although the quality of the current gravitational-wave data is not very good, we believe that the gradually mounting data in the future will place tighter constraints on various kinds of cosmological scenarios. To be more precise, we use the luminosity distance $420^{+150}_{-180}$ Mpc of two supermassive black holes as a complementary probe. The corresponding $\chi^2$ for GW150914 is expressed as $\chi^2_{GW}$. Naturally, the expected $\chi^2$ of the combined constraints from the SNe Ia, OHD, CMB and GW150914 data sets can be defined as $$\tilde{\chi}^2={\chi}^2_{SN}+{\chi}^2_{OHD}+\chi^2_{CMB}++\chi^2_{GW} \label{9}.$$

![$1\sigma$, $2\sigma$, and $3\sigma$ confidence ranges for the model parameter pair ($\Omega_{m0}$, $\Omega_{r_c}$) of the DGP braneworld scenario constrained by SNe Ia+OHD+GW data sets.[]{data-label="f1"}](1.jpg)

![$1\sigma$, $2\sigma$, and $3\sigma$ confidence ranges for the model parameter pair ($\Omega_{m0}$, $\Omega_{r_c}$) of the DGP braneworld scenario constrained by SNe Ia+OHD+Planck-2015+GW data sets.[]{data-label="f2"}](2.jpg)

![Evolutionary tendency of the EoS of the DGP braneworld scenario constrained by SNe Ia+OHD+Planck+GW data sets. The long-dashed (red) line represents the EoS when we take the best-fitting values of the model parameter pair ($\Omega_{m0}$, $\Omega_{r_c}$), and the short-dashed (blue) line represents the base cosmology scenario. The yellow region corresponds to the $1\sigma$ confidence band, and the red regions reflect the parts where the $2\sigma$ confidence band 