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Recently, a new class of fatigue crack growth models based on elastoplastic stress‐strain histories at the crack tip region and strain‐life fatigue damage models have been proposed. The fatigue crack propagation is understood as a process of continuous crack initializations, over elementary material blocks, which may be governed by strain‐life data of the plain material. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual crack driving force, taking into account mean stresses and loading sequential effects. The UniGrow model fits this particular class of fatigue crack propagation models. The purpose of this paper is to propose an extension of the UniGrow model to derive probabilistic fatigue crack propagation data, in particular the derivation of the P–da/dN–ΔK–R fields.

An existing deterministic fatigue crack propagation model, based on local strain‐life data is first assessed. In particular, an alternative methodology for residual stress computation is proposed, based on elastoplastic finite element analysis, in order to overcome inconsistencies found in the analytical approximate approaches often used in literature. Then, using probabilistic strain‐life fields, a probabilistic output for the fatigue crack propagation growth rates is generated. A new probabilistic fatigue field is also proposed to take mean stress effects into account, using the Smith‐Watson‐Topper (SWT) damage parameter. The proposed models are assessed using experimental data available for two materials representative from old Portuguese bridges.

A new method to generate probabilistic fatigue crack propagation rates (P–da/dN–ΔK–R fields) is proposed and verified using puddle iron from old Portuguese bridges, usually characterized by significant scatter in fatigue properties. Also, a new probabilistic fatigue field for plain material is proposed to deal with mean stress effects.

A relation between the P–ε–N and the P–da/dN–ΔK–R fields is firstly proposed in this research. Furthermore, a new P–SWT–N field is proposed to deal with mean stress effects.

The purpose of this study is to address the complexity involved in computing the fatigue life of casted structure with porosity effects in aero engine applications. The uncertainty of porosity defects is addressed by introducing probabilistic models.

One major issue of casted aluminium alloys in the application of aerospace industries is their internal defects such as porosities, which are directly affecting the fatigue life. Since there is huge cost and time effort involved in understanding the effect of fatigue life in terms of the presence of the internal defects, a probabilistic fatigue model approach is applied in order to define the realistic fatigue limit of the casted structures for the known porosity fractions. This paper describes the probabilistic technique to casted structures with measured porosity fractions and its relation to their fatigue life. The predicted fatigue life for various porosity fractions and dendrite arm spacing values is very well matching with the experimentally predicted fatigue data of the casted AS7G06 aluminium alloys with measured internal defects. The probabilistic analysis approach not only predicts the fatigue life limit of the structure but also provides the limit of fatigue life for the known porosity values of any casted aluminium bearing support structure used in aero engines.

The probabilistic fatigue model for addressing porosity in casting structure is verified with experimental results.

This is grey area in aerospace and automotive industry.

This work is original and not published anywhere else.

Studies in higher education tend to use different methods and methodologies, from documentary analysis to auto/biographical and observational studies. Most studies are either qualitative or qualitative. A mixed-methods approach has emerged in recent years, in which the qualitative approach generally plays an important role. The purpose of this chapter is to show the potential of a new methodology that is also appropriate for higher education research and widely used in the social sciences: probabilistic topic models. A probabilistic method can be used to analyse and categorise thousands of words. After collecting large sets of texts, content analysis is used to deeply analyse the meaning of these words. The huge number of texts published today pushes researchers to employ new techniques in their search for hidden structures built upon a set of core ideas. These methods are called topic modelling algorithms, with Latent Dirichlet Allocation being the basic probabilistic topic model. The application of these new techniques to the field of higher education is extremely useful, for two reasons: (1) studies in this area deal in some cases with a great volume of data and (2) these techniques allow one to devise models in a way that is unsupervised by humans (even when researchers operate on the resulting model); thus they are less subjective than other types of analyses and methods used for qualitative purposes. This chapter shows the foundations and recent applications of the technique in the higher education field, as well as challenges related to this new technique.

