An innovating analysis of the Nataf transformation from the copula viewpoint

This article gives new insight on the Nataf transformation, a widely used tool in reliability analysis. After recalling some basics concerning the copula theory, we explain this transformation in the light of the copula theory and we uncover all the hidden hypothesis made on the dependence structure of the probabilistic model when using this transformation.     

Do Rosenblatt and Nataf isoprobabilistic transformations really differ?

This article is the third in a series dedicated to the mathematical study of isoprobabilistic transformations and their relationship with stochastic dependence modelling, see [R. Lebrun, A. Dutfoy, An innovating analysis of the Nataf transformation from the viewpoint of copula, Probabilistic Engineering Mechanics (2008). doi: 10.1016/j.probengmech.2008.08.001] for an interpretation of the Nataf transformation in term of normal copula and [R. Lebrun, A. Dutfoy, A generalization of the Nataf transformation to distributions with elliptical copula, Probabilistic Engineering Mechanics (24) (2009), 172–178. doi:10.1016/j.probengmech.2008.05.001] for a generalisation of the Nataf transformation to any elliptical copula.In this article, we explore the relationship between two isoprobabilistic transformations widely used in the community of reliability analysts, namely the Generalised Nataf transformation and Rosenblatt transformation.First, we recall the elementary results of the copula theory that are needed in the remaining of the article, as a preliminary section to the presentation of both the Generalized Nataf transformation and the Rosenblatt transformation in the light of the copula theory.Then, we show that the Rosenblatt transformation using the canonical order of conditioning is identical to the Generalised Nataf transformation in the normal copula case, which is the most usual case in reliability analysis since it corresponds to the classical Nataf transformation. At this step, we also show that it is not possible to extend the Rosenblatt transformation to distributions with general elliptical copula the way the Nataf transformation has been generalised.Furthermore, we explore the effect of the conditioning order of the Rosenblatt transformation on the usual reliability indicators obtained from a FORM or SORM method. We show that in the normal copula case, all these reliability indicators, excepted the importance factors, are unchanged whatever the conditioning order one chooses.In the last section, we conclude the article with two numerical applications that illustrate the previous results: the equivalence between both transformations in the normal copula case, and the effect of the conditioning order in the normal and non-normal copula case.     

Data mining of vector–item patterns using neighborhood histograms

The representation of multiple continuous attributes as dimensions in a vector space has been among the most influential concepts in machine learning and data mining. We consider sets of related continuous attributes as vector data and search for patterns that relate a vector attribute to one or more items. The presence of an item set defines a subset of vectors that may or may not show unexpected density fluctuations. We test for fluctuations by studying density histograms. A vector–item pattern is considered significant if its density histogram significantly differs from what is expected for a random subset of transactions. Using two different density measures, we evaluate the algorithm on two real data sets and one that was artificially constructed from time series data.     

A generalization of the Nataf transformation to distributions with elliptical copula

In the first article [Lebrun R, Dutfoy A. An innovating viewpoint of the isoprobabilistic Nataf transformation with the copula theory within exceedance threshold uncertainty analysis. Probabilistic Structure Engineering Structural Reliability. 2008 [in press]], we showed that the Nataf transformation is a way to model the dependence structure of a random vector by a normal copula, parameterized by its correlation matrix. Following this analysis, we propose an extension of this transformation to any elliptical copula, and give the equivalent of the First Order Reliability Method (FORM) and the Second Order Reliability Method (SORM) for this generalization. In particular, we derive the Breitung asymptotic approximation in this new context.     

Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop

Mammals use two distinct gallops referred to as the transverse (where landing and take-off are contralateral) and rotary (where landing and take-off are ipsilateral). These two gallops are used by a variety of mammals, but the transverse gallop is epitomized by the horse and the rotary gallop by the cheetah. In this paper, we argue that the fundamental difference between these gaits is determined by which set of limbs, fore or hind, initiates the transition of the centre of mass from a downward–forward to upward–forward trajectory that occurs between the main ballistic (non-contact) portions of the stride when the animal makes contact with the ground. The impulse-mediated directional transition is a key feature of locomotion on limbs and is one of the major sources of momentum and kinetic energy loss, and a main reason why active work must be added to maintain speed in locomotion. Our analysis shows that the equine gallop transition is initiated by a hindlimb contact and occurs in a manner in some ways analogous to the skipping of a stone on a water surface. By contrast, the cheetah gallop transition is initiated by a forelimb contact, and the mechanics appear to have much in common with the human bipedal run. Many mammals use both types of gallop, and the transition strategies that we describe form points on a continuum linked even to functionally symmetrical running gaits such as the tölt and amble.     

