Modal parameter estimation in the presence of non-linearities

This paper investigates the use of time-frequency techniques to assist in the estimation of power system modes which are resolvable by a Digital Fourier Transform (DFT). The limitations of linear estimation techniques in the presence of large disturbances which excite system non-linearities, particularly the swing equation non-linearity are shown. Where a nonlinearity manifests itself as time varying modal frequencies the Wigner-Ville Distribution (WVD) is used to describe the variation in modal frequencies and construct a window over which standard linear estimation techniques can be used. The error obtained even in the presence of multiple resolvable modes is better than 2%.

Fixed-wing attitude estimation using temporal tracking of the horizon and optical flow

In this paper, a method has been developed for estimating pitch angle, roll angle and aircraft body rates based on horizon detection and temporal tracking using a forward-looking camera, without assistance from other sensors. Using an image processing front-end, we select several lines in an image that may or may not correspond to the true horizon. The optical flow at each candidate line is calculated, which may be used to measure the body rates of the aircraft. Using an Extended Kalman Filter (EKF), the aircraft state is propagated using a motion model and a candidate horizon line is associated using a statistical test based on the optical flow measurements and the location of the horizon. Once associated, the selected horizon line, along with the associated optical flow, is used as a measurement to the EKF. To test the accuracy of the algorithm, two flights were conducted, one using a highly dynamic Uninhabited Airborne Vehicle (UAV) in clear flight conditions and the other in a human-piloted Cessna 172 in conditions where the horizon was partially obscured by terrain, haze and smoke. The UAV flight resulted in pitch and roll error standard deviations of 0.42◦ and 0.71◦ respectively when compared with a truth attitude source. The Cessna flight resulted in pitch and roll error standard deviations of 1.79◦ and 1.75◦ respectively. The benefits of selecting and tracking the horizon using a motion model and optical flow rather than naively relying on the image processing front-end is also demonstrated.

Automatic in-bucket volume estimation for dragline operations

This paper presents a method for calculating the in-bucket payload volume on a dragline for the purpose of estimating the material’s bulk density in real-time. Knowledge of the bulk density can provide instant feedback to mine planning and scheduling to improve blasting and in turn provide a more uniform bulk density across the excavation site. Furthermore costs and emissions in dragline operation, maintenance and downstream material processing can be reduced. The main challenge is to determine an accurate position and orientation of the bucket with the constraint of real-time performance. The proposed solution uses a range bearing and tilt sensor to locate and scan the bucket between the lift and dump stages of the dragline cycle. Various scanning strategies are investigated for their benefits in this real-time application. The bucket is segmented from the scene using cluster analysis while the pose of the bucket is calculated using the iterative closest point (ICP) algorithm. Payload points are segmented from the bucket by a fixed distance neighbour clustering method to preserve boundary points and exclude low density clusters introduced by overhead chains and the spreader bar. A height grid is then used to represent the payload from which the volume can be calculated by summing over the grid cells. We show volume calculated on a scaled system with an accuracy of greater than 95 per cent.

Range sensor pose estimation

This paper presents a method of recovering the 6 DoF pose (Cartesian position and angular rotation) of a range sensor mounted on a mobile platform. The method utilises point targets in a local scene and optimises over the error between their absolute position and their apparent position as observed by the range sensor. The analysis includes an investigation into the sensitivity and robustness of the method. Practical results were collected using a SICK LRS2100 mounted on a P&H electric mining shovel and present the errors in scan data relative to an independent 3D scan of the scene. A comparison to directly measuring the sensor pose is presented and shows the significant accuracy improvements in scene reconstruction using this pose estimation method.

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.

The influence of platform walking on BRT station bus dwell time estimation

The common approach to estimate bus dwell time at a BRT station platform is to apply the traditional dwell time methodology derived for suburban bus stops. Current dwell time models are sensitive towards bus type, fare collection policy along with the number of boarding and alighting passengers. However, they fall short in accounting for the effects of passenger/s walking on a relatively longer BRT station platform. Analysis presented in this paper shows that the average walking time of a passenger at BRT platform is 10 times more than that of bus stop. The requirement of walking to the bus entry door at the BRT station platform may lead to the bus experiencing a higher dwell time. This paper presents a theory for a BRT network which explains the loss of station capacity during peak period operation. It also highlights shortcomings of present available bus dwell time models suggested for the analysis of BRT operation.

Machine prognostics based on health state probability estimation

The ability to accurately predict the remaining useful life of machine components is critical for machine continuous operation and can also improve productivity and enhance system’s safety. In condition-based maintenance (CBM), maintenance is performed based on information collected through condition monitoring and assessment of the machine health. Effective diagnostics and prognostics are important aspects of CBM for maintenance engineers to schedule a repair and to acquire replacement components before the components actually fail. Although a variety of prognostic methodologies have been reported recently, their application in industry is still relatively new and mostly focused on the prediction of specific component degradations. Furthermore, they required significant and sufficient number of fault indicators to accurately prognose the component faults. Hence, sufficient usage of health indicators in prognostics for the effective interpretation of machine degradation process is still required. Major challenges for accurate longterm prediction of remaining useful life (RUL) still remain to be addressed. Therefore, continuous development and improvement of a machine health management system and accurate long-term prediction of machine remnant life is required in real industry application. This thesis presents an integrated diagnostics and prognostics framework based on health state probability estimation for accurate and long-term prediction of machine remnant life. In the proposed model, prior empirical (historical) knowledge is embedded in the integrated diagnostics and prognostics system for classification of impending faults in machine system and accurate probability estimation of discrete degradation stages (health states). The methodology assumes that machine degradation consists of a series of degraded states (health states) which effectively represent the dynamic and stochastic process of machine failure. The estimation of discrete health state probability for the prediction of machine remnant life is performed using the ability of classification algorithms. To employ the appropriate classifier for health state probability estimation in the proposed model, comparative intelligent diagnostic tests were conducted using five different classifiers applied to the progressive fault data of three different faults in a high pressure liquefied natural gas (HP-LNG) pump. As a result of this comparison study, SVMs were employed in heath state probability estimation for the prediction of machine failure in this research. The proposed prognostic methodology has been successfully tested and validated using a number of case studies from simulation tests to real industry applications. The results from two actual failure case studies using simulations and experiments indicate that accurate estimation of health states is achievable and the proposed method provides accurate long-term prediction of machine remnant life. In addition, the results of experimental tests show that the proposed model has the capability of providing early warning of abnormal machine operating conditions by identifying the transitional states of machine fault conditions. Finally, the proposed prognostic model is validated through two industrial case studies. The optimal number of health states which can minimise the model training error without significant decrease of prediction accuracy was also examined through several health states of bearing failure. The results were very encouraging and show that the proposed prognostic model based on health state probability estimation has the potential to be used as a generic and scalable asset health estimation tool in industrial machinery.

