Reliability-based Assessment Research Articles

Remaining Useful Life prediction based on physics-informed data augmentation

Current approaches for monitoring machine health (SOH) and effective prognostics depend on the extensive use of complete degradation data trajectories, implying the reliance on data generation techniques that involve functional degradation of the real system until the failure state is reached. These commonly adopted approaches that depend on labeled target data remain operationally and economically nonviable for most industries and safety critical systems. This paper presents novel approaches that alleviate the existing dependence of most prognostics procedures on Remaining Useful Life (RUL) labeled data for training. To this end, firstly, a hybrid data augmentation procedure is proposed that enables the integration of system knowledge available a priori as well as physics of failure, within the training data. Secondly, an unsupervised Health Index (HI) extraction approach is developed, followed by a long-term prediction of this same HI, that leads to an efficient prediction of RUL without labeled data. Finally, a reliability-based assessment is performed to validate the proposed approach. This comprehensive approach (i.e. integrating all the various stages involved in achieving a RUL prediction based on unlabeled data) is tested on a real industrial aircraft system demonstrating the effectiveness of the proposed approach in real industrial context.

Reliability-based Assessment of the Structural Integrity of some Existing Reinforced Concrete Columns

Abnormal loading can initiate the progressive collapse of a reinforced concrete building. A progressive collapse may start as a local failure, followed by a sequence of reactions leading to a massive portion failure of an entire structure. Reinforced concrete columns are significant structural elements in ascertaining the integrity of framed buildings. This paper presents the report on the structural integrity of reinforced concrete columns of two selected university buildings labelled A and B investigated by using non-destructive testing techniques. First-Order Reliability Method (FORM) was deployed to process the data from the field in order to generate the implied safety indices for all accessed columns in the two buildings. The computed safety indices decrease as the simulated designed practical axial loads/moments increase for all the assumed steel ratios (0.4%, 1.59% and 6%) based on BS 8110:1997:1. When compared with the target safety level of 3.8 according to BS EN 1990:2002+A1:2005 for 50 years reference period of Class RC2 structural members in the ultimate limit state, almost all the columns passed the reliability test except the columns labelled 71 in building A; and C81A and C85 for building B. The highlighted critical columns show the direction for immediate repairs to forestall the initiation of eventual progressive failure of the buildings.

Sensitivity analysis of different parameterization schemes of the Weather Research and Forecasting (WRF) model to simulate heavy rainfall events over the Mahi River Basin, India

A reliability-based assessment of heavy rainfall events can provide insights for developing appropriate measures and predictions to control flood risk. One of the contemporary challenges is to model heavy rainfall events, which depend on different synoptic conditions and model configurations. In this study, the regional mesoscale Weather Research and Forecasting (WRF) model was used to evaluate the applicability of different parameterization schemes for simulating rainfall events over the Mahi River basin between 22 and 26 August 2020 with the maximum rainfall occurring on 23 August 2020. A high-resolution triple-nested (27, 9, and 3 km) WRF model was configured, and data for initial boundary conditions were obtained from NCEP/NCAR FNL with a resolution of 1° × 1° (six-hourly). The model results were evaluated using gridded rainfall of ECMWF Reanalysis v5 (ERA5) and India Meteorological Department (IMD) at a spatial resolution of 0.25° × 0.25°. Further to verify the model output, GPM-IMERG was used to compute the skill score (bias, threat score, probability of detection, and accuracy) metrics at 24 hourly and 3 hourly scales. Eight sensitivity tests were conducted to identify the optimal sets of microphysics (WSM6 and Goddard), cumulus (Kain and BMJ), and planetary boundary layer (YSU and ACM2) parameterization schemes for rainfall simulation of the selected events. The Kain-Goddard-YSU and Kain-Goddard-ACM2 parameterization schemes demonstrated the optimal performance for simulating the rainfall event. Relative humidity and reflectivity were used for analyzing moisture and cloud brightness temperature, respectively. The model score revealed that the Kain-Goddard scheme outperformed other schemes in case of heavy precipitation, with a threshold of 60 mm/day over the Mahi basin. The findings of this study showed that the simulation of heavy rainfall events with a set of selected combinations of parameterization schemes can reproduce the structure of convective organization as well as prominent synoptic features associated with heavy rainfall events over the Mahi basin. Moreover, this information may help to better understand the future forecast trend of precipitation and explore solutions for sustainable water management to support decision-makers and operational water managers.

