This paper proposes a novel framework to protect Physical Unclonable Function(PUF) against modeling attacks, denominated as Noisy PUF(NoPUF). NoPUF exploits structural unpredictability to improve overall security. We present several PUF architectures under the proposed framework to reconfigure a conventional reliable PUF to a noisy PUF. The reconfigured PUF becomes inherently unreliable and achieves a higher resistance against modeling attacks. Moreover, since only a small portion of the Challenge-Response Pairs are required for authentication, the designer can use the information obtained from the initial reliable PUF configuration to find CRPs, which are still reliable in the noisy PUF configuration for authentication.