Controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

The use of Mahalanobis squared distance–based novelty detection in statistical damage identification has become increasingly popular in recent years. The merit of the Mahalanobis squared distance–based method is that it is simple and requires low computational effort to enable the use of a higher dimensional damage-sensitive feature, which is generally more sensitive to structural changes. Mahalanobis squared distance–based damage identification is also believed to be one of the most suitable methods for modern sensing systems such as wireless sensors. Although possessing such advantages, this method is rather strict with the input requirement as it assumes the training data to be multivariate normal, which is not always available particularly at an early monitoring stage. As a consequence, it may result in an ill-conditioned training model with erroneous novelty detection and damage identification outcomes. To date, there appears to be no study on how to systematically cope with such practical issues especially in the context of a statistical damage identification problem. To address this need, this article proposes a controlled data generation scheme, which is based upon the Monte Carlo simulation methodology with the addition of several controlling and evaluation tools to assess the condition of output data. By evaluating the convergence of the data condition indices, the proposed scheme is able to determine the optimal setups for the data generation process and subsequently avoid unnecessarily excessive data. The efficacy of this scheme is demonstrated via applications to a benchmark structure data in the field.

Field validation of controlled Monte Carlo data generation for statistical damage identification employing Mahalanobis squared distance

This article presents the field applications and validations for the controlled Monte Carlo data generation scheme. This scheme was previously derived to assist the Mahalanobis squared distance–based damage identification method to cope with data-shortage problems which often cause inadequate data multinormality and unreliable identification outcome. To do so, real-vibration datasets from two actual civil engineering structures with such data (and identification) problems are selected as the test objects which are then shown to be in need of enhancement to consolidate their conditions. By utilizing the robust probability measures of the data condition indices in controlled Monte Carlo data generation and statistical sensitivity analysis of the Mahalanobis squared distance computational system, well-conditioned synthetic data generated by an optimal controlled Monte Carlo data generation configurations can be unbiasedly evaluated against those generated by other set-ups and against the original data. The analysis results reconfirm that controlled Monte Carlo data generation is able to overcome the shortage of observations, improve the data multinormality and enhance the reliability of the Mahalanobis squared distance–based damage identification method particularly with respect to false-positive errors. The results also highlight the dynamic structure of controlled Monte Carlo data generation that makes this scheme well adaptive to any type of input data with any (original) distributional condition.

Automatic solder joint defect classification using the Log-Gabor filter

This paper proposes the validity of a Gabor filter bank for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance measure based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Vision-based classification of solder joint defects

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure product quality and reliability. The solder joint inspection problem is more challenging than many other visual inspections because of the variability in the appearance of solder joints. Although many research works and various techniques have been developed to classify defect in solder joints, these methods have complex systems of illumination for image acquisition and complicated classification algorithms. An important stage of the analysis is to select the right method for the classification. Better inspection technologies are needed to fill the gap between available inspection capabilities and industry systems. This dissertation aims to provide a solution that can overcome some of the limitations of current inspection techniques. This research proposes two inspection steps for automatic solder joint classification system. The “front-end” inspection system includes illumination normalisation, localization and segmentation. The illumination normalisation approach can effectively and efficiently eliminate the effect of uneven illumination while keeping the properties of the processed image. The “back-end” inspection involves the classification of solder joints by using Log Gabor filter and classifier fusion. Five different levels of solder quality with respect to the amount of solder paste have been defined. Log Gabor filter has been demonstrated to achieve high recognition rates and is resistant to misalignment. Further testing demonstrates the advantage of Log Gabor filter over both Discrete Wavelet Transform and Discrete Cosine Transform. Classifier score fusion is analysed for improving recognition rate. Experimental results demonstrate that the proposed system improves performance and robustness in terms of classification rates. This proposed system does not need any special illumination system, and the images are acquired by an ordinary digital camera. In fact, the choice of suitable features allows one to overcome the problem given by the use of non complex illumination systems. The new system proposed in this research can be incorporated in the development of an automated non-contact, non-destructive and low cost solder joint quality inspection system.

