DE102010003698A1 - Method for laying out contour of control cam for controlling e.g. inlet valve of e.g. diesel engine, involves determining values for parameters of each of particles using particle swarm optimization algorithm - Google Patents

Abstract

The method involves defining one or more interpretation boundary conditions for a contour of a control cam (10). An interpretation target value is defined for the contour. An object function i.e. quality function, including the interpretation target value is defined for a particle swarm optimization algorithm. Values are determined for parameters of each of particles using the optimization algorithm such that an optimized target value of the object function is obtained based on interpretation boundary condition.

Description

The invention relates to a method for laying out the contour of a control cam.

Control cam, for example, in internal combustion engines z. B. for controlling the injection pump (as "injection cam") and also for controlling the gas exchange organs (as "inlet cam" or "Auslassnocke") used.

The goal in the production of a control cam is the development of an optimal contour of the control cam, which meets all the specified criteria and restrictions that exist for the control cam and the adjacent components. For example, the steady rise in injection pressures or rail pressures (eg in the case of the 2nd generation common rail, the rail pressure ≥ 2200 bar) entail higher component loads and thus require the optimization of injection components, such as injection valves. B. the injection cam.

To meet all requirements for the design of the contour of a control cam, it requires a closed optimization process. The known from the prior art, based on classical algorithms design method for the contour of a control cam, as z. In the publication "Research - Education - Further Education", Report No. 14, "A Mathematical Technique for Optimizing Cams", Hardy Moock, University of Kaiserslautern, Department of Mathematics, January 1986 are indicated, but are subject to narrow limits.

Out DE 10 2006 043 460 A1 a method for optimizing an injection nozzle for an internal combustion engine is known. The algorithm implemented there is a Particle Swarm Optimization (PSO) algorithm, which is a class of natural-analog stochastic optimization methods derived from the field of artificial intelligence.

DE 10 2006 043 460 A1 describes that the PSO algorithm is based on a population of particles (set of parameters as a possible solution) that, like birds in a flock, influence each other's movement in a search space and refers to this J. Kennedy, R. Eberhart: Particle Swarm Optimization. Proc. IEEE Int. Conf. on Neural Networks, 1995, pp. 1942-1948 ).

The invention has for its object to provide a method for designing the contour of a control cam, which is robust, effective and fast and with which the geometric design of the contour of the control cam can be realized in an optimal manner, so that the operating characteristics of the control cam and functionally to be added components in the entire application are adapted to existing requirements and limits and thus characterized by lower component loads.

This is achieved by a method according to claim 1. Further developments of the invention are defined in the dependent claims.

According to the invention, there is provided a method of designing the contour of a control cam, the method comprising: defining a predetermined number of parameters each having an initiation value for the contour of the control cam, defining a predetermined set of parameter sets each having the predetermined number of parameters as a predetermined one A set of particles for performing a Particle Swarm Optimization (PSO) algorithm, defining at least one design constraint on the contour of the control cam, defining at least one design target influenceable to the control cam contour, defining a Target function for the PSO algorithm including at least one of the defined design target values, and using the PSO algorithm, determining values for the parameters of each particle, so that taking into account the at least one n Design boundary condition is achieved on at least one optimization target optimized value of the objective function.

According to the invention, a PSO algorithm for optimal design of the contour of a control cam, such. B. a control cam for an internal combustion engine used. The aim of the PSO algorithm is to find the optimum of an examined objective function, which depending on the definition can represent a maximum or a minimum and according to one embodiment of the invention is a minimum. The optimum should preferably be the global optimum of the entire search space, i. H. Solution room, be.

The sets of parameters which according to the invention form the particles of the PSO algorithm are distributed stochastically and / or deterministically over the entire solution space at the beginning of the optimization, thus having a corresponding position therein. The particles are assigned to the initialization stochastic and / or determined velocity vectors.

For each further step of the PSO algorithm, each particle orients itself among other things on the location of the adjacent particles and its own best position so far. From the individual best solutions of each individual particle, the best solution of the swarm is selected by a comparison operation. The swarm thus tends as a whole toward the best positioned particle.

The orientation of the particles or parameter sets in the solution space is D-dimensional, depending on the number of design parameters.

The objective function can be formulated in such a way that several design target values with their own weighting are combined in it. It is then also referred to as a quality function (fitness). The design target values correspond to the mathematically determinable concrete requirements. By formulating a quality function, the variables determined in a calculation process can be evaluated and weighted both for themselves and against each other. The goal is to develop an optimal contour of a control cam depending on all criteria and limitations.

According to one embodiment of the invention, the design target values or values included in the target function are formed as normalized values, that is, they are related to a respective reference value.

According to a further embodiment of the invention, a weighting is carried out in each case for the design target variables included in the target function, the value of each parameter being set by the PSO algorithm such that the target function reaches a minimum.

According to one embodiment of the invention, when the Particle Swarm Optimization algorithm is executed, a predetermined number of iterations (loop repeats) are traversed, whereby in the Particle Swarm Optimization algorithm the current velocity in each dimension of a particle is multiplied by a constraint coefficient , and wherein in the first 60 percent of the predetermined number of iterations, the constraint coefficient of uniformly distributed random numbers in the interval [0,1; 1] is selected and then decreases linearly from a value of 1 to a value of 0.2087, up to 100 percent of the predetermined number of iterations.

