Analysis of fatigue surface crack using the probabilistic s-version finite element model

Fatigue failure is expected to contribute to injuries and financial losses in industries. The complex interaction between the load, time and environment is a major factor that leads to failure. In addition, the material selection, geometry, processing and residual stresses produce uncertainties and possible failure modes in the field of engineering. The conventional approach is to allow the safety factor approach to deal with the variations and circumstances as they occur within the engineering applications. The problems may persist in the computational analysis, where a complex model, such as a three-dimensional surface crack, may require many degrees of freedom during the analysis. The involvement of uncertainties in variables brings the analysis to a higher level of complexity due to the integration of non-linear functions during a probabilistic analysis. Probabilistic methods are applicable in industries such as the maintenance of aircraft structures, airframes, biomechanical systems, nuclear systems, pipelines and automotive systems. Therefore, a plausible analysis that caters for uncertainties and fatigue conditions is demanded. The main objective of this research work was to develop a model for uncertainties in fatigue analysis. The aim was to identify a probabilistic distribution of crack growth and stress intensity factors for surface crack problems. A sensitivity analysis of all the parameters was carried out to identify the most significant parameters affecting the results. The simulation time and the number of generated samples were presented as a measurement of the sampling efficiency and sampling convergence. A finite thickness plate with surface cracks subjected to random constant amplitude loads was considered for the fracture analysis using a newly developed Probabilistic S-version Finite Element Model (ProbS-FEM). The ProbS-FEM was an expansion of the standard finite element model (FEM). The FEM was updated with a refined mesh (h-version) and an increased polynomial order (p-version), and the combination of the h-p version was known as the S-version finite element model. A probabilistic analysis was then embedded in the S-version finite element model, and it was then called the ProbS-FEM. The ProbS-FEM was used to construct a local model at the vicinity of the crack area. The local model was constructed with a denser mesh to focus the calculation of the stress intensity factor (SIF) at the crack front. The SIF was calculated based on the virtual crack closure method. The possibility of the crack growing was based on the comparison between the calculated SIF and the threshold SIF. The fatigue crack growth was calculated based on Paris’ law and Richard’s criterion. In order to obtain an effective sampling strategy, the Monte Carlo and Latin hypercube sampling were employed in the ProbS-FEM. The specimens with a notch were prepared and subjected to fatigue loading for verification of the ProbS-FEM results. The ProbS-FEM was verified for the SIF calculation, the crack growth for mode I and the mixed mode, and the prediction of fatigue life. The major contribution of this research is to the development of a probabilistic analysis for the S-version finite element model. The formulation of uncertainties in the analysis was presented with the ability to model the distribution of the surface crack growth. The ProbS-FEM was shown to resolve the problem of uncertainties in fatigue analysis. The ProbS-FEM can be further extended for a mixed mode fracture subjected to variable amplitude loadings in an uncertain environment

Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels

Configurational Information as Potentially Negative Entropy: The Triple Helix Model

Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime

Data dependent energy modelling for worst case energy consumption analysis

Safely meeting Worst Case Energy Consumption (WCEC) criteria requires accurate energy modeling of software. We investigate the impact of instruction operand values upon energy consumption in cacheless embedded processors. Existing instruction-level energy models typically use measurements from random input data, providing estimates unsuitable for safe WCEC analysis. We examine probabilistic energy distributions of instructions and propose a model for composing instruction sequences using distributions, enabling WCEC analysis on program basic blocks. The worst case is predicted with statistical analysis. Further, we verify that the energy of embedded benchmarks can be characterised as a distribution, and compare our proposed technique with other methods of estimating energy consumption

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Point estimate method for voltage unbalance evaluation in residential distribution networks with high penetration of small wind turbines

Voltage unbalance (VU) in residential distribution networks (RDNs) is mainly caused by load unbalance in three phases, resulting from network configuration and load-variations. The increasing penetration of distributed generation devices, such as small wind turbines (SWTs), and their uneven distribution over the three phases have introduced difficulties in evaluating possible VU. This paper aims to provide a three-phase probabilistic power flow method, point estimate method to evaluate the VU. This method, considering the randomness of load switching in customers’ homes and time-variation in wind speed, is shown to be capable of providing a global picture of a network’s VU degree so that it can be used for fast evaluation. Applying the 2m + 1 scheme of the proposed method to a generic UK distribution network shows that a balanced SWT penetration over three phases reduces the VU of a RDN. Greater unbalance in SWT penetration results in higher voltage unbalance factor (VUF), and cause VUF in excess of the UK statutory limit of 1.3%