Fault Diagnosis in Internal Combustion Engines Using Nonlinear Multivariate Statistics

This paper presents a statistical-based fault diagnosis scheme for application to internal combustion engines. The scheme relies on an identified model that describes the relationships between a set of recorded engine variables using principal component analysis (PCA). Since combustion cycles are complex in nature and produce nonlinear relationships between the recorded engine variables, the paper proposes the use of nonlinear PCA (NLPCA). The paper further justifies the use of NLPCA by comparing the model accuracy of the NLPCA model with that of a linear PCA model. A new nonlinear variable reconstruction algorithm and bivariate scatter plots are proposed for fault isolation, following the application of NLPCA. The proposed technique allows the diagnosis of different fault types under steady-state operating conditions. More precisely, nonlinear variable reconstruction can remove the fault signature from the recorded engine data, which allows the identification and isolation of the root cause of abnormal engine behaviour. The paper shows that this can lead to (i) an enhanced identification of potential root causes of abnormal events and (ii) the masking of faulty sensor readings. The effectiveness of the enhanced NLPCA based monitoring scheme is illustrated by its application to a sensor fault and a process fault. The sensor fault relates to a drift in the fuel flow reading, whilst the process fault relates to a partial blockage of the intercooler. These faults are introduced to a Volkswagen TDI 1.9 Litre diesel engine mounted on an experimental engine test bench facility.

Summary statistics, educational achievement gaps and the ecological fallacy

Summary statistics continue to play an important role in identifying and monitoring patterns and trends in educational inequalities between differing groups of pupils over time. However, this article argues that their uncritical use can also encourage the labelling of whole groups of pupils as ‘underachievers’ or ‘overachievers’ as the findings of group-level data are simply applied to individual group members, a practice commonly termed the ‘ecological fallacy’. Some of the adverse consequences of this will be outlined in relation to current debates concerning gender and ethnic differences in educational attainment. It will be argued that one way of countering this uncritical use of summary statistics and the ecological fallacy that it tends to encourage, is to make much more use of the principles and methods of what has been termed ‘exploratory data analysis’. Such an approach is illustrated through a secondary analysis of data from the Youth Cohort Study of England and Wales, focusing on gender and ethnic differences in educational attainment. It will be shown that, by placing an emphasis on the graphical display of data and on encouraging researchers to describe those data more qualitatively, such an approach represents an essential addition to the use of simple summary statistics and helps to avoid the limitations associated with them.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

Higher order statistics for lognormal small-scale fading in mobile radio channels

This letter reports the statistical characterization and modeling of the indoor radio channel for a mobile wireless personal area network operating at 868 MHz. Line of sight (LOS) and non-LOS conditions were considered for three environments: anechoic chamber, open office area and hallway. Overall, the Nakagami-m cdf best described fading for bodyworn operation in 60% of all measured channels in anechoic chamber and open office area environments. The Nakagami distribution was also found to provide a good description of Rician distributed channels which predominated in the hallway. Multipath played an important role in channel statistics with the mean recorded m value being reduced from 7.8 in the anechoic chamber to 1.3 in both the open office area and hallway.

Higher order statistics for the κ–μ distribution

Closed-form expressions for the level crossing rate and average fade duration of a kappa–mu distributed fading signal envelope are presented. The proposed equations are validated by reduction to known Rice, Rayleigh and Nakagami-m special cases. They are also compared with measured data obtained from field trials analysing human body to body radio channels and shown to provide good agreement.

The structure of the Statistics Anxiety Rating Scale: A confirmatory factor analysis using UK psychology students

This study aimed to examine the structure of the statistics anxiety rating scale. Responses from 650 undergraduate psychology students throughout the UK were collected through an on-line study. Based on previous research three different models were specified and estimated using confirmatory factor analysis. Fit indices were used to determine if the model fitted the data and a likelihood ratio difference test was used to determine the best fitting model. The original six factor model was the best explanation of the data. All six subscales were intercorrelated and internally consistent. It was concluded that the statistics anxiety rating scale was found to measure the six subscales it was designed to assess in a UK population.

Fault reconstruction in linear dynamic systems using multivariate statistics

Treasure et al. (2004) recently proposed a new sub space-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.