According to yet another embodiment of the invention, when the Particle Swarm Optimization algorithm is executed, a particle exceeds or falls below a threshold value set in a particular dimension, a new location for the particle is determined equal to the predetermined threshold, with a current one Speed of the particle is determined as the difference between an upper parameter limit and previous location of the particle or as the difference between the previous location of the particle and a lower parameter limit.

According to yet another embodiment of the invention, when defining the predetermined number of parameters for the contour of the control cam, the parameters equally distributed random numbers receive corresponding initialization values.

According to a further embodiment of the invention, after a completed pass (with a predetermined number of iterations) of the Particle Swarm Optimization algorithm, the number of parameters per parameter set is increased, which is determined by means of the completed pass of the Particle Swarm Optimization algorithm Values of the parameters are passed to a pass of the Particle Swarm Optimization algorithm directly following the completed pass, interpolation being carried out on the basis of the transferred values of the parameters and the increased number of parameters per parameter set, and the values determined for the interpolation the parameters are used as initiation values for the subsequent pass of the Particle Swarm Optimization algorithm.

According to yet another embodiment of the invention, as the parameters for the contour of the control cam, points are defined on a plunger lift curve, wherein the contour of the control bag is calculated from the values of the parameters determined by the Particle Swarm Optimization algorithm.

According to one embodiment of the invention, the objective function may have squared differences of both speeds and accelerations of adjacent points on the ram stroke, where in the objective function the differences are multiplied by a factor of quality decreasing as the number of parameters per set of parameters increases.

According to yet another embodiment of the invention, up to a number of parameters per parameter set including the value of 36 for determining the initialization values for the directly following pass of the Particle Swarm Optimization algorithm, both the interpolated values of the parameters from the completed run of the Particle Swarm Optimization algorithm. Swarm optimization algorithm as well as equally distributed random numbers of a predetermined interval used.

In accordance with yet another embodiment of the invention, starting from a number of 41 parameters per parameter set for determining the initialization values for the direct pass of the Particle Swarm Optimization algorithm, only the interpolated values of the parameters from the completed pass of the Particle Swarm Optimization algorithm are used ,

According to yet another embodiment of the invention, as design constraints, at least one element, multiple elements or all elements of the following design constraint group are defined: a current ram velocity of a ram to be engaged with the control cam should be less than a ram speed of the ram , a current ram acceleration of the plunger should be smaller than a limit ram acceleration of the plunger, a cam drive torque should be minimal, a permissible pump chamber pressure of a fuel pump should be greater than a minimum required Grenzpumpenraumdruck the fuel pump (rising Stößelhubkurvenflanke), a limit speed (Abhebedrehzahl) should be greater than one Be the rotational speed of the control cam and a local radius of curvature of the cam should be smaller than a limit radius of curvature.

According to a further embodiment of the invention, as design target values at least one element, several elements or all elements of the following design target group are defined: the current ram speed, the current ram acceleration, the current cam drive torque, the allowable pump room pressure, the limit / lift speed and a current frictional force of the plunger.

According to further embodiments of the invention, the contour of a control cam for an internal combustion engine is designed with the inventive method, wherein the control cam preferably for controlling an injection pump (as "injection cam") or to control gas exchange organs (as "inlet cam" or "Auslassnocke") is.

In the following the invention will be described with reference to preferred embodiments and with reference to the accompanying figures.

1 shows a graduated schematic representation of the optimized contour of a triple cam according to an embodiment of the invention.

2 shows a schematic representation of the geometry of a control cam-tappet roller movement with Deachsierung.

3 shows in the representations 3A to 3E the genesis of a control cam according to an embodiment of the invention.

4 shows a diagram in which, according to an embodiment of the invention, the value profile of a restriction coefficient is shown.

An internal combustion engine (not shown in the figures), such as an internal combustion engine (eg, diesel engine) charged by a turbocharger (not shown in the figures), has a plurality of functional assemblies, and in the internal combustion engine, multiple processes are parallel and partially inter-related interlocked run off. An exemplary classification for a development process for the internal combustion engine is shown in the following Table 1: assemblies processes Motor engine engine process Injection system (injection cam) Control of fuel injection into the combustion chamber combustion chamber injection valve train Gas exchange; injection turbocharger Table 1

The following is with reference to the 1 to 4 a method for sweeping the contour of a control cam of an internal combustion engine according to embodiments of the invention described. The control cam is provided for controlling an injection pump (as "injection cam") of the engine or for controlling intake valves or exhaust valves (as "intake cam" or "exhaust cam") of the internal combustion engine.

The aim is to develop an optimal contour of a control cam, depending on all given criteria and limitations that are placed on the cams and the adjacent components. The entire contour of the control cam is discretized by a pre-set number of nodes. The number of nodes is usually determined by the manufacturing process used.

