-shell systems with porous FG core are presented. The results show that the power-law index and temperature can increase the frequency parameter of the structure. The smooth power spectral density (PSD) excitation only affects the amplitude of the response curve, and does not affect the frequency corresponding to the peak. In the analysis of non-stationary random vibration, the influence of modulation parameters on response is very significant.

Impact and tangential composite fretting wear of Zr-4 alloy tubes under random loading conditions

The fuel rod casing tube is a crucial component in pressurized water reactor (PWR) nuclear power plants. Flow-induced vibrations in the circulating water can result in complex alternating fretting wear between the casing tube and the positioning lattice frame. Existing research on fretting wear has primarily focused on unidirectional wear, with limited investigation into composite fretting wear under complex working conditions. This study conducted impact and tangential composite fretting wear tests on Zr-4 alloy tubes under varying constant and random impact loads to examine fretting wear behavior. The findings show that the peak friction coefficients in the impact and tangential composite fretting wear tests were consistent across the three constant load conditions, with higher peak friction coefficients observed under random load conditions and a longer time required to reach these peaks during micromotion tests. Comparative analysis revealed that random impact and tangential composite fretting wear caused the most severe damage. Under constant load conditions, wear damage became more severe with increasing load, transitioning from oxidized and adhesive wear to a peeling layer as the load intensified in the impact and tangential composite fretting wear tests.

Fatigue behaviors and life evaluation of AISI304 stainless steel under non-proportional multiaxial random loading

Fatigue tests on AISI304 stainless steel under non-proportional multiaxial random loading conditions were conducted with uniform hollow specimens at room temperature. The results revealed initial hardening and subsequent cyclic softening under uniaxial loadings and additional hardening under non-proportional multiaxial loadings. This shift from softening to additional hardening significantly reduced the failure life. Fractographic analysis and Electron Backscatter Diffraction (EBSD) observations identified planar slip as the dominant deformation mechanism under uniaxial loading. Multiple slip system activations, strong slip interactions, and martensitic transformation were key factors influencing changes in cyclic deformation behavior under non-proportional loadings. A novel life evaluation method based on the Itoh–Sakane (IS) method was established, demonstrating accurate evaluations for both uniaxial and non-proportional multiaxial fatigue life under random loading conditions.

The oxymoron of damage assessment in dynamics by static approach

The evaluation of fatigue damage of structural components within dynamic systems subjected to random loads is typically addressed using multibody models wherein one or more components are modeled as flexible using the modal approach. While incorporating flexible elements allows for consideration of their influence on the overall dynamic behavior of the system, certain components are intentionally designed to function as rigid bodies. Consequently, in this case the incorporation of flexible elements within multibody models merely leads to complex and time-consuming analysis. Hence, it would be more pragmatic to realize rigid body multibody models, with components characterized solely by their inertial properties, and subsequently extract the dynamic forces applied to the components to be verified. The assessment of stress can then be carried out by exploiting the principle of superposition of effects in the time domain. In this context, the objective of the present study is to develop this methodology in the frequency domain. This approach not only capitalizes on the simplicity of rigid multibody models but also harnesses the computational capabilities of the frequency-domain method for evaluating fatigue damage in components subjected to random loading conditions. This work, therefore, provides a rapid, effective, and robust method for verifying and designing rigid mechanical components integrated into dynamic systems subjected to random loads.

Study of the kurtoses transmission of linear structures under stationary non-Gaussian random loadings

Recent research has discovered that the kurtoses of non-Gaussian stress loadings can significantly impact the fatigue life of in-service structures. To predict potential damage, a fatigue life estimation method based on Gaussian damage and a kurtosis-related corrective coefficient has been developed. However, the transmission of kurtoses from excitations to responses has not been well studied, particularly in multi-input cases. This hinders efforts to accelerate fatigue damage by controlling input kurtoses. Therefore, this paper aims to establish a kurtoses transmission model for a linear structure under multiple uncorrelated stationary non-Gaussian excitations generated by zero-memory non-linear method. Firstly, a single-input kurtosis transmission equation is proposed to establish the relationship between excitation kurtosis and response kurtosis. Using this equation, the response kurtosis is formulated with input kurtosis and the system parameters of a linear structure. Secondly, the response kurtosis of multi-input cases is deduced, and the study shows that the response kurtosis is the weighted sum of the kurtosis induced by each excitation. Finally, numerical validation and experimental studies are conducted to verify the accuracy of both the single-input and multi-input kurtoses transmission models. The validations demonstrate that the proposed models can predict the response kurtoses with satisfactory precision, regardless of the input spectral shape and the number of uncorrelated input forces.

