## 1 Introduction
[22] proposed a CNN-LSTM method based on PSO optimization to improve its security and stability. After an attack exists in the system, research on defenses focus on how to mitigate the impact of the attack. Ref. [23] gave an optimal attack strategy for data tampering attacks in the framework of system identification based on binary observations, and finally a compensation algorithm to defend against data tampering attacks was given and verified. For data tampering attacks in finite impulse response systems, ref. [24] implemented the optimal attack strategy and further proposed an online defense strategy from the perspective of the defender. Ref. [25] designed a robust adaptive sliding mode observer to estimate the state of the power system, utilized the attack reconstruction method to estimate the FDI attack signals, and finally proposed a reliable sliding mode control strategy to eliminate the effects of the FDI attack. For the data tampering attack, in order to achieve the optimal attack, the traditional method uses the estimation error as the index, which is based on knowing the defender's identification algorithm, but how should the attacker construct the optimization index when the attacker has no knowledge of the defender's identification algorithm? In addition, after constructing the optimization metrics, so how should the attacker solve for the optimal attack strategy? In the actual attack, the data sequences are transmitted in real time in the network channel, how should the attacker meet the real-time requirement of online attack? In this paper, under the framework of system identification with multiple binary observations, the research is carried out from the attacker's perspective to pave the way for better defense. For the construction of indicators, since the defender mainly uses the information available in the data for identification, if the data contain less information, or if the data distribution is more concentrated due to the attack, then the identification of the defender will deviate more from the true value. Therefore, this paper introduces information entropy as an index to describe the effect of the attack, and at the same time models the problem of selecting the optimal data tampering attack under the multi-binary observations as an information entropy-based optimization problem with energy constraints. Due to the complexity of multi-observations, the optimization problem is a multi-parameter optimization task, so this paper gives the solution set of the optimal attack strategy based on the PSO algorithm. In order to solve the lag problem caused by the computation of the PSO algorithm, this paper carries out real-time optimization based on the BP network, and finally verifies the conclusion through simulation. In this paper, there are different attack strategies in each communication network, the objective to be optimized is the set of optimal attack strategies, the identification algorithm of the defender is unknown for the attacker, and in addition the online attack needs to meet the real-time requirement of the attack. The contributions of this paper are as follows:  
1. For the problem of attack indicators in multi-quantified observation linear systems, if the defender identification algorithm is unknown, this paper constructs the indicators based on the average entropy and turns the optimal data tampering attack problem into an optimization problem with energy constraints. 2. For the optimization problem where the average entropy expression is multi-parameter single-objective, this paper obtains the optimal solution based on the PSO algorithm and designs the estimation method for the unknown parameters. 3.