Reliability-Based Assessment of a Masonry Arch Bridge Considering Random Stereotomy

Reliability-Based Assessment of a Masonry Arch Bridge Considering Random Stereotomy

Assessment of the ultimate strength of stiffened panels of ships considering uncertainties in geometrical aspects: Finite element approach and simplified formula

The development of reliability-based assessments has improved the safety design of ship structures by considering the stochastic behaviour of structural components such as stiffened panels. However, previous studies generally considered the variation in the initial geometric imperfection of a stiffened panel as a single deterministic value. To enhance the analysis, in this study, a series of ultimate strength analyses of stiffened panels were carried out by varying and combining the stiffened panel parameters, including variations in the initial geometric imperfection (2.5%, 25%, 50%, 75%, and 100% of the maximum value), modes of the imperfection (column, local, and torsional imperfection modes), slenderness ratios (plate and web slenderness), and span-to-bay ratios (3 and 6). A total of 750 stiffened panel configurations were investigated through a nonlinear finite element method (FEM) analysis using ANSYS APDL incorporated with a code in MATLAB to model the imperfections based on idealised models. The obtained ultimate strength values were then formulated using a nonlinear correlation between the variables in the regression method to yield a new formula for predicting the ultimate strength of the stiffened panel. The results showed that combining the varied parameter values significantly affected the ultimate strength of the stiffened panel and collapse modes. The newly derived formula provided good accuracy with a standard error of only 2.08% when compared with the FEM results of stiffened panels having a significant disparity with the configuration of the idealised models. This confirms the validity of the formula as a reference for evaluating the ultimate strength value with the influence of an initial geometric imperfection.

Reliability-based assessment of reasonable mid-tower lateral stiffness for a three-tower suspension bridge

A reasonable lateral stiffness of the bridge mid-tower should ensure that the deflection-to-span ratio and sliding resistance coefficient satisfy the design requirements. However, if this stiffness is determined by the deterministic parametric analysis, the above two verification indices may exceed the threshold due to the randomness of the high-dimensional structure and load parameters. To satisfy the structural safety requirements of a three-tower suspension bridge during its design life, this study proposes a method to quickly and accurately evaluate the reliability indices of the deflection-to-span ratio and sliding resistance coefficient of the three-tower suspension bridge. Based on advanced first-order second-moment, the proposed method transforms the reliability problem into an optimization problem with constraint functions, uses the single-cable theory to establish the limit state function, and combines the manta ray foraging optimization algorithm and penalty function to derive the reliability index. The effectiveness of the proposed method is verified by performing Latin hypercube sampling for an examplary three-tower suspension bridge. These results prove that the new technique avoids tedious finite element simulation and surrogate model fitting, ensuring the accuracy of the reliability index while improving the calculation efficiency. The study further identifies critical structural parameters by parametric analysis. Based on the inverse reliability, the dimensionless stiffness range for the mid-tower with the randomness of the parameters is derived, and the preliminary design method of the lateral stiffness of the mid-tower based on the reliability is established.

Whole-life modelling of anchor capacity for floating systems: The RSN[sbnd]CSI approach

Successive episodes of cyclic loading cause the strength of soft soils to reduce, through pore pressure build-up, and then recover, through consolidation, as shown by model testing, field studies and theoretical considerations. These ‘whole-life’ changes in soil strength affect the capacity of anchoring systems for offshore infrastructure such as floating turbines or platforms. This paper introduces a new macro-model for assessing the through-life changes in seabed strength and anchor capacity as a result of variable cyclic loading and concurrent consolidation. The model combines SN curves for damage accumulation with a critical state soil mechanics framework for changes in soil strength and anchor capacity. These methods allow the full operational lifetime of an anchoring system to be rapidly analysed, encompassing timescales from individual wave-induced load cycles, through to annual seasons and soil consolidation processes. The approach provides a new basis for whole-life modelling of anchoring systems that is sufficiently fast to allow reliability-based assessments via a Monte Carlo method. In soft soils that exhibit beneficial gains in capacity, this method provides a basis for more efficient design through reductions in anchor size.

