Adaptive multiscale principal components analysis for online monitoring of wastewater treatment

Fault detection and isolation (FDI) are important steps in the monitoring and supervision of industrial processes. Biological wastewater treatment (WWT) plants are difficult to model, and hence to monitor, because of the complexity of the biological reactions and because plant influent and disturbances are highly variable and/or unmeasured. Multivariate statistical models have been developed for a wide variety of situations over the past few decades, proving successful in many applications. In this paper we develop a new monitoring algorithm based on Principal Components Analysis (PCA). It can be seen equivalently as making Multiscale PCA (MSPCA) adaptive, or as a multiscale decomposition of adaptive PCA. Adaptive Multiscale PCA (AdMSPCA) exploits the changing multivariate relationships between variables at different time-scales. Adaptation of scale PCA models over time permits them to follow the evolution of the process, inputs or disturbances. Performance of AdMSPCA and adaptive PCA on a real WWT data set is compared and contrasted. The most significant difference observed was the ability of AdMSPCA to adapt to a much wider range of changes. This was mainly due to the flexibility afforded by allowing each scale model to adapt whenever it did not signal an abnormal event at that scale. Relative detection speeds were examined only summarily, but seemed to depend on the characteristics of the faults/disturbances. The results of the algorithms were similar for sudden changes, but AdMSPCA appeared more sensitive to slower changes.

Quantificação da complexidade do ritmo cardíaco usando o método da Multiscale Entropy

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Nanocomposites: the contribution of multiscale modelling to improve the dispersion levels

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos

Urban image classification with semisupervised multiscale cluster kernels

This paper presents a semisupervised support vector machine (SVM) that integrates the information of both labeled and unlabeled pixels efficiently. Method's performance is illustrated in the relevant problem of very high resolution image classification of urban areas. The SVM is trained with the linear combination of two kernels: a base kernel working only with labeled examples is deformed by a likelihood kernel encoding similarities between labeled and unlabeled examples. Results obtained on very high resolution (VHR) multispectral and hyperspectral images show the relevance of the method in the context of urban image classification. Also, its simplicity and the few parameters involved make the method versatile and workable by unexperienced users.

Genetic diversity and differentiation processes in the ploidy series of Olea europaea L.: a multiscale approach from subspecies to insular populations.

Geographical isolation and polyploidization are central concepts in plant evolution. The hierarchical organization of archipelagos in this study provides a framework for testing the evolutionary consequences for polyploid taxa and populations occurring in isolation. Using amplified fragment length polymorphism and simple sequence repeat markers, we determined the genetic diversity and differentiation patterns at three levels of geographical isolation in Olea europaea: mainland-archipelagos, islands within an archipelago, and populations within an island. At the subspecies scale, the hexaploid ssp. maroccana (southwest Morocco) exhibited higher genetic diversity than the insular counterparts. In contrast, the tetraploid ssp. cerasiformis (Madeira) displayed values similar to those obtained for the diploid ssp. guanchica (Canary Islands). Geographical isolation was associated with a high genetic differentiation at this scale. In the Canarian archipelago, the stepping-stone model of differentiation suggested in a previous study was partially supported. Within the western lineage, an east-to-west differentiation pattern was confirmed. Conversely, the easternmost populations were more related to the mainland ssp. europaea than to the western guanchica lineage. Genetic diversity across the Canarian archipelago was significantly correlated with the date of the last volcanic activity in the area/island where each population occurs. At the island scale, this pattern was not confirmed in older islands (Tenerife and Madeira), where populations were genetically homogeneous. In contrast, founder effects resulted in low genetic diversity and marked genetic differentiation among populations of the youngest island, La Palma.

Local-global splitting for spatiotemporal-adaptive multiscale methods

We present a novel spatiotemporal-adaptive Multiscale Finite Volume (MsFV) method, which is based on the natural idea that the global coarse-scale problem has longer characteristic time than the local fine-scale problems. As a consequence, the global problem can be solved with larger time steps than the local problems. In contrast to the pressure-transport splitting usually employed in the standard MsFV approach, we propose to start directly with a local-global splitting that allows to locally retain the original degree of coupling. This is crucial for highly non-linear systems or in the presence of physical instabilities. To obtain an accurate and efficient algorithm, we devise new adaptive criteria for global update that are based on changes of coarse-scale quantities rather than on fine-scale quantities, as it is routinely done before in the adaptive MsFV method. By means of a complexity analysis we show that the adaptive approach gives a noticeable speed-up with respect to the standard MsFV algorithm. In particular, it is efficient in case of large upscaling factors, which is important for multiphysics problems. Based on the observation that local time stepping acts as a smoother, we devise a self-correcting algorithm which incorporates the information from previous times to improve the quality of the multiscale approximation. We present results of multiphase flow simulations both for Darcy-scale and multiphysics (hybrid) problems, in which a local pore-scale description is combined with a global Darcy-like description. The novel spatiotemporal-adaptive multiscale method based on the local-global splitting is not limited to porous media flow problems, but it can be extended to any system described by a set of conservation equations.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Multiscale phylogeography: glacial history and autopolyploidy of Biscutella laevigata L. (Brassicaceae) in the Western Alps

