Barkhausen　noise　(BN)　is　electromagnetic　pulse　sequence　that　could　be　used　to　nondestructively　predict　the　properties　of　materials　such　as　hardness,　residual　stress　and　carbon　content.　Current　BN　signal　analysis　methods　fail　to　describe　the　highly　variated　BN　signal　and　achieve　high　regression　accuracy　due　to　the　low　interpretability　of　neural　network　and　limited　capacity　of　mathematical　regression　tools.　In　this　paper,　two　multi-variable　regression　tools,　named　partial　Chebyshev　polynomial　regression　(PCPR)　and　Mutual　Information-based　Feature　Selection　with　Class-dependent　Redundancy　and　multi-variable　Chebyshev　polynomials　regression　(MIFS-CR+MCPR),　are　employed　for　the　first　time　to　predict　the　hardness　of　Cr12MoV　steel　(i.e.　X12m).　Combined　with　Chebyshev　polynomials,　ourregression　tools　are　designed　on　the　basis　of　cascaded　regression　and　mutual-information-based　feature　selection.　As　represented　by　the　experimental　results　for　predicting　the　hardness　of　X12m,　theproposed　method　outperforms　other　comparative　methods　including　neural　network　and　partial　linear　square　regression　method.　©　2020　The　authors　and　IOS　Press.