Reliability analysis of smart laminated composite plates under static loads using artificial neural networks

Reliability analysis of pipe whip impacts

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 94357, "Treating Uncertainties in Reservoir-Performance Prediction With Neural Networks," by J.P. Lechner, SPE, OMV A.G., and G. Zangl, SPE, Schlumberger Information Solutions, prepared for the 2005 SPE Europec/EAGE Annual Conference, Madrid, Spain, 13–16 June. In development projects, reservoir parameters are known only within certain ranges, which results in various realizations of the subsurface. Because of the computational time involved, simulation models to obtain a probability distribution of possible outcomes cannot cover all possible parameter combinations. Creating a response surface based on a reduced number of simulation runs becomes necessary. Such a response surface can be used to approximate results for several variations of input parameters. An approach in which reservoir response is captured by an artificial neural network (ANN) has been investigated. The trained ANN model was used in Monte Carlo simulations to generate the probability distribution of possible outcomes. Introduction Often, simulation models are built to design field-development plans. Because of the low level of information during the early development stage, a range of uncertainty in the prediction scenarios must be considered. Such uncertainties can be handled with ANNs. Numerical models (simulation models) are detailed and powerful predictive tools that can answer many questions regarding subsurface engineering. However, especially in the early development phase, uncertainties are large, and prediction results will span a broad range. To take into account the whole range of possible outcomes of reservoir simulation, optimization routines would have to run the numerical models perhaps thousands of times. Although the most likely solution that respects subsurface uncertainties is of interest, the most profitable solution for reservoir management must be found. Because of the computational time involved, these methodologies often are not used. Building a response surface that can predict many possible outcomes of a numerical simulation by processing a large variety of input parameters could provide a solution to this problem. The response surface must cover the non-linear dependencies between input and output parameters. Experimental design and response-surface modeling has been used to delineate subsurface uncertainty. Common applications include determining the probability distribution of original oil in place from geological models, quantifying uncertainty in predevelopment or preredevelopment projects, predicting production performance from different realizations of a geological model, and optimizing the location of new wells to maximize net profit. Methodology Fig. 1 shows the proposed workflow. As a first step, a limited number of simulation runs is carried out to define the most sensitive input parameters. In these runs, parameters are altered one at a time, either to the minimum or to the maximum. After selecting the most influential input parameters, three values (minimum, best-estimate, and maximum) are defined, and an experimental design is set up. The experimental design aims at obtaining the maximum information with a minimum number of simulation runs. However, practice showed that a minimum number of training data sets are required by the ANN to be able to make sufficiently accurate predictions. With these data sets containing varying input parameters and the corresponding output, an ANN is trained and tested with several additional simulation runs. After defining the probability distribution of the input parameters, the trained ANN is used as a proxy function for a Monte Carlo simulation. Thereby, a probability distribution of the desired output parameter (e.g., cumulative production after a certain number of years) is gained. The quality of the ANN is measured by the root-mean-square error of the deviation between the predicted and the actual output.

Uncertain material properties on wave dispersion behaviors of smart magneto-electro-elastic nanobeams

Analysis of composite plates with random material characteristics

Influence of micro-scale uncertainties on the reliability of fibre-matrix composites

This paper proposes a novel second-order reliability method (SORM) using non-central or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two errors by describing the quadratic failure surface with the linear combination of non-central chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function (PDF) over the linear failure surface and the second approach uses the cumulative distribution function (CDF) of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method (FORM), conventional SORM, and Monte Carlo simulation (MCS) results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.

The paper describes a computational simulation approach for durability, damage tolerance (D&DT) and reliability of composite wind turbine blade structures in presence of uncertainties in material properties. This computer-based prediction methodology combines composite mechanics with finite element analysis, damage and fracture tracking capability, probabilistic analysis and a robust design algorithm to reduce weight of turbine bales without loss in structural durability and reliability. A composite turbine blade was first assessed with finite element based multi-scale progressive failure analysis to determine failure modes and locations as well as the fracture load. Analysis D&DT results were validated with static test performed at Sandia National Laboratories. The work was followed by detailed weight analysis to identify contribution of various materials to the overall weight of the blade. The methodology ensured that certain types of failure modes, such as delamination progression, are contained to reduce risk to the structure. Probabilistic analysis indicated that composite shear strength has a great influence of the blade ultimate load under static loading. Weight was reduced by 12% with robust design without loss in reliability or D&DT. It was achieved by replacing a small volume of key materials with foam.