Real-time volume estimation of a dragline payload

This paper presents a method for measuring the in-bucket payload volume on a dragline excavator for the purpose of estimating the material's bulk density in real-time. Knowledge of the payload's bulk density can provide feedback to mine planning and scheduling to improve blasting and therefore provide a more uniform bulk density across the excavation site. This allows a single optimal bucket size to be used for maximum overburden removal per dig and in turn reduce costs and emissions in dragline operation and maintenance. The proposed solution uses a range bearing laser to locate and scan full buckets between the lift and dump stages of the dragline cycle. The bucket is segmented from the scene using cluster analysis, and the pose of the bucket is calculated using the Iterative Closest Point (ICP) algorithm. Payload points are identified using a known model and subsequently converted into a height grid for volume estimation. Results from both scaled and full scale implementations show that this method can achieve an accuracy of above 95%.

Prognostic modelling options for remaining useful life estimation by industry

Over recent years a significant amount of research has been undertaken to develop prognostic models that can be used to predict the remaining useful life of engineering assets. Implementations by industry have only had limited success. By design, models are subject to specific assumptions and approximations, some of which are mathematical, while others relate to practical implementation issues such as the amount of data required to validate and verify a proposed model. Therefore, appropriate model selection for successful practical implementation requires not only a mathematical understanding of each model type, but also an appreciation of how a particular business intends to utilise a model and its outputs. This paper discusses business issues that need to be considered when selecting an appropriate modelling approach for trial. It also presents classification tables and process flow diagrams to assist industry and research personnel select appropriate prognostic models for predicting the remaining useful life of engineering assets within their specific business environment. The paper then explores the strengths and weaknesses of the main prognostics model classes to establish what makes them better suited to certain applications than to others and summarises how each have been applied to engineering prognostics. Consequently, this paper should provide a starting point for young researchers first considering options for remaining useful life prediction. The models described in this paper are Knowledge-based (expert and fuzzy), Life expectancy (stochastic and statistical), Artificial Neural Networks, and Physical models.

Latent degradation indicators estimation and prediction : a Monte Carlo approach

Asset health inspections can produce two types of indicators: (1) direct indicators (e.g. the thickness of a brake pad, and the crack depth on a gear) which directly relate to a failure mechanism; and (2) indirect indicators (e.g. the indicators extracted from vibration signals and oil analysis data) which can only partially reveal a failure mechanism. While direct indicators enable more precise references to asset health condition, they are often more difficult to obtain than indirect indicators. The state space model provides an efficient approach to estimating direct indicators by using indirect indicators. However, existing state space models to estimate direct indicators largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires fixed inspection intervals. The discrete state assumption entails discretising continuous degradation indicators, which often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This paper proposes a state space model without these assumptions. Monte Carlo-based algorithms are developed to estimate the model parameters and the remaining useful life. These algorithms are evaluated for performance using numerical simulations through MATLAB. The result shows that both the parameters and the remaining useful life are estimated accurately. Finally, the new state space model is used to process vibration and crack depth data from an accelerated test of a gearbox. During this application, the new state space model shows a better fitness result than the state space model with linear and Gaussian assumption.

Critical gap estimation by numerical and statistical highest likelihood search

Many traffic situations require drivers to cross or merge into a stream having higher priority. Gap acceptance theory enables us to model such processes to analyse traffic operation. This discussion demonstrated that numerical search fine tuned by statistical analysis can be used to determine the most likely critical gap for a sample of drivers, based on their largest rejected gap and accepted gap. This method shares some common features with the Maximum Likelihood Estimation technique (Troutbeck 1992) but lends itself well to contemporary analysis tools such as spreadsheet and is particularly analytically transparent. This method is considered not to bias estimation of critical gap due to very small rejected gaps or very large rejected gaps. However, it requires a sufficiently large sample that there is reasonable representation of largest rejected gap/accepted gap pairs within a fairly narrow highest likelihood search band.

A Python package for Bayesian estimation using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) estimation provides a solution to the complex integration problems that are faced in the Bayesian analysis of statistical problems. The implementation of MCMC algorithms is, however, code intensive and time consuming. We have developed a Python package, which is called PyMCMC, that aids in the construction of MCMC samplers and helps to substantially reduce the likelihood of coding error, as well as aid in the minimisation of repetitive code. PyMCMC contains classes for Gibbs, Metropolis Hastings, independent Metropolis Hastings, random walk Metropolis Hastings, orientational bias Monte Carlo and slice samplers as well as specific modules for common models such as a module for Bayesian regression analysis. PyMCMC is straightforward to optimise, taking advantage of the Python libraries Numpy and Scipy, as well as being readily extensible with C or Fortran.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.