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This article uses acoustic emission (AE) analysis to diagnose an industrial-scale and slow-speed wind turbine blade bearing. The main challenge for AE analysis is that the fault signals are mingled with heavy noise. As a result, the objective of this article is to filter the raw AE signals and extract weak fault signals. To achieve this goal, a general linear and nonlinear auto-regressive (GLNAR) model is first developed to exploit the nonlinear characteristics of the AE signals. Then, the sparse augmented Lagrangian (SAL) algorithm is applied to learn the built GLNAR model and filter the raw AE signals. The characteristics of SAL is that it is a novel sparse representation technique which can convert the original filtering problem into a number of suboptimization problems, and these subproblems can be solved separately. Finally, as the blade bearing rotates at fluctuating speeds, the filtered signals are resampled so that the bearing fault type can be diagnosed in the order domain. The proposed diagnostic framework was validated in several experiments under time-varying low-speed and heavy-blade-load conditions. The results indicate that our proposed methods are effective and accurate. [ABSTRACT FROM AUTHOR]