Reliability-based assessment of ship hull girder ultimate strength

Abstract A reliability-based approach is presented to investigate the effects of structural and load uncertainties on the reliability estimation of ship hull girders. Structural uncertainties included randomness in material properties, geometric properties, initial geometric imperfections, and corrosion behavior. Load uncertainties included statistical uncertainties, model uncertainties, environmental uncertainties, and uncertainties related to nonlinearity. The hull girder ultimate strength was calculated using Smith’s method, and the probabilistic density function was evaluated by employing Monte Carlo simulations. In the load estimation, the still water bending moment and wave-induced bending moment were calculated using a simplified formula of the International Association of Classification Societies-Common Structural Rules code and then modified with load parameters. The reliability index was estimated using a first-order reliability method considering the operating time, the duration of the ship in the alternate hold loading condition, and the severity of the corrosion rate. As a result, sagging conditions dominated the collapse mode. The reliability indexes were obtained for the observed cases, and the viability of the ship was assessed accordingly.

Structural reliability and partial safety factor assessment of unreinforced masonry in vertical bending

ABSTRACT This paper focuses on a structural reliability-based assessment of clay brick unreinforced masonry (URM) walls subjected to uniformly distributed out-of-plane loads in one-way vertical bending. Stochastic models combining finite element analysis (FEA) and Monte Carlo simulations (MCS) are used to account for spatial variability of the flexural tensile bond strength when estimating the wall failure loads. The strength of URM walls is known to be influenced by the flexural tensile bond strength, which is subject to high spatial variability as batching, workmanship, and environmental exposure alter the strength of this bond. For this assessment, single skin walls have been considered with bond strength statistics seen in typical construction. The model error statistics available for similar walls are combined with the results of the spatial stochastic FEA and probabilistic load models to determine the reliability index corresponding to the Australian Standard for Masonry Structures AS 3700 design of members in vertical bending. It was found that existing levels of reliability exceed target reliabilities, and the capacity reduction factor can be increased from 0.60 to 0.65 for URM walls in one-way vertical bending while still providing an acceptable level of reliability. A sensitivity analysis showed this finding to be robust.

Reliability-based assessment of scour at pier in gravel beds

ABSTRACT Estimation of local scour depth at a bridge pier must be accurate and precise for the safety assessment of pier foundation. Many deterministic scour depth prediction models for bridge piers in sands and gravels have already been reported in the literature. However, the various types of uncertainties may be involved in the deterministic scour depth prediction models and thus affect the accuracy of the scour depth. To account for such uncertainties, a reliability analysis method is generally adopted. A sizable amount of laboratory and field data on scour has been procured in the present study to assess the performance of existing scour prediction models for gravel beds and develop a probabilistic scour prediction model using a First-Order Reliability Method (FORM) based on the object-oriented constraints optimization spreadsheet algorithm for the most appropriate selected deterministic scour prediction model. A new relationship of the silt factor has also been developed to estimate the scour depth in gravel bed as per Indian Practice. A safety factor based on the target reliability index has also been proposed in this study.

