Unless the noise is directly related to the connected load, I’m not sure there is much you can do about the sound, as this is usually the result of a physical change in the transformer as it ages.
A transformer is magnetically excited by an alternating voltage and current so that it becomes extended and contracted twice during a full cycle of magnetization. This change in dimension is independent of the direction of magnetic flux, occurring at twice the line frequency.
Over time, the transformer core adhesive starts to break apart and the laminated layers separate from each other slightly. The vibration of these layers is the humming noise you can hear and once the adhesive starts to break, the sound gets louder.
Sweep Frequency Response Analysis (SFRA) is a method to evaluate the mechanical integrity of core, windings and clamping structures within power transformers by measuring their electrical transfer functions over a wide frequency range.
If the noise is related to the core, it would probably need to be re-laminated. The SFRA test would provide a good visual indication. It is best performed during acceptance as a baseline and then used as a comparison for future tests.
Excessive magnetostriction can lead to mechanical stress and potential damage to the transformer. The load should also be investigated as it could have an effect over time.
You may find this article about Transformer Noise helpful:
