Quantum mechanics

Algorithm

Gaussian

Process (computing)

Statistics

Markov process

Hidden Markov model

Stochastic process

Markov chain

Operating system

Computer science

Mathematical optimization

Markov random field

Image segmentation

Mixture model

Physics

Segmentation

Mathematics

Gaussian process

Artificial intelligence

Maximization

Soft sensor

Machine learning

Accurate, real-time access to key performance indicators (KPIs) is critical to the overall performance of industrial processes. However, in many cases, it is difficult to obtain accurate and timely measurements, due to time delays or external disturbances in industrial processes. Soft sensors are one solution that can provide the necessary process information. This paper proposes a new approach for soft sensor design using Markov random fields (MRF). In which, a Gaussian mixture model (GMM) is firstly used to approximate the joint probability distribution in the soft sensor model, then the expectation maximization (EM) algorithm estimates the GMM parameters. Using this approach, a soft sensor is developed using industrial data for the alumina concentration process in the aluminum electrolysis industry, to show our proposed approach provides accurate estimation of the alumina concentration.

Development and Industrial Application of a Soft Sensor using Markov Random Fields