Application of polynomial transformation to normality in structural reliability analysis

1998 ◽  
Vol 25 (2) ◽  
pp. 241-249 ◽  
Author(s):  
Han Ping Hong
Keyword(s):  
Structural Reliability ◽  
Simulated Data ◽  
Approximate Solutions ◽  
Probability Of Failure ◽  
Accurate Estimation ◽  
Reliability Polynomial ◽  
Failure Simulation ◽  
Polynomial Transformation ◽  
Data Points ◽  
Polynomial Transformations

Polynomial transformations of a nonnormal variate to a normal variate are considered. Use of the polynomial transformations to normality representing some of the well-known distribution types is examined. Approximate solutions based on the polynomial transformation to normality models fitted to the simulated data points with fractile constraints are given to evaluate the probability of failure of a structural system. The approximate solutions do not require any stringent conditions on integrand or domain of integration. The approximation is easy to implement and can be used to reduce the required number of simulation cycles. Numerical examples indicate that using the approximate solutions accurate estimation of the failure probability can be obtained with fewer simulation cycles than the conventional simulation method.Key words: approximation, fractile, normality, reliability, polynomial, probability of failure, simulation, transformation.

scholarly journals Comparison of several non-linear-regression methods for fitting the Michaelis-Menten equation

1985 ◽  
Vol 231 (1) ◽  
pp. 171-177 ◽  
Author(s):  
L Matyska ◽  
J Kovář
Keyword(s):  
Simulated Data ◽  
Confidence Regions ◽  
Parameter Estimates ◽  
Interval Parameter ◽  
Variance Matrix ◽  
Regression Methods ◽  
Parameter Estimations ◽  
Data Points ◽  
Relative Weighting

The known jackknife methods (i.e. standard jackknife, weighted jackknife, linear jackknife and weighted linear jackknife) for the determination of the parameters (as well as of their confidence regions) were tested and compared with the simple Marquardt's technique (comprising the calculation of confidence intervals from the variance-co-variance matrix). The simulated data corresponding to the Michaelis-Menten equation with defined structure and magnitude of error of the dependent variable were used for fitting. There were no essential differences between the results of both point and interval parameter estimations by the tested methods. Marquardt's procedure yielded slightly better results than the jackknives for five scattered data points (the use of this method is advisable for routine analyses). The classical jackknife was slightly superior to the other methods for 20 data points (this method can be recommended for very precise calculations if great numbers of data are available). The weighting does not seem to be necessary in this type of equation because the parameter estimates obtained with all methods with the use of constant weights were comparable with those calculated with the weights corresponding exactly to the real error structure whereas the relative weighting led to rather worse results.

Reliability Based Assessment of Deck Elevations for Offshore Jacket Platforms

2004 ◽  
Vol 126 (4) ◽  
pp. 331-336 ◽  
Author(s):  
Ernesto Heredia-Zavoni ◽  
Dante Campos ◽  
Gallegher Ramı´rez
Keyword(s):  
Reliability Index ◽  
Structural Reliability ◽  
Failure Modes ◽  
Probability Of Failure ◽  
Upper And Lower Bounds ◽  
Series System ◽  
Wave Loading ◽  
System Components ◽  
Storm Wave ◽  
Wave Heights

Structural reliability analyses of fixed marine platforms subjected to storm wave loading are performed to assess deck elevations. Platforms are modeled as a series system consisting of the deck and jacket bays. The structural reliability analyses are carried out assuming dominant failure modes for the system components. Upper and lower bounds of the probability of failure are computed. The variation of the reliability index per bay component as a function of wave height, with a focus on those wave heights that generate forces on the deck, is analyzed. A comparison is given for the deck probability of failure and the lower bound probability of failure of the jacket in order to assess how the deck or the jacket controls the probability of failure of the system. Results are also given for reliability analyses considering different deck elevations. Finally, an analysis of the total probabilities of failure, unconditioned on wave heights, is given.

Efficient Reliability Assessment With the Conditional Probability Method

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Conditional Probability ◽  
Structural Reliability ◽  
A Priori ◽  
Reliability Assessment ◽  
Probability Of Failure ◽  
Assessment Method ◽  
Probability Method ◽  
Probability Of Survival ◽  
Design Variables ◽  
Reliability Method

Reliability assessment is an important procedure in engineering design in which the probability of failure or equivalently the probability of survival is computed based on appropriate design criteria and model behavior. In this paper, a new approximate and efficient reliability assessment method is proposed: the conditional probability method (CPM). Focus is set on computational efficiency and the proposed method is applied to classical load-strength structural reliability problems. The core of the approach is in the computation of the probability of failure starting from the conditional probability of failure given the load. The number of function evaluations to compute the probability of failure is a priori known to be 3n + 2 in CPM, where n is the number of stochastic design variables excluding the strength. The necessary number of function evaluations for the reliability assessment, which may correspond to expensive computations, is therefore substantially lower in CPM than in the existing structural reliability methods such as the widely used first-order reliability method (FORM).

