Convergence of orthogonal series to $+\infty$

For any sequence $\{b_n\}$ such that $\sum_{n=1}^\infty b_n^2=\infty$, a uniformly bounded system $\{\Phi_n(x)\}$, orthonormal on $[0, 1]$, is constructed such that the series $\sum_{n=1}^\infty b_n\Phi_n(x)$ diverges to $+\infty$ on some set $E\subset[0, 1]$, $0<\mathrm{mes}\, E<1$, for any order of the terms.