As in 1 For example, in a triple cam (embodiment of a common injection cam contour in the common rail system as a result of the method described herein) and a resolution of 0.5 degrees cam rotation angle and 120 degrees cam rotation angle for a control cam contour a total of 241 support points. For a double cam, the swept area for a control cam contour is 180 degrees cam rotation angle and thus results in 361 nodes (at 0.5 degrees resolution).

2 shows a schematic representation of the geometry of a control cam-tappet roller assembly 1 , being a control cam 10 in mechanical cooperation with a cylindrical plunger roller 20 (Part of a not fully illustrated plunger) is shown. The control cam 10 has a basic radius R _G and the tappet roller 20 has a roller radius R _R.

An optimal control cam contour meets the requirements placed on it (eg from a specification sheet, constructive aspects, etc.) at each individual support point. There is therefore a free lift curve (ram stroke) of the plunger roller 20 created without additional conditions (eg linear velocity gradients). So the potentials are maximized. However, such conditions can be imposed prinipally but at any point or in regions of the ram stroke curve. Each support point of the control cam contour is thus basically within the selected requirements and restrictions independent of all others. The interpolation points are thus used as independent parameters in the optimization calculations. The presented method provides optimal control cam contours for pre-defined requirements and constraints.

The like in 2 shown geometric conditions during the rolling of the plunger roller 20 on the control cam 10 and the physical processes are calculated closed. For this purpose, the required equations are set up and compiled in a calculation process. Thus, those are for the design of the contour of the control cam 10 mathematically recorded important company variables. This mathematical model of a control cam 10 can now be coupled with an optimization process.

The extremely complex calculations and the large number of boundary conditions and target values to be adhered to require a closed optimization procedure in order to achieve an optimum contour for the control cam 10 to be able to realize.

These requirements are met in a particularly expedient manner by the Particle Swarm Optimization (PSO) algorithm. The PSO algorithm is robust, effective and fast and can be used for almost any mathematical context. As a parameter for the design of the contour of the control cam 10 become points on a ram stroke (as in 3 shown), wherein the contour of the control cam 10 from values determined by means of the PSO algorithm, the parameter is calculated.

The parameters are influenced by other criteria from the contour design, which must also be taken into account as design boundary conditions: a current ram speed of the ram roll 20 (or the plunger) should be smaller than a limit ram speed of the plunger roller 20 (or the plunger), a current ram acceleration of the plunger roller 20 (or the plunger) should be smaller than a limit plunger acceleration of the plunger roller 20 (or the plunger), a cam drive torque should be minimal, an allowable pump chamber pressure of a fuel pump of the internal combustion engine should be greater than a minimum required Grenzpumpenraumdruck the fuel pump, a limit speed should be greater than a speed of the control cam and a local radius of curvature of the control cam 10 soff be less than a Grenzkurwürungsradius.

For an optimal contour for the control cam 10 All parameters must be specified according to their dependencies and limits. Accordingly, the design target values are defined as: the actual ram speed, the current ram acceleration, the current cam drive torque, the allowable pump room pressure, the limit / retract speed, and a current frictional force of the ram.

The design constraints, design targets, and parameters for contouring a control cam of an internal combustion engine according to an embodiment of the invention are listed in Tables 2 through 4 below, where the limits shown there are formed from numerical values to be specified for each application. boundary condition size Basic / origin v <v _limit [m / s] ram speed Avoid breaking film, empirical value a <a _limit [m / s ² ] slide acceleration mechanical load, empirical value M _d → MIN [Nm] Cam drive torque mechanical load camshaft empirical value p _zul > p _limit [bar] permissible pump chamber pressure hydraulic load pump cylinder n _pGrenz > n _limit [min ^-1 ] Limit speed Avoidance Lifting plunger roller + safety RP <RP _limit [mm] local radius of curvature Ensure point bearing cam on ram roller + safety Table 2 symbols target optimization goal v [m / s] ram speed minimize a [m / s ² ] slide acceleration minimize M _d [Nm] Cam drive torque minimize P _zul [bar] permissible pump chamber pressure maximize n _pGrenz [min ^-1 ] Limit speed maximize F _friction [N] Frictional force of the tappet roller minimize Table 3 symbols parameter reference h [mm] ram stroke Cam rotation angle Table 4

The design target variables listed in Table 3 can be normalized (based on a respective reference value) and weighted in a quality function (objective function), which is set up at the end of the calculations, depending on the optimization target and summed up with the corresponding sign. In the present application, the value of the quality function is minimized with the PSO algorithm. Thus, design goals to be minimized in the objective function or quality function have a positive sign, while design parameters to be maximized have a negative sign.

At the end of a calculation cycle, the calculated support points of the tappet roller stroke (corresponding to a tappet stroke curve) are output as the result, which are then converted into the points of an optimal control cam contour.

Since the PSO algorithm can find both local optima and the global optimum of the established objective function, several different optimal control cam contours can be found in repeated calculations. The speeds v of the tappet roller 20 are each numerically as ram stroke increase of the plunger roller 20 of the previous interpolation point (i-1). The accelerations a are interpreted as a speed increase to the following interpolation point (i + 1). This results in the acceleration a at the current support point i in each case from the ram strokes of the neighboring support points. Taking into account a disaccentration e, an advance angle α and a cam elevation h _N can now be analytically calculated (see 2 ). To reduce the cam drive torque M _d can be a as in 2 shown desachsierte arrangement of the plunger roller 20 above a neck center 11 be provided.

