# Soft Sensor Transferability: A Survey
###### Abstract  
Soft Sensors (SSs) are inferential dynamical models employed in industries to perform prediction of process hard-to-measure variables based on their relation with easily accessible ones. They allow implementation of real-time control and monitoring of the plants and present other advantages in terms of costs and efforts. Given the complexity of industrial processes, these models are generally designed with data-driven black-box machine learning (ML) techniques. ML methods work well only if the data on which the prediction is performed share the same distribution with the one on which the model was trained. This is not always possible, since plants can often show new working conditions. Even similar plants show different data distributions, making SSs not scalable between them. Models should then be created from scratch with highly time-consuming procedures. Transfer Learning (TL) is a field of ML that re-uses the knowledge from one task to learn a new different, but related, one. TL techniques are mainly used for classification tasks. Only recently TL techniques have been adopted in the SS field. The proposed survey reports the state of the art of TL techniques for nonlinear dynamical SSs design. Methods and applications are discussed and the new directions of this research field are depicted.  
soft sensor; inferential model; dynamical model; process system monitoring; system identification; machine learning; transfer learning. +
Footnote †: 2021: 11, 7710. [[https://doi.org/10.3390/app1167710](https://doi.org/10.3390/app1167710)]([https://doi.org/10.3390/app1167710](https://doi.org/10.3390/app1167710))  
a new model from scratch, requiring large amounts of computational power and large datasets. Moreover, either in presence of new working conditions or when new processes are considered, the number of available data is too low to design a new model [8].  
Nowadays, the gaps between domains and distributions of data and changes in the processes are the main obstacles of ML techniques for SS modelling for complex industrial processes.  
The reported issues can be mitigated by Transfer Learning (TL), a set of approaches, increasingly popular in the ML field, which take advantage of the knowledge already acquired by a model on a source task to transfer it to a target task [9]. TL would allow reduction in the amount and quality of data needed by transferring knowledge among tasks. TL can also be used to approach model scalability from a process to a similar one [10; 11].  
TL has increasingly gained attention since the issue of inconsistency of data distribution is a common barrier in many general ML applications. TL was then been applied to different fields, as reviewed by different publications, such as in medical imaging [12], email spam [13] and speech recognition [14]. On the other side, in the industrial automation field, it still is a new research topic. Most of the studies focus on classification problems, anomaly detection, fault diagnosis and quality monitoring [15]. Only in the last two years have applications of TL methods for SSs design appeared in the literature.  
This survey covers the recent developments of TL techniques to nonlinear dynamical SSs design. Methods and applications reported in the recent literature are discussed along with the description of the future trends in the field.  
The remaining of the paper is organized as follows: firstly, a brief description of SSs and their design procedure is given in Section 2 to explain the need of TL; the main TL methodologies are then introduced in Section 3; in Section 4 current applications of TL methods for SSs are examined and classified. Final discussions and future trends are drawn in Section 5.