Chance-Constrained Optimization for Torque Tracking Control with Improving Fuel Economy in Spark-Ignition Engines

Shen, Xun; Shen, Tielong

doi:10.9746/jcmsi.11.365

Cited by 6 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[16] and [17] performed stochastic optimization aiming to quantify and minimize uncertainty resulting from different driving cycles. In [18] chance-constrained optimization was performed to improve thermal efficiency. [19] did some early work on stochastic optimization of spark ignition engines considering spark advance and injection time uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A stochastic design optimization methodology to reduce emission spread in combustion engines

Mourat

Eckstein

Koch

2020

Automot. Engine Technol.

View full text Add to dashboard Cite

This paper introduces a method for efficiently solving stochastic optimization problems in the field of engine calibration. The main objective is to make more conscious decisions during the base engine calibration process by considering the system uncertainty due to component tolerances and thus enabling more robust design, low emissions, and avoiding expensive recalibration steps that generate costs and possibly postpone the start of production. The main idea behind the approach is to optimize the design parameters of the engine control unit (ECU) that are subject to uncertainty by considering the resulting output uncertainty. The premise is that a model of the system under study exists, which can be evaluated cheaply, and the system tolerance is known. Furthermore, it is essential that the stochastic optimization problem can be formulated such that the objective function and the constraint functions can be expressed using proper metrics such as the value at risk (VaR). The main idea is to derive analytically closed formulations for the VaR, which are cheap to evaluate and thus reduce the computational effort of evaluating the objective and constraints. The VaR is therefore learned as a function of the input parameters of the initial model using a supervised learning algorithm. For this work, we employ Gaussian process regression models. To illustrate the benefits of the approach, it is applied to a representative engine calibration problem. The results show a significant improvement in emissions compared to the deterministic setting, where the optimization problem is constructed using safety coefficients. We also show that the computation time is comparable to the deterministic setting and is orders of magnitude less than solving the problem using the Monte-Carlo or quasi-Monte-Carlo method.

show abstract

Section: Introductionmentioning

confidence: 99%

A stochastic design optimization methodology to reduce emission spread in combustion engines

Mourat

Eckstein

Koch

2020

Automot. Engine Technol.

View full text Add to dashboard Cite

show abstract

“…Thus, they are called chance constraints. In recent years, chance constrained program has been applied to automotive powertrain control, model predictive control, system identification, machine learning and many other fields [3,4].…”

Section: Introductionmentioning

confidence: 99%

Parallel Randomized Algorithm for Chance Constrained Program

Shen,

Zhuang,

Zhang

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address chance constrained program. Randomized optimization is applied to search the optimizer which satisfies chance constraints in a framework of parallel algorithm. Firstly, multiple decision samples are extracted uniformly in the decision domain without considering the chance constraints. Then, in the second sampling layer, violation probabilities of all the extracted decision samples are checked by extracting the disturbance samples and calculating the corresponding violation probabilities. The decision samples with violation probabilities higher than the required level are discarded. The minimizer of the cost function among the remained feasible decision samples are used to update optimizer iteratively. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach. The proposed method exhibits better robustness in finding probabilistic feasible optimizer.

show abstract

“…Chance constraints are constraints within uncertain parameters which are required to hold with specified probability levles [3]. In recent 30 years, chance constrained program has been applied from economics and management fileds to various problems, such as model predictive control [4], automotive control [5,6] , machine learning [7], system identification and prediction [8].…”

Section: Introductionmentioning

confidence: 99%

Approximate Uncertain Program

2019

Self Cite

View full text Add to dashboard Cite

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address chance constrained program. Firstly, a single layer neural-network is used to approximate the function from decision domain to violation probability domain. The algorithm for updating parameters in single layer neural-network adopts sequential extreme learning machine. Based on the neural violation probability approximate model, a randomized algorithm is then proposed to approach the optimizer in the probabilistic feasible domain of decision. In the randomized algorithm, samples are extracted from decision domain uniformly at first. Then, violation probabilities of all samples are calculated according to neural violation probability approximate model. The ones with violation probability higher than the required level are discarded. The minimizer in the remained feasible decision samples is used to update sampling policy. The policy converges to the optimal feasible decision. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach and parallel randomized algorithm. The result shows that proposed method have improved performance.

show abstract

Chance-Constrained Optimization for Torque Tracking Control with Improving Fuel Economy in Spark-Ignition Engines

Cited by 6 publications

References 16 publications

A stochastic design optimization methodology to reduce emission spread in combustion engines

A stochastic design optimization methodology to reduce emission spread in combustion engines

Parallel Randomized Algorithm for Chance Constrained Program

Approximate Uncertain Program

Contact Info

Product

Resources

About