To determine a surface pressure between the control cam 10 and the tappet roller 20 becomes a local radius of curvature RP of the control cam 10 needed. Since there is no continuous contour curve for the calculation algorithm, a numerical calculation method was developed for this purpose.

The strain of the control cam 10 , which is to be minimized, is due to the dynamics of the combined lifting and rolling movement of the tappet roller 20 on the contour of the control cam 10 certainly.

The mathematical description of the dynamics of the control cam ram roller arrangement 1 In addition to the values listed in Table 3, (pairing) provides the pressure and shear forces that occur.

With the PSO algorithm, it is possible to control the contour of the control cam 10 optimally designed so that the operating characteristics of the control cam 10 and functionally to be added components (such as the plunger roller 20 and a camshaft) are adapted to the existing requirements and limit values in the entire field of application and are thus characterized by lower component loads and lower costs.

Based on natural swarms, such as bird swarms or schools of fish, the PSO algorithm involves a population of particles representing the swarm. Each of these particles has a unique position within a given, multidimensional search space, which simultaneously represents the domain of definition of a given function or objective function to be optimized.

According to the invention, as particles for the execution of the PSO algorithm, a predetermined amount each of a predetermined number of parameters (points according to a like in FIG 2 Defined ram stroke) having parameter sets defined.

In addition, each particle still has one velocity vector per parameter, which indicates the direction and length of movement of each individual parameter. These velocity vectors are initially initialized based either on empirical values or randomly.

The particles now start at the initialized positions and move through the search space, whereby the target function value is evaluated at each position. The goal is according to this embodiment of the invention to find a minimum target function point. The movement of the particles is dependent on the respective velocity vectors and positions of the respective best results of the target function found so far, both of adjacent particles and of themselves.

• WIEDERHOLE
• Für jeden Partikel führe aus
• Ermittle Zielfunktionswert an der Stelle der aktuellen Position des
• Partikels
• Ende
• Für jeden Partikel führe aus
• Aktualisieren der persönlich besten Position des
• Partikels
• Ende
• Aktualisieren der globalen besten Position
• Für jeden Partikel führe aus
• Aktualisieren des Geschwindigkeitsvektors
• Neue Position berechnen
• Ende
• BIS Abbruchkriterium erfüllt

An abstract scheme (pseudo code for the PSO algorithm to solve static problems) is as follows: Initialize a population of particles with positions and velocities of each particle in D dimensions in the search space

• REPEAT
• For each particle perform
• Determine target function value at the location of the current position of the
• particle
• The End
• For each particle perform
• Updating the personal best position of the person
• particle
• The End
• Update the global best position
• For each particle perform
• Update the speed vector
• Calculate new position
• The End
• BIS Abort criterion met

According to this very simple scheme, the particles start at z. For example, random positions and evaluate their solution quality (objective function value). Then, the best local positions and the best global positions are stored by the PSO algorithm (providing variables that hold these positions), and then new speeds and new positions are calculated for each particle, which depend on the stored best results. The position of a particle in the search space is composed of the individual positions in the individual dimensions. This will be explained in more detail by means of the following objective function optimization.

Given are the solution problem dimensions D {number of dimensions of the search space) and the objective function to be optimized: f (x ₁ , ..., x _D ) → Min (1)

The PSO algorithm now has the task of finding the global extremum of the objective function (in the present embodiment: MINIMUM).

This is based on a number m of particles. For each of these numbers of particles, the PSO algorithm stores the positions x _m = (x ₁₁ , ..., x _mD ) and the velocity v _m = (v ₁₁ , ..., v _mD ) both of the current iteration step t as also of the preceding iteration step t - 1 in each case of the dimension D.

In order to process the best positions of each particle, another variable p _m = (p ₁₁ , ..., p _mD ) is introduced and managed. The location of each particle in the D-dimensional search space is determined from a concrete position in dimension D. In addition, there is an index g, which identifies the particle with the best global positions.

Thus, the PSO algorithm is set up so that an optimization can be carried out.

The following is intended to illustrate how the updating of the velocity vectors for each particle and the calculation of the new positions of each particle can be realized.

To update the velocity vectors of a respective particle, the previous best positions of the particles of the neighborhood and the best position of the respective particle itself are used.

Depending on the chosen scheme, the neighborhood can have different topologies and describes the exchange of information among the particles with regard to the best positions found so far. The most common sociometries are the so-called gbest and lbest topologies, where each particle is affected by the best previous position of the entire swarm or by the best previous position of the particles in the immediate vicinity. The topology patterns influence the swarm behavior in terms of convergence rate and degree of parallelism of the search.

This is to ensure that the particles are to some extent in the direction of the best self-found positions and to a certain extent in the direction of the best found so far Move positions of the swarm. For determining or influencing the respective extent, the parameters and r are provided.

