Stochastic Bayesian optimization for predicting borderline knock

Tang, Jian; Pal, Anuj; Wen, Desheng; Archer, Chad; Yi, James; Zhu, Guoming

doi:10.1177/14680874211065237

Cited by 9 publications

(15 citation statements)

References 28 publications

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“…With all these, the model has three unknowns to be solved for the Kriging model and they are scalar σ , parameter vector β and θ . They are determined by maximizing the likelihood function (see Tang et al 4 for details) over the observed points. Accordingly, the predicted mean μ and mean square error s 2 for y ( x ) are predicted by the following equations:…”

Section: Offline Trained Surrogate Model Through Bayesian Optimizatio...mentioning

confidence: 99%

“…3 The knock combustion is affected by many aspects such as spark timing, trapped gas composition and temperature as a result of gas exchange process due to EGR, intake and exhaust valve timings. 4 In order to avoid undesired knock and achieve the best possible engine efficiency, the control parameters (such as spark timing, EGR and valve timings, etc.) need to be optimized through an extensive calibration process.…”

Section: Introductionmentioning

confidence: 99%

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Borderline knock adaptation based on online updated surrogate models

Tang

Wen

Archer

et al. 2022

International Journal of Engine Research

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Spark ignition engines are often desired to be operated close to its knock borderline limit, when MBT (maximum brake torque) cannot be achieved, to optimize engine efficiency. Traditionally, engine knock is closed-loop controlled using a dual-rate PID scheme with the help of feedforward control based on off-line calibrated borderline knock limit along with associated corrections. Note that the feedforward control is often not accurate and very conservative. This paper proposed a data-driven knock baseline control architecture consisting of two-key components: (a) offline training knock borderline Surrogate models under the worst and lightest knock conditions and (b) online updating the composite Surrogate model for adaptation. A Bayesian-based multi-objectives optimization algorithm is used to obtain optimal knock control parameters with significantly improved calibration efficiency, where the offline trained models are obtained using spark and intake valve timings as control parameters, and indicated specific fuel consumption (ISFC) and knock intensity (KI) as two competing performance measures to be minimized. Based on our early results, two Kriging surrogate models with two corresponding Pareto fronts (most and least advanced timing) can be obtained, and the purpose of this paper is to generate a composite real-time Kriging model for compensating engine aging and operational environmental changes such as fuel type, temperature, humidity, etc. In order to reduce the number of control parameters used in online updating, principal component analysis is conducted to find dominated control parameter, and in this case, the spark timing is the most sensitive factor of Pareto front. During the online updating process, a likelihood ratio controller with short- and long-term buffers was proposed to update the surrogate model in real-time and to adapt to fast and slow environmental and engine variations so that the optimal borderline knock limit can be found based on the intersection of mean and variance of Pareto front from the real-time updated composite Kriging model; and accordingly, the optimal control parameters can be located in the design space using surrogate model. Both simulation and test results indicate that the proposed online updating scheme is able to update the machine-learned stochastic surrogate models and adjust the feedforward borderline knock control parameters adapted to engine aging and operational environment.

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Section: Offline Trained Surrogate Model Through Bayesian Optimizatio...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Borderline knock adaptation based on online updated surrogate models

Tang

Wen

Archer

et al. 2022

International Journal of Engine Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, our early study on knock stochastic properties 10 shows that the knock intensity probability density function (PDF) is not a symmetric Gaussian random process but has a log-nominal distribution, which was also verified by other researchers. 13 Thus a distribution conversion 11 is necessary to make it possible to implement the system identification algorithm. On the other hand, the fluctuation and absolute amplitude of δ temperature have a much larger range than these of the knock intensity; see Figures 10 and 12.…”

Section: System Identification and Model Verificationmentioning

confidence: 99%

“…The overall knock control architecture is shown below in Figure 1. The offline trained stochastic surrogate model 11 is updated in real-time and provides the baseline spark timing to the engine controller. This paper focuses on the δ spark timing compensation, which is the red path shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Cycle-based LQG knock control using identified exhaust temperature model

