Bridging the gap: a novel approach to mathematics support

The ever growing gap between secondary and university level mathematics is now becoming a major concern to higher education institutions. The increase in diversity of students’ background in mathematics, from students who have studied the more traditional A-level programmes to students with BTEC or international qualifications and part-time students who have been out of education for long periods, means that they are often unprepared for the marked shift in levels and catering for all abilities is difficult in the normal lecture, tutorial format. Lack of sufficient mathematical knowledge not only affects students’ success on courses but also leads to disengagement and thus a high drop-out rate in the first 2 years of study. Many universities now offer a maths support service in an attempt to overcome this but their success is varied. This paper presents a novel approach to maths support designed and adopted by the University of Lincoln, School of Engineering, to bridge this transition gap for students, offer continued support through assessment for learning (AFL) and Individual Learning Plans (ILP’s) and ultimately increase student success, engagement and retention. The paper then extends this proven approach and discusses proposed enhancements through the use of on-line diagnostic testing and implementation of a ‘student expert’ system to harness mathematical knowledge held by those gifted and talented students often overlooked by higher education institutions and to promote peer-to-peer mentoring. The paper shows that with the current support system in place, there is a marked increase in student retention, compared with national benchmark data, and an increase in student engagement and success measured through student feedback and presented retention data

Increasing the impact of mathematics support on aiding student transition in higher education

The ever growing gap between secondary and university level mathematics is a major concern to higher education institutions. The increase in diversity of students’ background in mathematics, with entry qualifications ranging from the more traditional A-level programmes to BTEC or international qualifications is compounded where institutions attempt to widen participation. For example, work-based learners may have been out of education for prolonged periods, and consequently, are often unprepared for the marked shift in levels, and catering for all abilities is difficult in the normal lecture, tutorial format. Lack of sufficient mathematical knowledge not only affects students’ achievement on courses but also leads to disengagement and higher drop-out rates during the first two years of study. Many universities now offer a maths support service in an attempt to overcome these issues, but their success is varied. This paper presents a novel approach to maths support designed and adopted by the University of Lincoln, School of Engineering, to bridge this transition gap for students, offer continued support through assessment for learning (AFL) and Individual Learning Plans (ILP’s), and ultimately increase student achievement, engagement and retention. The paper then extends this proven approach and discusses recently implemented enhancements through the use of on-line diagnostic testing and a ‘student expert’ system to harness mathematical knowledge held by those gifted and talented students (often overlooked by higher education institutions) and to promote peer-to-peer mentoring. The paper shows that with the proven system in place, there is a marked increase in student retention compared with national benchmark data, and an increase in student engagement and achievement measured through student feedback and assessments. Although the on-line enhancements are in the early stages of implementation it is expected, based on these results, that further improvements will be shown

Applied Sensor Fault Detection, Identification and Data Reconstruction

Sensor fault detection and identification (SFD/I) has attracted considerable attention in military applications, especially when safety- or mission-critical issues are of paramount importance. Here, two readily implementable approaches for SFD/I are proposed through hierarchical clustering and self-organizing map neural networks. The proposed methodologies are capable of detecting sensor faults from a large group of sensors measuring different physical quantities and achieve SFD/I in a single stage. Furthermore, it is possible to reconstruct the measurements expected from the faulted sensor and thereby facilitate improved unit availability. The efficacy of the proposed approaches is demonstrated through the use of measurements from experimental trials on a gas turbine. Ultimately, the underlying principles are readily transferable to other complex industrial and military systems

Fault detection and diagnosis based on extensions of PCA

The paper presents two approaches for fault detection and discrimination based on principal component analysis (PCA). The first approach proposes the concept of y-indices through a transposed formulation of the data matrices utilized in traditional PCA. Residual errors (REs) and faulty sensor identification indices (FSIIs) are introduced in the second approach, where REs are generated from the residual sub-space of PCA, and FSIIs are introduced to classify sensor- or component-faults. Through field data from gas turbines during commissioning, it is shown that in-operation sensor faults can be detected, and sensor- and component-faults can be discriminated through the proposed methods. The techniques are generic, and will find use in many military systems with complex, safety critical control and sensor arrangements

Aiding student transition through a novel approach to mathematics support

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Measuring the impact of an on-line maths support system

