Prediction Of Failure Probability Research Articles

Modeling the Causes and Manifestation of Bank Stress: An Example from the Financial Crisis

In this study, I model the predictors and manifestation of bank stress during the financial crisis using a Multiple Indicator Multiple Cause model. Unlike most early warning models that predict failure probabilities, this article describes a framework for predicting a broader notion of bank stress that need not rely on regulatory decisions. As such, this method can be easily applied to large institutions, and avoids the complications associated with modelling a regulatory decision such as failure or a CAMELS downgrade. Using bank reliance on Term Auction Facility funds and the out-of-sample incidence of failures and acquisitions, I demonstrate that the measure of bank stress generated here accords with other notions of bank-level distress. Finally, this method catalogues predictors of distress during the financial crisis. Thus, this article can help assess the validity of several recent regulatory proposals. I find that those banks entering the crisis with more Tier 1 capital, more liquid balance sheets, ...

Application of subset simulation in reliability estimation of underground pipelines

This paper presents a computational framework for implementing an advanced Monte Carlo simulation method, called Subset Simulation (SS) for time-dependent reliability prediction of underground flexible pipelines. The SS can provide better resolution for low failure probability level of rare failure events which are commonly encountered in pipeline engineering applications. Random samples of statistical variables are generated efficiently and used for computing probabilistic reliability model. It gains its efficiency by expressing a small probability event as a product of a sequence of intermediate events with larger conditional probabilities. The efficiency of SS has been demonstrated by numerical studies and attention in this work is devoted to scrutinise the robustness of the SS application in pipe reliability assessment and compared with direct Monte Carlo simulation (MCS) method. Reliability of a buried flexible steel pipe with time-dependent failure modes, namely, corrosion induced deflection, buckling, wall thrust and bending stress has been assessed in this study. The analysis indicates that corrosion induced excessive deflection is the most critical failure event whereas buckling is the least susceptible during the whole service life of the pipe. The study also shows that SS is robust method to estimate the reliability of buried pipelines and it is more efficient than MCS, especially in small failure probability prediction.

New models for prediction of high cycle fatigue failure based on highly loaded regions

The stress gradient and the structural size are known to be very important factors affecting the fatigue life of metallic mechanical components. For multiaxial stress conditions, a relevant criterion must be used to account for both these effects as well as the history of a non-homogeneous stress state. The new probabilistic HCF models in this work fulfill these requirements. A stress field resulting from rotating bending is analyzed. Also, the well-known weakest link model has be compared to the new proposed HCF models based on the concept of the highly loaded regions. The new models take the highly loaded regions (volume, area) and the stress gradient effect into account. These models show significant improvement of failure probability prediction capability compared to the weakest link integral.

Prediction of failure probability of oil wells

We consider parametric accelerated failure time models with random effects to predict the probability of possibly correlated failures occurring in oil wells. In this context, we first consider empirical Bayes predictors (EBP) based on aWeibull distribution for the failure times and on a Gaussian distribution for the random effects.We also obtain empirical best linear unbiased predictors (EBLUP) using a linear mixed model for which the form of the distribution of the random effects is not specified. We compare both approaches using data obtained from an oil-drilling company and suggest how the results may be employed in designing a preventive maintenance program.

Assessment of the efficiency of Kriging surrogate models for structural reliability analysis

This paper presents an assessment of the efficiency of the Kriging interpolation models as surrogate models for structural reliability problems involving time-consuming numerical models such as nonlinear finite element analysis structural models. The efficiency assessment is performed through a systematic comparison of the accuracy of the failure probability predictions based on the first-order reliability method using the most common first- and second-order polynomial regression models and the Kriging interpolation models as surrogates for the true limit state function. An application problem of practical importance in the field of marine structures that requires the evaluation of a nonlinear finite element structural model is adopted as numerical example. The accuracy of the failure probability predictions is characterised as a function of the number of support points, dispersion of the support points in relation to the so-called design point and order of the Kriging basis functions. It is shown with the application problem considered that the Kriging interpolation models are efficient surrogate models for structural reliability problems and can provide significantly more accurate failure probability predictions as compared with the most common polynomial regression models.

