Co-simulation computer system

Abstract

A computer system (CPS) for digital modular simulation of a system (SYS) and a computer-implemented method thereof, comprising: (a) decomposing the system (SYS) into at least two sub-units (SSY) simulation subsystems (SMNs), and (b) progressively and repeatedly simulating the respective sub-units (SSYs) during the respective subsystem time steps (SMPs), generating subsystem step outputs (MSOs) based on subsystem step inputs (MSIs). To improve accuracy and performance, the method includes the following additional steps: (c) sending a subsystem step input (MSI) to the receiving subsystem (SMR) and simulating the subsystem (SMN) over a delay time (DLT) before generating a subsystem step output (MSO); (d) receiving a connection interface variable (TRD) from the transmitting subsystem (SMS), the connection interface variable including at least one of the following: - digital data (DTA), - parameters of at least the data prediction model (DEM) of the digital data (DTA), - the data prediction model (DEM) assigned to the digital data (DTA); (e) predicting the digital data (DTA) by the data prediction model (DEM) over the delay time (DLT) to obtain predicted digital data (EDT) of the interface variable (TRD) provided by the transmitting subsystem (SMS); and (f) initiating the next simulation step of the receiving subsystem (SMR) and generating the next subsystem step output (MSO) based on the subsystem step input (MSI), wherein the subsystem step input (MSI) includes the predicted digital data (EDT).

Description

Technical Field

[0001] This invention relates to computer-implemented simulation.

[0002] More specifically, the present invention relates to simulations implemented by at least two computers that simulate tasks in parallel to achieve a common result. Background Technology

[0003] The industrial applications of electromechanical simulation have now reached a point where modular simulation is necessary beyond simple practical aspects. Modular representation couples / decouples sub-units, simulates and verifies them separately, and then connects them together to obtain a fully digital representation of the entire architecture. In fact, co-simulation is a hot topic more for design reasons than performance considerations, as runtime simulation models have a modular structure of interconnected sub-units (blocks representing specific physical domains with their own internal dynamics, control boxes, etc.). Co-simulation is a way of simulating such a model by simulating each entity separately and managing their corresponding knowledge of information about other sub-units; this can often be referred to as communication. This is primarily because it is impossible to group these sub-units into a large model due to platform incompatibility, for example, different software developed for each sub-unit, or different internal solvers used by each sub-unit. Therefore, we typically obtain the following results from co-simulation:

[0004] Because communication occurs in discrete time rather than continuously, co-simulation may be less accurate than individual simulations of the assembled system. Sampling of exchanged signals can lead to digital artifacts and instabilities throughout the simulation.

[0005] - Co-simulation may take longer to process. Although sub-cells can be smaller in terms of the number of variables and can use parallel machine architectures, communication often introduces discontinuities, which leads to untimely restarts of the internal solvers in each of these sub-cells.

[0006] Methods for handling the following problems are known:

[0007] - Digital artifacts introduced by signal sampling at the interface.

[0008] - Signal reconstruction between communications

[0009] Point to:

[0010] • Use the Gauss-Seidel exchange instead of the Jacobi exchange.

[0011] • Energy savings at the interface via signal correction

[0012] • Use the output history to predict the input.

[0013] • The use of Jacobi information

[0014] • Iterative co-simulation with rollback functionality.

[0015] Generally, using a larger time step for data exchange can mitigate the efficiency issues arising from co-simulation. Less frequent information exchange may worsen the accuracy of the global solution. A simple approach to improving this dilemma is to use predictions between data exchanges.

[0016] A known tool (COSIMATE, provided by KiasTek, with DPA (Data Prediction Algorithm)) uses predictions to reduce communication frequency. Essentially, it predicts values ​​based on the past.

[0017] Another approach (Martin Benedikt: Model.connect derived from AVL, using the NEPCE algorithm: Nearly Energy Preserving Coupling Element) provides correction for communication variables based on energy conservation between each sub-unit.