Status and perspectives of renewable energy policy and deployment in the European Union—What is needed to reach the 2020 targets?

This article evaluates the status of current RES deployment, policies and barriers in the EU-27 member states and compares it to the required to meet the 2020 targets. The evaluation relies strongly on the quantitative deployment status and policy effectiveness indicators. European RES deployment and policy has progressed strongly in recent years, but the growth here has been mainly driven by effective policies in a small or medium number of top runner countries. Across Europe, the highest average policy effectiveness over six years was reached for onshore wind (4.2%), biofuels (3.6%) and biomass electricity (2.7%), while in the heat sector, all technologies score below 2%. Comparing the recent progress to the required growth for meeting the 2020 target, it appears that some countries largely exceed the interim targets of the RES Directive 2009/28/EC. Despite this, Europe will need additional policy effort to reach the 2020 target. Critical success factors include implementing effective and efficient policies that attract sufficient investments, reducing administrative and grid related barriers, especially in currently less advanced countries, upgrading the power grid infrastructure, dismantling financial barriers in the heat sector, realising sustainability standards for biomass, and lowering energy demand through increased energy efficiency efforts.     

ISO 9001 within the Swedish construction sector

This study analysed how the ISO 9000 framework could be employed in the construction process. Interviews were conducted at twelve companies in Sweden that utilized the quality system standard ISO 9001. Many of the concepts contained in the quality system standard were experienced as being too abstract and too difficult to comprehend. Frequently quality mangement was considered as serving the function of improving the company's competitiveness and allowing the company to be more efficient. It appeared difficult, however, in view of the many stages the construction process encompasses and the diverging interests represented, to meet the needs of the construction sector by the use of ISO 9001 alone. Some of the paragraphs it contains also tended to be confused with one another and to be misinterpreted. Others, although useful elsewhere, appeared scarcely to find application in the construction sector. Developments in the area appear to be going in the direction away from using large bureaucratic inspection systems and quality handbooks aimed at impressing customers and towards employing more diversified systems. Certification was found to be a matter of concern to all of the companies investigated.     

Influence of precursors on the formation of 3‐MCPD and glycidyl esters in a model oil under simulated deodorization conditions

To find new ways for reducing the potential of palm oil to form 3‐monochloropropane‐1,2‐diol (3‐MCPD) and glycidyl esters during refining it is helpful to know more about the influence of different precursors like diacylglycerols (DAGs) and monoacylglycerols (MAGs), lecithin, and chlorine containing compounds. After adding increasing amounts of the different precursors to a model oil obtained by removal of polar compounds from crude palm oil and heating the mixture under standardized conditions to 240°C for 2 h the contents of 3‐MCPD and glycidyl esters were analyzed according to the standard procedure of DGF C‐VI 18 (10). DAGs and MAGs were found to increase the potential of palm oil to form 3‐MCPD and glycidyl esters, but refined lecithin showed no influence. Sodium chloride as well as tetra‐n‐butylammoniumchloride (TBAC) led to higher contents of the esters. Whereas the addition of TBAC raised the amount of glycidyl esters as well as 3‐MCPD esters, sodium chloride largely raised the amount of 3‐MCPD esters. An addition of 5 mmol of sodium carbonate/kg model oil spiked with sodium chloride reduced the amount of glycidyl esters almost completely; the 3‐MCPD esters were reduced by 50%. About 1 mmol sodium hydrogen carbonate/kg oil reduced both 3‐MCPD and glycidyl esters almost completely. Practical applications : For the mitigation of the formation of 3‐MCPD esters and related compounds in refined edible oils, it is helpful to know more about the effect of different possible precursors. Using a broader data basis, it is possible to adopt the oil processing but especially the choice of the raw material to the demands of the market for lower contents of the esters in the refined products.