Multi-objective constrained optimization of engine maps

International audienceNowadays, automotive manufacturers are submitted to strong constraints in engine calibration: lowest fuel consumption, emission-control legislation and driver requests for driving comfort and performances. These constraints lead to an increasingly complexity of the engines and thus an increasingly number of parameters to be tuned, making the empirical engine calibration by a scan of parameter values impossible at engine test-bench. New methodologies in automated engine calibration based on statistics and optimization have emerged in order to limit the number of experimental tests to be run. The optimization problem of engine calibration consists in the determination of engine tuning parameter maps that minimize the cumulated fuel consumption and pollutant emissions, under combustion noise constraints, on a driving cycle. The usual way to get this result is to select specific operating points representing this cycle in the engine working range and to define upper bounds applied on the different engine responses (allocations) for each of them, in order to obtain a weighted sum of these local responses respecting the global targets. The underlying problem is a multi-objective optimization problem: different compromises between fuel consumption, noise and pollutant emissions on each operating point are possible. We propose an adapted optimization method based on the MO-CMA-ES method (Multi-objective Covariance Adaptation Evolution Strategy) which takes into account the non trivial limits of the engine parameter variation domains and some robustness constraints. An other point addressed in this paper is the map optimization which consists in a global optimization of engine responses cumulated on the driving cycle. This method avoids the cumbersome choice of allocations for each considered operating point and includes directly the map regularity constraints in map parameterizations. Finally, application on real dataset obtained at automated test-bench for a diesel engine are presented

A derivative free optimization method for reservoir characterization inverse problem

International audienceThese data (pressure, oil/water/gas rates at the wells and 4D seismic data) are compared with simulated data to determine petrophysical properties of the reservoir. The underlying optimization problem requires dedicated techniques : derivatives are often not available, the associated forward problems are CPU time consuming and some constraints may be introduced to handle a priori information. In this paper, we propose a derivative free optimization method based on trust region approach coupled with local quadratic interpolating models of the cost function and of non linear constraints. Results obtained with this method on a synthetic reservoir application with the joint inversion of production data and 4D seismic data are presented. Its performances are compared with a classical sequential quadratic programming method in terms of numbers of simulation of the forward problem

Optimization for engine calibration

International audienceNowadays, automotive manufacturers are submitted to strong constraints in engine calibration such as: low fuel consumption, emission-control legislation and driver requests for driving comfort and performances. These constraints lead to an increasing complexity of the engines and thus an increasing number of parameters to be tuned, making the empirical engine calibration by a scan of parameter values impossible at engine test-bench. New methodologies in automated engine calibration based on statistics and optimization have emerged in order to limit the number of experimental tests to be run. The optimization problem of engine calibration consists in the determination of engine tuning parameters that minimize the cumulated fuel consumption and pollutant emissions on a driving cycle generally associated with legislation norms. This cycle is decomposed in a set of stationary operating points of the engine characterized by its speed and its torque (the transient behaviors of the engine are not taken into account in the stabilized calibration). Then, the optimal tuning parameters of the engine should be defined for each operating points, the functions defining these parameters on the whole engine operating domain are called the engine maps. These two-dimensional optimal engine maps are then integrated in the engine control unit in the vehicle. We illustrate the difficulties associated with this application and propose adapted optimization methodologies: LoLiMoT models for engine map parameterization in order to handle intrinsic constraints on the map regularity, multi-objective optimization method based on CMA-ES approach. Finally , application on real dataset obtained at IFP automated test-bench for a diesel engine are presented. 2. Keywords: Engine calibration, LoLiMoT, Multi-objective optimization, Evolutionary algorithm 3. Introduction Engine calibration consists in fulfilling the engine tuning maps that are used in engine controls of the vehicle, i.e. in defining the optimal tuning of parameters used by engine control strategies. Due to the highly increased number of these parameters (especially for diesel engines but spark ignition engines are following the same trend) and the reduction of the development schedule available for the calibration process, manual tuning of engine parameters is now replaced by mathematically assisted calibration process. Such a process is based on the design of experiments with associated modeling methods, in order to reduce the number of tests used to build engine response models depending on engine control parameters, and optimization techniques to determine the optimal settings within the model definition domain. In order to perform the tests in a more productive way, these mathematical techniques are generally associated with test automation, requiring well controlled measurement methods and reliable test equipments. This paper describes the optimization methods developed for this application and illustrates their effectiveness on a real case of a common rail diesel Engine. The first section introduces the classical steps of the calibration process and discusses the associated difficulties. In the second section, we propose the Multi-Objective Covariance-Adaptation Evolutionary Strategy method for solving the optimization problem associated with a given engine operating point defined by the engine speed and the engine load. In the third part, an integrated approach is proposed in order to directly optimize the engine maps on the whole driving cycle (associated with legislation norms) instead of the individual optimization of each engine operating point. 4. Engine calibration 4.1. Sketch of the engine calibration process The emission calibration workflow is classically divided into four steps: 1. a preliminary phase consisting in choosing a sample of operating points (referred to as OP in the