A finite difference-based approach for strain demand prediction of inelastic pipes subjected to permanent ground displacements

Permanent ground displacement triggered by geohazards constitutes a major threat to the integrity of long-distance pipelines. In this study, a novel and simple method is proposed to evaluate inelastic pipes’ behavior under ground movements considering soil-pipe interaction based on the finite difference method. The existing finite difference-based method previously proposed by the authors for strain analysis of buried pipelines subjected to ground movements excludes material nonlinearity in pipes, which limits its applicability in engineering practice. To remedy this situation, the method presented herein maintains the well-established concepts of the existing finite-difference-based method but also introduces the scheme to consider the inelastic material behavior of steel pipes. More specifically, the expressions of internal axial force and bending moment, required in the finite difference equations, are explicitly derived based on the actual stress distribution on the pipe cross-section. The proposed method is validated against the finite element method (one-dimensional beam model) in terms of the strain and deformation demands using two indicative case studies, referred to as symmetric and non-symmetric soil resistance conditions, respectively. The comparison between finite element analysis and the proposed method indicates good agreement. Additionally, the proposed method is compared with four existing analytical methods for pipes subjected to strike-slip fault displacement. The proposed method is a simple but general technique to analyze pipes’ response under a wide range of geohazards, and thus can be potentially used as an alternative method for preliminary design, safety prescreening, and reliability-based assessment of pipes against geohazards.

Reliability-based assessment of progressive collapse in horizontally irregular multi-story concrete buildings

Structures’ resistance against progressive collapse varies depending on their design and taxonomy. However, despite numerous studies addressing the impact of geometric configuration, limited attention is given to the effect of irregularity. This study presents a reliability-based approach to evaluate the effect of horizontal irregularity on the progressive collapse potential of seismically designed concrete buildings. Incremental dynamic analysis is performed on three-dimensional nonlinear finite element models of six prototype buildings with different levels of horizontal irregularity subjected to four column removal scenarios. Probabilistic demand models are then derived to construct fragility curves based on the first-order reliability method. In addition, an analysis of covariance is performed to measure the sensitivity of demand models to column removal scenarios in terms of floor and location. The results show that the studied irregular buildings do not pose a greater risk of progressive collapse than the regular building. In addition, while the probability of collapse under sudden column removal is significantly low for the seismically designed concrete frames, all buildings are expected to experience significant damage under such abnormal loads.

Reliability-based assessment and optimization for the two-way shear design of lightweight reinforced concrete slabs using the ACI and EC2

Recent brittle two-way shear failures have made assessing strength models a topic of interest. In addition, the economic alternatives have made lightweight reinforced concrete slabs (LWRCS) a popular choice of construction in many areas around the world. However, researchers have rarely tackled the two-way shear strength models of LWRCS using accurate structural reliability analysis methods. Most of the research investigations evaluated the performance of the two-way shear strength models for the LWRCS with respect to an experimental database using statistical measures. While it did not implement structural reliability methods, which could include the variability due to the following: (1) the governing variable’s random distribution; (2) the size of the experimental database; and (3) errors in measurements, construction, and design. Thus, this current study aims to apply structural reliability methods for the two-way shear of LWRCS. Two internationally renowned design codes were selected using an extensive experimental database. A brief outline of existing structural reliability methods is presented and compared. A selected reliability method was used to assess the reliability of the design-chosen codes. The reliability and sensitivity indices were calculated for the American and European design code provisions of two-way shear of lightweight concrete and compared with each other as well as international standard reliability. The American design code were found to be less reliable compared with the European, which might be due to not considering the flexure reinforcement ratio in the model. In addition, model accuracy is the main factor affecting reliability, however, the variability of basic parameters including concrete density, concrete strength and cross section depth have larger effect compared to flexure reinforcement ratio and loading area dimensions. Moreover, in order to achieve target reliability indices value of 3.8, 3.7, or 3.6 a reduction factor value of 0.8, 0.75, or 0.70 could be implemented. These findings could be helpful in design code developments. However, the results are limited to the selected variability of the random variables.

