Research on online perception and uncertainty quantification of fuel injection characteristics based on variational Bayesian methods

Intelligent perception and control of fuel injection characteristics represent a key cutting-edge technology for achieving controllable and efficient combustion in engines. Existing methods primarily rely on deterministic point estimates, lacking a quantitative assessment of the reliability of perception results, which limits their decision-making and application in closed-loop control under complex, time-varying operating conditions. To address this, this paper proposes an online injection rate perception method (VB-BiLSTM) that integrates variational Bayesian inference with a bidirectional long short-term memory (BiLSTM) network. This method uses the injector inlet pressure fluctuation signal and the solenoid valve drive current as coupled time-series inputs. By distributing network parameters and training the model to maximize the evidence lower bound (ELBO), combined with Monte Carlo sampling and Gaussian reparameterization, it achieves stable gradient optimization and real-time forward inference, thereby providing a posterior confidence interval alongside the output fuel injection rate curve. The offline-trained model was embedded into LabVIEW for online deployment and validated on a high-pressure common-rail system test bench. Test results demonstrate that the proposed VB-BiLSTM model achieves high-precision injection rate estimation, with an R 2 value for injection rate consistently exceeding 0.9811 and an injection volume error consistently below 3.7%, while providing a stable 95% posterior confidence interval. Uncertainty exhibits adaptive variation characteristics during the injection rise, peak, and fall phases, effectively reflecting confidence differences caused by dynamic pressure changes.