The increase in the market for supersized LNG (liquefied natural gas) vessels, with double wall cargo tanks, has led to concerns regarding their safe operation. If both the primary and secondary wall of the cargo tank fail simultaneously, the hull of the vessel can be exposed to the LNG. This has the potential to cause brittle failure of the hull structure. This study presents a new acoustic emission (AE) technique approach that can be implemented for monitoring the structural condition of the cargo containment. The new technique approach is based on a feature of the AE waveform, calculated using quadratic Renyi’s entropy. The presented technique is capable of providing information regarding critical damage so that appropriate maintenance can be carried out to avoid failure. The new AE technique is based on an AE feature that is independent of acquisition settings (e.g., threshold and timing), unlike many traditional AE features. The effectiveness of the proposed feature was evaluated by comparison with traditional AE features under ideal conditions for a range of varying acquisition settings. Unlike the traditional feature, the new feature demonstrated no variance with variation of the acquisition settings and was effective in capturing the collective information in the waveform. The proposed AE feature was validated through tensile and fatigue testing on standard specimens of austenitic stainless steel (material of the primary wall). The results suggest that the proposed AE feature is sensitive in identifying the critical damages irrespective of some data acquisition settings.