The approach integrated micro and macro composite mechanics, laminate theories, finite element methods, and probability algorithms, and was implemented using the IPACS computer code. A few years later, Chamis [14] used the PICAN computer code to simulate the probabilistic mechanical behaviour of composites at all scale levels. Elseifi et al. [15] simulated the curing process of a thick composite plate with uncertainties in the material and process parameters.

Future studies should consider increasing the sample size of subjects to improve the reliability of the study results. In the future, a longitudinal approach could be adopted to accurately explore individual emotions related to physical education and their evolving processes, thereby offering more targeted and practical guidance for physical education instructors. Fourthly, the sample of this study exhibited a relatively low representation of females, ethnic minorities, individuals from rural backgrounds, and sophomore students.

S-BORM: Reliability-based optimization of general systems using buffered optimization and reliability method

This chapter describes an approach to the development of color morphological scale-spaces using area openings and closings based on the identification and processing of vector extrema. The properties, development and implementation of the resulting color area morphology scale-spaces are described and studies of their application to color image segmentation and noise reduction are presented. In this research project we are computing the probability of failure and constructing a distribution function for a critical response. We have developed innovative BEM methods using sensitivity  formulation coupled with ffirst and second order Reliability Method for predicting the reliability index of structures subjected to fatigue loading.

multi-scale reliability analysis

This multi-scale reliability analysis procedure has been applied to analyse laminated fibre reinforced composites made of AS4/3501 carbon/epoxy. Firstly, a comparative study has been conducted to evaluate the performance of the assumed homogenization methods for the reliability of composites, and to identify advantages compared with a single scale analysis. The results show that multi-scale analysis can provide more accurate reliability estimates.

Probabilistic evaluation of fuselage-type composite structures

Renormalisation groups [Wilson, 1979] provide useful insights for multiscale analysis. Renormalisation operates by abstracting interdependencies between fine scale variables into interdependencies between coarse scale variables, and can be applied recursively. This allows an analyst to identify which details and relationships in the fine scale representation of a system have large scale implications, and which details disappear at coarser scales. Renormalisation may not apply directly to many defence systems, since it only applies when the system is close to a critical point, and in addition it abstracts away potentially important local details, losing context.

A complete and adequate assessment of validity must include both theoretical and empirical approaches. As shown in Figure 7.4, this is an elaborate multi-step process that must take into account the different types of scale reliability and validity. Concurrent validity examines how well one measure relates to other concrete criterion that is presumed to occur simultaneously. For instance, do students’ scores in a calculus class correlate well with their scores in a linear algebra class?

Performance evaluation of the proposed method with a theoretical example

This could potentially undermine the extent to which these findings can be applied to these specific demographic groups. Hence, it is recommended that future research endeavors incorporate additional validation measures. In this research the reliability of a 2D elastostatic BEM model is evaluated for various levels of uncertainty in design parameters such as the applied stress and the dimensions of the model. To overcome the computational cost of built-up structures with multiple random variables, multi-fidelity (MF) modelling has been developed.

  • This can have serious implications in areas like medical research where, for example, a new form of treatment may be evaluated.
  • The powerful graphical analysis capabilities of computer vision allow identification of microscopic image features of composite materials, establishing a bridge between the microscopic world of the material and structure reliability.
  • Of course, this approach requires a detailed description of the entire content domain of a construct, which may be difficult for complex constructs such as self-esteem or intelligence.
  • If not, the method of measurement may be unreliable or bias may have crept into your research.

In order to quantify the safety of FRP composite structures subjected to uncertainties, reliability analysis has been commonly applied to evaluate the failure probability of structural components and system [15], [16], [17], [18], [19]. Most of the studies only focus on the uncertainty of single-scale parameters and stochastic response to https://wizardsdev.com/en/news/multiscale-analysis/ structural performance [14], [20]. However, uncertainties exist in various parameters, such as material properties at different length scales. For instance, variations arising from manufacturing defects in constituent materials are at microscale, while uncertainties in ply thickness are in mesoscale and applied loads are at macroscale.

Simulation of a 3-D Lid-Driven Cavity Flow by a Parallelised Lattice Boltzmann Method

If possible and relevant, you should statistically calculate reliability and state this alongside your results. Compare your paper to billions of pages and articles with Scribbr’s Turnitin-powered plagiarism checker.

multi-scale reliability analysis

It also enables us to deal with statistical dependence both in spatial and temporal senses through the decomposition of the reliability analysis in space and time aspects. In these regards, the proposed approach performs a reliability analysis with the dynamic responses in time domain. This dynamic reliability analysis approach can consider uncertainties in system parameters and earthquake excitations simultaneously. In addition, the peak response over a time duration is used to describe the limit state of the structural system, which provides a more realistic measure of the failure probability of a structural system than instantaneous probability. In order to demonstrate the proposed approach, a 3-story shear-type building equipped with an optimal active control device is considered.

These scores should be related concurrently because they are both tests of mathematics. Unlike convergent and discriminant validity, concurrent and predictive validity is frequently ignored in empirical social science research. Criterion-related validity can also be assessed based on whether a given measure relate well with a current or future criterion, which are respectively called concurrent and predictive validity. Predictive validity is the degree to which a measure successfully predicts a future outcome that it is theoretically expected to predict.

multi-scale reliability analysis

An alternative and more common statistical method used to demonstrate convergent and discriminant validity is exploratory factor analysis . This is a data reduction technique which aggregates a given set of items to a smaller set of factors based on the bivariate correlation structure discussed above using a statistical technique called principal components analysis. These factors should ideally correspond to the underling theoretical constructs that we are trying to measure. The general norm for factor extraction is that each extracted factor should have an eigenvalue greater than 1.0. A more sophisticated technique for evaluating convergent and discriminant validity is the multi-trait multi-method (MTMM) approach. This technique requires measuring each construct (trait) using two or more different methods (e.g., survey and personal observation, or perhaps survey of two different respondent groups such as teachers and parents for evaluating academic quality).

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