A very high cycle fatigue thermal dissipation investigation for titanium alloy TC4

Titanium alloy TC4 is widely used in aeronautics applications where it is subjected to high frequency fatigue loads. Tests are performed to investigate the alloy fatigue behavior sustaining ultrasonic fatigue load in Very High Cycle Fatigue (VHCF) regime. Thermal dissipation for the alloy in 20kHz frequency is studied and a model is proposed to describe the temperature increment in the framework of thermodynamics by estimation of the anelastic and inelastic thermal dissipation at microscopic active sites in the reference element volume. The failure probability prediction method is used to evaluate the VHCF dispersion based on the two scale model and fatigue thermal dissipation analysis.

Probabilistic fracture mechanics analysis of thermally aged nuclear piping in a pressurized water reactor

A predicting program for pipe break probability based on thermal aging embrittlement was developed. In order for life prediction, evolutions of fracture toughness and tensile strength were estimated for a Z3CN20-09M piping steel using the Argonne National Laboratory (ANL) procedure. To understand the influence of thermal aging on failure probability, different evolutions of fracture toughness, tensile strength and fatigue crack growth rate were employed in the prediction of cumulative failure probability. The results show that the cumulative failure probability for 40-year thermal aging increases by almost four times compared to without consideration of fracture toughness degradation. The cumulative failure probability is slightly affected by fatigue crack growth rate. The increase of tensile strength due to thermal aging reduces the risk of pipe failure. This work demonstrates that the degradation of fracture toughness due to thermal aging should be fully considered in the probabilistic fracture mechanics analysis of nuclear pressure pipes.

Analysis of Residual and Operational Thermal Stresses in a Planar SOFC

A structural model has been developed for analysis of residual stresses for anode- and electrolyte-supported planar solid oxide fuel cells (SOFC). This model was also used for analysis of thermally induced stresses during operation for three different case studies with the electrolyte-supported geometry. Temperature distribution in the solid parts of the cell was modeled by means of an in-house electrochemical model, and the results were exported to the structural model. In the case studies, the impact of air and fuel inlet temperatures, steam reforming, and operation voltages on thermal stresses were studied. Weibull statistics were used for the prediction of failure probabilities and design considerations. Base case geometry for the electrolyte-supported cell was 50, 150, and 50 μm for anode, electrolyte, and cathode thicknesses, respectively, and for the anode-supported cell 1000, 20, and 50 μm, respectively. Analysis of residual stresses showed that, compared with the anode-supported cell, the electrolyte-supported cell experienced considerably higher stress levels in the anode and cathode due to the thick electrolyte, while the stress levels in the electrolyte were lower. For the anode-supported cell, maximum stress levels were 57, −12, and −678 MPa in the anode, cathode, and electrolyte, respectively, with negative values indicating compressive and positive values, tensile stresses. For the electrolyte-supported geometry, the corresponding levels were 282, 100, and −308 MPa, respectively. With a failure probability of 1E-6 and an electrolyte thickness of 10 μm, the minimum allowable anode thickness was estimated to be 1000 μm. For an electrolyte-supported cell, optimal thicknesses of electrolyte and anode were considered to be 100 and 100 μm, respectively, while the thickness of the cathode showed low impact. During operation, the stress levels were reduced considerably, since high operating temperatures reduce the temperature difference to the sintering temperature (1250 °C). Concerning the presence of methane in the fuel and the effect of steam reforming, small amounts of methane—as low as 10% of molar mass—were found to induce a cooling effect with correspondingly high gradients. With 45% methane in the fuel, the tensile stress level in the anode was about 130 MPa; the impact of thermal gradients was considered to be 40 MPa and the cooling effect also 40 MPa.

