Performance of artificial neural network models in the presence of instrumental noise and measurement errors

#The present invention relates to a method for improving prediction accuracy and generalization performance of artificial neural network models in presence of input-output data containing instrumental noise and/or measurement errors.

#Artificial neural networks (ANNs) are suitable for modeling complex multiple input-multiple output nonlinear processes owing to their ability of approximating nonlinear relationships to an arbitrary degree of accuracy (Poggio, T. and Girosi, F. Regularization algorithms for learning that are equivalent to multilayer networks. Science, 247, 978, 1990). As a result, ANNs have been extensively used in industries for making on-line and off-line predictions of process variables. The industrial applications of ANNs include process identification, steady-state and dynamic process modeling, fault detection and diagnosis, soft-sensor development, and nonlinear process control and monitoring. These ANN applications have been comprehensively reviewed by Tambe and co-authors (Tambe, S. S., Kulkarni, B. D., Deshpande, P. B. Elements of Artificial Neural Networks with Selected Applications in Chemical Engineering, and Chemical & Biological Sciences, Simulation & Advanced Controls Inc.: Louisville, USA, 1996). During any process operation, huge amounts of process input-output data are generated, which can be used to develop ANN models that can predict in advance the values of process output variables. The desirable characteristics of an ANN model are: (i) it should accurately predict the outputs contained in the input-output example dataset used for its construction, and (ii) it possesses good generalization capability. Conventionally, ANN models are trained using a suitable weight-adjustment algorithm that minimizes a pre-specified cost (error) function. It may be noted that the form of the cost function completely determines the stochastic properties (noise sensitivity) of the resulting ANN model. For instance, most widely used error-back-propagation (EBP) (Rumelhart, D., Hinton, G., Williams, R., Learning representations by backpropagating errors. Nature, 323,533,1986) algorithm performs minimization of the root-mean-squared-error (RMSE) function. In any large set of process data, presence of instrumental noise and/or measurement errors is imminent. The presence of noise and/or errors in the input-output data used for network training creates a threshold limit for the accuracy of model predictions and the generalization performance exhibited by the model. This happens mainly because the network tries to approximate (learn) the average relationship existing between the input and the output data containing noise and/or errors. Since the network ignores the noise and errors in the data, the average relationship captured by it is fraught with inaccuracies. The inaccuracies in the prediction, if they are significant, cannot be tolerated since a significant number of control and policy decisions regarding the process operation are based on the predictions made by the model. For example, in polymerisation reactors, prediction of quality variables, such as melt flow index (MFI), stress exponent (Sex), etc., are important in deciding the grade of the polymer produced. An ANN model capable of generalization not only accurately predicts the outputs in the data (example set) used for its development, but also those corresponding to a new or novel input data. Thus, it is critically important that an ANN model possesses not only excellent prediction accuracy, but also a good generalization property.

#It has been observed by Gorp and coworkers (Gorp, J. V., Schoukens, J., Pintelon, R., Learning neural networks with noisy inputs using the errors-in-variables approach, Transactions on Neural Networks A. 180, 1-14, 1999) that in commercial software, most of the ANN models are trained using a simple output error (OE) cost function and this can lead to severe biased errors in the network predicted output when input data are noisy. The authors show that presence of noise actually suppresses the higher order derivatives of ANN model's transfer function and a bias is introduced if the conventional least-squares cost functions are employed. Accordingly, a method for improving ANN's generalization performance recommends replacement of the RMSE cost function with a novel cost function, for instance, the Errors-In-Variables (EIV) cost function (Gorp, J. V., Schoukens, J., Pintelon, R., Learning neural networks with noisy inputs using the errors-in-variables approach, Transactions on Neural Networks A. 180, 1-14, 1999). The drawback of the EIV method is that its implementation requires the knowledge of variances pertaining to the inputs and outputs. In many practical settings, this information is not available, thus severely limiting the utility of the EIV method. The methodology, though works better for the noisy measurements, it also requires large memory and can be caught into a local minimum. Alternative methodologies, such as: (i) using EIV method as a post-processing tool after application the OE method, (ii) usage of the measured input and output values instead of the estimated values, and (iii) modified learning and optimization schemes, are variedly proposed and illustrated (Gorp, J. V., Schoukens, J., Pintelon, R., The errors in variables cost function for learning neural networks with noisy inputs, Intelligent Engineering Systems Through Artificial Neural Networks, 8, 141-146, 1998).

#FIG. 1: represents a schematic of a typical Feed-forward neural network such as the Multilayer Perceptron (MLP).

#FIG. 2: represents the flow-chart detailing steps in the invention.

#Accordingly, the present invention, provides a method for improving the prediction accuracy and generalization performance of nonlinear artificial neural network models when the input-output data, known as the example set, available for constructing the network model, comprises instrumental noise and/or measurement errors, said method comprising the steps of:

#(a) generating noise-superimposed enlarged input-output sample data set using computer simulations;

#(b) generating for each input-output pattern in the example set, M number of noise-superimposed sample input-output patterns (vectors) using computer simulations;