Axel Hochstein

Switching vector autoregressive models with higher-order regime dynamics Application to prognostics and health management

Regime switching vector autoregressive (RSVAR) models are typically used to model changing dependency structures of multivariate time series. These changing regimes are represented by using a first-order Markov process where the transition distribution reflects the probabilities of moving to one of the other regime in the subsequent time step. Instead of representing the state of the system at different points in time, we extend this framework by using an explicit time representation that allows us to query against probability distributions of when particular regime changes take place. In contrast to continuous time based approaches such as continuous time Bayesian networks or continuous time Markov processes, we do not rely on intensity matrices that describe trajectories of consecutive states. Here we define regime changes as events and understand time as context of an event. This allows us to integrate dependencies at different time granularities while being able to perform inference in a decomposed way. As a consequence, we can efficiently consider higher-order effects stretching across a large number of consecutive regimes. The underlying assumption is that timely evolution of variables between regime switches is completely captured by the VAR model or possibly a set of VAR models with varying measuring rates and that there is a representative set of multiple time series exhibiting similar higher-order regime dynamics. In this paper we show how such dynamics can be learned integrative with learning RSVAR model parameters and how the regime dynamics can be considered in the RSVAR inference procedures. We demonstrate the benefits of our approach based on a simple scenario. Further, an application to a typical prognostics scenario is presented, leading to the highest score in the IEEE PHM 2014 Data Challenge for the industrial track.

Analytical Pathway Methodology: Simplifying Business Intelligence Consulting

The implementation and use of advanced analytics to identify patterns and discover the non-obvious from structured and unstructured data sources to improve business performance or establish a competitive advantage is becoming more commonplace in enterprises. Delivering complex advanced analytical systems to mine unstructured data sources requires a complex decision-making process by the business analytics user to perform an analysis. In general, analytics is a process that often times requires continual iteration of the content sources(s) to locate, examine and interpret information to address an issue or hypothesis. This problem led us to explore a method to communicate, and eventually automate, an analytical pathway to be implemented with an analytical services system. In this paper we describe some of the challenges in the use of complex advanced analytics for business intelligence, an initial breakdown of the process and an approach to bringing repeatability to the analysis process.

Survival analysis for HDLSS data with time dependent variables: Lessons from predictive maintenance at a mining service provider

In gene expression analysis it is often the goal to predict survival given a high-dimensional space of covariates. In corresponding literature models are described that deal with low sample size which is a typical feature of such studies. This is also the case in asset management services where downtime of assets is very costly and thereby replacements are scheduled long before the actual risk of failure increases. Although sometimes good surrogates of the true failure probability are available, it is in practice often the case that a number of weak predictors exist which needed to be filtered from a large set of candidates. Although the challenge is similar to gene expression analysis, a crucial difference is that covariates in condition monitoring are dynamic whereas genes are not. The result is that in gene expression analysis any data in between failure can be omitted, which leads to a potentially high bias in variable selection for condition monitoring. The authors are not aware of any survival models that deal with high dimensional low sample size (HDLSS) data in case of time-dependent covariates. In this paper we evaluate the performance of different modeling techniques in case of HDLSS survival data including the definition of a discrete time model where survival is modeled as a locally independent, binary outcome variable. We thereby study the trade-off between omitting measurements between times of failure and disregarding temporal dependencies. The analysis is based on a real life case study where 39 components of 50 mining haul trucks were monitored in operations over almost 6 years.

Optimal control of HVAC operations based on sensor data

We present a comprehensive approach for leveraging sensor networks in order to improve HVAC (Heating, Ventilation, and Air Conditioning) services in terms of occupants preferences as well as sustainability. A two-step approach is presented with a data-driven model estimation for each HVAC configuration and an optimization step taking into account dynamic trade-offs between changing preferences of occupants and energy usage with possibly time-varying penalty constants. We further enable consideration of potentially available forecasts of relevant variables such as outside temperatures. Application of suggested approach is illustrated based on a case study and benefits as well as limitations are discussed.