The ever growing gap between secondary and university level mathematics continues to be a major concern to higher education institutions. The increase in diversity of students’ background in mathematics, from students who have studied the more traditional A-level programmes to students with BTEC or international qualifications and part-time students who have been out of education for long periods, means that they are often unprepared for the marked shift in levels and catering for all abilities is difficult in the normal lecture, tutorial format. Lack of sufficient mathematical knowledge not only affects students’ success on courses but also leads to disengagement and thus a high drop-out rate in the first 2 years of study. Many universities now offer a maths support service in an attempt to overcome this but their success is varied. Previously, the author presented a novel on-line approach to maths support designed and adopted by the University of Lincoln, School of Engineering and funded as part of the National HE STEM Programme, to bridge this transition gap for students, offer continued support through assessment for learning (AFL) and ultimately increase student success, engagement and retention. On-line diagnostic tests, containing levelled exam style questions, are administered after each taught topic which highlights specific support areas for each student. Support is then offered via numerous on-line resources and more traditional weekly timetabled sessions tailored to individual student needs. The system also incorporates a ‘student expert’ system as a way of encouraging peer-to-peer support and harnessing the knowledge of gifted and talented students. The on-line system builds on a previous system developed by Lincoln which was proven to increase student success, retention and engagement. Since its implementation in September 2012, the new on-line system has proven to be a huge success not only in terms of monitoring the progress of students and offering targeted support but also as a way of addressing the issues surrounding poor engagement in maths support. Results show that with this system in place there is further improvement in student achievement for all students. They also show that for those students who still did not engage in the more traditional ‘out of hours’ support sessions, they still achieved high marks purely through the on-line system. This paper presents these results

Applied sensor fault detection, identification and data reconstruction based on PCA and SOMNN for industrial systems

The paper presents two readily implementable approaches for Sensor Fault Detection, Identification (SFD/I) and faulted sensor data reconstruction in complex systems, in real-time. Specifically, Principal Component Analysis (PCA) and Self-Organizing Map Neural Networks (SOMNNs) are demonstrated for use on industrial turbine systems. In the first approach, Squared Prediction Error (SPE) based on the PCA residual space is used for SFD. SPE contribution plot is employed for SFI. A missing value approach from an extension of PCA is applied for faulted sensor data reconstruction. In the second approach, SFD is performed by SOMNN based Estimation Error (EE), and SFI is achieved by EE contribution plot. Data reconstruction is based on an extension of the SOMNN algorithm. The results are compared in each examining stage. The validation of both approaches is demonstrated through experimental data during the commissioning of an industrial 15MW turbine

Applied sensor fault detection and identification during steady-state and transient system operation

The paper presents two readily implementable methods for sensor fault detection and identification (SFD/I) for complex systems. Specifically, principal component analysis (PCA) and self-organizing map neural network (SOMNN) based algorithms are demonstrated for use on industrial gas turbine (IGT) systems. Two operational regimes are considered viz. steady-state operation and operation during transient conditions. For steady-state operation, PCA based squared prediction error (SPE) is used for SFD, and through the use of contribution plots, SFI. For SFD/I under operational conditions with transients, a proposed ‘y-index’ is introduced based on PCA with transposed input matrix that provides information on anomalies in the sensor domain (rather than in the time domain as with the traditional PCA approach). Moreover, using a SOMNN approach, during steady-state operation the estimation error (EE) is used for SFD and EE contribution plots for SFI. Additionally, during transient operation, SOMNN classification maps (CMs) are used through comparisons with ‘fingerprints’ taken during normal operation. Validation of the approaches is demonstrated through experimental trial data taken during the commissioning of IGTs. Although the attributes of the techniques are focused on a particular industrial sector in this case, ultimately their use is expected to be much more widely applicable to other fields and systems

Self-organising symbolic aggregate approximation for real-time fault detection and diagnosis in transient dynamic systems

The development of accurate fault detection and diagnosis (FDD) techniques are an important aspect of monitoring system health, whether it be an industrial machine or human system. In FDD systems where real-time or mobile monitoring is required there is a need to minimise computational overhead whilst maintaining detection and diagnosis accuracy. Symbolic Aggregate Approximation (SAX) is one such method, whereby reduced representations of signals are used to create symbolic representations for similarity search. Data reduction is achieved through application of the Piecewise Aggregate Approximation (PAA) algorithm. However, this can often lead to the loss of key information characteristics resulting in misclassification of signal types and a high risk of false alarms. This paper proposes a novel methodology based on SAX for generating more accurate symbolic representations, called Self-Organising Symbolic Aggregate Approximation (SOSAX). Data reduction is achieved through the application of an optimised PAA algorithm, Self-Organising Piecewise Aggregate Approximation (SOPAA). The approach is validated through the classification of electrocardiogram (ECG) signals where it is shown to outperform standard SAX in terms of inter-class separation and intra-class distance of signal types

Plasma Potential Measurements in the Discharge Channel of a 6-kW Hall Thruster

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76785/1/AIAA-2008-5185-902.pd