Use of Fragile Geologic Structures as Indicators of Unexceeded Ground Motions and Direct Constraints on Probabilistic Seismic Hazard Analysis

Abstract We present a quantitative procedure for constraining probabilistic seismic hazard analysis results at a given site, based on the existence of fragile geologic structures at that site. We illustrate this procedure by analyzing precarious rocks and undamaged lithophysae at Yucca Mountain, Nevada. The key metric is the probability that the feature would have survived to the present day, assuming that the hazard results are correct. If the fragile geologic structure has an extremely low probability of having survived (which would be inconsistent with the observed survival of the structure), then the calculations illustrate how much the hazard would have to be reduced to result in a nonnegligible survival probability. The calculations are able to consider structures the predicted failure probabilities of which are a function of one or more ground‐motion parameters, as well as structures that either rapidly or slowly evolved to their current state over time. These calculations are the only way to validate seismic hazard curves over long periods of time.

Failure probability prediction based on condition monitoring data of wind energy systems for spare parts supply

The feasibility of maintenance processes relies on the availability of spare parts. Spare part inventory planning is capital intensive. It is based on demand forecasting, which possesses a high potential in reducing inventories. Even if condition monitoring systems are installed in technical systems, condition monitoring information is barely used to predict the failure probability of units. Therefore, an enhanced forecast model, which integrates SCADA information, has been developed. This leads to more accurate spare part demand forecasts. The approach presented in the paper is based on data mining, the proportional hazards model (PHM) and a binomial distribution. It has been validated with maintenance data of wind energy systems.

A rapid scatter prediction method for very high cycle fatigue

ABSTRACTVery high cycle fatigue (VHCF) tests are often performed by a high‐frequency fatigue test system, such as ultrasonic fatigue test machine. In the paper, simple VHCF tests and cumulative fatigue (low cycle fatigue plus VHCF) tests are performed to investigate the fatigue behaviour, respectively, for a low carbon manganese steel. The test results in Wöhler diagram show a large scatter in VHCF regime. Continuum damage mechanics model is extended to VHCF region to estimate the remaining fatigue life. A rapid fatigue failure probability prediction method is applied and extended to VHCF regime in order to evaluate the fatigue dispersion based on multi‐scales model and fatigue dissipation analysis.

Probabilistic fracture mechanics analysis of linear-elastic cracked structures by spline fictitious boundary element method

Abstract The inherent uncertainties in crack geometry, material properties and loadings have large influence on fracture response characteristics of cracked structures. This paper presents the probabilistic fracture mechanics analysis of linear-elastic cracked structures subjected to mixed-mode loading conditions using the spline fictitious boundary element method (SFBEM). The response surface method (RSM) is used to predict the fracture probability of the cracked structure. To determine the unknown coefficients of the response surface function, the SFBEM based on the Erdogan fundamental solutions for infinite cracked plates is adopted to perform deterministic analyses of stress intensity factors (SIFs) corresponding to different test points with given parameters. Numerical examples based on mode-I and mixed-mode crack problems are presented to illustrate the present method. The results show that the predicted failure probability obtained by the present approach is accurate in comparison with the Monte Carlo simulation (MCS) results. Since a much lesser number of numerical tests are required in RSM as compared with that needed in MCS, and since the SFBEM based on the Erdogan fundamental solutions has been used to conduct the numerical tests, reliability analysis of cracked structures can be performed efficiently using the present method.

A numerical method for structural uncertainty response computation

A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration (DRI), C-type Gram-Charlier (CGC) series, and finite element (FE) model, is proposed to assess the probability distribution of structural performance. From the relationship between the weighting function of orthogonal polynomial and probability density function (PDF) of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering applications for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation (MCS), the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function (CDF), results have shown the satisfying estimators for small probabilities, say, P ∈ [10−4, 10−3]. That implies the method could be trusted for structural failure probability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration (NI) and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element (SFE) codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.

