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EP2791827A2 - Procédé permettant d'évaluer la solution d'un problème d'optimisation à plusieurs critères - Google Patents

Procédé permettant d'évaluer la solution d'un problème d'optimisation à plusieurs critères

Info

Publication number
EP2791827A2
EP2791827A2 EP12795756.1A EP12795756A EP2791827A2 EP 2791827 A2 EP2791827 A2 EP 2791827A2 EP 12795756 A EP12795756 A EP 12795756A EP 2791827 A2 EP2791827 A2 EP 2791827A2
Authority
EP
European Patent Office
Prior art keywords
space
solution
variation
model
variables
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
EP12795756.1A
Other languages
German (de)
English (en)
Inventor
Klemens WALLNER
Alejandra GARCIA
Adnand DRAGOTI
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
AVL List GmbH
Original Assignee
AVL List GmbH
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by AVL List GmbH filed Critical AVL List GmbH
Publication of EP2791827A2 publication Critical patent/EP2791827A2/fr
Ceased legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/02—Circuit arrangements for generating control signals
    • F02D41/14—Introducing closed-loop corrections
    • F02D41/1401—Introducing closed-loop corrections characterised by the control or regulation method
    • F02D41/1406—Introducing closed-loop corrections characterised by the control or regulation method with use of a optimisation method, e.g. iteration
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
    • G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/20—Drawing from basic elements, e.g. lines or circles
    • G06T11/206—Drawing of charts or graphs
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design