This study aims to identify empirically proven strategies for reducing healthcare supply chain inventory costs.

The author conducted in-depth interviews in 80 hospitals covering different supply chains. The author treated the healthcare firm as the unit of analysis and examined Vrat's taxonomy of inventory models based on the static and dynamic complexity theories of inventory models to identify an appropriate approach. The author addressed 33 highly priced and moderately priced stock-keeping units from 1,432 items and test several inventory policies. Next, the author applied combinations of inventory models, testing probabilistic hybrid inventory models.

The study finds that medical supplies, equipment, and medications are indispensable for a quality healthcare system. Hence, healthcare supply chain management (SCM) professionals must adopt basic inventory cost-reduction strategies, implementing inventory software functionalities effectively and efficiently. This study shows that probabilistic hybrid inventory techniques in healthcare SCM effectively determine an optimal stocking level, significantly reducing costs.

This study analyzes data from primary care and (to some extent) secondary care institutions. Although tertiary and quaternary care systems do not represent a large portion of the healthcare system, future research should also address these highly specialized organizations' needs.

This study proposes practical strategies to help continuously improve supply chain operations in healthcare organizations worldwide.

This study suggests probabilistic hybrid inventory models as empirically proven solutions for evaluating stock-keeping units in the healthcare sector. In doing so, the study provides a new healthcare supply chain approach, proposing a modified taxonomy of inventory models.

This paper aims to develop the Hybrid feature descriptor and probabilistic neuro-fuzzy system for attaining the high accuracy in face recognition system. In recent days, facial recognition (FR) systems play a vital part in several applications such as surveillance, access control and image understanding. Accordingly, various face recognition methods have been developed in the literature, but the applicability of these algorithms is restricted because of unsatisfied accuracy. So, the improvement of face recognition is significantly important for the current trend.

This paper proposes a face recognition system through feature extraction and classification. The proposed model extracts the local and the global feature of the image. The local features of the image are extracted using the kernel based scale invariant feature transform (K-SIFT) model and the global features are extracted using the proposed m-Co-HOG model. (Co-HOG: co-occurrence histograms of oriented gradients) The proposed m-Co-HOG model has the properties of the Co-HOG algorithm. The feature vector database contains combined local and the global feature vectors derived using the K-SIFT model and the proposed m-Co-HOG algorithm. This paper proposes a probabilistic neuro-fuzzy classifier system for the finding the identity of the person from the extracted feature vector database.

The face images required for the simulation of the proposed work are taken from the CVL database. The simulation considers a total of 114 persons form the CVL database. From the results, it is evident that the proposed model has outperformed the existing models with an improved accuracy of 0.98. The false acceptance rate (FAR) and false rejection rate (FRR) values of the proposed model have a low value of 0.01.

This paper proposes a face recognition system with proposed m-Co-HOG vector and the hybrid neuro-fuzzy classifier. Feature extraction was based on the proposed m-Co-HOG vector for extracting the global features and the existing K-SIFT model for extracting the local features from the face images. The proposed m-Co-HOG vector utilizes the existing Co-HOG model for feature extraction, along with a new color gradient decomposition method. The major advantage of the proposed m-Co-HOG vector is that it utilizes the color features of the image along with other features during the histogram operation.

Learning field of events is characterized by the occurrenceof random and uncertain phenomena, all of which have probabilistic distributions. The meaning of learning is exchange by interdependence between interacting agents. Such agents are both the human entities and the non‐human ones. Thus, in a learning field of probabilistic events there are complex forms of interaction between the domains of mind (human cognition) and matter (world‐system). The purpose of this paper is to formalize and study such interactions by the epistemology of unity of being and becoming of relations between given variables in analytical perspective.

The critical argumentation and search in this paper leads to the premise of the episteme of unity of knowledge. It is found singularly in the doctrine of the paired universe of the Quran. The episteme of oneness of the monotheistic law and its consequential forms establish the axiomatic basis of the criterion function representing the phenomenon of probabilistic learning field. The authors refer to this criterion as wellbeing. It conceptualizes and measures the degree of unity of being and becoming that exists between the variables of a specific problem under investigation.

