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Estimation of Heat Transfer Coefficient in Heat Exchangers from closed-loop data using Neural Networks

Ramachandran Anantharaman, Carlos Gonzalez Rojas, Luna Artemis van Leeuwen, Leyla Özkan

TL;DR

The paper addresses estimating a time-varying heat transfer coefficient $U(t)$ in heat exchangers using closed-loop data without external excitation. It first establishes local identifiability of $U(t)$ through an observability analysis of an augmented HEX model with an unknown controller gain, then introduces Per-PINN, a physics-regularized NN that learns $U(t)$ by enforcing the known ODE structure as a hard constraint. The approach is compared to standard PINN formulations via numerical HEX data, showing that Per-PINN provides more accurate state predictions, better physical consistency, and simpler training. The work advances fouling monitoring and maintenance planning in industrial HEXs under realistic closed-loop conditions by enabling reliable inference of $U(t)$ from limited data.

Abstract

Heat exchangers (HEXs) play a central role in process industries for thermal energy transfer. Fouling, the gradual accumulation of solids on heat transfer surfaces, causes a time-varying decrease in the overall heat transfer coefficient (U(t)), significantly impacting the efficiency of heat transfer. Good estimation and modeling of fouling (the heat transfer coefficient) will lead to better fouling mitigation strategies. This study investigates the identifiability of the time-varying $U(t)$ in HEXs from closed-loop operational data, without external excitation of reference signals or knowledge of the controller parameters. We establish that while the complete system model cannot be identified under these given constraints, the time-varying heat transfer coefficient $U(t)$ remains identifiable. Further, we propose a neural network based architecture, called (Per-PINN), for estimation and modeling the heat transfer coefficient from the closed-loop system data. This Per-PINN model is shown to perform better than the existing Physics-Informed Neural Networks (PINN) based models for inverse parameter learning as it inherently fixes the underlying physical equations and learns only the time-varying parameter U(t).

Estimation of Heat Transfer Coefficient in Heat Exchangers from closed-loop data using Neural Networks

TL;DR

The paper addresses estimating a time-varying heat transfer coefficient in heat exchangers using closed-loop data without external excitation. It first establishes local identifiability of through an observability analysis of an augmented HEX model with an unknown controller gain, then introduces Per-PINN, a physics-regularized NN that learns by enforcing the known ODE structure as a hard constraint. The approach is compared to standard PINN formulations via numerical HEX data, showing that Per-PINN provides more accurate state predictions, better physical consistency, and simpler training. The work advances fouling monitoring and maintenance planning in industrial HEXs under realistic closed-loop conditions by enabling reliable inference of from limited data.

Abstract

Heat exchangers (HEXs) play a central role in process industries for thermal energy transfer. Fouling, the gradual accumulation of solids on heat transfer surfaces, causes a time-varying decrease in the overall heat transfer coefficient (U(t)), significantly impacting the efficiency of heat transfer. Good estimation and modeling of fouling (the heat transfer coefficient) will lead to better fouling mitigation strategies. This study investigates the identifiability of the time-varying in HEXs from closed-loop operational data, without external excitation of reference signals or knowledge of the controller parameters. We establish that while the complete system model cannot be identified under these given constraints, the time-varying heat transfer coefficient remains identifiable. Further, we propose a neural network based architecture, called (Per-PINN), for estimation and modeling the heat transfer coefficient from the closed-loop system data. This Per-PINN model is shown to perform better than the existing Physics-Informed Neural Networks (PINN) based models for inverse parameter learning as it inherently fixes the underlying physical equations and learns only the time-varying parameter U(t).

Paper Structure

This paper contains 11 sections, 2 theorems, 18 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Identification from closed-loop data
  3. Identification of HEX from data
  4. Problem formulation
  5. Identification of the heat transfer coefficient using Neural Networks
  6. Organization of the paper
  7. Identifiability of Heat Transfer Coefficient
  8. Per-PINN architecture and its application to parameter identification
  9. Numerical Results - Per-PINN for HEX
  10. Discussions on the numerical study
  11. Conclusions and Future scope

Key Result

Proposition 1

The time-varying parameter $U (t)$ of eq:Id1 is identifiable.

Figures (11)

  • Figure 1: closed-loop Identification
  • Figure 2: Heat Exchanger
  • Figure 3: HEX in a closed-loop
  • Figure 4: Block diagram of HEX in closed-loop
  • Figure 5: Per-PINN
  • ...and 6 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Theorem 1