Definitions

  • the present invention relates to a method for evaluating the solution of a multi-criteria optimization problem.
  • Such multicriteric optimization problems generally exist if target values of several objective functions are to be optimized simultaneously depending on several restrictions (such as boundary conditions, physical limits, etc.). However, if the objective functions are in conflict with each other, the simultaneous optimization of all objective functions is often a problem.
  • multicriteria optimization problems usually can not find unique solutions but only a set of possible multidimensional solution points in a multi-dimensional space a multi-dimensional surface, the so-called Pareto front, which all represent an optimal compromise of the multi-criteria optimization problem. Individual points of this Pareto front therefore represent different, but in each case optimal, compromises between the objective functions.
  • Such multi-criteria optimization problems are known per se and there are also a number of mathematical methods for solving such problems.
  • a method is known with which an ECU is optimized during operation by means of a multi-criteria optimization problem with respect to an exhaust gas soot consumption compromise.
  • a single aggregate objective function (AOF) is used, which combines the weighted objective functions into a functional one common solution is the linearly weighted summation of the objective functions described here.
  • Each objective function is assigned a weighting factor. tor, from which a scalar objective function is derived as the sum.
  • the actual optimization can be carried out using conventional approaches, for example by means of sequential quadratic programming (SQP), an effective, iterative method for nonlinear limited optimization, which is necessary for the desired reduction of the required computing power.
  • SQL sequential quadratic programming
  • US Pat. No. 7,921,371 B1 describes a method for visualizing the solution of a multi-dimensional multi-criteria optimization problem. All target values are displayed on parallel, adjacent axes, whereby also the smallest and largest value of the found optimal solution is visualized, which represent the entire possible range of the optimal solutions for a target size. Therefore, the pareto front is represented in the form of parallel axes for the number of target variables. For each target size, there is a fixed target value, also shown in the diagram, with the parallel axes shifted vertically so that the target values all lie on a horizontal line.
  • WO 01/67395 A1 discloses a method in which, in a representation of all possible optimal solutions, those are marked (here by a different color), which satisfy a certain user-specified criterion, such as a constraint.
  • the solutions are projected onto two or three-dimensional surfaces in order to be able to recognize connections.
  • This object is achieved according to the invention by representing the set of optimal solutions of the multicriteria optimization problem in a model space as a two- or three-dimensional diagram of the objective functions and simultaneously displaying at least one of the objective functions as a function of at least one variation variable in a variation space
  • Model space and the variation space are interactively interconnected by marked for each selected solution in the model space, the solution size underlying the solution in the variation space.
  • a mathematical model can be used as the objective function, which is determined from a number of measurements of the objective function as a function of the variables. This makes it possible to apply the inventive method practically to any optimization problems.
  • MOP Multi-Criteria Optimization Problems
  • the variation quantities x are e.g. during a calibration, the settings, e.g. at the test bench where the calibrator carries out his measurements. Since these variation quantities x represent valid points in the variation space, the calibrator knows that he can adjust the variation quantities x in this range. For this reason, in this variation space, around the variation quantities x, an envelope is laid, which is referred to as design space.
  • the design room thus contains all the variables x valid for the respective application.
  • evolutionary algorithms for multicriteria optimization do not require any weighting or a priori information, so that these methods have been increasingly used in recent years and in particular have proven to be effective and robust methods.
  • genetic algorithms - based on selection, recombination and mutation - were used to achieve a continuous approach to a desired target. They are easy to apply to a wide range of problems and are very robust in the search for global optima, even if there are a variety of local optima.
  • conflicting requirements are searched for in a set of compromise solutions that approximate the best possible solutions.
  • the quality of an approximation can be quantified by the volume dominated by it in the target space, the S metric. Maximizing the S-metric is a desirable goal and, at the same time, sufficient scalar replacement of the original objective function.
  • a genetic algorithm uses these within the selection and thus achieves excellent results, especially when more than three goals have to be optimized where other multicriteria genetic algorithms fail.
  • the currently most popular genetic algorithm for determining the Pareto front is the Non-Dominated Sorting Genetic Algorithm (NSGA-II), which has proven to be extremely efficient, especially for the determination of a global optimum.
  • NSGA-II is a high-performance, elitist algorithm that prioritizes non-dominating individuals and preserves the diversity of solutions. The algorithm creates an initial population within the vector of variational magnitudes x and approaches iteratively in an iterative process that is based on selection,
  • the peculiarity of the visual presentation lies in a split representation of model space 1 and variation space 2, as shown in FIG.
  • f 2 (x) "NOX” and f 3 (x) "Fuel Consumption” The illustration of the design space game of FIG. Three-dimensional space, the fi through the objective functions (x) "Smoke”, is spanned. the valid range 3 in which the solutions can move is contained in this model space 1.
  • the Pareto front 4 contains the solutions found for the multi-criteria optimization problem within this valid range 3.
  • the Model space 1 can also be represented by several two- or three-dimensional representations of the k dimensions of the model space. These dimensions of the k dimensions in the two- or three-dimensional representations can be made dependent on the multi-criteria optimization problem and the preference of the user is represented by a number of two or three-dimensional representations of objective functions f j (x) and variation quantities x In Place.
  • the objective function is f 3 (x) each represented as a function of the three varying sizes x- ⁇ "exhaust gas temperature" x 2 "EGR rate” and x 3 "rail pressure".
  • any combinations of objective functions f j (x) and variation quantities x are conceivable here.
  • the objective functions f j (x) can be known functions of the variables x.
  • an objective function f j (x) is a mathematical model that is determined from measurements or experiments. In this case, measurements are carried out on the object of the multi-criteria optimization problem, eg on an internal combustion engine, a drive train, a transmission, a vehicle, etc., for example on corresponding test benches or in the course of test drives.
  • the desired objective functions f j are measured as a function of the variables x and possibly other variables. Mathematical models of the objective functions f j are then created from these measured variables.
  • Mathematical models of the objective functions f j are then created from these measured variables.
  • Possible models include a polynomial regression model, a fast neural network or an intelligent neural network. Because of this approach, additional measurements, ie real measurements, will not necessarily be 100% accurate on this model.
  • the methods for determining the models therefore also provide a model confidence interval indicating the bandwidth in which further measurements are likely to move. This means that a model with a slim model confidence range fits relatively well on the measurements made and has accordingly good explanatory power. The closer the model confidence interval, the better the models fit the measurements, and the more likely the model-determined solutions to the multi-criteria optimization problem will actually yield the sought-after values.
  • well-known objective functions ( ⁇ ) can also have a model confidence range, which in turn indicates how exactly an objective function f j agrees with a real measurement.
  • the model confidence range is thus a measure of the accuracy of the model or a target function with respect to real measurements.
  • the model confidence ranges 5 can also be shown in the individual diagrams, for example in the form of an upper and lower limit as shown in FIG.
  • the special feature of this type of representation is that the objective functions ( ⁇ ) in the model space 1 and the Pareto front 4 are represented as a set of possible optimal solutions of the multi-criteria optimization problem together with the variables x and therefore can also be analyzed together.
  • the representation in the variation space 2 is interactively adapted to a selection of a point in the model space 1.
  • a crosshair 6 is provided. With the example, an interesting point 7 of the Pareto front 4, or the valid area 3, is selected.
  • the crosshair 6 automatically marks the variation quantities x for this punk 7 in the model space 1.
  • the respective values of the variables x at this point can also be indicated, as indicated in FIG. 1.
  • the model trust area 5 can be represented so that the user additionally receives information about how trustworthy the underlying objective function fj (or mathematical model) is on this point.
  • this type of representation also allows the analysis of the effects of changes in the specification of the constraints g, and / or the range x min , x ma x of the variables x.
  • changes lead to other solutions that can then be easily compared directly.
  • it can be provided, for example, to change the limits of the range of variation variables x, for example by means of a slider in the variation space 2, whereby the representation of the solution in the model space 1 can change at the same time.
  • a number of measurements are performed on the internal combustion engine, wherein the target variables of the target functions f j (x) NOx, soot and consumption depending on the variables x, eg exhaust gas temperature, EGR rate, rail pressure, are measured.
  • the number and the amount of measurements can be predetermined, eg by a given Design of Experiment.
  • the measurements are used to determine mathematical models and model confidence regions 5 for the objective functions f j (x).
  • the multicriteria optimization problem for optimizing the objective functions f j (x) can be solved and the solution in the split representation of model space 1 and variation space 2 can be analyzed.
  • the calibrator can examine various optimal solutions of the pareto-front 4 with regard to the underlying variation variables x and the model confidence region 5. From these possible optimal solutions, the calibrator then determines one of the solutions as the best possible compromise.
  • the experience of the calibrator plays a major role.
  • the model confidence ranges and the Dependencies of the variables x are also the values of additional model channels that have not been optimized as target functions, as well as the robustness of the settings, eg whether the models in the vicinity of the optimum changes greatly, low influenceability due to component tolerances, etc., are taken into account.
  • This can be repeated for all operating points required for the calibration (eg speed, torque, load) of the internal combustion engine.
  • a predetermined number of operating points eg ten to twenty operating points, are generally required.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Data Mining & Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Health & Medical Sciences (AREA)
  • Medical Informatics (AREA)
  • Evolutionary Computation (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • Operations Research (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Mechanical Engineering (AREA)
  • Combined Controls Of Internal Combustion Engines (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Image Processing (AREA)