Deep-learning approach based on multi-data fusion for damage recognition of marine platforms under complex loads

This paper presents an innovative deep-learning network underpinned by advanced data-fusion techniques developed explicitly for detecting structural damage in marine platforms. This study commences with a rigorous validation of the proposed methodology employing detailed experimental procedures and subsequently applies this method to identify damage under specific random load conditions utilizing state-of-the-art finite element analysis software. This entails the meticulous construction of an extensive database mirroring the real-life conditions encountered by a deep-water jacket platform in the South China Sea. By conducting thorough simulations based on the characteristic environmental loads of this marine area, the study succeeds in closely replicating real-world conditions. The developed damage-identification model, which is specifically adapted to the distinctive requirements of non-Gaussian white-noise loads, exhibits notable accuracy. The experimental outcomes derived from the application of the proposed deep-learning algorithm for data fusion indicate an impressive accuracy rate of 92.01%. In simulated scenarios involving complexly loaded jacket platforms, the model attains an accuracy of 88.25%, highlighting the robustness of the method and its wide applicability in the field of marine structural health monitoring.

Experimental investigation and phenomenological modeling of fatigue crack growth in X80 pipeline steel under random loading

Ocean structures are subjected to random environmental loads during their service life. Under the action of random loads, fatigue crack growth within pipeline steel exhibits transient behaviors such as retardation or acceleration. This poses significant challenges in predicting the fatigue life of ocean structures under random loadings. To establish a predictive model for fatigue crack growth in X80 pipeline steel under random loadings, this study first conducts fatigue crack growth experiments under constant amplitude and random loading conditions. Then, based on deep learning methods and the fracture yield zone theory, a phenomenological model is developed to predict fatigue crack growth in X80 pipeline steel under random loading conditions. The results show that under random loading conditions, the fatigue crack growth curve of X80 pipeline steel maintains a relatively clear logarithmic-linear feature during the stable crack growth stage. However, due to the continuous variation of stress ratio with loading sequence, the fatigue crack growth curve exhibits strong fluctuation characteristics; The phenomenological model established in this study for predicting fatigue crack growth under random loading conditions can relatively accurately reflect the overall trend of fatigue crack growth under random loadings, with a maximum prediction error of less than 10%.

Vibration improvement of offshore wind turbines under multiple hazards

The slenderness ratio, particularly pronounced in offshore wind turbines (OWTs) with values exceeding five, renders them highly susceptible to dynamic sensitivity when exposed to lateral loads, setting them apart from conventional structures. The simultaneous interaction of wind and wave forces often results in the generation of extreme vibrations, ultimately jeopardizing the structural integrity of offshore wind turbines. This study is dedicated to assessing the effectiveness of distributed tuned mass dampers (d-TMDs) in mitigating responses in OWTs when subjected to the concurrent action of wind and wave forces. The finite element model (FEM) for the OWT, accounting for its multi-degree of freedom (MDOF) nature, is meticulously constructed using ANSYS software. The analysis encompasses uncontrolled offshore wind turbines (NC), those equipped with single tuned mass dampers (STMD), and variants featuring d-TMDs. These structures are exposed to random wind and wave loading conditions, mirroring real-world scenarios and necessitating the deployment of control schemes to counteract the adverse vibrations induced. Consequently, wind and wave spectra are generated using the Kaimal spectrum and Pierson and Moskowitz spectrum, respectively, with drag wave forces calculated through Morison's equation. Moreover, the study takes into account the impact of soil-structure interaction (SSI), incorporating both rotational and lateral springs. The results, comprising displacement and acceleration responses at the pinnacle of the OWT, facilitate a comprehensive comparison between the responses of the NC, STMD, and d-TMD configurations. In single hazard analysis, it is evident that TMDs exhibit greater efficacy in mitigating wind-induced responses in offshore wind turbines compared to wave-induced responses. Furthermore, d-TMD schemes demonstrate superior performance in enhancing the response of flexible base offshore wind turbines as opposed to their fixed base counterparts.

