Abstract: Acoustic anomaly detection (AAD) identifies anomalies by analyzing the normal patterns of acoustic signals. Most existing mainstream AAD models extract Mel features based on (integer-order) Fourier transform (FT), achieving excellent performance with uniform sampling. However, in reality, uniform sampling is often difficult to guarantee, resulting in non-uniform of the obtained signals. Although non-uniform FT (NUFT) can directly analyze non-uniform (sampling) signals, it is limited by integer order and can only extract frequency domain representations, missing temporal information. The fractional FT (FrFT) can project uniform signals to any angle in the fractional domain on the time-frequency plane through the fractional order parameter α, compensating for the shortcomings of FT. However, the value of α usually relies on manual tuning, leading to suboptimal performance and lack of flexibility. To overcome these limitations, and considering the maturity and effectiveness of Mel feature application in mainstream AAD models, a non-uniform FrFT (NUFrFT) Mel feature extraction algorithm that can be used as an independent module for plug-and-play is proposed. The fractional order parameter is jointly optimized with the AAD model to achieve adaptive optimization. Experimental results show that on the non-uniformized ICBHI2017 and ToyADMOS datasets, embedding the algorithm module proposed into existing AAD models obviously improves performance metrics such as accuracy and area under curve (AUC). Another analysis shows that the adaptively optimized fractional order parameters not only ensure consistency in time-frequency preference selection with the characteristics of each dataset, but also enhance the interpretability of the AAD model at the feature level.