Simultaneous Temperature and Volume Estimation in Variable-Load Micro-Reaction Systems via Online Thermal Parameter Identification: Application to Ultrafast qPCR

Non-invasive temperature estimation during online operation is a critical challenge in enclosed micro-reaction systems, particularly when the thermal mass of the working fluid varies dynamically or is uncertain. Conventional model-based approaches typically rely on fixed thermal parameters, leading to significant estimation errors when the actual reagent volume deviates from nominal conditions. To address this limitation, this study proposes a volume-adaptive temperature estimation framework applied to an ultrafast quantitative polymerase chain reaction (qPCR) system. By modeling the heat-transfer pathways via a simplified resistance–capacitance (RC) network, a nonlinear least squares (NLS) algorithm within an output-error (OE) framework is employed to identify key thermal parameters online. The framework separates the estimation into an offline calibration stage—where a thermocouple-equipped chip provides ground-truth data—and an online deployment stage that relies solely on non-invasive external measurements. This approach allows the system to explicitly compensate for volume-induced variations in thermal inertia. Validation experiments on an ultrafast qPCR platform with reagent volumes ranging from 100 to 250 μL and heating rates exceeding 20 °C/s demonstrate that the method achieves robust performance, maintaining a mean absolute error (MAE) of reagent temperature at 0.24 °C and restricting the average volume estimation error to within 1.37 μL. DNA gel electrophoresis results further confirm the biological reliability of the temperature prediction strategy by verifying amplification specificity. This work provides a generalised solution for precise thermal management in micro-systems subject to variable thermal loads.