Prognostics and health management (PHM) is an engineering discipline that aims to maintain system behaviour and function and ensure mission success, safety and effectiveness. Prognostics is defined as the estimation of remaining useful life. It is the most critical part of this process and is a key feature of maintenance strategies since the estimation of the remaining useful life (RUL) is essential to avoiding unscheduled maintenance. Prognostics is relatively immature compared to diagnostics, and a challenging task facing the research community is to overcome some of the major barriers to the application of PHM technologies to real-world industrial systems. This thesis presents research into methods for addressing these challenges for industrial applications. The thesis work focuses on prognostic approaches for three different engineering systems with different characteristics in terms of the prognostics of operation and maintenance aspects. The aim of this thesis is to facilitate better operation and maintenance decision making. The main benefits of prognostics are in anticipating future failures to increase uptime, implementing dynamic maintenance planning toward decreasing total costs and decreasing energy consumption. Therefore, there is a need for methods that can be used in these cases to classify the health states and predict the remaining useful life of assets. The studied engineered systems in this thesis are railway tracks, batteries and rolling element bearings.

In a railway system, the track geometry has to be maintained to provide a safe and functional track. Therefore, track degradation of ballasted railway track systems has to be measured on a regular basis to determine when to maintain the track by tamping. Tamping aims to restore the geometry to its original state to ensure an efficient, comfortable and safe transportation system. To minimise the disruption introduced by tamping, this action has to be planned in advance. Track degradation forecasts derived from regression methods are used to predict when the standard deviation of a specific track section will exceed a predefined maintenance or safety limit. In this thesis, a particle-filter-based prognostic approach for railway track degradation for railway switches is proposed. The particle-filter-based prognostic will generate a probabilistic prediction result that can facilitate risk-based decision making.

Li-ion batteries are another important components in engineering system and battery life prediction matters. Li-ion batteries are commonly used in a wide range of consumer electronic devices, electric vehicles of all types, military electronics,  maritime applications, astronaut suits, and space systems. Many critical operations depend on such batteries as a reliable power source. It is therefore important for the user to get an accurate estimate of the battery end of discharge because an unforeseen discharge of a battery could have catastrophic consequences. To address this issue, a Bayesian hierarchical model (BHM)-based prognostics approach was applied to Li-ion batteries, where the goal was to analyse and predict the discharge behaviour of such batteries with variable load profiles and variable amounts of available discharge data. The BHM approach enables inferences for both individual batteries and groups of batteries. Estimates of the hierarchical model parameters and the individual battery parameters are presented, and dependencies on load cycles are inferred. The operational and reliability aspects, end of life (EoD) and end of life (EoL), are studied; it is shown that predictions of the EoD can be made accurately with a variable amount of battery data. Without access to measurements, e.g., predicting performance of a new battery, the predictions are based only on the prior distributions describing the similarity within a group of batteries and their dependency on the load cycle. A discharge cycle dependency is identified helping with estimation of battery reliability.

Batteries have become a very important engineering system, rotating machines have played an important role, possibly the most important role, in the field of engineering. They have been used to drive the industrialisation of the world.

For rotating machinery, rolling element bearings are a vital component and have several failure modes. Hence, there is  significant need to monitor the health of bearings and detect degraded  states and  upcoming  failures  as  early  as  possible  to avoid serious accidents and equipment failure. For  rolling element bearings, an investigation in using FEM models for estimating bearing forces from acceleration measurements was conducted. This study was performed at a paper mill where a bearing monitoring system was installed. The purpose of the study was to feed the bearing rating life L₁₀ (a bearing life length calculation) with estimations of the dynamic bearing forces  to continuously update the L₁₀ calculation by generating a dynamic L₁₀. In a second study for bearing lifetime prediction, a Bayesian hierarchical modelling (BHM) approach , which includes different data sources, such as enveloped acceleration data, in combination with degradation models and prior distributions of other parameters, was developed, in which the bearing rating life calculation can be included. The proposed prognostics methodology can be used in cases where there is less  or noisy data. The above approach can even be used in cases whereby there is no prior knowledge of the system or little measurement data on the conditions. The presented BHM approach can also be used to predict the remaining useful life (RUL) of bearings both in situations in which the bearing is considered to be in a healthy state and in situations after a defect has been detected.