Operational modal analisys using joint statistical analysis of multiple records

In Operational Modal Analysis (OMA) of a structure, the data acquisition process may be repeated many times. In these cases, the analyst has several similar records for the modal analysis of the structure that have been obtained at di�erent time instants (multiple records). The solution obtained varies from one record to another, sometimes considerably. The differences are due to several reasons: statistical errors of estimation, changes in the external forces (unmeasured forces) that modify the output spectra, appearance of spurious modes, etc. Combining the results of the di�erent individual analysis is not straightforward. To solve the problem, we propose to make the joint estimation of the parameters using all the records. This can be done in a very simple way using state space models and computing the estimates by maximum-likelihood. The method provides a single result for the modal parameters that combines optimally all the records.

Joint statistical analysis of multiple measurement setups for the estimation of vibrational modes

Computing the modal parameters of large structures in Operational Modal Analysis often requires to process data from multiple non simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors that are fixed for all the measurements, while the other sensors are moved from one setup to the next. One possibility is to process the setups separately what result in different modal parameter estimates for each setup. Then the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global modes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a state space model that can be used to process all setups at once so the global mode shapes are obtained automatically and subsequently only a value for the natural frequency and damping ratio of each mode is computed. We also present how this model can be estimated using maximum likelihood and the Expectation Maximization algorithm. We apply this technique to real data measured at a footbridge.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Accurate reconstruction of a known HIV-1 transmission history by phylogenetic tree analysis.

Phylogenetic analyses are increasingly used in attempts to clarify transmission patterns of human immunodeficiency virus type 1 (HIV-1), but there is a continuing discussion about their validity because convergent evolution and transmission of minor HIV variants may obscure epidemiological patterns. Here we have studied a unique HIV-1 transmission cluster consisting of nine infected individuals, for whom the time and direction of each virus transmission was exactly known. Most of the transmissions occurred between 1981 and 1983, and a total of 13 blood samples were obtained approximately 2-12 years later. The p17 gag and env V3 regions of the HIV-1 genome were directly sequenced from uncultured lymphocytes. A true phylogenetic tree was constructed based on the knowledge about when the transmissions had occurred and when the samples were obtained. This complex, known HIV-1 transmission history was compared with reconstructed molecular trees, which were calculated from the DNA sequences by several commonly used phylogenetic inference methods [Fitch-Margoliash, neighbor-joining, minimum-evolution, maximum-likelihood, maximum-parsimony, unweighted pair group method using arithmetic averages (UPGMA), and a Fitch-Margoliash method assuming a molecular clock (KITSCH)]. A majority of the reconstructed trees were good estimates of the true phylogeny; 12 of 13 taxa were correctly positioned in the most accurate trees. The choice of gene fragment was found to be more important than the choice of phylogenetic method and substitution model. However, methods that are sensitive to unequal rates of change performed more poorly (such as UPGMA and KITSCH, which assume a constant molecular clock). The rapidly evolving V3 fragment gave better reconstructions than p17, but a combined data set of both p17 and V3 performed best. The accuracy of the phylogenetic methods justifies their use in HIV-1 research and argues against convergent evolution and selective transmission of certain virus variants.

Half tetrad analysis in alfalfa using multiple restriction fragment length polymorphism markers.

A maximum likelihood approach of half tetrad analysis (HTA) based on multiple restriction fragment length polymorphism (RFLP) markers was developed. This procedure estimates the relative frequencies of 2n gametes produced by mechanisms genetically equivalent to first division restitution (FDR) or second division restitution and simultaneously locates the centromere within a linkage group of RFLP marker loci. The method was applied to the diploid alfalfa clone PG-F9 (2n = 2x = 16) previously selected because of its high frequency of 2n egg production. HTA was based on four RFLP loci for which PG-F9 was heterozygous with codominant alleles that were absent in the tetraploid tester. Models including three linked and one unlinked RFLP loci were developed and tested. Results of the HTA showed that PG-F9 produced 6% FDR and 94% second division restitution 2n eggs. Information from a marker locus belonging to one linkage group was used to more precisely locate the centromere on a different linkage group. HTA, together with previous cytological analysis, indicated that in PG-F9, FDR 2n eggs are likely produced by diplospory, a mechanism common among apomictic species. The occurrence of FDR 2n eggs in plant species and their importance for crop evolution and breeding is discussed together with the potential applicability of multilocus HTA in the study of reproductive mutants.

Evolution of chlorophyll and bacteriochlorophyll: the problem of invariant sites in sequence analysis.

Competing hypotheses seek to explain the evolution of oxygenic and anoxygenic processes of photosynthesis. Since chlorophyll is less reduced and precedes bacteriochlorophyll on the modern biosynthetic pathway, it has been proposed that chlorophyll preceded bacteriochlorophyll in its evolution. However, recent analyses of nucleotide sequences that encode chlorophyll and bacteriochlorophyll biosynthetic enzymes appear to provide support for an alternative hypothesis. This is that the evolution of bacteriochlorophyll occurred earlier than the evolution of chlorophyll. Here we demonstrate that the presence of invariant sites in sequence datasets leads to inconsistency in tree building (including maximum-likelihood methods). Homologous sequences with different biological functions often share invariant sites at the same nucleotide positions. However, different constraints can also result in additional invariant sites unique to the genes, which have specific and different biological functions. Consequently, the distribution of these sites can be uneven between the different types of homologous genes. The presence of invariant sites, shared by related biosynthetic genes as well as those unique to only some of these genes, has misled the recent evolutionary analysis of oxygenic and anoxygenic photosynthetic pigments. We evaluate an alternative scheme for the evolution of chlorophyll and bacteriochlorophyll.

