To　address　the　inverse　problem　of　thermal　growth　oxide　(TGO)　thickness　in　thermal　barrier　coatings　(TBCs),　a　novel　multi-scale　analysis　(MSA)　method　based　on　terahertz　time-domain　spectroscopy　(THz-TDS)　is　introduced.　The　proposed　method　involves　a　MSA　technique　based　on　four　wavelet　basis　functions　(db4,　sym3,　haar,　coif3).　Informative　feature　parameters　characterizing　the　TGO　thickness　were　extracted　by　performing　continuous　wavelet　transform　(CWT)　and　max-pooling　operations　on　representative　wavelet　coefficients.　Subsequently,　multi-linear　regression　and　machine　learning　regression　models　were　employed　to　predict　and　assess　the　wavelet　feature　parameters.　Experimental　results　revealed　a　discernible　trend　in　the　wavelet　feature　parameters　obtained　through　CWT　and　max-pooling　in　the　MSA,　wherein　the　visual　representation　of　TGO　thickness　initially　increases　and　then　gradually　decreases.　Significant　variations　in　these　feature　parameters　with　changes　in　both　thickness　and　scale　enabled　the　effective　inversion　of　TGO　thickness.　Building　upon　this,　multi-linear　regression　and　machine　learning　regression　prediction　were　performed　using　multi-scale　data　based　on　four　wavelet　basis　functions.　Partial-scale　data　were　selected　for　multi-linear　regression,　while　full-scale　data　were　selected　for　machine　learning　regression.　Both　methods　demonstrated　high　accuracy　prediction　performance.　In　particular,　the　haar　wavelet　basis　function　exhibited　excellent　predictive　performance,　as　evidenced　by　regression　coefficients　of　0.9763　and　0.9840,　further　confirming　the　validity　of　MSA.　Hence,　this　study　effectively　presents　a　feasible　method　for　the　inversion　problem　of　TGO　thickness,　and　the　analysis　confirms　the　promising　application　potential　of　terahertz　time-domain　spectroscopy’s　multi-scale　analysis　in　the　field　of　TBCs　evaluation.　These　findings　provide　valuable　insights　for　further　reference.　©　2023　by　the　authors.