A general form of equation for determining the new velocity vector for a dimension of a particle is as follows: v _mD (t) = w · v _mD (t - 1) + n ₁ · r ₁ · (p _mD - x _mD (t - 1)) + n ₂ · r ₂ · (p _gD - x _mD (t - t)) 1)) (2)

In equation (2), v _m (t) and x _m (t) are vectors in the D-dimensional search space. The addition is thus a vector addition and geometrically easy to interpret by combining two vectors. In the following, the individual components of the new vector v _mD (t) consisting of the summands of the above formula are explained.

The component w is a weighting or the inertia of the speed and determines the influence of the old (previous) speed of a design parameter and is called Inertia Weight. Thus, the old velocity vector can be compressed or stretched by the factor w. The component w can z. B. can be implemented so that their value changes linearly with time: w = (w _start - w _end ) · ((Max Epochs) / Max Epochs) + w _end (3) where w _{start is} the power value and w _{end is} the end value for w. Epochs stands for the number and MaxEpochs for the maximum number of loop repetitions (iterations) of the PSO algorithm. A large starting value and small final value result in a globally weighted search with large movements at the beginning and a locally weighted search at the end of the optimization process.

The vector p _m denotes the best positions of a particle in the dimension D. Thus, the term (p _mD -x _mD (t-1)) is the vector which is from the current position of the particle m to the best position so far in the dimension D of the particle m. This vector can be compressed or stretched by the factor n ₁ · r ₁ , where n _{1 is} a so-called acceleration coefficient and r _{1 is} an equally distributed random number from the interval [0,1]. The factor n ₁ corresponds to a cognitive parameter, since it controls the movement of the particle with respect to its best previous positions in the D-dimensional space. Like n ₂ , in standard applications it is a positive constant whose value is commonly used at 2.05.

Thus, it is clear that the vector is minimally a zero vector to the best position so far and is lengthened maximally by the factor n ₁ . This influence on the new speed is controlled by the random number r ₁ , so that the updating of the speed has randomized influences.

The last component of the new velocity vector is similar to that just described, except that it forms a vector from the current position to the best global position p _gD among all the particles of the swarm.

The parameters n ₂ and r ₂ have the same function as n ₁ and r ₁ and hereby influence the extent to which the new velocity vector tends toward the best global position in the D-dimensional space. Therefore, n _{2 is} also referred to as the social parameter, which is also given as n ₁ in standard applications with 2.05.

The new position of the particle in D-dimensional space is now determined by adding the old position to the new velocity vector. Geometrically, the particle moves from the old position along the new velocity vector, giving it the new position, as defined below: x _mD (t) = x _mD (t - 1) + v _mD (t) (4)

For optimal design of the contour of the control cam 10 are therefore a predetermined number of parameters each having an initialization value for the contour of the control cam 10 defined, wherein the number of parameters corresponds to the degrees of freedom for the optimization. Further, a predetermined amount of parameter sets each having the predetermined number of parameters as a predetermined amount of particles for performing the PSO algorithm and a predetermined number of design constraints and a predetermined number of the parameters influencing design target variables for the contour of the control cam 10 defined as shown in Tables 2 and 3.

According to the invention, a target function or quality function for the PSO algorithm is defined taking into account a certain number of the defined design target values and values for the parameters of each particle are determined using the PSO algorithm, so that taking into account a certain number (preferred all) of the design boundary conditions on respective optimization targets (see Table 3, right column) optimized values of the design target variables for the contour of the control cam 10 the internal combustion engine and thus optimized to the optimization target value (here a minimum) of the target function can be achieved.

A weighting is performed on each of the design target variables included in the objective function, with the value of each parameter being adjusted by the PSO algorithm until the objective function reaches a minimum.

Preferably, all defined design target variables are used to define the target function.

An example could be an objective function for the optimal design of the contour of the control cam 10 be constructed as follows. Fitness = G ₁ * Z _1N -G ₂ * Z _2N + G ₃ * Z _3N + G ₄ * Z _4N + G ₅ * Z _5N , (5) where Z ₁ to Z _{5 are} the different design target values, the index N indicates that the respective values are normalized, that is, refer to a reference value, and the factors G ₁ to G _{5 are} weighting factors for the design target values.

In the objective function, weighting factors are thus weighted according to the invention. Design target sizes to be minimized receive a positive sign, while design target sizes to be maximized receive a negative sign. In addition, a series of penalty terms (not shown) can be included in the objective function or quality function. If design boundary conditions are not met, a penalty value is given a positive value, so that the optimizer or the PSO algorithm attempts to select the parameters in such a way that the penalty term is eliminated, ie the objective function is minimized.

Any weights for optimizing the contour of the control cam 10 may, for example, be made in the light of the importance of compliance with the design constraints or design goals.

According to the PSO algorithm has been further developed and the problem of optimizing the contour of the control cam 10 customized. The PSO algorithm is thus more powerful and the global search property is better than the original version.

In addition, not a single optimization pass for all degrees of freedom / parameters is performed together, but the optimization task is broken down into several sub-steps. Due to the number of degrees of freedom as well as the optimization problem to be solved, the task is too complex to be solved in an optimization run. Theoretically, this is possible, but the expected effort or the expected time to solution is disproportionately high.