Solder joint defects classification using the Log-Gabor Filter, the Discrete Wavelet Transform and the Discrete Cosine Transform

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure project quality and reliability. This paper proposes the use of the Log-Gabor filter bank, Discrete Wavelet Transform and Discrete Cosine Transform for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Divergência genética de cultivares de arroz quanto à resistência a Tibraca limbativentris Stål (Hemiptera: Pentatomidae)

A divergência genética de 16 cultivares de arroz quanto à resistência ao percevejo-do-colmo-do-arroz, Tibraca limbativentris Stål, foi avaliada por meio de técnicas de análise multivariada. O experimento foi conduzido em casa de vegetação, em delineamento experimental de blocos ao acaso, com oito repetições. Na avaliação foram considerados oito caracteres de resistência ao ataque do inseto. A divergência genética foi avaliada por procedimentos multivariados: distância generalizada de Mahalanobis (D²), método de agrupamento de otimização de Tocher e técnica de variáveis canônicas. As cultivares mais dissimilares foram Bico Ganga e Marabá Branco, enquanto Agulha e Branco Tardão foram as mais similares. Foram formados cinco grupos pelo método de otimização de Tocher. As três primeiras variáveis canônicas explicaram 88,5% da variabilidade total disponível. Conclui-se que as técnicas de análise multivariada são eficientes para a análise da divergência genética entre as cultivares de arroz, com destaque para Marabá Branco e Bico Ganga, consideradas as mais promissoras a serem utilizadas em futuros cruzamentos para melhoramento visando resistência ao percevejo-do-colmo-do-arroz.

Seleção de genótipos parentais de acerola com base na divergência genética multivariada

Este trabalho teve por objetivo identificar e selecionar genótipos parentais de acerola (Malpighia emarginata L.) adequadas a programas de melhoramento genético. Nove caracteres quantitativos de maior importância agronômica foram usados para determinação da distância genética e formação de grupos similares de acessos. O agrupamento pelo método de Tocher, a partir das distâncias generalizadas de Mahalanobis, possibilitou a divisão de 14 genótipos em três grupos. Com base na divergência genética e no caráter agronômico-chave (teor de vitamina C), destacaram-se como mais promissores os cruzamentos dos genótipos: AM Mole pertencente ao grupo III, com os genótipos PR AM, N° 18, PR 17, PR 16, Eclipse, AM 22 e Dominga, todos pertencentes ao grupo I.

Comparação de métodos de agrupamento para o estudo da divergência genética em cultivares de feijão

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análises genéticas em progênies de Pinus caribaea Morelet var. caribaea por caracteres quantitativos e marcadores moleculares

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Rapid morphological changes in populations of hybrids between Africanized and European honey bees

African honey bees, introduced to Brazil in 1956, rapidly dominated the previously introduced European subspecies. To better understand how hybridization between these different types of bees proceeded, we made geometric morphometric analyses of the wing venation patterns of specimens resulting from crosses made between Africanized honey bees (predominantly Apis mellifera scutellata) and Italian honey bees (A. mellifera ligustica) from 1965 to 1967, at the beginning of the Africanization process, in an apiary about 150 km from the original introduction site. Two virgin queens reared from an Italian parental were instrumentally inseminated with semen from drones from an Africanized parental. Six F-1 queens from one of these colonies were open mated with Africanized drones. Resultant F-1 drones were backcrossed to 50 Italian and 50 Africanized parental queens. Five backcross workers were collected from each of eight randomly selected colonies of each type of backcross (N = 5 bees x 8 colonies x 2 types of backcrosses). The F-1 progeny (40 workers and 30 drones) was found to be morphologically closer to the Africanized than to the European parental (N = 20 drones and 40 workers, each); Mahalanobis square distances = 21.6 versus 25.8, respectively, for the workers, and 39.9 versus 46.4, respectively, for the drones. The worker progenies of the backcrosses (N = 40, each) were placed between the respective parental and the F-1 progeny, although closer to the Africanized than to the Italian parentals (Mahalanobis square distance = 6.2 versus 12.1, respectively). Consequently, the most common crosses at the beginning of the Africanization process would have generated individuals more similar to Africanized than to Italian bees. This adds a genetic explanation for the rapid changes in the populational morphometric profile in recently colonized areas. Africanized alleles of wing venation pattern genes are apparently dominant and epistatic.

Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index

Parent, L. E., Natale, W. and Ziadi, N. 2009. Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index. Can. J. Soil Sci. 89: 383-390. Compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index (CND - r(2)) with assumed chi(2) distribution. The Mahalanobis distance D(2), which detects outliers in compositional data sets, also has a chi(2) distribution. The objective of this paper was to compare D(2) and CND - r(2) nutrient imbalance indexes in corn (Zea mays L.). We measured grain yield as well as N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn concentrations in the ear leaf at silk stage for 210 calibration sites in the St. Lawrence Lowlands [2300-2700 corn thermal units (CTU)] as well as 30 phosphorus (2300-2700 CTU; 10 sites) and 10 nitrogen (1900-2100 CTU; one site) replicated fertilizer treatments for validation. We derived CND norms as mean, standard deviation, and the inverse covariance matrix of centred log ratios (clr) for high yielding specimens (>= 9.0 Mg grain ha(-1) at 150 g H(2)O kg(-1) moisture content) in the 2300-2700 CTU zone. Using chi(2) = 17 (P < 0.05) with nine degrees of freedom (i.e., nine nutrients) as a rejection criterion for outliers and a yield threshold of 8.6 Mg ha(-1) after Cate-Nelson partitioning between low- and high-yielders in the P validation data set, D(2) misclassified two specimens compared with nine for CND -r(2). The D(2) classification was not significantly different from a chi(2) classification (P > 0.05), but the CND - r(2) classification differed significantly from chi(2) or D(2) (P < 0.001). A threshold value for nutrient imbalance could thus be derived probabilistically for conducting D(2) diagnosis, while the CND - r(2) nutrient imbalance threshold must be calibrated using fertilizer trials. In the proposed CND - D(2) procedure, D(2) is first computed to classify the specimen as possible outlier. Thereafter, nutrient indices are ranked in their order of limitation. The D(2) norms appeared less effective in the 1900-2100 CTU zone.

On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions

Many existing engineering works model the statistical characteristics of the entities under study as normal distributions. These models are eventually used for decision making, requiring in practice the definition of the classification region corresponding to the desired confidence level. Surprisingly enough, however, a great amount of computer vision works using multidimensional normal models leave unspecified or fail to establish correct confidence regions due to misconceptions on the features of Gaussian functions or to wrong analogies with the unidimensional case. The resulting regions incur in deviations that can be unacceptable in high-dimensional models. Here we provide a comprehensive derivation of the optimal confidence regions for multivariate normal distributions of arbitrary dimensionality. To this end, firstly we derive the condition for region optimality of general continuous multidimensional distributions, and then we apply it to the widespread case of the normal probability density function. The obtained results are used to analyze the confidence error incurred by previous works related to vision research, showing that deviations caused by wrong regions may turn into unacceptable as dimensionality increases. To support the theoretical analysis, a quantitative example in the context of moving object detection by means of background modeling is given.

Semantic spaces : measuring the distance between different subspaces

Semantic Space models, which provide a numerical representation of words’ meaning extracted from corpus of documents, have been formalized in terms of Hermitian operators over real valued Hilbert spaces by Bruza et al. [1]. The collapse of a word into a particular meaning has been investigated applying the notion of quantum collapse of superpositional states [2]. While the semantic association between words in a Semantic Space can be computed by means of the Minkowski distance [3] or the cosine of the angle between the vector representation of each pair of words, a new procedure is needed in order to establish relations between two or more Semantic Spaces. We address the question: how can the distance between different Semantic Spaces be computed? By representing each Semantic Space as a subspace of a more general Hilbert space, the relationship between Semantic Spaces can be computed by means of the subspace distance. Such distance needs to take into account the difference in the dimensions between subspaces. The availability of a distance for comparing different Semantic Subspaces would enable to achieve a deeper understanding about the geometry of Semantic Spaces which would possibly translate into better effectiveness in Information Retrieval tasks.