Verification and validation of neural networks for safety-critical applications

Onboard nonlinear models are a key enabling technology for virtual sensors, model-based control, reconfigurable control and model-based diagnostic algorithms. Before such models can be used in safety-critical applications, such as civilian aircraft, they must undergo extensive testing to verify that there is no combination of inputs that will generate an undesirable output. This paper presents analysis techniques that can be used as part of a verification procedure for polynomial neural networks (PNNs) that are trained to replace lookup tables in a variety of safety-critical control applications. The technique builds on previous research that uses Lipschitz constants to provide guaranteed bounds on network output and error for all possible inputs without having to test the network at all possible input combinations. The focus of the work presented here is on static, feedforward, multilayer networks, with polynomial basis functions. The methods described form the basis of a software tool, which is in the process of being qualified by the FAA for use in verifying neural networks for safety-critical flight control applications.