Therefore, the entire optimization task (the generation of an optimal control cam contour) is broken down into several subtasks. Starting from a small number of parameters / interpolation points that fulfill the requirements set in the objective function or the design boundary conditions, the number of degrees of freedom (number of parameters per parameter set) is increased with each optimization pass, as in 3 shown.

3 shows in the illustrations 3A to 3E the genesis of a control cam 10 according to an embodiment of the invention, wherein 3A a number of 8 degrees of freedom, 3B a number of 12 degrees of freedom, 3C a number of 16 degrees of freedom, 3D a number of 20 degrees of freedom and 3E show a number of 241 degrees of freedom.

First, the program starts with the initialization of the particles. Each particle is characterized by the fact that it carries a solution combination of the parameters or degrees of freedom, ie of one Parameter set of certain number of parameters is formed. Each parameter represents a point on the ram stroke (see 3 ). The case according to 3 shows 30 particles on their way from 200 iterations starting from a stochastic initialization with 8 degrees of freedom ( 3A ) until convergence at the point of best / lowest goodness value of the best particle with 12, 16 and 20 degrees of freedom ( 3B - 3D ).

As the calculation proceeds, the contour of the ram stroke is generated. On the left side of each 3A - 3D the time is shown approximately in the middle of the allowed iterations and at the end of an iteration. The initially stochastically distributed swarm begins to converge. The curve drawn with solid points shows the best particle at the end of an iteration. The curves drawn with unfilled dots (rings) represent the other particles that are positioned worse in the search space and carry the higher quality function values.

Each in the middle of the 3A - 3E is shown how the particle swarm converges toward the best particle with the lowest merit value until finally the swarm accumulates at the end of the iterations at the best point of the previously evaluated search space (plotted curves on the right hand side of the 3A - 3E ).

The increments of the degrees of freedom specified in the program continue this process until the end of a control cam 10 with in the present case 241 Parameters is generated. This approach has proven to be effective.

The results of an optimization run are passed on to the next optimizer run with the next highest degree of freedom. For this purpose, a 1-D data interpolation is created from the results and the next highest degree of freedom. These new nodes serve as initialization solutions for the particle swarm in the next higher optimization stage. The calculation starts with 8 degrees of freedom. The initialization takes place with equally distributed random numbers. It has proved successful to initialize with free values and then pass the results on. The resulting control cam contour is thus created completely free and does not result from an example given cosine function.

In other words, after a completed pass of the PSO algorithm, the number of parameters per parameter set is increased, passing the values of the parameters determined by the completed pass of the PSO algorithm to a pass of the PSO algorithm directly following the completed pass, On the basis of the transferred values of the parameters and the increased number of parameters per parameter set, an interpolation is performed and the values of the parameters determined with the interpolation are used as initialization values for the following pass of the PSO algorithm.

Up to a degree of freedom of 36 inclusive, both the interpolated results of the previous calculation run and evenly distributed random numbers in the interval from 0 to a maximum ram stroke are used as initialization. From a degree of freedom of 41, only the interpolated results of the previous calculation run are applied.

In other words, up to a number of parameters per parameter set including the value of 36 for determining the initialization values for the directly following pass of the PSO algorithm, both the interpolated values of the parameters from the completed run of the PSO algorithm and evenly distributed random numbers of a predetermined one Interval used. From a number of 41 parameters per parameter set, only the interpolated values of the parameters from the completed run of the PSO algorithm are used to determine the initialization values for the directly following pass of the PSO algorithm.

A corresponding program window offers, after the calculations, the possibility of all operating data of the control cam 10 at each support point and to visualize the ram stroke curve.

Furthermore, the optimization described herein includes some peculiarities. An integral further development of the PSO algorithm used compared to the original version is the use of a so-called restriction or constriction coefficient, which eliminates the assignment of the sensitive variable v _max . In the versions of the PSO algorithm used so far, the variable v _{max determines} the maximum allowable velocity of a particle in one dimension, such as in Kennedy, J .; Eberhart, RC; "Swarm Intelligence"; Morgan Kaufmann Publishers, San Francisco, USA 2001 described.

A too small constraint coefficient allows only a very limited local search, too high a value can lead to massive restriction of the local search property. The constraint coefficient determines the freedom of movement of the particles in the search space. The equation for calculating the current particle velocity (equation (2) without w or inertia weight) is multiplied by the value of the restriction coefficient. It has proved expedient to calculate the coefficients in the first 60 percent of the iterations with uniformly distributed random numbers in the interval [0,1; 1] to choose. Then it decreases linearly from 1 to 0.2087 until the end of all iterations, as in 4 shown.

This strategy gives the particles enough freedom of movement to safely reach an optimum found in the stochastic part of the constraint coefficient allocation as a point of convergence. The value 1 has been determined empirically while the constraint coefficient end value of 0.2087 is set to the in Clerc, M .; Particle Swarm Optimization; ISTE - Hermes Science Puplishing, London, UK, 2006 described calculation for φ = φ ₁ + φ ₂ = 2 + 5 = 7 is due. The increased weighting of φ ₂ results in increased particle movement toward the particle with the best functional value found so far, and has been found to be most suitable for optimizing a control cam contour.

