Hierarchical model-based prognostics for Li-ion batteries


Recent global trend towards a fossil-fuel-free society has yielded the rapid soar in demand of electrically powered systems. Specifically, the demand for battery powered systems has fueled the desire to have better performing batteries with lithium-ion batteries being the most widely used. Presently, for application in unmanned vehicles, exploratory rovers, submarines among others demand a better comprehension of battery performance metrics. Case and point, battery capacity and state of charge have become increasingly vital when it comes to determining the end of discharge. As of now, several techniques have already been established for determining such parameters. Unfortunately, their prognostic capability for determining remaining battery charge is still not optimal. Therefore, there is a need to develop prognostic and health management technology for critical systems (such as Mars rovers) to successfully predict and manage the lifetime of batteries, monitor their health state in real time, evaluate the performance and predict the remaining useful life.

To this note, Luleå University of Technology researchers in Sweden: Dr. Madhav Mishra, Dr. Jesper Martinsson, and Dr. Matti Rantatalo in collaboration with Dr. Kai Goebel at NASA in the United States proposed a study whose main objective was to measure the battery discharge and predict the end of discharge considering the operating conditions for lithium ion batteries. To be precise, they purposed on employing a Bayesian Hierarchical Model (BHM)-based end of discharge prognostic for Li-ion batteries. Their work is currently published in the research journal, Reliability Engineering and System Safety.

The research technique employed entailed the utilization of two batteries with 16 discharge events with a simplified battery circuit model of the battery. Next, the research team examined the detailed discharge voltage profiles during different discharging cycles with variable load profiles. They then proceeded to demonstrate the BHM approach and group-level dependencies by utilizing more than one battery and more than one discharge cycle.

The authors observed that the BHM approach enabled inferences for both individual batteries and groups of batteries. The researchers then recorded the estimates of the hierarchical model parameters and the individual battery parameters after which their dependencies on load cycles were inferred. In addition, they noted that by using the BHM approach the predictions of end of discharge could be made accurately with a variable amount of battery data. Furthermore, this technique was seen to applicable even for new batteries without prior recorded data where the predictions were based only on the prior distributions describing the similarity within the group of batteries and their dependency on the load cycle.

In conclusion, the study presented a Bayesian hierarchical model (BHM)-based prognostics approach for Li-ion batteries, where the goal was to analyze and predict the discharge behavior of such batteries with variable load profiles and variable amounts of available discharge data. The results obtained showed that the technique could address cases with or without data. Altogether, the proposed method can capture additional relationships between parameters and use it to improve prognostics. Lastly, the BHM approach has been seen to permit inference at both the individual battery level and group of battery level.

Hierarchical model-based prognostics for Li-ion batteries - Advances in Engineering

About the author

Dr. Madhav Mishra is a senior researcher at the Division of Operation and Maintenance Engineering within the framework of the SKF-University of Technology Centre (UTC). His research focus is on prognostics and health management to improve the RUL prognosis of an asset by developing models. He obtained Master degree in Control Systems Engineering with specialisation in Mechatronics from the Netherlands.

He worked at Philips Semiconductors/NXP in Nijmegen in the Netherlands as a Senior Design Engineer Mechatronics where he has involved in design and developed of the high speed rotating machine.

About the author

Dr. Jesper Martinsson is a senior lecturer at the Division of Mathematical Science at Luleå University of Technology in Sweden. His research interests are in applied Bayesian data analysis and statistical signal processing, with applications ranging from health sciences to geophysics.

He is also a senior researcher in statistical data analysis at Luossavaara-Kiirunavaara AB (LKAB) in Sweden, where he is developing Bayesian prediction models of mining-induced seismic events

About the author

Dr. Matti Rantatalo is an associate professor at the Division of Operation, Maintenance and Acoustics at Luleå University of Technology in Sweden with a focus on simulation and measurement of vibrations for condition-based maintenance (CBM) applications. He is working as a supervisor, teacher and researcher and is responsible for coordinating the research and innovation projects at Luleå Railway Research Centre (JVTC). He is currently involved in numerous research projects on condition monitoring and predictive maintenance.

About the author

Dr. Kai Goebel works at NASA Ames Research Center where he founded the Prognostics Center of Excellence. He is the Area Lead for Discovery and Systems Health in the Intelligent Systems Division. He received a Diplom-Ingenieur degree from Technische Universitaet Muenchen in 1990 and a Ph.D. from the University of California at Berkeley in 1996. Dr. Goebel worked at General Electric’s Corporate Research Center in upstate New York where he was also an Adjunct Professor at Rensselaer Polytechnic Institute.

Kai is co-founder of a professional society (Prognostics and Health Management Society) and an associate Editor of the International Journal of PHM, and he is on the Board of Directors of several non-profit organizations. He holds eighteen patents and has published more than 300 technical papers.


Madhav Mishra, Jesper Martinsson, Matti Rantatalo, Kai Goebel. Bayesian hierarchical model-based prognostics for lithium-ion batteries. Reliability Engineering and System Safety, volume 172 (2018) page 25–35.

Go To Reliability Engineering and System Safety

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