A heterogeneous ensemble approach for the prediction of the remaining useful life of packaging industry machinery

Abstract

We present a method based on heterogeneous ensemble learning for the prediction of the Remaining Useful Life (RUL) of cutting tools (knives) used in the packaging industry. Ensemble diversity is achieved by training multiple prognostic models using different learning algorithms. The combination of the outcomes of the models in the ensemble is based on a weighted averaging strategy, which assigns weights proportional to the individual model performances on patterns of a validation set. The proposed heterogeneous ensemble has been applied to real condition monitoring knife data. It has provided more accurate RUL predictions compared to those of each individual base model. radation beyond which the equipment fails performing its function (failure threshold). Examples of modeling techniques used in degradationbased approaches are Auto-Regressive models (Gorjian et al., 2009), Relevance Vector Machines (Di Maio et al., 2012) and Semi-Markov Models (Cannarile et al., 2017a) (Cannarile et al., 2018). Direct RUL predictions approaches, instead, typically resort to machine learning techniques that directly map the relation between the observable parameters and the equipment RUL, without the need of predicting the equipment degradation state evolution towards a failure threshold (Schwabacher et al., 2007). Techniques used in direct RUL prediction approaches are, for example, Artifical Neural Networks (Wang & Vachtsenavos, 2001), Extreme Learning Machines (ELM) (Yang et al., 2017), Gaussian Processes (GP) (Baraldi et al., 2015b), etc. When few run-to-failure degradation trajectories are available, direct RUL approaches may overfit, i.e., these algorithms customize themselves too much to learn the relationship between the observable parameters and the corresponding RUL in the training set. Therefore, these methods tend to lose their generalization power, which leads to poor performance on new data. To overcome this, ensemble approaches, based on the aggregation of multiple model outcomes, have been introduced (Baraldi et al., 2013a). The basic idea is that the diverse models in the ensemble complement each other by leveraging their strengths and overcoming their drawbacks. Thus, the combination of the outcomes of the individual models in the ensemble improves the accuracy of the predictions compared to the performance of a single model (Brown et al., 2005) (Baraldi et al., 2013a). Different methods, such as ANN (Baraldi et al., 2013b), Support Vector Machine (SVM) (Liu et al., 2006) and kernel learning (Liu et al., 2015), have been used with success to build the individual models. For example, an ensemble of feedforward Artificial Neural Networks (ANN) has been embedded into a Particle Filter (PF) for the prediction of crack length evolution (Baraldi et al., 2013b) and an ensemble of datadriven regression models has been exploited for the RUL prediction of lithium-ion batteries (Xing et al., 2013). In (Rigamonti et al., 2017) a local ensemble of Echo State Networks (ESN) has been proposed to improve the RUL prediction accuracy of turbofan engines. The objective of this work is to predict the RUL of knives installed on Tetra Pak® A3/Flex filling machines used to cut package material. The prognostic task is complicated by the fact that few run-to-failure degradation trajectories are available, and a failure threshold is not available. To cope with these issues, this work proposes an ensemble formed by multiple datadriven direct RUL prediction models, capable of aggregating the RUL predictions for good performance throughout the entire degradation trajectory of a knife. Ensemble diversity is achieved by heterogeneous ensemble generation, i.e., by training the models using different prognostics algorithms. Aggregation is obtained by averaging the output of the individual base models with weights proportional to the inverse of their Empirical Generalization Error (EGE) on retrieved patterns in a validation set. The application of the proposed heterogeneous ensemble method to real condition monitoring knife data has shown to provide more accurate RUL prediction compared to that of each individual base learner in the ensemble. The paper is organized as follows: in Section 2, the objectives of this work and the assumptions are discussed; in Section 3, ensemble learning main concepts for data-driven direct RUL prediction are illustrated; in Section 4, performance metrics to compare different prognostic models are discussed. The application of the methodology to Tetra Pak® A3/Flex filling data is described in Section 5, whereas Section 6 draws the work conclusions. 2 ASSUMPTIONS AND OBJECTIVES We assume to have available run-to-failure degradation trajectories of N pieces of equipment similar to the one currently monitored (test equipment). Let xi(τi) ∈ R , i = 1, . . , N; τ = 1, ... , ni be the vector of m features extracted from signal measurements performed at time τi on the i equipment, with ni indicating the total number of data acquisitions performed on the i equipment before its failure. The ground truth RUL of the i piece pf equipment at time τi will be referred to as yi(τi), i = 1, ... , N; τi = 1, ... , ni . We consider a case in which the failure thresholds for the extracted features are not known. In this setting, fault prognostics is framed as a regression problem: given the historical dataset U formed by N realizations (degradation trajectories) {xi(τi), yi(τi), τi = 1, ... , ni}, i = 1, ... , N, of a stochastic process (X(τ), Y(τ)) ∈ Rx (0, +∞), our task is to find a function f: R → (0, +∞) such that it associates to a test pattern xtest(τtest) ∈ R , the corresponding output ytest(τtest). In what follows, we refer to f as base model or base learner (Zhou, 2012). 3 ENSEMBLE LEARNING FOR FAULT PROGNOSTICS In contrast to ordinary learning approaches which try to construct one base learner from training data, ensemble methods try to construct a set of learners f1̃, ... , f?̃? and combine them to obtain an ensemble learner fen?̃?. In this work, we consider combination of base learners based on weighted averaging (Zhou, 2012), i.e., the combined output fen?̃? is obtained by averaging the output of the individual learners with different weights αh, which implies that the different learners have different importance fen?̃?(x(τ)) = ∑ αh H