# Gaussian Processes for Signal Processing and Representation in Control Engineering
## 5 Gaussian Process Usage in Terms of Electrical Energy  
### Prediction of Battery Condition Parameters  
Other areas of interest are complex objects in terms of modeling. The exemplary problem is predicting the life parameters of batteries. This issue can be found in several papers, where authors focus on different aspects of battery condition values, but always using GP as a method of calculating these. All of the selected articles face the same problem of lithium-ion cells, which degrade in time on their own and while being used. This causes a significant decrease of total capacity and an increase of inner resistance. So it is really important to have a way to predict and simulate the state of the remaining usability of a battery, even with economics reasons. The process and description of cell degradation is very complex and depends on various variables. Classical methods are based on fitting a somewhat arbitrary parametric function to laboratory data and, on the other hand, electrochemical modelling of the physics of degradation. Alternative solutions are machine learning ones or non-parametric such as support-vector machine or GP [24; 25]. The authors of each paper benchmarked their proposal solutions on an open source data base, which belongs to NASA, of various different batteries. However, they researched dissimilar kind of problem with divergent approaches. In [24; 25; 26] the main purposes are to calculate State of Health (SoH) and prognose Remaining Useful Life (RUL) states of battery. SoH refers to reducing capacity and increasing resistance over time and RUL can be described as the time that elapses from now until the end of the total useful life. In [27], the authors aim to calculate the \"knee point\". Achieving knee point indicates that significant deterioration has occurred and the battery suddenly accelerates in ageing. At this point it is often suggested to replace cells [27]. Everyone admits that the GP fits very well in solving such a problem and is surprisingly uncommon as a used method. Moreover it has a crucial advantage over other approaches such as neural networks, because of its ability to capture model uncertainty. Methods of using GP were slightly different in each scenario. Approaches used in [24; 25] were based on simple assumption of mean value. The distinction comes with choosing the kernel function. In [25] four models were created, two based on the Matern kernel, and the other two on a linear one. Additionally two models were using gradient boosting regression (GBR) as a point of reference. Moreover, each pair uses different methods of capturing long term trends. On the other hand, in [24] the authors used different settings of covariance functions, where they use multikernel GP approach. They combine the Radial Basis Function (RBF), the Matern, Rotational Quadratic (RQ) and Exp Sine Squared (ESS) in various sets. The first set of hyperparameters is constant and then optimized over time with ML methods. GP in test produced satisfying results and compared to other data-driven approaches it offers great flexibility with a relatively high accuracy on mean capacity predictions (5% of the actual values). The conclusion of the multikernel approach was that the combination of Matern kernels (Ma1.5 + Ma2.5) gave the best results. The authors draw attention to the future use of GP in other aspects connected with battery cells as well as researching other approaches based on the GP method [24; 25]. Other methods based on GP can be seen in the approach presented in [26]. Of course, the authors solving the same problem of predicting the end of life time of the cells and SoH in general, but in a very different manner. They propose deep Gaussian Process variations, which use GP to model mapping between layers, and matrix-variate Gaussian distribution to model the correlation between nodes of a give layer [26]. That allows to estimate the capacity of the cell using partial charge-discharge time series data (voltage, current, temperature). It also eliminates the need for input feature extraction.