For a square matrix \( M \), its energy \( E(M) \) is the sum of its singular values.Let \( {\cal H} \) be a \( k \)-uniform hypergraph, and let \( B({\cal H}) \) be the incidence matrix of \( {\cal H} \).The incidence energy \( BE({\cal H}) \) of \( {\cal H} \) is the energy of \( B({\cal H}) \).

Let \( {\cal T}{ _{n,d}} \) be the set of \( k \)-uniform hypertrees of order \( n \) and size \( r \) with diameter \( 3 \le d \le r -1 \).In this article, the \( k \)-uniform hypertrees with minimum incidence energy over \( {\cal T}{ _{n,d}} \) are characterized.In addition, we have obtained the incidence energy of a hyperstar,and determined which hyperstar has the maximum and minimum incidence energy among all hyperstars with \( n \) vertices.