The conclusion is that when the PSO algorithm is performed, a predetermined number of iterations are run through, wherein in the PSO algorithm, an actual particle velocity of the particles is multiplied by a constraint coefficient, and wherein in the first 60 percent of the predetermined number of iterations, the constraint Coefficient of uniformly distributed random numbers in the interval [0,1; 1] is selected and then decreases linearly from a value of 1 to a value of 0.2087, up to 100 percent of the predetermined number of iterations.

Equally important has been the selection of a suitable limit violation behavior when implementing the PSO algorithm. This describes or controls the behavior of the particles if a violation of the permissible range occurs when calculating a new speed and subsequently a new location in a dimension of a particle. For the application of optimizing a control cam contour, it is crucial for success how this limit violation behavior is selected.

The present version of the PSO algorithm uses the following mechanism: If, when performing the PSO algorithm, a particle exceeds or falls below a limit specified in a given dimension, a new location for the particle is determined to be equal to the predetermined limit, where a current velocity of the particle is determined as the difference between an upper parameter boundary and previous location of the particle or as the difference between the previous location of the particle and a lower parameter boundary.

Another special feature of the optimization of a control cam contour described here is the use of a dynamic quality factor. For non-compliance with design boundary conditions, relatively high penalty values are awarded to the objective function or quality function. If, for example, a particle with its parameters (plunger strokes) has an impermissibly high acceleration at one point (parameter), then a penalty is assigned for this parameter.

In general, the penalty terms in the values stand out from the optimization goals. The optimization goals and the penalty terms are included in the merit function and are summed up there in the present application case (search of the optimization algorithm to a minimum). In this context, relatively high sentences are awarded as soon as design boundary conditions are not fulfilled. The comparatively high punitive values ensure that all design boundary conditions are initially met.

In principle, then the optimization of the control cam contour. The swarm converges to a minimum on a successful computation pass. This minimum is characterized by the satisfaction of all design constraints (i.e., no penalty term) and a corresponding control cam contour (minimization of the differences defined below).

In essence, the cam contour is generated by taking the differences in both the accelerations and the speeds of adjacent points on the ram stroke contour and then squared. Squaring evaluates positive and negative values of the differences equally. It also ensures that the resulting quality value is always positive, thus maintaining the direction of optimization (minimum search). The inclusion of minimizing the squared differences from the speeds and accelerations of adjacent points ceases Rounding the cam contour. Using the minimization of the squared differences from the adjacent points on the ram stroke results in a linear ram stroke curve.

As the number of degrees of freedom increases, so does the sum of the above-mentioned differences. So that these do not take such large values that the marginal conditions penalties are superimposed, a quality factor is introduced. As the number of parameters (number of degrees of freedom) increases, the quality factor becomes smaller. The so-called differences are multiplied by the quality factor. Thus, the focus of the optimization continues to be on the fulfillment of the design boundary conditions or constraints and subsequently on the generation and rounding of the control cam contour.

In conclusion, with regard to the PSO algorithm used in accordance with the invention, it should be noted that this according to embodiments of the invention is based on that described in the document "Particle Swarm Optimization - An Overview", R. Poli, J. Kennedy, T. Blackwell, Springer Science 2007 described PSO algorithms possibly with the extensions shown there and / or based on the in the article of J. Kennedy and R. Eberhart "A New Optimizer Using Particle Swarm Theory", pages 39-43, from Proc. IEEE Int. Conf. on Neural Networks, 1996 described PSO algorithms may be performed or realized with the extensions shown there.

Further possibilities for implementing or realizing the PSO algorithm used according to the invention and a need-based adaptation thereof are described in the seminar report of the University of Dortmund by Niels Pothmann, Seminar "Optimization and decision support" Lecture "Swarm Intelligence", under point 3, pages 7-14 (available on the Internet at: http://ls2-www.cs.uni-dortmund.de/-jansen/seminare/opt2006/nielspothmann. pdf) described.

LIST OF REFERENCE NUMBERS

1

Cam-follower roller assembly

10

control cam

11

Cam center

20

tappet roller

h _N

cam lobe

e

axial offset

α

lead angle

H

ram stroke

L1

Center distance without desalination

L

Center distance with offset

R _R

roller radius

R _G

base radius

M _d

Cam drive torque

v

current ram speed

v _limit

Cross ram speed

a

current ram acceleration

a _border

Cross slide acceleration

p _perm

permissible pump chamber pressure

p _limit

Border pump chamber pressure

n _pGrenz

Limit speed

n _limit

Limit speed control cam

RP

local radius of curvature control cam

RP _limit

Boundary curvature radius control cam

F _rubbing

Frictional force of the tappet roller (ram)

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 102006043460 A1 [0005, 0006]