Nonlinear bending and thermal postbuckling of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators

The development of accurate codes for the design of bridges and the evaluation of existing structures requires adequate assessment of site-specific heavy traffic loading and also the dynamic interaction that may occur as this traffic traverses the structure. Shortcomings in current design codes occur due to the relatively independent manner in which critical static loading values and the corresponding allowance for dynamic amplification factor (DAF) are obtained. It is important that an approach is adopted that allows for the reduced probability of both high static loading and high dynamic amplification occurring simultaneously. Consideration of only relevant critical loading events will allow for efficient and accurate determination of independent values for characteristic (lifetime-maximum) static and total load effects. This paper proposes a method whereby initially the critical static loading scenarios for a chosen bridge are determined, from Monte Carlo simulation using weigh-in-motion (WIM) data from a typical European route. The development of a database of 3-dimensional finite element bridge and truck models allows for the analysis of these various different combinations of vehicular loading patterns. Thus the bridge specific critical loading scenarios are modelled and analysed individually to obtain the critical total (dynamic + static) load effect. It will then be possible to obtain a correlation between critical static load effect and corresponding total load effect/DAF and to extrapolate a characteristic DAF. This approach can lead to significant savings in structural design/assessment where site-specific maximum design load effects are determined from measured traffic data and experimental bridge-truck dynamic interaction.

Evaluation of tunnel support structure reliability

This paper proposes to apply the convolution integral method to the novel second-order reliability method (SORM) to further improve its computational efficiency. The novel SORM showed better accuracy in estimating the probability of failure than conventional SORMs by utilizing a linear combination of noncentral or general chi-squared random variables. However, the novel SORM requires significant computational time when integrating the linear combination to calculate the probability of failure. In particular, when the dimension of performance functions is higher than three, the computational time for full integration increases exponentially. To reduce this computational burden for the novel SORM, we propose to obtain the distribution of the linear combination using the convolution and to use the distribution for the probability of failure estimation. Since it converts an N-dimensional full integration into one-dimensional integration, the proposed method is computationally very efficient. Numerical study illustrates that the accuracy of the proposed method is almost the same as the full integral method and Monte Carlo simulation (MCS) with much improved efficiency.

Sustainable development (SD) has recently emerged as a critical axis in industrial strategic management and debate. Apart from the scarcity of resources, the influence of economic difficulties on human life and society has increased the relevance of SD. However, estimating and analyzing the SD of any business are still in its infancy. Thus, the SD of the sports goods industry is assessed using a multilayer artificial perceptron neural network (MLP) technique employing eight distinct characteristics connected to production efficiency, international and internal environment, export, and domestic development by using Statistica software. To discover an ideal model for SD in the sports goods business, stepwise models with varied input parameters were built. The identity activation function was used to create and train an error propagation algorithm-based network. The results of various eight network models revealed that, among other models, the accuracy of our fifth model, which incorporates production efficiency, international and internal environment, strategic management, and domestic distribution organization, gives the best answer. This model has the lowest root-mean-square error (RMSE) = 0.002 and the greatest R square = 0.922, demonstrating its efficacy and effectiveness in terms of SD. Based on these findings, it is possible to conclude that using artificial neural networks is beneficial in determining an optimal solution for SD and other similar problems since this tool is important and would be utilized for forecasting and decision-making in any business.

The effect of interference of corrosion pits on the failure probability of a reinforced concrete beam

Effect of Pit Distance on Failure Probability of a Corroded RC Beam

A probabilistic framework for durability assessment of concrete structures in marine environments was proposed in terms of reliability and sensitivity analysis, which takes into account the uncertainties under the environmental, material, structural and executional conditions. A time-dependent probabilistic model of chloride ingress was established first to consider the variations in various governing parameters, such as the chloride concentration, chloride diffusion coefficient, and age factor. Then the Nataf transformation was adopted to transform the non-normal random variables from the original physical space into the independent standard Normal space. After that the durability limit state function and its gradient vector with respect to the original physical parameters were derived analytically, based on which the first-order reliability method was adopted to analyze the time-dependent reliability and parametric sensitivity of concrete structures in marine environments. The accuracy of the proposed method was verified by comparing with the second-order reliability method and the Monte Carlo simulation. Finally, the influences of environmental conditions, material properties, structural parameters and execution conditions on the time-dependent reliability of concrete structures in marine environments were also investigated. The proposed probabilistic framework can be implemented in the decision-making algorithm for the maintenance and repair of deteriorating concrete structures in marine environments.