Accelerated Life Testing Dataset for Lithium-Ion Batteries with Constant and Variable Loading Conditions

The development of new modes of transportation, such as electric vertical takeoff and landing (eVTOL) aircraft and the use of drones for package and medical delivery, has increased the demand for reliable and powerful electric batteries. The most common batteries in electric-powered vehicles use Lithium-ion (Li-ion). Because of their long cycle life, they are the preferred choice for battery packs deployed over a lifespan of many years. Thus, battery aging needs to be well understood to achieve safe and reliable operation, and life cycle experiments are a crucial tool to characterize the effect of degradation and failure. With the importance of battery durability in mind, we present an accelerated Li-ion battery life cycle data set, focused on a large range of load levels, for batteries composed of two 18650 cells. We tested 26 battery packs grouped by: (i) constant or random loading conditions, (ii) loading levels, and (iii) number of load level changes. Furthermore, we conducted load cycling on second-life batteries, where surviving cells from previously-aged packs were assembled to second-life packs. The goal is to provide the PHM community with an additional data set characterized by unique features. The aggressive load profiles create large temperature increases within the cells. Temperature effects becomes therefore important for prognosis. Some samples are subject to changes in amplitude and number of load levels, thus approaching the level of variability encountered in real operations. Reassembling of survival cells into new packs created additional data that can be used to evaluate the performance of recommissioned batteries. The data set can be leveraged to develop and test models for state-of-charge and state-of-health prognosis. This paper serves as a companion to the data set. It outlines the design of experiment, shows some exemplifying time-series voltage curves and aging data, describes the testbed design and capabilities, and also provides information about the outliers detected thus far. Upon acceptance, the data set will be made available on the NASA Ames Prognostics Center of Excellence Data Repository.

An Equivalent Structural Stress-Based Frequency-Domain Fatigue Assessment Approach for Welded Structures under Random Loading

Welded structures under random loadings are usually susceptible to fatigue-induced failures that lead to significant economic and safety effects. However, accurately predicting these structures’ fatigue damage and life in the frequency domain remains challenging due to the limitations associated with using traditional weld stress extrapolation methods, such as nominal, hotspot, and notch stress methods. These methods struggle with precisely defining and characterizing the stresses at the weld toe and root as they vary depending on factors like weld stress concentration effects, joint geometry, and loading modes. This research introduces an Equilibrium Equivalent Structural Stress (EESS)-based frequency-domain fatigue analysis approach for welded structures subjected to random loading. The proposed method utilizes the EESS formulations, which are based on the decomposition and characterization of weld toe stresses with a single stress parameter, together with incorporating structural dynamic properties’ effects on the stresses acting on the weld joints and the corresponding accumulated fatigue damage of the structure. The numerical demonstration and validation of the proposed method have been performed using a welded Rectangular Hollow Section (RHS) T-joint structure subjected to stationary random fatigue loading. The proposed method’s fatigue damage and life results are compared with the fatigue test data and the equivalent hotspot stress extrapolation-based technique results.

Thermal Load Model of a Proportional Solenoid Valve Based on Random Load Conditions

Drastic changes in the random load of an electromechanical system bring about a reliability problem for the proportional solenoid valve based on a thermal effect. In order to accurately and effectively express the thermal load of a proportional solenoid valve under random load conditions and to meet the requirements of online acquisition, adaptive anomaly detection, and the missing substitution of thermal load data, a thermal load prediction model based on the Kalman filter algorithm is proposed. Taking the compound operation process of an excavator as the object and based on the field testing of an excavator and the independent testing experiment of a proportional solenoid valve in a non-installed state, a method of obtaining historical samples of the proportional solenoid valve’s power and thermal load is given. The k-means clustering algorithm is used to cluster the historical samples of the power and thermal load corresponding to the working posture of a multi-tool excavator. The Grubbs criterion is used to eliminate the outliers in the clustering samples, and unbiased estimation is performed on the clustering samples to obtain the prediction model. The results show that the cross-validation of the sample data under the specific sample characteristics of the thermal load model was carried out. Compared with other methods, the prediction accuracy of the thermal load model based on the Kalman filter is higher, the adaptability is strong, and the maximum prediction deviation percentage is stable within 5%. This study has value as a reference for random cycle thermal load analyses of low-frequency electromechanical products.

Random vibration analysis of composite laminated conical–cylindrical cabin structures of air vehicles considering thermal load

This study proposes a novel semi-analytical random dynamic model using the meshless method to precisely predict and quickly analyze the frequency-domain random response properties of composite laminated conical–cylindrical cabin structures (CL-CCCSs) of air vehicles under stationary random loads. In addition, thermal load is considered in the analysis. The first-order shear deformation theory (FSDT) is used to develop a random dynamic theoretical model for CL-CCCSs based on the spectro-geometric method (SGM) and pseudo-excitation method (PEM). Variable stiffness springs are employed to handle diverse boundary cases and compatibility conditions in the current model. Also, the displacement admissible functions for laminated conical shell and cylindrical shell are uniformly depicted with SGM, which depends on sine and cosine functions. After that, the PEM is employed to transform stationary random loads into pseudo harmonic loads. Subsequently, the energy variation principle is used to derive theoretical discrete random dynamic equations for vibration model of CL-CCCSs considering the thermal effect. The results of numerical vibration analyses are compared to confirm the reliability of the established model. Finally, the effect of certain parameters, such as the lamination scheme, layer number, and temperature, on the random vibration response of a CL-CCCS is thoroughly explained.