[0018] Simulation setups using iterative co-simulation methods are difficult to implement because sub-cells generated by different authoring tools do not provide the ability to perform integration over time intervals that have already been simulated (the so-called "rollback" capability).

[0019] One objective of this invention is to improve the accuracy of co-simulation.

[0020] Another objective of this invention is to make co-simulation more effective.

[0021] Another objective of this invention is to enable co-simulation to be applied more flexibly to a wide range of systems, regardless of their capabilities. Summary of the Invention

[0022] The objective of this invention is achieved by the independent claims. The dependent claims describe advantageous improvements and modifications to the invention.

[0023] According to the present invention, a solution to the above-mentioned problem is provided by a method with additional steps as initially defined:

[0024] (a) Decompose the system into at least two sub-unit simulation subsystems.

[0025] (b) Simulate the corresponding sub-unit by progressively and repeatedly generating the sub-system step output based on the sub-system step input during the corresponding sub-system time step (which can be considered as 'operating / simulating the sub-system').

[0026] It is characterized by the following additional steps:

[0027] (c) Receive connection interface variables from the transmitting subsystem, the connection interface variables including at least digital data and prediction subsystem outputs—where the digital data belongs to the transmitting subsystem—including details about at least one piece of information from the transmitting subsystem to be sent to at least one receiving subsystem.

[0028] The transmitting subsystem and the receiving subsystem are corresponding subsystems.

[0029] (d) Delay the forwarding of received connection interface variables by a delay time, during which these system simulation time steps (b) are performed.

[0030] (e) Predicting digital data by generating a data prediction model based on past digital data generated by the system within a delay time, thereby obtaining predicted digital data from the digital data provided by the transmitting subsystem.

[0031] (f) Start receiving the next simulation step of the subsystem, and generate the next subsystem step output based on the subsystem step input, wherein the subsystem step input includes predicted digital data.

[0032] This invention enables robust, accurate, and effective simulation.

[0033] According to another preferred embodiment, the data prediction model is selected as a polynomial function of degree 0, 1, or 2.

[0034] According to another preferred embodiment, the method may include an additional step of extending the polynomial order of the data prediction model (DEM) obtained by Hermite interpolation (e.g., *Computational Mathematics*, Vol. 71, No. 239, pp. 1043-1074, S0025-5718(02)01446-1, published electronically on January 17, 200). Regardless of the polynomial degree (0, 1, or 2) of the given data prediction input to the subsystem step, it can preferably be extended to order 3 by Hermite interpolation. The constraints of this Hermite interpolation extension may be:

[0035] -The last value reached by the predictor at the current moment (Digital Data (DTA)).

[0036] - The value predicted by the predictor at the end of the current time step (Digital Data (DTA)).

[0037] -The last time derivative of the digital data (DTA) reached by the predictor at the current time, and

[0038] - The time derivative of the digital data (DTA) predicted by the predictor at the end of the current time step. Therefore, the smoothness of the subsystem-level inputs is not compromised at the current communication time. If this can be done at every time step, then all inputs can be guaranteed to have C1 smoothness (continuity and the continuity of their derivatives).

[0039] A subsystem can be understood as a simulation unit, or a corresponding sub-unit.

[0040] Another preferred embodiment provides one of the described methods, the corresponding advanced method including the following additional steps:

[0041] - The data prediction model is determined by selecting the data prediction model type from a set of predefined functions, and

[0042] - The data prediction model is calibrated based on the digital data of the corresponding transmission subsystem output from the current and previous subsystem steps of steps 1, 2, 3 or more. - This can preferably generate polynomial data prediction models of different orders.

[0043] - The absolute error of each data prediction model is determined by comparing the numerical data calculated by the data prediction model based at least on the steps preceding the latest subsystem step output with the latest numerical data output by the subsystem step at the same point in time when the subsystem is being sent.

