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Federated learning, as a new security exchange paradigm, is widely used in medical care, driverless cars, finance, and other fields. However, federated learning still faces the problem of sybil attacks common in distributed frameworks. The existing schemes mainly defend against malicious model attacks with distance comparison, neural network, and confidence vote. But they are significantly limited in dealing with collusive sybil attacks. Therefore, we propose a federated learning malicious model detection method based on feature importance (Fed-Fi). Firstly, we screen important features by feature importance reasoning method based on LRP and compare the similarity based on Hamming distance between important features. Then, we adjust model learning rate adaptively to reduce the effect of collusive sybil attacks on the global model. The experimental results indicate that it can effectively resist the attack of collusive sybils in federated learning.

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Research of mathematical model is an important work in control filed. According as the abstract concept of the Hammerstein model, this paper studies modelling method based on balance points of controlled object, taking objects of thermal control field as research background, establishes corresponding mathematical models of coordinate controlled object for boiler-turbine generator units whose boilers are respectively deployed with steam drum boiler, subcritical press once-through boiler or supercritical press once-through boiler. And the models are confirmed by some projects experiment. Mathematical analysis to a pathological mathematical model is given. A method to validate mathematical model has presented. Another method to estimate system dynamic responds with some uncertainty has proposed by design and application of an observer of coal calorific value. Its validity and practicability has been testified by project practice too.