Recent advances in Artificial Intelligence raise interest in its participation in design activity, which is commonly considered to be complex and human-dominated. In this work, we aim to examine AI roles in early design stages. The human ideation components and design tools related to AI are discussed in a framework of AI-augmented design support. The framework develops a hierarchy of design cognition (basis), approaches and principles. The cognitive models are constructed in an empirical study of 30 designers (26 for analysis, 4 for pilot study) by concurrent Think-Aloud protocol and behavior analysis. The process of producing new design ideas is explained by a transparent analysis of designers' language and behaviors. Three strategies to organize cognitive activities in design ideation are summarized: develop structured consideration, relate to a scenario, and stick-to designing. These strategies suggest AI could act as (1) representation creation, (2) empathy trigger and (3) engagement, in principles of knowledge-driven and decompose-and-integrate. The design support with AI provides new perspectives on computer-based design tools that limit to well-defined design variables. The framework is built on a generic notion of design activity and mimic human design rationales, expected to benefit research of domain-independent computational design supports and cognitive supports.