Abstract
This study presents the development of soft sensors based on just-in-time learning (JITL) and dynamic time warping (DTW) for online quality prediction in multi-grade processes. Most industrial chemical processes are multi-grade processes that produce multiple products with distinct properties. Multi-grade processes, however, are difficult to monitor and control due to frequent process transitions and abrupt changes in operating conditions. The DTW-based JITL soft sensor modeling approach is proposed as a solution to the complexity of multi-grade process modeling. In the JITL modeling approach, a local model is trained online using historical samples that are similar to the query sample, allowing the model to account for multi-grade characteristics and process drifts. To account for process dynamics and temporal correlations, the suggested approach utilizes a data sequence as an input rather than a single data point. DTW calculates the similarity of data sequences by stretching the sequences to determine an optimal warping path. Additionally, sensitivity analyses of model hyperparameters are performed and a cross-correlation-based hyperparameter optimization approach is proposed. The advantages of the proposed approach are verified via multi-grade simulation studies. As a result, the proposed model outperforms a conventional JITL model based on the Euclidean distance.
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Abbreviations
- CA0 :
-
concentration of A in the feed stream into the first reactor [mol l−1]
- CAi :
-
concentration of A in the i-th reactor (i= 1, 2, 3) [mol l−1]
- C p :
-
heat capacity of the reaction mixture [cal g−1 K−1]
- C pc :
-
heat capacity of the coolant [cal g−1 K−1]
- DTW:
-
distance calculated by dynamic time warping
- ED:
-
euclidean distance
- E/R:
-
fraction of the activation energy divided by the gas constant [K]
- hA:
-
product of the heat transfer coefficient and heat transfer area [cal min−1 K−1]
- k0 :
-
pre-exponential factor [min−1]
- KLD:
-
Kullback-Leibler divergence
- MD:
-
mahalanobis distance
- qc :
-
flowrate of coolant for the second and third reactor [l min−1]
- qi :
-
flowrate of feed stream into the i-th reactor (i=1, 2, 3) [l min−1]
- qin :
-
flowrate of coolant for the first reactor [l min−1]
- T0 :
-
temperature of the feed stream into the first reactor [K]
- Tc :
-
temperature of coolant [K]
- Ti :
-
temperature of the i-th reactor (i= 1, 2, 3) [K]
- Vi :
-
volume of the i-th reactor (i=1, 2, 3) [l]
- ΔH:
-
heat of reaction [cal mol−1]
- ρ :
-
density of the reaction mixture [g l−1]
- ρ c :
-
density of coolant [g l−1]
- ANN:
-
artificial neural network
- CSTR:
-
continuous stirred tank reactor
- DTW:
-
dynamic time warping
- GPR:
-
Gaussian process regression
- JITL:
-
just-in-time learning
- LSTM:
-
long short-term memory network
- MAPE:
-
mean absolute percentage error
- PCA:
-
principal component analysis
- PLS:
-
partial least squares
- RMSE:
-
root mean squared error
- SVM:
-
support vector machine
- TIC:
-
Theil’s inequality coefficient
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Song, M.J., Ju, S.H. & Lee, J.M. Soft sensor development based on just-in-time learning and dynamic time warping for multi-grade processes. Korean J. Chem. Eng. 40, 1023–1036 (2023). https://doi.org/10.1007/s11814-022-1335-5
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DOI: https://doi.org/10.1007/s11814-022-1335-5