The results of this study formalize the probabilistic model of learning. The simulated evaluation of the probabilistic form of the wellbeing function brings out the synonymous results between unity of knowledge and its impact on the unity of the world‐system induced by the knowledge‐flows. Such a transformation of a world‐system presents the meaning of endogenous (or systemically self‐regenerated) ethics and morality in such broader fields of choices involving embedded learning systems.

The dynamics of pervasive complementarities arising from learning by unity of knowledge, and considerations of ethics and morality remain exogenous factors in economic theory. This paper, instead, has formalized ethical endogeneity in models of decision‐making with probabilistic learning fields that remain embedded in complementarities by interaction and integration across economic, social and ethical systems.

The purpose of this paper is to discuss the application of a method for combining multiple criteria based on the transformation of numerical evaluations into probabilities of preference. It is applied to compare failure risks and to measure efficiency in the retail trade sector.

The main conceptual aspect of the method employed is taking into account uncertainty. Its other important feature is allowing for the combination of evaluations in terms of joint probabilities. This avoids the need of assigning weights to the criteria. In the context of failure modes and effects analysis (FMEA) it provides a probabilistic derivation for priority scores. An application of FMEA to the sector of services is discussed. Another area of application investigated is the assessment of efficiency.

Details of the application of the probabilistic composition in the evaluation of modes of failure and in the comparison of operational efficiencies of retail stores are evidenced.

The study is limited to the retail market. Other factors might be considered in the reliability analysis and other inputs and outputs might be added to the productivity evaluation. The extension of the study to other cases and sectors is straightforward.

Features of the evaluation of modes of failure and of productivity in the retail sector are revealed.

The main contribution of this paper is showing how to use a probabilistic framework to measure efficiency in services management.

The author presents new estimates of the probability weighting functions found in rank-dependent theories of choice under risk. These estimates are unusual in two senses. First, they are free of functional form assumptions about both utility and weighting functions, and they are entirely based on binary discrete choices and not on matching or valuation tasks, though they depend on assumptions concerning the nature of probabilistic choice under risk. Second, estimated weighting functions contradict widely held priors of an inverse-s shape with fixed point well in the interior of the (0,1) interval: Instead the author usually finds populations dominated by “optimists” who uniformly overweight best outcomes in risky options. The choice pairs used here mostly do not provoke similarity-based simplifications. In a third experiment, the author shows that the presence of choice pairs that provoke similarity-based computational shortcuts does indeed flatten estimated probability weighting functions.

Most epidemic transmission forecasting methods can only provide deterministic outputs. This study aims to show that probabilistic forecasting, in contrast, is suitable for stochastic demand modeling and emergency medical resource planning under uncertainty.

Two probabilistic forecasting methods, i.e. quantile regression convolutional neural network and kernel density estimation, are combined to provide the conditional quantiles and conditional densities of infected populations. The value of probabilistic forecasting in improving decision performances and controlling decision risks is investigated by an empirical study on the emergency medical resource planning for the COVID-19 pandemic.

The managerial implications obtained from the empirical results include (1) the optimization models using the conditional quantile or the point forecasting result obtain better results than those using the conditional density; (2) for sufficient resources, decision-makers' risk preferences can be incorporated to make tradeoffs between the possible surpluses and shortages of resources in the emergency medical resource planning at different quantile levels; and (3) for scarce resources, the differences in emergency medical resource planning at different quantile levels greatly decrease or disappear because of the existing of forecasting errors and supply quantity constraints.

Very few studies concern probabilistic epidemic transmission forecasting methods, and this is the first attempt to incorporate deep learning methods into a two-phase framework for data-driven emergency medical resource planning under uncertainty. Moreover, the findings from the empirical results are valuable to select a suitable forecasting method and design an efficient emergency medical resource plan.