Random vibrations of laminated planar frames

In this study, the normal mode method is used to determine the response of a generalized laminated planar frame structure subjected to random loading conditions. The model, which is based on the Timoshenko–Ehrenfest beam theory, accounts for the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy. The free vibration analysis of the frame is formulated and solved, and the orthogonality condition derived. Following this, the normal mode method is applied to determine expressions for the mean square longitudinal, transverse and rotational displacements in terms of the excitation spectral density. Although the proposed model is capable of analyzing a wide range of problems, the numerical analysis conducted in this paper is centered on investigating the response of inclined two-member and three-member frames excited by a point force, whose spectrum is band-limited white noise. It is shown that in cases where the modal cross-correlation is negligible and the boundary conditions are symmetric, the spatial response of the mean square displacements are nearly symmetric about the center point of the frame. Contrarily, as the influence of the modal cross-correlation on the overall response increases, the featured spatial symmetry vanishes. An interesting characteristic of frame structures, is that the spacing between the natural frequencies is dependent on the frame angle. Consequently, modal cross-correlations can have a much greater effect on certain frame angles compared to others, even when the damping is fairly low. The study also investigates the effects of bending-extension material coupling on the random response of asymmetrically laminated cross-ply frames. The numerical results presented in this work are verified with independent finite element simulations conducted in the software package, Ansys® Parametric Design Language (APDL).

Spectral-Tchebychev technique for the free and stochastic vibration analysis of functionally graded plates with piezoelectric patches

This paper presents a Spectral-Tchebychev (S-T) dynamic model to examine the free and random vibration properties of functionally gradient plates with piezoelectric patches (FGPPP) under random excitation. Firstly, the plate is divided into several sub-plates according to the position of the piezoelectric patches through the multi-partitioning strategy. Then, the dynamical equations for each sub-plate are derived based on the first-order shear deformation theory (FSDT) and Hamilton's variational principle. The boundary conditions and the coupling relationships of the adjacent plates are handled using the artificial spring technique. Finally, the free and stochastic vibration characteristics of FGPPP are obtained using the Spectral-Tchebychev technique, where the stationary random load is introduced by the pseudo-excitation method (PEM). The rationality and validity of the S-T model in predicting the vibration characteristics of FGPPP are verified by the comparison with the results from literature and FEM. The influence mechanism of some key parameters including the thickness ratio, area ratio, patching position, patching type, power law index, etc., on the vibration characteristics are systematically investigated.

Real-Time Response Estimation of Structural Vibration with Inverse Force Identification

Virtual sensing is an effective method to identify the inaccessible state of the structural systems by compensating the limitations of the conventional physical sensing techniques. Recently, it becomes popular in structural vibration field and their relevant physical domains such as civil, mechanical, aerospace engineering, thermal dynamics, and acoustics. This study aimed to develop a virtual sensing algorithm of structural vibration for the real-time identification of unmeasured information. First, certain local point vibration responses (such as displacement and acceleration) are measured using physical sensors, and the data sets are extended using a numerical model to cover the unmeasured quantities through the entire spatial domain in the real-time computation process. A modified time integrator is then proposed to synchronize the physical sensors and the numerical model using inverse dynamics. In particular, an efficient inverse force identification method is derived using implicit time integration. The second-order ordinary differential formulation and its projection-based reduced-order modeling are used to avoid two times larger degrees of freedom within the state-space form. Then, the Tikhonov regularization noise-filtering algorithm is employed instead of Kalman filtering. The performance of the proposed method is investigated on both numerical and experimental testbeds under sinusoidal and random excitation loading conditions. In the numerical test, the system could identify the status of the motor housing structure in the speed of 16,181 S a m p l e s / s . The FDE and RMSE values are bounded under 0.1816 and 1503.2. In the case of the experimental test, the algorithm is implemented to the beam structure using a single-board computer, including inverse force identification and unmeasured response prediction. Even in the limited computational environment, the system could identify the applied forces in real time in the speed of 2,173 S a m p l e s / s . Through all experimental cases, FDE and RMSE values are bounded under 0.2925 and 0.1660. The results show that the virtual sensing algorithm can accurately identify unmeasured information, forces, and displacements throughout the vibration model in real time in a very limited computing environment.