Cited non-patent literature

• "Research - Education - Further Education", Report No. 14, "A Mathematical Method for Optimizing Cams", Hardy Moock, University of Kaiserslautern, Department of Mathematics, January 1986 [0004]
• J. Kennedy, R. Eberhart: Particle Swarm Optimization. Proc. IEEE Int. Conf. on Neural Networks, 1995, pp. 1942-1948 [0006]
• Kennedy, J .; Eberhart, RC; "Swarm Intelligence"; Morgan Kaufmann Publishers, San Francisco, USA 2001 [0095]
• Clerc, M .; Particle Swarm Optimization; ISTE - Hermes Science Puplishing, London, UK, 2006 [0097]
• "Particle Swarm Optimization - An Overview", R. Poli, J. Kennedy, T. Blackwell, Springer Science 2007 [0106]
• J. Kennedy and R. Eberhart "A New Optimizer Using Particle Swarm Theory", pages 39-43, from Proc. IEEE Int. Conf. on Neural Networks, 1996 [0106]
• "Optimization and decision support" Lecture "Swarm Intelligence", under point 3, pages 7-14 (available on the Internet at: http://ls2-www.cs.uni-dortmund.de/-jansen/seminare/opt2006/nielspothmann. pdf) [0107]

Claims (12)

Method for laying out the contour of a control cam ( 10 ), comprising: defining a predetermined number of control cam contour parameters each having an initialization value ( 10 ), Defining a predetermined set of parameter sets each having the predetermined number of parameters as a predetermined amount of particles for performing a Particle Swarm Optimization algorithm, defining at least one design constraint for the contour of the control cam ( 10 ), Defining at least one design target variable that can be influenced by the parameters for the contour of the control cam ( 10 ), Defining a target function for the Particle Swarm Optimization algorithm involving at least one of the defined design target values, and using the Particle Swarm Optimization algorithm, determining values for the parameters of each particle such that at least a design constraint is achieved an optimized target value value for an optimization target. The method of claim 1, wherein weighting is performed on each of the design target variables included in the objective function, and wherein the value of each parameter is adjusted by the PSO algorithm until the objective function reaches a minimum. The method of claim 1 or 2, wherein in performing the Particle Swarm Optimization algorithm, a predetermined number of iterations are traversed, wherein in the Particle Swarm Optimization algorithm, an actual particle velocity of the particles is multiplied by a constraint coefficient, and wherein in the first 60 percent of the predetermined number of iterations, the constraint coefficient of uniformly distributed random numbers in the interval [0,1; 1] is selected and then decreases linearly from a value of 1 to a value of 0.2087, up to 100 percent of the predetermined number of iterations. A method according to any one of claims 1 to 3, wherein, when performing the Particle Swarm Optimization algorithm, when a particle exceeds or falls below a threshold value set in a particular dimension, a new location for the particle is determined equal to the predetermined threshold value, and wherein an actual velocity of the particle is determined as the difference between an upper parameter boundary and previous location of the particle and a difference between the previous location of the particle and a lower parameter boundary. Method according to one of claims 1 to 4, wherein in defining the predetermined number of parameters for the contour of the control cam ( 10 ) the parameters equally distributed random numbers receive corresponding initialization values. Method according to one of claims 1 to 5, wherein after a completed pass of the Particle Swarm Optimization algorithm, the number of parameters per parameter set is increased, wherein the values of the parameters determined by means of the completed pass of the Particle Swarm Optimization algorithm Passing a pass directly following the completed pass of the Particulate Swarm Optimization algorithm, interpolating on the basis of the passed values of the parameters and the increased number of parameters per set of parameters and the values for the parameters determined by the interpolation as initialization values be used for the next pass of the Particle Swarm Optimization algorithm. Method according to claim 6, wherein as the parameters for the contour of the control cam ( 10 ) Points are defined on a ram stroke, and wherein the contour of the control cam ( 10 ) is calculated from the values of the parameters determined by the Particle Swarm Optimization algorithm. The method of claim 7, wherein the objective function has squared differences in both velocities and accelerations of adjacent points on the ram stroke, and wherein in the objective function the differences are multiplied by a factor of quality decreasing as the number of parameters per set of parameters increases. Method according to one of Claims 6 to 8, wherein up to a number of parameters per parameter set including the value of 36 for determining the initialization values for the directly following pass of the Particle Swarm Optimization algorithm both the interpolated values of the parameters from the completed pass of the Particle Swarm Optimization algorithm, as well as gated distributed random numbers of a predetermined interval. Method according to one of claims 6 to 9, wherein, starting from a number of 41 parameters per parameter set for determining the initialization values for the directly following pass of the particle swarm optimization algorithm, only the interpolated values of the parameters from the completed pass of the particle swarm Optimization algorithm can be used. Method according to one of claims 1 to 10, wherein as design boundary conditions at least one element, several elements or all elements of the following design boundary condition group are defined: a current ram speed of one with the control cam ( 10 A current ram acceleration of the ram should be smaller than a ram acceleration of the plunger, a cam drive torque should be minimal, a permissible pump chamber pressure of a fuel pump should be greater than a minimum required Grenzpumpenraumdruck the fuel pump , a limit speed should be greater than a speed of the control cam and a local radius of curvature of the control cam ( 10 ) should be smaller than a radius of curvature boundary. The method of claim 11, wherein at least one of an element, a plurality of elements, or all elements of the following design target group are defined as design targets: the current ram speed, the current ram acceleration, the current cam drive torque, the allowable pump room pressure, the limit / ramp down speed and a current frictional force of the plunger.

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