Engine calibration: multi-objective constrained optimization of engine maps

International audienceWe present two new approaches to address the optimization problem associated with engine calibration. In this area, the tuning parameters are traditionally determined in a local way, i.e., at each engine operating point, via a single-objective minimization problem. To overcome these restrictions, the first method we propose is able to cope with several objective functions simultaneously in the local formulation. The second method we put forward relies on a global formulation, which allows the whole driving cycle to be taken into account while remaining single-objective. At the practical level, the two methods are implemented by combining various existing techniques such as the LoLiMoT (Local Linear Model Tree) parameterization and the MO-CMA-ES (Multi-Objective Covariance Matrix Adaptation Evolution Strategy) algorithm. A better compromise appears to be achieved on real case applications. Keywords Engine calibration · Response surface · LoLiMoT · Multi-objective optimization · Evolutionary algorithm Nomenclature Abbreviations (by alphabetical order

A Derivative Free Optimization method for reservoir characterization inverse problem

International audienceReservoir characterization inverse problem aims at building reservoir models consistent with available production and seismic data for better forecasting of the production of a field. These observed data (pressures, oil/water/gas rates at the wells and 4D seismic data) are compared with simulated data to determine unknown petrophysical properties of the reservoir. The underlying optimization problem is usually formulated as the minimization of a least-squares objective function composed of two terms : the production data and the seismic data mismatch. In practice, this problem is often solved by nonlinear optimization methods, such as Sequential Quadratic Programming methods with derivatives approximated by finite differences. In applications involving 4D seismic data, the use of the classical Gauss-Newton algorithm is often infeasible because the computation of the Jacobian matrix is CPU time consuming and its storage is impossible for large datasets like seismic-related ones. Consequently, this optimization problem requires dedicated techniques: derivatives are not available, the associated forward problems are CPU time consuming and some constraints may be introduced to handle a priori information. We propose a derivative free optimization method under constraints based on trust region approach coupled with local quadratic interpolating models of the cost function and of non linear constraints. Results obtained with this method on a synthetic reservoir application with the joint inversion of production data and 4D seismic data are presented. Its performance is compared with a classical SQP method (quasi-Newton approach based on classical BFGS approximation of the Hessian of the objective function with derivatives approximated by finite differences) in terms of number of simulations of the forward problem

Optimisation sans dérivées sous contraintes : deux applications industrielles en ingénierie de réservoir et en calibration des moteurs

Optimization takes place in many IFPEN applications: for instance estimation of parameters of numerical models from experimental data in geosciences or for engine calibration. These optimization problems consist in minimizing a complex function, expensive to estimate, and for which derivatives are often not available. Moreover, additional difficulties arise with the introduction of nonlinear constraints and even several objectives to be minimized. In this thesis, we developed the SQA method (Sequential Quadratic Approximation), an extension of a derivative-free optimization method proposed by M.J.D Powell for optimization with constraints with known or unknown derivatives. This method consists in solving optimization sub-problems based on local quadratic interpolation models of objective function and derivative-free constraints built with a limited number of function evaluations. If the solution of this sub-problem does not progress toward a solution of the original problem, new simulations are performed to try to improve the model quality. Numerical results on benchmarks show that SQA is an effective method for constrained derivative-free optimization. Finally, SQA has been tested with success on two industrial applications in reservoir engineering and in engine calibration. An other problem studied in this thesis is multi-objective minimization under constraints. The MO-CMA-ES method (Multi-Objective - Covariance Matrix Adaptation - Evolution Strategy) adapted to take into account constraints has been successful to determine different compromises for an engine calibration application.L'optimisation intervient dans de nombreuses applications IFPEN, notamment dans l'estimation de paramètres de modèles numériques à partir de données en géosciences ou en calibration des moteurs. Dans ces applications, on cherche à minimiser une fonction complexe, coûteuse à estimer, et dont les dérivées ne sont pas toujours disponibles. A ces difficultés s'ajoutent la prise en compte de contraintes non linéaires et parfois l'aspect multi-objectifs. Au cours de cette thèse, nous avons développé la méthode SQA (Sequential Quadradic Approximation), une extension de la méthode d'optimisation sans dérivées de M.J.D. Powell pour la prise en compte de contraintes à dérivées connues ou non. Cette méthode est basée sur la résolution de problèmes d'optimisation simplifiés basés sur des modèles quadratiques interpolant la fonction et les contraintes sans dérivées, construits à partir d'un nombre limité d'évaluations de celles-ci. Si la résolution de ce sous-problème ne permet pas une progression pour l'optimisation originale, de nouvelles simulations sont réalisées pour tenter d'améliorer les modèles. Les résultats de SQA sur différents benchmarks montrent son efficacité pour l'optimisation sans dérivées sous contraintes. Enfin, SQA a été appliqué avec succès à deux applications industrielles en ingénierie de réservoir et en calibration des moteurs. Une autre problématique majeure en optimisation étudiée dans cette thèse est la minimisation multi-objectifs sous contraintes. La méthode évolutionnaire Multi-Objective Covariance Matrix Adaptation, adaptée à la prise en compte des contraintes, s'est révélée très performante dans l'obtention de compromis pour la calibration des moteurs

Engine calibration: multi-objective constrained optimization of engine maps

International audienceWe present two new approaches to address the optimization problem associated with engine calibration. In this area, the tuning parameters are traditionally determined in a local way, i.e., at each engine operating point, via a single-objective minimization problem. To overcome these restrictions, the first method we propose is able to cope with several objective functions simultaneously in the local formulation. The second method we put forward relies on a global formulation, which allows the whole driving cycle to be taken into account while remaining single-objective. At the practical level, the two methods are implemented by combining various existing techniques such as the LoLiMoT (Local Linear Model Tree) parameterization and the MO-CMA-ES (Multi-Objective Covariance Matrix Adaptation Evolution Strategy) algorithm. A better compromise appears to be achieved on real case applications