Résumé Les changements climatiques du Quaternaire ont eu une influence majeure sur la distribution et l'évolution des biota septentrionaux. Les Alpes offrent un cadre spatio-temporel bien étudié pour comprendre la réactivité de la flore et le potentiel d'adaptation d'une espèce végétale face aux changements climatiques. Certaines hypothèses postulent une diversification des espèces en raison de la disparition complète de la flore des Alpes et d'un isolement important des espèces dans des refuges méridionaux durant les dernières glaciations (Tabula Rasa). Une autre hypothèse stipule le maintien de poches de résistance pour la végétation au coeur des Alpes (Nunataks). Comme de nombreuses espèces végétales présentant un grand succès écologique semblent avoir réagi aux glaciations par la multiplication de leur génome (autopolyploïdie), leur étude en milieu naturel devrait permettre de comprendre les avantages inhérents à la polyploïdie. Biscutella laevigata est un modèle emblématique de biogéographie historique, diverses études ayant montré que des populations diploïdes sont actuellement isolées dans les zones restées déglacées durant le dernier maximum glaciaire, alors que des tétraploïdes ont recolonisé l'ensemble des zones alpines mises à nu par le retrait des glaciers. Si le contexte périglaciaire semble avoir favorisé ce jeune complexe autopolyploïde, les circonstances et les avantages de cette mutation génomique ne sont pas encore clairs. Y a-t-il eu de multiples événements de polyploïdisation ? Dans quelle mesure affecte(nt)il(s) la diversité génétique et le potentiel évolutif des polyploïdes ? Les polyploïdes ont-ils une grande flexibilité génomique, favorisant une radiation adaptative, ou doivent-ils leur succès à une grande plasticité écologique ? Cette étude aborde ces questions à différentes échelles spatiales et temporelles. L'échelle régionale des Alpes occidentales permet d'aborder les facteurs distaux (aspects historiques), alors que l'échelle locale cherche à appréhender les facteurs proximaux (mécanismes évolutifs). Dans les Alpes occidentales, des populations ont été densément échantillonnées et étudiées grâce à (1) leur cytotype, (2) leur appartenance taxonomique, (3) leur habitat et (4) des marqueurs moléculaires de l'ADN chloroplastique, en vue d'établir leurs affinités évolutives. Á l'échelle locale, deux systèmes de population ont été étudiés : l'un où les populations persistent en périphérie de l'aire de distribution et l'autre au niveau du front actif de colonisation, en marge altitudinale. Les résultats à l'échelle des Alpes occidentales révèlent les sites d'intérêt (refuges glaciaires, principales barrières et voies de recolonisation) pour une espèce représentative des pelouses alpines, ainsi que pour la biodiversité régionale. Les Préalpes ont joué un rôle important dans le maintien de populations à proximité immédiate des Alpes centrales et dans l'évolution du taxon, voire de la végétation. Il est aussi démontré que l'époque glaciaire a favorisé l'autopolyploïdie polytopique et la recolonisation des Alpes occidentales par des lignées distinctes qui s'hybrident au centre des Alpes, influençant fortement leur diversité génétique et leur potentiel évolutif. L'analyse de populations locales en situations contrastées à l'aide de marqueurs AFLP montre qu'au sein d'une lignée présentant une grande expansion, la diversité génétique est façonnée par des forces évolutives différentes selon le contexte écologique et historique. Les populations persistant présentent une dispersion des gènes restreinte, engendrant une diversité génétique assez faible, mais semblent adaptées aux conditions locales de l'environnement. À l'inverse, les populations colonisant la marge altitudinale sont influencées par les effets de fondation conjugués à une importante dispersion des gènes et, si ces processus impliquent une grande diversité génétique, ils engendrent une répartition aléatoire des génotypes dans l'environnement. Les autopolyploïdes apparaissent ainsi comme capables de persister face aux changements climatiques grâce à certaines facultés d'adaptation locale et de grandes capacités à maintenir une importante diversité génétique lors de la recolonisation post-glaciaire. Summary The extreme climate changes of the Quaternary have had a major influence on species distribution and evolution. The European Alps offer a great framework to investigate flora reactivity and the adaptive potential of species under changing climate. Some hypotheses postulate diversification due to vegetation removal and important isolation in southern refugia (Tabula Rasa), while others explain phylogeographic patterns by the survival of species in favourable Nunataks within the Alps. Since numerous species have successfully reacted to past climate changes by genome multiplication (autopolyploidy), studies of such taxa in natural conditions is likely to explain the ecological success and the advantages of autopolyploidy. Early cytogeographical surveys of