In recent years, the research on the robustness of interdependent networks has attracted lots of attention. Considering a type of two-layer edge-coupled networks with edge-coupling relationships in practical networks, this paper studies the effects of network structure and load capacity model parameters on the robustness of edge-coupled networks when there is an edge failure in the network. The results show that the network structure tends to be more heterogeneous, and the system is more robust. The load capacity parameters of the directly attacked network can effectively change the percolation behaviors of the network, and the increasing of the initial capacity makes the percolation behaviors change from first-order phase transitions to hybrid-phase transitions, and then to the second-order phase transitions, but it is unable to increase the survival scale of the network under large-scale attacks and it costs too much to improve the robustness. The increasing of initial capacity parameter of the indirectly attacked network can significantly improve the robustness of the network, and is affected by the initial load distribution of the network. Further research finds that the different initial load models function leads to the different initial load distributions, which can optimize the value of the critical load capacity parameter. Finally, the capacity parameter settings for optimizing the robust performance of the coupled network under cost constraints are analyzed.