# hLSTM-Aging: A Hybrid LSTM Model for Software Aging Forecast
## 2 Related Works  
A diverse range of machine learning models has been developed to forecast error propagation and detect potential software failures before they happen in the field of software aging. In this section, we present some research findings in this area, as well as those demonstrating ways to predict time series in other fields that might be applicable to computer system aging forecasting. [PERSON] et al. [11] proposed a way of interpreting Just-in-Time software defect prediction using the random forest classifier as the base for a defect forecasting model as a solution to software aging problems. Compared to random prediction, their method increased accuracy by 36.8% on average. An investigation by [PERSON] and [PERSON] [12] aimed to build machine learning classifiers that could predict defects in NASA datasets with imbalance. The authors' results suggest that machine learning classifiers by themselves cannot predict effectively. However, by applying oversampling methods, they can improve predictions. Using the ARIMA model to predict Eucalyptus Cloud resource consumption, [PERSON] et al. [13] showed the utility of probabilistic methods to the prediction of software aging. Using a machine learning model called Error Rate Reduction Pruning (ERP), [PERSON] et al. [14] constructed a framework for predicting the average failure rate of virtual machines in different cloud regions. [PERSON] et al. [15] used LSTM to predict software aging on Android systems in 2018. The authors evaluated performance using traditional metrics such as MAPE and MSE and found that LSTM had superior performance to other deep learning algorithms. [PERSON] et al. [6] investigated the aging of cloud computing software using a hybrid ARIMA and LSTM method. The results obtained by their method were better than those of individual methods. Unfortunately, there is little information on why ARIMA and the Vanilla-LSTM model are effective for the hybrid algorithm. There are many different probabilistic methods and LSTM networks available in the current state of the art, and it would be helpful to have a better understanding of which ones are the most effective. We discuss related studies on other subjects related to this research and indicate a number of techniques suitable to be implemented for data forecasting of software aging problems in the following paragraphs. [PERSON] et al. [16] employed a hybrid method of the ARIMA algorithm and the BI-LSTM neural network to predict the early stabilization time of electrolytic capacitors. This work indicatesthat probabilistic models such as ARIMA can handle the linear parts of a time series, while the BI-LSTM is better for extracting the non-linear features. As for the analysis of the fundamentals of software aging, [PERSON] et al. [1] demonstrated that the accumulation of internal errors in cloud software should lead to software aging problems and very likely an eventual software crash. Energy efficiency and carbon dioxide emission reduction can be interpreted as time series, and [PERSON] et al. [17] proposed using auto-regressive models (AR) to analyze this type of data and were able to identify very important factors in reducing carbon dioxide emissions, such as energy efficiency. The moving average model (MA), employed by [PERSON] et al. [18] for accurate projection of the number of guests quarterly for one year in the future, allows sufficient preparation time for all parties engaged in the tourist sector. Other auto-regression models are also used for time-series analysis, such as the auto-regressive moving average (ARMA) used by [PERSON] et al. [19] to model the electricity demand loads in Greece--the model developed can be used to successfully predict the price of electricity--and the auto-regressive integrated moving average (ARIMA) used by [PERSON] et al. [8] to predict sugarcane production in India. Studies indicated that between 2015 and 2017 sugarcane production would have an average growth rate of approximately 3% per year.