Biscutella laevigata have shed light on the links between autopolyploidy and glaciations by indicating that diploids are now spatially isolated in never-glaciated areas, while autotetraploids have recolonised the zones covered by glaciers- during the last glacial maximum. A periglacial context apparently favoured this young autopolyploid complex but the circumstances and the advantages of this genomic mutation remain unclear. What is the glacial history of the B. laevigata autopolyploid complex? Are there multiple events of polyploidisation? To what extent do they affect the genetic diversity and the evolutionary potential of polyploids? Is recolonisation associated with adaptive processes? How does long-term persistence affect genetic diversity? The present study addresses these questions at different spatiotemporal scales. A regional survey at the Western Alps-scale tackles distal factors (evolutionary history), while local-scale studies explore proximal factors (evolutionary mechanisms). In the Western Alps, populations have been densely sampled and studied from the (1) cytotypic, (2) morphotaxonomic, (3) habitat point of views, as well as (4) plastid DNA molecular markers, in order to infer their relationships and establish the maternal lineages phylogeography. At the local scale, populations persisting at the rear edge and populations recolonising the attitudinal margin at the leading edge have been studied by AFLPs to show how genetic diversity is shaped by different evolutionary forces across the species range. The results at the regional scale document the glacial history of a widespread species, representative of alpine meadows, in a regional area of main interest (glacial refugia, main barriers and recolonisation routes) and points out to sites of interest for regional biodiversity. The external Alps have played a major role in the maintenance of populations near the central Alps during the Last Glacial Maximum and influenced the evolution of the species, and of vegetation. Polytopic autopolyploidy in different biogeographic districts is also demonstrated. The species has had an important and rapid radiation because recolonisation took place from different refugia. The subsequent recolonisation of the Western Alps was achieved by independent lineages that are presently admixing in the central Alps. The role of the Pennic summit line is underlined as a great barrier that was permeable only through certain favourable high-altitude passes. The central Alps are thus viewed as an important crossroad where genomes with different evolutionary histories are meeting and admixing. The AFLP analysis and comparison of local populations growing in contrasted ecological and historical situations indicate that populations persisting in the external Alps present restricted gene dispersal and low genetic diversity but seem in equilibrium with their environment. On the contrary, populations colonising the attitudinal margin are mainly influenced by founder effects together with great gene dispersal and genotypes have a nearly random distribution, suggesting that recolonisation is not associated with adaptive processes. Autopolyploids that locally persist against climate changes thus seem to present adaptive ability, while those that actively recolonise the Alps are successful because of their great capacity to maintain a high genetic diversity against founder effects during recolonisation.

Multiscale determinants of tree frog (Hyla arborea L.) calling ponds in western Switzerland

A tree frog (Hyla arborea L., 1758) metapopulation in western Switzerland was studied during spring 2001. All potential calling ponds in an area of 350 km(2) were searched for tree frog calling males. Twenty-nine out of 111 ponds sheltered between 1 and 250 callers. Most ponds were occupied by less than 12 males. Pond parameters were measured at three different levels using field analysis and a Geographical Information System (GIS). The first level was water chemistry and pond-associated measures. The second level was the surrounding land use in a 30 m buffer around the pond. The third level consisted of landscape indices on a broader scale (up to 2 km). Logistic regression was applied to identify parameters that can predict the presence of calling males in a pond. Response variable was the presence or absence of callers. Four significant parameters allowed us to explain about 40% of the total deviance of the observed occupational pattern. Urbanization around the pond had a highly negative impact on the probability of presence of calling males. Hours of direct sunlight on the pond was positively correlated with callers. Higher water conductivity was associated with a lesser probability of species presence. Finally, the further the closest two-lane road, the higher the probability of callers presence. Our results show that presence or absence of callers is influenced by factors acting at various geographical scales.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.