Ensemble of Data-Driven Prognostic Algorithms with Weight Optimization and K-Fold Cross Validation



Chao Hu Byeng D. Youn Pingfeng Wang


The traditional data-driven prognostic approach is to construct multiple candidate algorithms using a training data set, evaluate their respective performance using a testing data set, and select the one with the best performance while discarding all the others. This approach has three shortcomings: (i) the selected standalone algorithm may not be robust, i.e., it may be less accurate when the real data acquired after the deployment differs from the testing data; (ii) it wastes the resources for constructing the algorithms that are discarded in the deployment; (iii) it requires the testing data in addition to the training data, which increases the overall expenses for the algorithm selection. To overcome these drawbacks, this paper proposes an ensemble data-driven prognostic approach which combines multiple member algorithms with a weighted- sum formulation. Three weighting schemes, namely, the accuracy-based weighting, diversity-based weighting and optimization-based weighting, are proposed to determine the weights of member algorithms for data-driven prognostics. The k-fold cross validation (CV) is employed to estimate the prediction error required by the weighting schemes. Two case studies were employed to demonstrate the effectiveness of the proposed prognostic approach. The results suggest that the ensemble approach with any weighting scheme gives more accurate RUL predictions compared to any sole algorithm and that the optimization-based weighting scheme gives the best overall performance among the three weighting schemes.

How to Cite

Hu, C. ., D. Youn, B., & Wang, P. . (2010). Ensemble of Data-Driven Prognostic Algorithms with Weight Optimization and K-Fold Cross Validation. Annual Conference of the PHM Society, 2(1). https://doi.org/10.36001/phmconf.2010.v2i1.1860
Abstract 149 | PDF Downloads 164



Ensemble, K-fold cross validation, Weighting schemes, Data-driven prognostics, RUL prediction

Dekker, R. (1996). Applications of maintenance optimization models: a review and analysis, Reliability Engineering and System Safety, vol. 51, no. 3, pp. 229–240.

Luo, J., Pattipati, K.R., Qiao, L. & Chigusa, S. (2008). Model-based prognostic techniques applied to a suspension system, IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 38, no. 5, pp. 1156–1168.

Gebraeel, N. & Pan, J. (2008). Prognostic degradation models for computing and updating residual life distributions in a time-varying environment, IEEE Transactions on Reliability, vol. 57, no. 4, pp. 539– 550.

Gebraeel, N., Elwany, A. & Pan J. (2009). Residual life predictions in the absence of prior degradation knowledge, IEEE Transactions on Reliability, vol. 58, no. 1, pp. 106–117.

Schwabacher, M. (2005). A survey of data-driven prognostics, Proceedings of AIAA Infotech@Aerospace Conference, Arlington, VA.

Wang, T., Yu, J., Siegel, D. & Lee, J. (2008). A similarity-based prognostics approach for remaining useful life estimation of engineered systems, IEEE, International Conference on Prognostics and Health Management, Denver, CO, Oct 6-9.

Zio, E. & Di Maio, F. (2010). A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear power plant, Reliability Engineering and System Safety, vol. 95, no. 1, pp. 49–57.

Coble, J.B. & Hines, J.W. (2008). Prognostic algorithm categorization with PHM challenge application, IEEE, International Conference on Prognostics and Health Management, Denver, CO, Oct 6-9.

Heimes, F.O. (2008) Recurrent neural networks for remaining useful life estimation, IEEE, International Conference on Prognostics and Health Management, Denver, CO, Oct 6-9.

Kozlowski, J.D., Watson, M.J., Byington, C.S., Gargam A.K. & Hay, T.A. (2001). Electrochemical cell diagnostics using online impedance measurement, state estimation and data fusion techniques, Proceedings of 36th Intersociety Energy Conversion Engineering Conference, Savannah, Georgia.

Goebel, K., Eklund, N. & Bonanni, P. (2006). Fusing Competing Prediction Algorithms for Prognostics, Proceedings of 2006 IEEE Aerospace Conference, New York.

Saha, B., Goebel, K., Poll, S. & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a Bayesian framework, IEEE Transaction on Instrumentation and Measurement,vol. 58, no. 2, pp. 291–296.

Perrone, M.P., and Cooper, L.N. (1993). When networks disagree: ensemble methods for hybrid neural networks, Neural Networks for Speech and Image Processing. R.J. Mammone, ed., Chapman- Hall, 1993.

Bishop, C.M. (2005). Neural networks for pattern recognition. Oxford University Press.

Goel, T., Haftka, R.T., Shyy, W. & Queipo, N.V. (2007). Ensemble of surrogates, Structural and Multidisciplinary Optimization, vol. 33, no. 3, pp. 199–216.

Acar, E. & Rais-Rohani, M. (2009). Ensemble of metamodels with optimized weight factors, Structural and Multidisciplinary Optimization, vol. 37, no. 3, pp. 279–294.

Hu, J., Y ang, Y .D. & Kihara, D. (2006). EMD: an ensemble algorithm for discovering regulatory motifs in DNA sequences, BMC bioinformatics, vol. 7, no. 342.

Chen, S., Wang, W. & Zuylen, H. (2009). Construct support vector machine ensemble to detect traffic incident, Expert Systems with Applications, vol. 36, no. 8, pp. 10976–10986.

Evensen, G. (2003). The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynamics, vol. 53, no. 4, pp. 343–367.

Kohavi, R. (1995). A study of cross-validation and bootstrap for accuracy estimation and model selection, Proceedings of the International Joint Conference on Artificial Intelligence - IJCAI'95'.

Tipping, M.E. (2001). Sparse Bayesian learning and the relevance vector machine, Journal of Machine Learning Research, vol. 1, p211–244.

Smola, A.J. & Schölkopf, B. (2004). A tutorial on support vector regression, Statistics and Computing, vol. 14, no. 3, pp. 199–222.

Cernansky, M., Makula, M. & Cernansky, L., (2007). Organization of the state space of a simple recurrent network before and after training on recursive linguistic structures, Neural
Networks, vol. 20, no. 2, pp. 236–244.

Saxena, A. & Goebel, K. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation, IEEE, International Conference on Prognostics and Health Management, Denver, CO, Oct 6-9.

Leibfried, T. (1998). Online monitors keep transformers in service, IEEE. Computer Applications in Power, vol. 11, no. 3, pp. 36–42.

Rivera, H.L., Garcia-Souto, J.A. & Sanz, J. (2000)Measurements of mechanical vibrations at magnetic cores of power transformers with fiber-optic interferometric intrinsic sensor, IEEE Journal on Selected Topics in Quantum Electronics, vol. 6, no. 5, p788–797.

Xu, H. & Rahman, S. (2005). Decomposition methods for structural reliability analysis, Probabilistic Engineering Mechanics, vol. 20, no. 3, pp. 239–250.
Technical Research Papers

Most read articles by the same author(s)