# Hybrid multiscale forecasting of SRU sulfur gas concentrations using VMD CEEMDAN and optimized PatchTST

## TL;DR

This paper introduces a new forecasting method for sulfur gas concentrations in SRUs, combining advanced decomposition and optimization techniques to improve accuracy and stability.

## Contribution

A novel hybrid framework using VMD-CEEMDAN, PatchTST-PSA, and PIMO for multi-scale forecasting of SRU gas concentrations.

## Key findings

- The framework outperforms six baseline models in RMSE, MAE, MAPE, and R2 metrics.
- Dual-stage VMD-CEEMDAN effectively separates trends and high-frequency disturbances.
- PIMO optimization enhances model accuracy and stability.

## Abstract

The sulfur recovery process in SRUs is highly nonlinear and non-stationary, making accurate forecasting of H2S and SO2 concentrations challenging yet crucial for efficient, low-carbon operation. Many existing models fail to handle multi-scale fluctuations, high-frequency noise, and complex variable couplings, limiting their accuracy. This study presents a multi-scale framework combining variational mode decomposition (VMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), an enhanced patch time-series transformer with ProbSparse attention (PatchTST-PSA), and projection iterative modeling optimization (PIMO). VMD decomposes the concentration series into intrinsic mode functions, and CEEMDAN suppresses noise while preserving dynamics. PatchTST-PSA captures nonlinear variable interactions, while PIMO optimizes hyperparameters. Experiments on SRU data from an Italian refinery demonstrate that the framework provides improved results in RMSE, MAE, MAPE, and R2 compared to six baseline models, highlighting its robustness and industrial relevance.

•Dual-stage VMD-CEEMDAN separates trend and high-frequency disturbances•Sample-entropy-guided reconstruction reduces noise and dimensional redundancy•Probabilistic sparse attention in PatchTST retains key long-range dependencies•PIMO jointly tunes hyperparameters, improving accuracy and stability

Dual-stage VMD-CEEMDAN separates trend and high-frequency disturbances

Sample-entropy-guided reconstruction reduces noise and dimensional redundancy

Probabilistic sparse attention in PatchTST retains key long-range dependencies

PIMO jointly tunes hyperparameters, improving accuracy and stability

Chemistry; Computer science; Engineering