Adjusting Environmental Contours for Specified Expected Number of Unwanted Events

2020 ◽  
Author(s):  
Erik Vanem
Keyword(s):  
Reliability Analysis ◽  
Return Period ◽  
Environmental Conditions ◽  
Structural Reliability ◽  
Probability Of Failure ◽  
Expected Number ◽  
Probability Of Exceedance ◽  
Underlying Distribution ◽  
Extreme Loads ◽  
Time Period

Abstract Environmental contours are applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. Typically, they are constructed to correspond to a certain return period and a probability of exceedance with regards to the environmental conditions that can again be related to the probability of failure of a structure. Thus, they describe events with a certain probability of being exceeded one or more times during a certain time period, which can be found from a certain percentile of the underlying distribution. In this paper, various ways of adjusting such environmental contours to account for the expected number of exceedances within a certain time period are discussed. Depending on how such criteria are defined, one may get more lenient or more stringent criteria compared to the classical return period.

Reduction Factors for Estimating the Probability of Failure of Mechanical Damage Due to External Interference

2008 ◽  
Author(s):  
Andrew Cosham ◽  
Jane Haswell ◽  
Neil Jackson
Keyword(s):  
Structural Reliability ◽  
Historical Data ◽  
Mechanical Damage ◽  
Probability Of Failure ◽  
Risk Assessments ◽  
External Interference ◽  
Failure Data ◽  
Major Accident ◽  
The Uk ◽  
Reduction Factors

Quantified risk assessments (QRAs) are widely used in the UK to assess the significance of the risk posed by major accident hazard pipelines on the population and infrastructure in the vicinity of the pipeline. A QRA requires the calculation of the frequency of failures and the consequences of failures. One of the main causes of failures in onshore pipelines is mechanical damage due to external interference, such as a dent, a gouge, or a dent and gouge. In the published literature, two methods have been used to calculate the probability of failure due to external interference: • historical failure data and • limit state functions combined with historical data (i.e. structural reliability-based methods). Structural reliability-based methods are mathematically complicated, compared to using historical failure data, but have several advantages, e.g. extrapolation beyond the limited historical data, and the identification of trends that may not be apparent in the historical data. In view of this complexity, proposed supplements to the UK pipeline design codes IGE/TD/1 (natural gas) and PD 8010 (all substances) — on the application of QRAs to proposed developments in the vicinity of major accident hazard pipelines — include simple ‘reduction factors’ for use in ‘screening’ risk assessments. These ‘reduction factors’ are based on a comprehensive parametric study using a structural reliability-based model to calculate the probability of failure due to mechanical damage, defined as: gouges, and dents and gouges. The two ‘reduction factors’ are expressed in terms of the design factor and wall thickness of the pipeline. It is shown that, through appropriate normalisation, the effects of diameter, grade and toughness are secondary. Reasonably accurate, but conservative, estimates of the probability of failure can be obtained using these ‘reduction factors’. The proposed methodology is considerably simpler than a structural reliability-based analysis. The development and verification of these ‘reduction factors’ is described in this paper.

Simplified Strength Reliability and Integrity Analysis of TTRs

2014 ◽  
Author(s):  
Mir Emad Mousavi ◽  
Sanjeev Upadhye ◽  
Kevin Haverty
Keyword(s):  
Extreme Events ◽  
Structural Reliability ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Reliability Assessment ◽  
Cost Effective ◽  
Probability Of Failure ◽  
Annual Probability ◽  
Reliability Methods ◽  
Integrity Analysis

The design of riser systems can be improved if structural reliability methods are used to assess their safety and integrity and confirm that such design meets a target annual probability of failure. TTRs are typically multi–bore assemblies involving several sub-assemblies. The failure of any of the components of a TTR under extreme or service environmental conditions can lead to an immediate failure of the entire assembly and impose a direct risk of damaging the wellheads, conductors, casing and tubing hangers, or other subsea equipment, because they are installed directly on top of the wellhead. However, the actual strength safety of the TTR cannot be examined unless after it is installed and examined under extreme events. Because of the numerous uncertainties associated with the design of TTRs, a probabilistic approach based on structural reliability methods can account for many of those uncertainties and serve as a basis for their reliable and cost-effective design. In turn, a comprehensive reliability assessment of a TTR requires extensive analysis that is considerably more complex and time consuming compared to a conventional deterministic-based analysis. This paper presents a probabilistic-based simplified methodology for the strength reliability assessment of TTR systems. In this method, marginal values on some uncertain model inputs are considered similar to the conventional analysis methods but, some key random variables related to environmental demands and component capacities are considered with their associated probability distributions. As a result, this method can be used to estimate the minimum level of safety of the TTR under extreme events. Additionally, results of the proposed method are discussed for integrity analysis and integrity-based optimal design of the TTR system, which compare the safety of the TTR components and estimate the component Optimality Factors for improving the design integrity and meeting a target minimum annual probability of failure.