Reliability-Based Assessment of Galloping Instability of Thin-Walled Steel Beams

Abstract Galloping instability relating to cross-wind vibrations can be found in flexible and lightly damped structures. In the present paper, the reliability of a thin-walled steel beam in maintaining its galloping stability was examined using a probabilistic approach. The analysis considered random variation in the cross-sectional geometrical properties of the beam, the material elastic modulus, the structural damping and the wind speed. A large number of Monte Carlo simulations were performed with normal and Gumbel distributions applied to the random variables to determine the probability distribution function of the safety margin. The limit state is considered violated when the wind speed exceeds the onset wind velocity of galloping, resulting in the aerodynamic damping being greater than the structural damping. It was shown by a conventional codified safety factor method that the beam was robust enough for galloping stability. By contrast, the probability-based assessment revealed that the beam failed to achieve the target reliability index in case the coefficient of variation of wind speed was greater than 5%. The analysis results suggested that the code-satisfied slenderness of the beam should be reduced by a factor of 1.5-1.7 under the action of wind speed with a coefficient of variation in the range 30-40%.

Reliability-Based Assessment of Concrete Decks Designed Using Approximate Method at the Strength I Limit State

The Approximate Method coupled with the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications (BDS) is applied for designing reinforced concrete bridge decks. Although the LRFD BDS has an intrinsic design return period of 75 years and a target reliability index of 3.5 at the Strength I Limit State, many concrete bridge decks exhibit much shorter service life. Besides the limitations of the crack control limit state at service, the inadequate nominal resistance at the Strength Limit State could contribute to the shortened service life. This paper presents a reliability-based assessment of the current concrete deck design provisions by utilizing actual truck load spectra collected from the national weigh-in-motion (WIM) data. Axle groups, including single axles, tandem axles, and tridem axles, were identified from the WIM data. The moment effects are obtained from influence surface analysis, formulating the live load statistics, particularly for the decks that are supported by girders. It was found that the current design load is not able to represent and envelop the actual traffic load. Additionally, the reliability indices are calculated for a series of reinforced concrete decks on account of both bending moment capacity and arching action moment capacity. The arching action was found to greatly enhance the reliability index for the positive moment region, providing satisfactory reliability indices. The negative moment region may or may not meet the target reliability index depending on the design criteria.

Reliability-Based Assessment of LTF and CLT Shear Walls under In-Plane Seismic Loading Using a Modified Bouc-Wen Hysteresis Model

AbstractThis paper reports on the reliability-based assessment of light timber frame (LTF) and cross-laminated timber (CLT) shear walls. The outcomes of cyclic tests on 17 timber shear wall specime...

Reliability-based assessment of the partial factor for shear design of fibre reinforced concrete members without shear reinforcement

Fibre reinforced concrete (FRC) is increasingly used for structural purposes owing to its many benefits, especially in terms of improved overall sustainability of FRC structures relative to traditional reinforced concrete (RC). Such increased structural use of FRC requires safe and reliable models for its design in ultimate limit states (ULS). Particularly important are models for shear strength of FRC members without shear resistance due to the potential of brittle failure. The fib Model Code 2010 contains a model for the shear strength of FRC members without shear reinforcement and the same partial factor accepted for RC structures is accepted for FRC elements. This approach, however, is potentially on the unsafe side since the uncertainties of some design-determining mechanical properties of FRC (i.e., residual flexural strength) are larger than those for RC. Therefore, in this study, a comprehensive reliability-based calibration of the partial factor γc for the shear design of FRC members without shear reinforcement according to the fib Model Code 2010 model is performed. As a first step, the model error δ is assessed on 332 experimental results. Then, a parametric analysis of 700 cases is performed and a relationship between the target failure probability βR and γc is established. The results demonstrate that the current model together with the prescribed value of γc = 1.50 does not comply with the failure probabilities accepted for the different consequences of failure of FRC members over a 50-year service life. Therefore, changes to the shear resistance model are proposed in order to achieve the target failure probabilities.

