This paper presents an anomaly-based methodology for reliable detection of integrity attacks in cyber-physical critical infrastructures. Such malicious events compromise the smooth operation of the infrastructure while the attacker is able to exploit the respective resources according to his/her purposes. Even though the operator may not understand the attack, since the overall system appears to remain in a steady state, the consequences may be of catastrophic nature with a huge negative impact. Here, we apply a computational intelligent technique which incorporates the merits of two of the heterogeneous modeling approaches (linear time-invariant and neural networks), while considering both temporal and functional dependencies existing among the elements of an infrastructure. The experimental platform includes a power grid simulator of the IEEE 30 bus model and a cyber network emulator. Subsequently, we implemented a wide range of integrity attacks (replay, ramp, pulse, scaling, and random) with different intensity levels. A thorough evaluation procedure is carried out while the results demonstrate the ability of the proposed method to produce a desired result in terms of false positive rate, false negative rate, and detection delay.