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• VEW-MWPLS is proposed to enhance the prediction performance of NOx emission. • With adjustable forgetting factor, VEW-MWPLS can change modeling data window. • An efficient updated scheme with detailed derivations is provided. • Computational efficiency of VEW-MWPLS and past methods are analyzed and compared. The efficiency of selective catalytic reduction denitrification heavily depends on the amount of ammonia injection, which is determined by the emission of nitrogen oxides (NOx) in flue gas. To accurately predict NOx emission of the coal-fired boiler with strong variable correlations, nonlinear and time-varying characteristics for determining the amount of injected ammonia, a soft sensor modeling method based on the moving window partial least squares (MWPLS) and locally weighted regression, referred to as variable exponentially weighted MWPLS (VEW-MWPLS), is proposed. It adjusts the window size in disguised form by automatically strengthen or weaken the information in the selected window according to the prediction errors of the current model. In this work, with the added new sample and the removed old sample, a series of rank-1 modification formulations are used to calculate both, the means and standard deviations among the input and output variables and the covariance and cross-covariance matrices so that a quick and adaptive update can be done for the PLS model. The numerical results have demonstrated that VEW-MWPLS algorithm can reduce the mean and standard deviation of prediction errors by one order of magnitude, and reduce the computational complexity by two orders of magnitude when being compared with other algorithms. Thus the proposed VEW-MWPLS is more suitable for predicting NOx emission online. [ABSTRACT FROM AUTHOR]