Reliability-based assessment of bond strength models for near-surface mounted FRP bars and strips to concrete

This article investigates the reliability of three existing near-surface mounted (NSM) fiber-reinforced polymer (FRP) bond strength models including the ACI 440.2R-17 model and two fracture mechanics-based models. Various load combinations and strength reduction factors included in the ACI 440.2R-17 guidelines and the CSA S806-12(17) standard are considered. The uncertainty of the bond models is evaluated using the data gathered from 451 experimental specimens available in the literature with careful consideration of the reported modes of failure and their combinations. A reliability analysis based on the first-order second-moment (FOSM) method is conducted on the three bond models for both strips and bars against the dead, live, snow, and wind loads accounting for uncertainties due to geometrical and mechanical properties of the NSM FRP-to-concrete joints. This article provides a platform for choosing the proper strength reduction factors for a practical range of target reliability indices. The results show that the strength reliability of the considered bond models with respect to the existing strength reduction factors requires major improvements. The proposed strength reduction factors in this study are able to improve the reliability indices of the bond models significantly for provisions of ACI and CSA when different load combinations are considered.

Reliability-Based Assessment of Potential Risk for Lane-Changing Maneuvers

Despite the urgent need for continuous risk assessments during autonomous driving, achieving reliable assessment results is still challenging because of the unpredictable behaviors of adjacent human drivers and the resulting complexity. Such complexity increases particularly during lane changes because several vehicles need to interact with other vehicles. Therefore, this paper proposes a new framework to analyze lane-changing risk on freeways considering the forecastability in adjacent vehicles. Virtual lane-change scenarios are constructed based on historical maneuvers in adjacent vehicles, and the risk of potential lane change is evaluated through the safety evaluation result of the scenario. Adjacent vehicles’ future maneuvers are predicted using a multivariate Bayesian structural time series model, and the forecastability is estimated as the standard error of the predicted values. The failure probability of those lane-changing scenarios is obtained through the first-order reliability method, assuming that failure occurred when any time-to-collision value for adjacent vehicles was less than a threshold at the end of the lane change. This study tested two scenarios with three levels of uncertainty to show the effect of uncertainty on the level of risk. The results showed that the reduced uncertainty allowed a clearer distinction between risky situations. The proposed framework differentiates itself from existing methods by estimating higher risk in an adjacent vehicle’s more significant uncertainties. It is expected that the outcome of this study will be valuable in developing reliable lane-change strategies in autonomous driving.

Reliability-based assessment and calibration of standards for the lateral vibration of pedestrian bridges

Ensuring vibrations remain tolerable to occupants is central to the serviceability limit state (SLS) design of lightweight pedestrian bridges. In general, pedestrians tend to be more sensitive to lateral bridge vibrations compared to vertical vibrations, which underscores the importance of serviceability limit state (SLS) design in the lateral direction. Significant uncertainties associated with the pedestrian loading and bridge behaviour motivate the need to treat serviceability design provisions from a reliability standpoint. This paper is a first attempt towards such an assessment and code calibration of SLS provisions applicable to the lateral direction in the existing major pedestrian bridge design guidelines (ISO 10137, Eurocode 5 and SÉTRA). For this purpose, this study adopts a reliability-based framework, which accounts for the uncertainties arising from the pedestrian loading, perceptions of vibration by pedestrians, and structural damping. Furthermore, SLS design generally considers commonly occurring design traffic densities only. However, several historical lateral vibration serviceability failures of pedestrian bridges have occurred under infrequent loading events. Hence, this paper also incorporates infrequent traffic event (load case) in the reliability assessment and calibration of the design guidelines. Results show that metal truss-type pedestrian bridges under design and infrequent traffic events need to be designed to a higher reliability level (through calibration) than currently achieved by these provisions under the design event. Adopting traffic density and frequency-dependent acceleration limits can mitigate overdesigns resulting from the calibration exercise. The desired reliability index required to achieve minimum acceptable performance of the designs under both the design and infrequent events is estimated iteratively in the proposed procedure, followed by the calculation of design calibration factors. This study shows that the calibration of some design provisions (e.g., SÉTRA) depends on amplitude-dependent damping values, while this is not the case with other provisions. This dependency can be attributed to differences in the form of the limit state function. Finally, it is shown that the proposed calibration process achieves sufficient and consistent reliability across all bridge classes under design and infrequent traffic events in the lateral direction, while ensuring economic designs using traffic density and frequency-based comfort limits.