Recent studies have demonstrated the feasibility of predicting open-hole triple combo data from cased-hole pulsed neutron data using neural networks. For a single network realization, it is desirable to select methodically an individual model, developed from a training well or wells, that furnishes the best predictions of new data from application wells. However, the robustness of a single model may be a problem because of the limited availability and diversity of the training well data. A possible solution is to use neural network ensembles (NNE) to reduce the risk of inadvertently applying a single neural network (NN) that is rendered statistically inferior as a result of early termination of the training, lack of generalization, and other uncertainties associated with network configuration and data partitioning.
One open question in NNE studies is how to construct or select member networks. Pre-existing methods have shown significant limitations in their compatibility with conventional training software and in their credibility in processing well logging data. This paper presents a new method that allows the use of conventional algorithms to generate a number of individual NNs from the training well(s), followed by ensemble selection utilizing a novel multi-objective genetic algorithm (MOGA). The multi-objective function (MOF) is formulated as a weighted sum of the prediction error on the ensemble validation data, the ensemble complexity, and the negative correlation of the member networks. The weighting coefficients of the MOF can be either pre-selected according to the nature of the training well data or can be automatically determined if the data from an additional test well are available and if high computational overhead of the automatic selection process is not an issue.
Implementation of the proposed method and testing the results with different data partitions and MOF weighting factors are discussed through case studies. Compared with single NN realizations and random NNE generation, the MOGA-selected neural-network ensembles are more robust in producing accurate open-hole triple-combo logs using acquired cased-hole pulsed neutron inputs. The method developed from this study and the principles in selecting MOF coefficients could be extended to many other applications.