# Input Selection Methods for Soft Sensor Design: A Survey
## 2 SS Design Stages  
SS design stages follow the typical steps of pattern recognition [50] as well as system identification theory [51]. In an industrial environment, ad-hoc experiments to collect suitable identification datasets are, in general, not possible as in the system identification practice. So, data have to be retrieved from industries historical databases. SS design steps can be summarized as follows [1]:  
1. Data collection and filtering;
2. Input variables selection;
3. Model structure choice;
4. Model identification;
5. Model validation. Each of these steps is crucial for the good success of the further one. Data is stored by industries in historical databases, generally provided from a supervisory control and data acquisition (SCADA) control system [52] or a distributed control system (DCS) [53]. Collected data must be capable of representing the whole dynamics of the system, since the model cannot provide more information than the one stored in the data itself. After data are collected, the first stage of the design regards its filtering and preprocessing [1,2]. This is due to unprocessed data from databases coming with well-known problems, such as oversampling, outliers and missing data and accuracy problems, such as offsets, seasonal effects and high-frequency noise. Therefore, the designer should carefully deal with them and prepare data to become suitable for the next designing steps [54; 55; 56]. Common preprocessing stages consist of resampling, noise filtering, outlier detection and removal and normalization. Data collected in plant databases usually come with different sample rates. Easy-to-measure variables are automatically measured with online available sensors; while hard-to-measure ones cannot be measured automatically, but more commonly only sporadically, at high cost and with high delays, such as in the case of laboratory analysis [1,57]. For this reason, the former usually present high sample rates, even higher than the one required by the sampling theorem, while the latter tend to be downsampled [58; 59]. High sample rate can lead to huge datasets that can suffer from data collinearity. Therefore, resampling becomes necessary to synchronize the variables back together [60] and to avoid dealing with huge datasets. Missing data and outliers are quite common problems in databases collected from industries. The former occur when values are missing in the observation of a variable; the latter are actually inconsistent data with the majority of the recorded ones that greatly deviate from the typical range of values, such as peaks, saturations, flat trends and discontinuities. They can both be caused by sensor or process faults and measurement noise. They are usually handled by removing the samples that contain them or by filling the missing observations with some imputing method. Outlier detection is, however, a tough task achieved through statistical techniques, such as the 3\(\sigma\)-rule, and the final validation has to be manually performed by a plant expert to avoid outlier masking (a false negative) and outlier swamping (false positive) [61]. High frequency noise is generally induced by measurement instruments and can be filtered out with low-pass filters. The appropriate bandwidth is chosen by using spectral analysis. Once data have been preprocessed, selection of input variables is one critical step in the SS designing process. The importance of this stage is addressed in the next section along with the main techniques adopted. The further step consists of the choice of the model structure, which is based on the a priori knowledge of the system. Mechanistic (or white-box) models are the ones obtained on the basis of first principles analysis, such approach requires a deep physical knowledge of the process.