Tang

Wen

Archer

et al. 2022

International Journal of Engine Research

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Spark ignition engines are often desired to be operated close to their knock borderline when MBT (maximum brake torque) cannot be achieved for optimizing combustion efficiency. Under this circumstance, a calibrated baseline spark timing, along with other control parameters such as intake and exhaust valve timings, is found for the engine control system to maximize fuel economy, and a stochastic scheme can be used for the control based on a large number of history data. However, cycle-to-cycle combustion variations still exist, resulting in a relatively conservative baseline control. To reduce cycle-to-cycle combustion variations, a real-time cycle-wised knock compensation is required. The correlation between exhaust temperature at the current cycle and knock intensity at the next cycle was found in our earlier research. In this paper, a cycle-to-cycle spark timing compensation scheme is developed based on the measured exhaust temperature when the engine is operated close to its knock borderline. To make model-based control possible, [Formula: see text]-Markov COVER (COVariance Equivalent Realization) system identification was used to obtain a linearized engine exhaust system model from incremental spark timing to associated exhaust temperature and knock intensity. Accordingly, a Linear–Quadratic–Gaussian (LQG) controller is designed, based on the identified model, to minimize the knock intensity fluctuations based on incremental exhaust temperature variation. The LQG control strategy was integrated with the existing entire knock control architecture, where the baseline spark timing is generated based on the offline machine training with an online updating scheme developed earlier, and demonstrated experimentally. Note that the cycle-based compensation only adds incremental spark timing to the baseline control so that knock combustion variations can be reduced. Three test scenarios are used to demonstrate the effectiveness of the proposed cycle-to-cycle compensation scheme when the engine is knock-limited. With the help of cycle-to-cycle based compensation, it was demonstrated that engine spark timing can be further advanced about one crank degree while maintaining the same knock intensity up-limit due to reduced knock combustion variations. Note that this is corresponding to 0.5%–1.0% fuel economy for this engine when it is operated under knock condition.

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“…The approach has been validated in easing the computational burden for various problems ranging from parameter calibration and control design. References [16], [17], [18], [19], [20], [21], [22] implemented the Bayesian optimization framework in automotive domain for performing the engine calibration. Apart from automotive applications, the Bayesian optimization approach has also been successfully implemented in other applications such as analog/rf circuit design [23], groundwater reactive transport model [24], actuator modeling [25], and designing natural-gas liquefaction plant [26].…”

Section: Introductionmentioning

confidence: 99%

Sample-efficient Model Predictive Control Design of Soft Robotics by Bayesian Optimization

Pal¹,

He²,

Wei³

2022

Preprint

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This paper presents a sample-efficient data-driven method to design model predictive control (MPC) for cableactuated soft robotics using Bayesian optimization. Instead of modeling the complex dynamics of the soft robots, the proposed approach uses Bayesian optimization to search the best-guessed low-dimensional prediction model and its associated controller to minimize the objective function of closed-loop responses. The prediction model is updated by Bayesian optimization from the closed-loop input-output data in each iteration. A linear MPC is then designed based on the updated prediction model, and evaluated based on the closed-loop responses. Different from directly searching controller parameters, the closed-loop system stability, and inputs/outputs constraints can be easily handled in the MPC design. After a few iterations, a convergent solution of a (sub-)optimal controller can be obtained, which minimizes the user-defined closed-loop performance index. The proposed method is simulated and validated by a high-fidelity simulation of a cable-actuated soft robot. The simulation results demonstrate that the proposed approach can achieve desired tracking controller for the soft robot without a prior-known model.

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Stochastic Bayesian optimization for predicting borderline knock

Cited by 9 publications

References 28 publications

Borderline knock adaptation based on online updated surrogate models

Borderline knock adaptation based on online updated surrogate models

Cycle-based LQG knock control using identified exhaust temperature model

Sample-efficient Model Predictive Control Design of Soft Robotics by Bayesian Optimization

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