Reliability analysis of large structural systems

Brute force Monte Carlo simulation methods can, in principle, be used to calculate accurately the reliability of complicated structural systems, but the computational burden may be prohibitive. A new Monte Carlo based method for estimating system reliability that aims at reducing the computational cost is therefore proposed. It exploits the regularity of tail probabilities to set up an approximation procedure for the prediction of the far tail failure probabilities based on the estimates of the failure probabilities obtained by Monte Carlo simulation at more moderate levels. In this paper, the usefulness and accuracy of the estimation method is illustrated by application to a particular example of a structure with several thousand potentially critical limit state functions. The effect of varying the correlation of the load components is also investigated.

Predicting the Failure Probability of Device Features in MEMS

In the MEMS industry today, device reliability is commonly evaluated by simulating the loads applied to a device using finite element (FE) analysis and setting a threshold for the allowable first principal stress ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ). This is a potentially misleading practice for the analysis of brittle structures, but it is used because better reliability tools have not been validated and adopted for MEMS design. In this paper, we detail and validate pragmatic FE-based MEMS analysis capabilities: local (device feature) failure probability prediction and surface-specific failure probability intensity (FPI, μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ) plotting, which quantitatively identify the most probable locations of fracture on a MEMS device and provide a more meaningful and higher contrast visualization versus corresponding plots of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . To validate prediction effectiveness, fractographic analysis was completed on micromirrors (a representative MEMS device) loaded in two distinct complex stress states (primarily, tension or torsion) until failure, thus determining the locations of fracture initiation and their relative probabilities. Our method improves the simulation-driven design of brittle microstructures by providing not only the failure probability of the total structure but also probable failure locations as a function of load, all of which are essential for intelligent design iteration.

Materials of large wind turbine blades: recent results in testing and modeling

ABSTRACTThe reliability of rotor blades is the pre‐condition for the development and wide use of large wind turbines. In order to accurately predict and improve the wind turbine blade behavior, three main aspects of the reliability and strength of rotor blades were considered: (i) development of methods for the experimental determination of reliable material properties used in the design of wind turbine blades and experimental validation of design models, (ii) development of predictive models for the life prediction, prediction of residual strength and failure probability of the blades and (iii) analysis of the effect of the microstructure of wind turbine blade composites on their strength and ways of microstructural optimization of the materials. By testing reference coupons, the effect of testing parameters (temperature and frequency) on the lifetime of blade composites was investigated, and the input data for advanced design of wind turbine blades were collected. For assessing the residual strength and stiffness of wind turbine blades subjected to irregular cyclic loads, a shell‐based finite element numerical methodology was developed, taking into account the non‐linear response of plies, and experimentally validated. Two methods of structural reliability estimation of the blade, which take into account the stochastic nature of the anisotropic material properties and loads, were developed on the basis of the response surface method and the Edgeworth expansion technique, respectively. The effects of fiber clustering, misalignments, interface properties and other factors on the strength and lifetime of the wind turbine blade materials were investigated in the micromechanical finite element simulations. The results described in this paper stem from the Rotor Structure and Materials task of the UPWIND project. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Logistic regression model for predicting the failure probability of a landslide dam

Landslides may obstruct river flow and result in landslide dams; they occur in many regions of the world. The formation and disappearance of natural lakes involve a complex earth–surface process. According to the lessons learned from many historical cases, landslide dams usually break down rapidly soon after the formation of the lake. Regarding hazard mitigation, prompt evaluation of the stability of the landslide dam is crucial. Based on a Japanese dataset, this study utilized the logistic regression method and the jack-knife technique to identify the important geomorphic variables, including peak flow (or catchment area), dam height, width and length in sequence, affecting the stability of landslide dams. The resulting high overall prediction power demonstrates the robustness of the proposed logistic regression models. Accordingly, the failure probability of a landslide dam can also be evaluated based on this approach. Ten landslide dams (formed after the 1999 Chi-Chi Earthquake, the 2008 Wenchuan Earthquake and 2009 Typhoon Morakot) with complete dam geometry records were adopted as examples of evaluating the failure probability. The stable Tsao-Ling landslide dam, which was induced by the Chi-Chi earthquake, has a failure probability of 27.68% using a model incorporating the catchment area and dam geometry. On the contrary, the Tangjiashan landslide dam, which was artificially breached soon after its formation during the Wenchuan earthquake, has a failure probability as high as 99.54%. Typhoon Morakot induced the Siaolin landslide dam, which was breached within one hour after its formation and has a failure probability of 71.09%. Notably, the failure probability of the earthquake induced cases is reduced if the catchment area in the prediction model is replaced by the peak flow of the dammed stream for these cases. In contrast, the predicted failure probability of the heavy rainfall-induced case increases if the high flow rate of the dammed stream is incorporated into the prediction model. Consequently, it is suggested that the prediction model using the peak flow as causative factor should be used to evaluate the stability of a landslide dam if the peak flow is available. Together with an estimation of the impact of an outburst flood from a landslide-dammed lake, the failure probability of the landslide dam predicted by the proposed logistic regression model could be useful for evaluating the related risk.