Abstract

Il est difficile d'apporter des solutions à un problème d'optimisation présentant plusieurs critères et plusieurs dimensions, les corrélations et les interdépendances entre solutions, fonctions cibles et grandeurs variables ne pouvant être que difficilement déterminées. Afin de faciliter cette démarche, l'invention propose l'affichage d'un espace de modèle (1) et d'un espace de variations (2) interconnectés de manière simultanée et interactive.
EP12795756.1A 2011-12-12 2012-11-08 Procédé permettant d'évaluer la solution d'un problème d'optimisation à plusieurs critères Ceased EP2791827A2 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
AT0182011A AT510328A2 (de) 2011-12-12 2011-12-12 Verfahren zur auswertung der lösung eines multikriteriellen optimierungsproblems
PCT/EP2012/072165 WO2013087307A2 (fr) 2011-12-12 2012-11-08 Procédé permettant d'évaluer la solution d'un problème d'optimisation à plusieurs critères

Publications (1)

Publication Number Publication Date
EP2791827A2 true EP2791827A2 (fr) 2014-10-22

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EP12795756.1A Ceased EP2791827A2 (fr) 2011-12-12 2012-11-08 Procédé permettant d'évaluer la solution d'un problème d'optimisation à plusieurs critères

Country Status (5)

Country Link
US (1) US9760532B2 (fr)
EP (1) EP2791827A2 (fr)
JP (1) JP5940667B2 (fr)
AT (1) AT510328A2 (fr)
WO (1) WO2013087307A2 (fr)

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EP4235319A1 (fr) 2022-02-25 2023-08-30 Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen Étalonnage de fonction automatisé

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EP3612011A1 (fr) 2018-08-14 2020-02-19 ABB Schweiz AG Procédé pour commander le refroidissement dans un centre de données
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Publication number Priority date Publication date Assignee Title
EP4235319A1 (fr) 2022-02-25 2023-08-30 Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen Étalonnage de fonction automatisé
DE102022104648A1 (de) 2022-02-25 2023-08-31 Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen, Körperschaft des öffentlichen Rechts Automatisierte funktionskalibrierung

Also Published As

Publication number Publication date
JP5940667B2 (ja) 2016-06-29
AT510328A2 (de) 2012-03-15
US9760532B2 (en) 2017-09-12
WO2013087307A2 (fr) 2013-06-20
JP2014533387A (ja) 2014-12-11
WO2013087307A3 (fr) 2013-09-06
US20140344320A1 (en) 2014-11-20

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