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EN
Deep learning is widely used in remaining useful life (RUL) prediction because it does not require prior knowledge and has strong nonlinear fitting ability. However, most of the existing prediction methods are point prediction. In practical engineering applications, confidence interval of RUL prediction is more important for maintenance strategies. This paper proposes an interval prediction model based on Long Short-Term Memory (LSTM) and lower upper bound estimation (LUBE) for RUL prediction. First, convolutional auto-encode network is used to encode the multi-dimensional sensor data into one-dimensional features, which can well represent the main degradation trend. Then, the features are input into the prediction framework composed of LSTM and LUBE for RUL interval prediction, which effectively solves the defect that the traditional LUBE network cannot analyze the internal time dependence of time series. In the experiment section, a case study is conducted using the turbofan engine data set CMAPSS, and the advantage is validated by carrying out a comparison with other methods.
2
Content available Optymalizacja neuronowego modelu prognostycznego
PL
W pracy przedstawiono metodę prognozowania wartości symptomu w oparciu o optymalizowany neuronowy model prognostyczny. Heurystyczna optymalizacja modelu odbywała się dwoma metodami: w oparciu o ocenę błędu ex post (błąd prognozy oceniany na podstawie różnic wartości prognozowanych i pomiarów), oraz przewidywanie szerokości przedziału predykcji ex ante (w tym samym kroku czasowym, w którym budowana jest prognoza). Omawiane metody zastosowano dla danych pochodzących z młynów wentylatorowych. Ostatecznie najlepsze rezultaty uzyskano stosując średnią ważoną prognoz generowanych przez różne typy i struktury sieci. Wagi uzależnione były od błędów prognozy ex post uzyskiwanych przez daną sieć. Przy zastosowaniu wspomnianej metody udało się zapewnić średni błąd prognozy na poziomie 4,5%.
EN
The paper presents a method for prediction of symptom values based on an optimized neural predictive model. The heuristic model optimization was carried out by means of two methods: based on ex post error evaluation (the error of prediction evaluated based on the difference between the predicted and measured values), and on ex ante estimation of a prediction interval width (at the same time step, at which the prediction is made). The above methods were applied to measurement data obtained from fan mills. Finally, the best results were obtained when a weighted average of predictions generated by different types and topologies of networks was used. The weights were dependent on the ex post prediction errors obtained by the given network. With use of the method it was possible to guarantee the average error of prediction at the level of 4.5%.
3
Content available remote Prediction intervals for stationary time series using the sieve bootstrap metod
EN
We consider the problem of constructing prediction intervals for future observations of stationary time series. Our approach relies on the sieve bootstrap procedure introduced by Blihimann (1997, 1998) which is asymptotically valid for the rich class of linear stationary processes which can be inverted and represented as an autoregressive processes of order infinity (AR(oo)). We extend the results obtained earlier by Stine (1987) for autoregressive time series of known order. A more traditional Gaussian strategy is also presented. We verify accuracy of the proposed methods via numerical comparison including both Gaussian and non-Gaussian data.
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