Performance Analysis of On-Chip Communication Structures under Device Variability

On-chip communication is becoming an important bottleneck in the design and operation of high performance systems where it has to face additional challenges due to device variability. Communication structures such as tapered buffer drivers, interconnects, repeaters, and data storage elements are vulnerable to variability, which can limit the performance of the on-chip communication networks. In this regard, it becomes important to have a complete understanding of the impact that variability will have on the performance of these circuit elements in order to design high yield and reliable systems. In this paper, the authors have characterized the performance of the communication structures under the impact of random dopant fluctuation (RDF) for the future technology generations of 25, 18, and 13 nm. For accurate characterization of their performance, a Monte Carlo simulation method has been used along with predictive device models for the given technologies. Analytical models have been developed for the link failure probability of a repeater inserted interconnect which uses characterization data of all communication structures to give an accurate prediction of the link failure probability. The model has also been extended to calculate the link failure probability of a wider communication link.

Performance assessment of topologically diverse power systems subjected to hurricane events

Large tropical cyclones cause severe damage to major cities along the United States Gulf Coast annually. A diverse collection of engineering and statistical models are currently used to estimate the geographical distribution of power outage probabilities stemming from these hurricanes to aid in storm preparedness and recovery efforts. Graph theoretic studies of power networks have separately attempted to link abstract network topology to transmission and distribution system reliability. However, few works have employed both techniques to unravel the intimate connection between network damage arising from storms, topology, and system reliability. This investigation presents a new methodology combining hurricane damage predictions and topological assessment to characterize the impact of hurricanes upon power system reliability. Component fragility models are applied to predict failure probability for individual transmission and distribution power network elements simultaneously. The damage model is calibrated using power network component failure data for Harris County, TX, USA caused by Hurricane Ike in September of 2008, resulting in a mean outage prediction error of 15.59% and low standard deviation. Simulated hurricane events are then applied to measure the hurricane reliability of three topologically distinct transmission networks. The rate of system performance decline is shown to depend on their topological structure. Reliability is found to correlate directly with topological features, such as network meshedness, centrality, and clustering, and the compact irregular ring mesh topology is identified as particularly favorable, which can influence regional lifeline policy for retrofit and hardening activities to withstand hurricane events.

Application of relevance vector machine and logistic regression for machine degradation assessment

Degradation parameter or deviation parameter from normal to failure condition of machine part or system is needed as an object of prediction in prognostics method. This study proposes the combination between relevance vector machine (RVM) and logistic regression (LR) in order to assess the failure degradation and prediction from incipient failure until final failure occurred. LR is used to estimate failure degradation of bearing based on run-to-failure datasets and the results are then regarded as target vectors of failure probability. RVM is selected as intelligent system then trained by using run-to-failure bearing data and target vectors of failure probability estimated by LR. After the training process, RVM is employed to predict failure probability of individual units of machine component. The performance of the proposed method is validated by applying the system to predict failure time of individual bearing based on simulation and experimental data. The result shows the plausibility and effectiveness of the proposed method, which can be considered as the machine degradation assessment model.