Reliability-based fatigue life assessment using random road load condition and local damage criteria

This study presents a fatigue reliability assessment of a vehicle coil spring based on random road load conditions for fatigue life characterisation. Fatigue life data characterisation was carried out to accelerate the durability analysis by retaining the higher amplitude cycles in the original strain signals and thus indicate the fatigue damage. To collect experimental data, road testing was conducted using various road profiles, which contributed significantly to the fatigue failure performance of the vehicle coil spring. Fatigue reliability analysis was performed to assess the failure behaviour of the coil spring utilising the probabilistic Gumbel distribution model to forecast the probability distribution of the fatigue life data. Furthermore, the highest and lowest mean-cycles-to-failure (McTF) of 5.44 × 107 and 2.46 × 105 blocks were estimated for the Coffin-Manson and Smith-Watson-Topper models from the highway and rural road profiles. The findings demonstrate that the lowest hazard rate corresponded to the highest McTF, making this an acceptable model to be implemented in reliability assessments of road profiles. Hence, the fatigue reliability assessment provided a hazard rate based on the fatigue life predictions for risk assessments when characterising the fatigue life data.

Uncertainty of Estimated Rainflow Damage in Stationary Random Loadings and in Those Stationary per partes

The uncertainty of rainflow fatigue damage is evaluated for stationary loadings and for non-stationary switching loadings with a finite number of stationary states. The approach is based on confidence intervals constructed after direct analysis of stress-time histories. The accuracy of confidence intervals is verified first by numerical simulations, and then by experimental data measured in a mountain bike traveling under various driving and road surface conditions, yielding stationary and non-stationary switching loadings. Stationarity and non-stationarity of loading records is checked by a statistical method (run test). In experiments, a small set of records (validation set) is also collected and used to approximate the expected damage, which serves for verification purposes. Not only do numerical and experimental results confirm the correctness of the proposed confidence interval for damage, but they also emphasize its usefulness in real engineering applications.

Failure Strength of Automotive Steering Knuckle Made of Metal Matrix Composite

This article presents the static performance of composite steering knuckle due to drive on an equivalent road, including different types of roughness and maneuvers. To achieve this purpose, the driving of a full-vehicle model was simulated using the multi-body dynamics (MBD) method, and the imposed loads on connection points of the steering knuckle to different components of the suspension system were extracted considering various maneuvers. Next, CATIA software was used to prepare a smooth model of the steering knuckle by employing coordinate measuring machine (CMM) data. Stress analysis was performed under the maximum value of the loading history in finite element (FE) software. Eventually, the safety factor was calculated based on some well-known criteria for static failure of the composite materials. Moreover, the optimum value of tungsten carbide as a reinforcing substance in aluminum composite was estimated to increase failure strength. The results show that an increase in tungsten carbide leads to an increase in the strength of the steering knuckle under purely axial loads (normal stress criterion) and also that an increase in this substance leads to a decrease in the strength of the part under shear loads (shear stress criterion). Therefore, based on the nature of the loads (i.e., multi-axial non-proportional random amplitude loading conditions) applied to the automotive steering knuckle due to actual conditions, this metal matrix composite (aluminum matrix and tungsten carbide as reinforcement) is not practical.

Decentralized Optimized Integral Sliding Mode-Based Load Frequency Control for Interconnected Multi-Area Power Systems

In this paper, a decentralized load frequency control (LFC) is proposed for the frequency regulation of multi-area power systems applying optimized integral sliding mode control (OISMC) scheme. A modified particle swarm optimization (MPSO) algorithm is utilised to optimize the control variables of the proposed controller for improving the performance of frequency response. A comprehensive model of a multi-area power system is developed where each area is considered to power from conventional sources, renewable energy resources (RERs), and electrical vehicle (EV) aggregators. Different types of interconnectors have been considered to tie different power regions. This system is subjected to random generation and loading conditions, as well as model uncertainties, which cause its frequency and area control error (ACE) to deviate from their nominal values. A decentralised OISMC is implemented for the proposed model to keep the frequency variation within the nominal range. Further, a validation study investigates the performance of the proposed control technique in MATLAB simulation environment to mimic the real power system operation. This study includes different test scenarios considering the dynamic events such as variations in load demand, amount of generated power, participation factor of EV reserve, system parameters, disturbances, and time delay. The simulated results support better frequency regulation with the suggested OISMC compared to other alternative control approaches.