Nonlinear System Identification in Offshore Structural Reliability

1995 ◽  
Vol 117 (3) ◽  
pp. 171-177 ◽  
Author(s):  
P. D. Spanos ◽  
R. Lu
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Structural Reliability ◽  
Transfer Functions ◽  
Nonlinear System Identification ◽  
Simulated Data ◽  
Wave Force ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Analysis And Design

Nonlinear forces acting on offshore structures are examined from a system identification perspective. The nonlinearities are induced by ocean waves and may become significant in many situations. They are not necessarily in the form of Morison’s equation. Various wave force models are examined. The force function is either decomposed into a set of base functions or it is expanded in terms of the wave and structural kinematics. The resulting nonlinear system is decomposed into a number of parallel no-memory nonlinear systems, each followed by a finite-memory linear system. A conditioning procedure is applied to decouple these linear sub-systems; a frequency domain technique involving autospectra and cross-spectra is employed to identify the linear transfer functions. The structural properties and the force transfer parameters are determined with the aid of the coherence functions. The method is verified using simulated data. It provides a versatile and noniterative approach for dealing with nonlinear interaction problems encountered in offshore structural analysis and design.

Hybrid ℓ1/ℓ2 minimization with applications to tomography

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1183-1195 ◽  
Author(s):  
Kenneth P. Bube ◽  
Robert T. Langan
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Full Rank ◽  
Approximate Solutions ◽  
Seismic Inversion ◽  
Smooth Transition ◽  
Data Points ◽  
Linear Problems ◽  
Data Error

Least squares or [Formula: see text] solutions of seismic inversion and tomography problems tend to be very sensitive to data points with large errors. The [Formula: see text] minimization for 1 ≤ p < 2 gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions to these [Formula: see text] problems. We apply IRLS to a hybrid [Formula: see text] minimization problem that behaves like an [Formula: see text] fit for small residuals and like an [Formula: see text] fit for large residuals. The smooth transition from [Formula: see text] to [Formula: see text] behavior is controlled by a parameter that we choose using an estimate of the standard deviation of the data error. For linear problems of full rank, the hybrid objective function has a unique minimum, and IRLS can be proven to converge to it. We obtain a robust efficient method. For nonlinear problems, a version of the Gauss‐Newton algorithm can be applied. Synthetic crosswell tomography examples and a field‐data VSP tomography example demonstrate the improvement of the hybrid method over least squares when there are outliers in the data.

System Reliability of Existing Jacket Platform in Malaysian Water (Failure Path and System Reliability Index)

2014 ◽  
Vol 567 ◽  
pp. 307-312 ◽  
Author(s):  
V. John Kurian ◽  
Mohamed Mubarak Abdul Wahab ◽  
T.S. Kheang ◽  
Mohd Shahir Liew
Keyword(s):  
System Reliability ◽  
Reliability Index ◽  
Structural Reliability ◽  
Pushover Analysis ◽  
Probability Of Failure ◽  
Jacket Platform ◽  
First Order ◽  
Failure Path ◽  
Reliability Method ◽  
Two Parameters

The objective of this work is to determine the structural reliability of an existing jacket platform in Malaysia, by determining the system probability of failure and its corresponding reliability index. These two parameters are important indicators for assessing the integrity and reliability of the platform, and will point out whether the platform is suitable for continued operation. In this study, pushover analysis is used to determine possible failure paths of the structure, while First Order Reliability Method (FORM) and Simple Bound Formula are used to determine the failure probability and reliability index. Three failure paths of the platform are established. The reliability index of these paths is found with the highest Reliability Indexto be 18.82 from the 315-degree path, while the system reliability index is 9.23. This illustrates that the platform is robust and the chances of collapse is very small.

Performance of In-Line Inspection Tools and Their Influence on the Structural Reliability of Corroded Pipeline

2006 ◽  
Author(s):  
Jose´ de Jesu´s Leal Carvajalino ◽  
Fa´bio de Castro Marangone ◽  
Jose´ Luiz de Franc¸a Freire
Keyword(s):  
Sequential Analysis ◽  
Structural Reliability ◽  
Field Measurements ◽  
Visual Basic ◽  
Probability Of Failure ◽  
First Order ◽  
Reliability Method ◽  
Minimum Number ◽  
Corrosion Defects ◽  
Reference Tool

This paper presents: i) the assessment of in-line inspection (ILI) tools’ performance in the measurement of defects caused by corrosion; ii) different methods for calculating the probability of failure (POF) of corroded pipeline based on the ILI report. The ILI report is compared to the geometry of defects measured by a reference tool (field measurements) and the errors associated with each measurement system are analyzed and assessed through different statistical methods. The minimum number of field measurements necessary to verify the performance of the ILI in sizing the corrosion defects is determined by implementing a test based on sequential analysis. The POF of a pipeline is calculated using two methods: i) first order reliability method (FORM) and ii) propagation of uncertainties. The comparison between calculated and acceptable POF enables the determining of the next reinspection period. When the calculated POF exceeds the acceptable POF before completing the amount of time desired for the next inspection, the developed procedure enables determining the number of repairs that must be made to reach the desired time when the next ILI will be performed. Finally, a software in Visual Basic® language was developed to implement this work.

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