## 1 Introduction  
The sensors are the basic instruments of the structural health monitoring system, while the measurements of sensors are the necessary information for estimating the structural safety. However, the operation duration of a sensor is limited and the sensor measurements may be abnormal because of sensor failure or environmental influences [1]. The technique for reconstructing the sensor information should be developed as a result, which can ensure saving the complete monitoring information for structural safety estimation. The monitoring information is diverse in the different measured locations and the different types of structural responses, which are correlated with each other to some extent [2]. That is to say, it is necessary to reconstruct the information for the failure sensor using the effective correlation model between the failure sensor and the other normal sensors.  
For the sensor information reconstruction, the researchers proposed several methods to solve the question. For the problem of data distortion in the structural health monitoring system of a bridge, [PERSON] [3] analyzed the relationship of the monitoring data by using Granger causality testing [4] in which the sensor data with a closer relationship is selected to be the input vector for an extreme learning machine to recover the missing sensor signal data. However, the individual prediction value could be a large error, and the training results need to be further improved because the tendency of the predicted data is not consistent with the theory value. The radial basis function (RBF) neural network model is another method to recover the unreliable data, which is also easy to fall into a local optimum [5]. The Kalman filtering method was proposed to build the model between structural displacements and structural accelerations [6], in which the structural model parameters and external excitation should be known in advance. The method of data compression sampling is used for data recovery of wireless sensors, while the recovery data error would be larger for the accelerations when the sparse of the original data becomes worse [7]. [PERSON] [8] proposed a data recovery method based on a least square support vector machine. A forecasting model based on the method is established, and signal recovery is accomplished by on-line learning diagnosis. However, this method mainly aims at the data reconstruction of the sensor within short duration, and the effect is not good for a high sampling rate and for long-term failure prediction.  
This paper, thus, focuses on the structural responses and the correlation model between the reconstructed variable and the response variable is established, which can be used for reconstructing the sensor information. In this paper, the correlation degree and the partial least square method are applied to the data reconstruction of the fault sensors. As the strain sensors are placed on the roof steel structure of Shenzhen Bay Stadium, the strain measurements represent the distributed responses of the structure and have an inherent association, which is suitable to verify the effectiveness of the proposed method in the paper as well.