  In view of the difficulty in calculating the atomic structure parameters of
high-$Z$ elements, the HFR (Hartree-Fock with relativistic corrections) theory
in combination with the ridge regression (RR) algorithm rather than the Cowan
code's least squares fitting (LSF) method is proposed and applied. By analyzing
the energy level structure parameters of the HFR theory and using the fitting
experimental energy level extrapolation method, some excited state energy
levels of the {Yb~I} ($Z=70$) atom including the $4f$ open shell are
calculated. The advantages of the ridge regression algorithm are demonstrated
by comparing it with Cowan's least squares results. In addition, the results
obtained by the new method are compared with the experimental results and other
theoretical results to demonstrate the reliability and accuracy of our
approach.
