The scaling properties of multi-unit soft sensors
Industrial processes often consist of replicated process units, such as pumps, compressors, and tanks. This is because profit margins depend on production at scale, which often requires parallel production lines. Our most recent research explores the advantages of utilizing data from multiple, similar process units when developing soft sensors. This is the first of two blog posts, where we present the highlights of this research and demonstrate its application to data-driven virtual flow metering in oil and gas.
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- Author
- Jens Nikolai Alfsen
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- · 3 min read
A soft sensor, also known as a virtual sensor, is a system used in industrial process environments to infer the value of a hard-to-measure variable. The sensor is essentially a mathematical model that takes more readily available measurements as input. The main assumptions for the input measurements are that they contain relevant information about the hard-to-measure variable and that they are more frequently available.
The motivation for developing an on-line soft sensor is typically to monitor some key performance indicator. The process can then be optimized in real time - based on the inferred values. There are two established approaches to developing a soft sensor; model-based, in which the underlying process is modeled from first-principle physics, and data-driven which has gained significant traction in recent years. Due to the typical complexity of the process and expensive maintenance of a model-based soft sensor, a data-driven approach is proposed. The main challenge, though, is that a soft sensor is most valuable in information-poor environments, where one would expect data-driven methods to perform poorly. To achieve a good predictive performance in such environments, it is imperative to be data efficient.
«The main challenge is that a soft sensor is most valuable in information-poor environments, where one would expect data-driven methods to perform poorly. To achieve a good predictive performance in such environments, it is imperative to be data efficient.»
A data-driven soft sensor is a type of soft sensor that primarily relies on data to make estimates or predictions about a process or a system. Unlike model-based soft sensors, which are built upon theoretical models and understanding of the process mechanics, data-driven soft sensors utilize statistical and machine learning methods to learn from historical data.
The proposed solution is inspired by transfer learning, the technique of taking knowledge acquired by solving a source task and utilizing it to improve generalization on a target task. Applied to the soft sensor challenge, the unidirectional transfer of knowledge is generalized to be multidirectional. Multiple soft sensors, or units, are learned simultaneously and knowledge transfer is enabled through parameter sharing.
«The soft sensor performance increases with the number of units. The convergence rate matches a theoretical estimate, and can be used to indicate when a good base model is found.»
![](https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=334&q=90&w=600&s=8fd2fbb0cf02aefd867978f42851e9bc 600w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=390&q=90&w=700&s=6fa17b52da41cbb29dadfa6f43c5441d 700w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=446&q=90&w=800&s=f7927e985de19f69cd852de6ce1f2870 800w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=501&q=90&w=900&s=25a0a29b7bea1a08cc1bcc036a9c069e 900w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=557&q=90&w=1000&s=16f17bd27ab077513827525806f7cdc8 1000w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=613&q=90&w=1100&s=f26ac07b3346efcb1c305c50cc923229 1100w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=668&q=90&w=1200&s=6722c56c87b6f23ce5ecea4f759869cf 1200w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=724&q=90&w=1300&s=7b30b0b26c6e86633096c451ef7c7fb7 1300w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=780&q=90&w=1400&s=f23f71aa91473788d7fe2ce9049d8106 1400w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=835&q=90&w=1500&s=af62f8a67878d64d6d3472732646bb63 1500w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=891&q=90&w=1600&s=8d4f75c6136e69709690122f38af4d45 1600w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=947&q=90&w=1700&s=996345ebe758813c6d78cc0505c98862 1700w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1002&q=90&w=1800&s=587a40b504f32e95c77f378e83a40b8c 1800w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1058&q=90&w=1900&s=2a80fa74c0787a6ba5ebdfb1f76d5862 1900w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1114&q=90&w=2000&s=e49afa93b3f08ac6bce2fceade015142 2000w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1169&q=90&w=2100&s=7827b4f54613424a26044c1e7430317b 2100w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1225&q=90&w=2200&s=a93e346364730b72ed109c8671410485 2200w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1281&q=90&w=2300&s=878e5b1271140b06d305e71ccb6b132a 2300w, https://solutionseeker2021.imgix.net/images/mtl_map_scaling.png?auto=compress%2Cformat&crop=focalpoint&cs=srgb&fit=crop&fp-x=0.5&fp-y=0.5&h=1337&q=90&w=2400&s=4cb595b7a5da9e51ab82a87be8eade75 2400w)
The hypothesis of increasing soft sensor performance is tested in an empirical study on the problem of Virtual Flow Metering. In the study, the average soft sensor performance is, in fact, shown to increase as expected with the number of soft sensors (M). The figure shows the empirical result against theoretical expected learning rate as a function of the number of units (M) in the dataset. Notice the diminishing returns after M ≃ 40. Also worth noticing is that for M=80, the test error is about half that of single-unit soft sensors (M=1).
In an upcoming article, we will see how this insight can be used to develop data-driven soft sensors which work using extremely little data. Read the full paper at Multi-unit soft sensing permits few-shot learning.
References
- Naiju Zhai et al. “Soft Sensor Model for Billet Temperature in Multiple Heating Furnaces Based on Transfer Learning”. en. In: IEEE Transactions on Instrumentation and Measurement 72 (2023), pp. 1–13. issn: 0018-9456, 1557-9662. doi: 10 . 1109 / TIM . 2023 . 3267520. (Visited on 08/18/2023).
- Yuxin Huang et al. “Modeling Task Relationships in Multivariate Soft Sensor With Balanced Mixture-of-Experts”. en. In: IEEE Transactions on Industrial Informatics 19.5 (May 2023), pp. 6556–6564. issn: 1551-3203, 1941-0050. doi: 10.1109/TII.2022.3202909. (Visited on 08/18/2023).
- Yu Zhang and Qiang Yang. “A Survey on Multi-Task Learning”. In: IEEE Transactions on Knowledge and Data Engineering 4347.c (2021), pp. 1–20. doi: 10.1109/TKDE.2021.3070203.
- Bjarne Grimstad et al. "Multi-unit soft sensing permits few-shot learning"