Acoustic scene analysis (ASA) relies on the dynamic sensing and understanding of stationary and non-stationary sounds from various events, background noises and human actions with objects. However, the spatio-temporal nature of the sound signals may not be stationary, and novel events may exist that eventually deteriorate the performance of the analysis. In this study, a self-learning-based ASA for acoustic event recognition (AER) is presented to detect and incrementally learn novel acoustic events by tackling catastrophic forgetting. The proposed ASA framework comprises six elements: (1) raw acoustic signal pre-processing, (2) low-level and deep audio feature extraction, (3) acoustic novelty detection (AND), (4) acoustic signal augmentations, (5) incremental class-learning (ICL) (of the audio features of the novel events) and (6) AER. The self-learning on different types of audio features extracted from the acoustic signals of various events occurs without human supervision. For the extraction of deep audio representations, in addition to visual geometry group (VGG) and residual neural network (ResNet), time-delay neural network (TDNN) and TDNN based long short-term memory (TDNN-LSTM) networks are pre-trained using a large-scale audio dataset, Google AudioSet. The performances of ICL with AND using Mel-spectrograms, and deep features with TDNNs, VGG, and ResNet from the Mel-spectrograms are validated on benchmark audio datasets such as ESC-10, ESC-50, UrbanSound8K (US8K), and an audio dataset collected by the authors in a real domestic environment.