Influence analysis of robust Wald-type tests

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

Partitioned likelihood support and the evaluation of data set conflict

In simultaneous analyses of multiple data partitions, the trees relevant when measuring support for a clade are the optimal tree, and the best tree lacking the clade (i.e., the most reasonable alternative). The parsimony-based method of partitioned branch support (PBS) forces each data set to arbitrate between the two relevant trees. This value is the amount each data set contributes to clade support in the combined analysis, and can be very different to support apparent in separate analyses. The approach used in PBS can also be employed in likelihood: a simultaneous analysis of all data retrieves the maximum likelihood tree, and the best tree without the clade of interest is also found. Each data set is fitted to the two trees and the log-likelihood difference calculated, giving partitioned likelihood support (PLS) for each data set. These calculations can be performed regardless of the complexity of the ML model adopted. The significance of PLS can be evaluated using a variety of resampling methods, such as the Kishino-Hasegawa test, the Shimodiara-Hasegawa test, or likelihood weights, although the appropriateness and assumptions of these tests remains debated.

Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm. to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker. demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

A preliminary phylogenetic analysis of the Capsalidae (Platyhelminthes : Monogenea : Monopisthocotylea) inferred from large subunit rDNA sequences

Phylogenetic relationships within the Capsalidae (Monogenea) were examined Using large subunit ribosomal DNA sequences from 17 capsalid species (representing 7 genera, 5 subfamilies), 2 outgroup taxa (Monocotylidae) plus Udonella caligorum (Udonellidae). Trees were constructed using maximum likelihood, minimum evolution and maximum parsimony algorithms. An initial tree, generated from sequences 315 bases long, Suggests that Capsalinae, Encotyllabinae, Entobdellinae and Trochopodinae are monophyletic, but that Benedeniinae is paraphyletic. Analyses indicate that Neobenedenia, currently in the Benedeniinae, should perhaps be placed in 2 separate subfamily. An additional analysis was made which omitted 3 capsalid taxa (for which only short sequences were available) and all outgroup taxa because of alignment difficulties. Sequence length increased to 693 bases and good branch support was achieved. The Benedeniinae was again paraphyletic. Higher-level classification of the Capsalidae, evolution of the Entobdellinae and issues of species identity in Neobenedenia are discussed.

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Sparsely spread CDMA - A statistical mechanics-based analysis

Sparse code division multiple access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of nonzero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code. © 2007 IOP Publishing Ltd.

Molecular analysis of evolutionary relationships of Phaseolus dumosus with the gene pool of common bean

Valuable genetic variation for bean breeding programs is held within the common bean secondary gene pool which consists of Phaseolus albescens, P. coccineus, P. costaricensis, and P. dumosus. However, the use of close relatives for bean improvement is limited due to the lack of knowledge about genetic variation and genetic plasticity of many of these species. Characterisation and analysis of the genetic diversity is necessary among beans' wild relatives; in addition, conflicting phylogenies and relationships need to be understood and a hypothesis of a hybrid origin of P. dumosus needs to be tested. This thesis research was orientated to generate information about the patterns of relationships among the common bean secondary gene pool, with particular focus on the species Phaseolus dumosus. This species displays a set of characteristics of agronomic interest, not only for the direct improvement of common bean but also as a source of valuable genes for adaptation to climate change. Here I undertake the first comprehensive study of the genetic diversity of P. dumosus as ascertained from both nuclear and chloroplast genome markers. A germplasm collection of the ancestral forms of P. dumosus together with wild, landrace and cultivar representatives of all other species of the common bean secondary gene pool, were used to analyse genetic diversity, phylogenetic relationships and structure of P. dumosus. Data on molecular variation was generated from sequences of cpDNA loci accD-psaI spacer, trnT-trnL spacer, trnL intron and rps14-psaB spacer and from the nrDNA the ITS region. A whole genome DArT array was developed and used for the genotyping of P. dumosus and its closes relatives. 4208 polymorphic markers were generated in the DArT array and from those, 742 markers presented a call rate >95% and zero discordance. DArT markers revealed a moderate genetic polymorphism among P. dumosus samples (13% of polymorphic loci), while P. coccineus presented the highest level of polymorphism (88% of polymorphic loci). At the cpDNA one ancestral haplotype was detected among all samples of all species in the secondary genepool. The ITS region of P. dumosus revealed high homogeneity and polymorphism bias to P. coccineus genome. Phylogenetic reconstructions made with Maximum likelihood and Bayesian methods confirmed previously reported discrepancies among the nuclear and chloroplast genomes of P. dumosus. The outline of relationships by hybridization networks displayed a considerable number of interactions within and between species. This research provides compelling evidence that P. dumosus arose from hybridisation between P. vulgaris and P. coccineus and confirms that P. costaricensis has likely been involved in the genesis or backcrossing events (or both) in the history of P. dumosus. The classification of the specie P. persistentus was analysed based on cpDNA and ITS sequences, the results found this species to be highly related to P. vulgaris but not too similar to P. leptostachyus as previously proposed. This research demonstrates that wild types of the secondary genepool carry a significant genetic variation which makes this a valuable genetic resource for common bean improvement. The DArT array generated in this research is a valuable resource for breeding programs since it has the potential to be used in several approaches including genotyping, discovery of novel traits, mapping and marker-trait associations. Efforts should be made to search for potential populations of P. persistentus and to increase the collection of new populations of P. dumosus, P. albescens and P. costaricensis that may provide valuable traits for introgression into common bean and other Phaseolus crops.