Soft sensor: Cubist Regresion

Model Identification

Cubist is a rule-based model that is an extension of Quinlan’s M5 model tree. A tree is grown where the terminal leaves contain linear regression models. These models are based on the predictors used in previous splits. This soft sensor ML (version V.1.0) has the ID 0003[R]penicillinCUBIST. Its authors are Acosta-Pavas, J. C., Robles-Rodriguez, C. E., Griol, D., Daboussi, F., Aceves-Lara, C. A., & Corrales, D. C., and it is associated with the publication available at the DOI link: https://doi.org/10.1016/j.compchemeng.2024.108736 The model was created on 22-01-2024, belongs to a project described in Industrial-scale penicillin simulation, and its current status is online, meaning it is loaded and ready to generate predictions.

Model Description

The model uses a CUBIST learner and is classified as interpretable. It is implemented in R 4.3.3, and the corresponding model file is 0003_[R]_penicillin_CUBIST.rds.

The implementation relies on:

Package: Cubist
Version: 0.4.4

Model summary: The Cubist learner is an advanced version of M5 that explores nonlinear relationships in observed data

Input Time Interval:

One measurement is expected every 12 minutes.
No aggregation method is applied (set to "NaN").

Training Information

The training dataset contains 89,800 instances.

Hyperparameters used:

Minimum number of instances per leaf: 12,000
Number of committees: 1
Instance-based corrections: 3

The model was validated using 10-fold cross-validation with 3 repetitions. It was trained using experiments with the following IDs: [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 33, 34, 36, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99].

Model Inputs

The model receives a set of sensor measurements, actuator settings, and computed variables, each with defined units, expected ranges, and no feature scaling applied.

Features

Name	Type	Description	Units	Scaling	Expected Min	Expected Max
temperature	Sensor	Current temperature (T) in the bioreactor	K	none	298	308
pH	Sensor	Current pH level in the bioreactor	pH	none	5.5	7.5
dissolved_oxygen_concentration	Sensor	Dissolved oxygen (DO) concentration	mg/L	none	0	10
agitator	Actuator	Agitation speed (rpm)	rpm	none	100	1200
CO2_percent_in_off_gas	Sensor	CO₂ percentage in off-gas (CO₂,og)	%	none	0	10
oxygen_in_percent_in_off_gas	Sensor	O₂ percentage in off-gas (O₂,og)	%	none	10	21
vessel_volume	Computed variable	Total vessel volume (V)	L	none	1	1000
sugar_feed_rate	Actuator	Sugar feed rate (Fs) into the bioreactor	L/h	none	0	2