[0044] - Select a data prediction model with the order corresponding to the minimum absolute error from the selected data prediction model type.

[0045] - If all data prediction models of the data prediction model type produce errors greater than a given threshold, use constant prediction (order 0) as a safety measure.

[0046] Ideally, all data prediction models are polynomials of different orders.

[0047] Preferably, the data prediction model type can be selected at the beginning of the co-simulation, or even more preferably only at the beginning of the co-simulation and remain unchanged (without dynamic changes) during the co-simulation, where co-simulation refers to the co-simulation steps. Most preferably, the change of the data prediction model type can be completed or is only possible before the start of the co-simulation.

[0048] Preferably, dynamic changes during co-simulation can be performed for at least one (preferably for all data prediction models) polynomial.

[0049] In a simulation time context, if the reference time and the virtual simulation time are not significantly different according to the context, then the reference time refers to the virtual simulation time.

[0050] After determining the data prediction model (which can be done by selecting the data prediction model type with the smallest absolute error from a (pre)selected data prediction model type) and optionally calculating the order (polynomial degree) of the data prediction model, the coefficients of the associated polynomial function can be calculated. These coefficients can then be transmitted to the connected input, allowing the latter to have their time-dependent formulas or to inject the calculated digital data during the co-simulation step of its system. Since the simulation can be asynchronous, the data prediction model (e.g., the polynomial function) does not necessarily need to be directly evaluated; instead, it can be sent to a receiving subsystem that can use the separately transmitted data prediction model to determine the digital data itself. This option can be implemented alternatively and can be best suited to each combination of receiving / transmitting subsystems.

[0051] The calculation of this coefficient can be done in two different ways: by extrapolation or by constrained least squares, which is a least squares fit that forces the data to reach a specific value at a specific time.

[0052] A preferred embodiment provides an "extrapolation" mode that uses the latest digital data provided from the transmitting subsystem to determine and calibrate the order of the data prediction model. This method can reduce any influence or effect from too far in the past, but can also produce small discrepancies between the set of values ​​already used to determine the order (as before) and the set of values ​​used to calibrate the polynomial function intended for use with the receiving subsystem or as a time-dependent input to the receiving subsystem.

[0053] As an alternative preferred embodiment, the "constrained least squares" mode can fit a data prediction model, for example, an nth-degree polynomial function over the n+2 most recent digital data provided by the transmitting subsystem when the determined order is n (during calibration). This ensures that all points considered for determining the order are also considered for polynomial function calibration. Moreover, this makes current and near-future values ​​depend on older values ​​(older than in the extrapolation mode).

[0054] Another preferred embodiment provides a step (in other words, a stage) to convert a polynomial function into a lower-order polynomial function, particularly for systems where time-dependent numerical data may not be generated by a sufficiently high-order data prediction model polynomial function. This keeps the behavior close to the initially defined behavior and also maintains the values ​​that the system should reach at the end of the co-simulation steps. Preferably, this step (in other words, the stage) can be performed after each predictor calibration as a post-processing step (it is post-processing of the calibration, but pre-processing of the computations of the co-simulation steps). This can transform the predictor requested by the method up to this step into a more feasible predictor for the system.

[0055] Another preferred embodiment of the previously defined example provides polynomial order reduction for systems that only support order 1 or lower: when a 2nd order polynomial function is injected as a time-dependent input, the order reduction can be used as a replacement based on the values ​​at the beginning and end of the corresponding macrostep, and in the case of order 0, this is only the value at the end of the step.

[0056] Another preferred embodiment of the previously defined examples provides a reduction step for the system. It can be applied to transform predictor models such as:

[0057] The values ​​that should be reached at the end of the co-simulation step of the system while maintaining the input will be preserved as is at the moment of calculating the error and injected into the time step.

[0058] This transition phase can preferably be applied to systems that support orders no higher than 1.

[0059] When a second-order polynomial function according to this method can be injected as a time-dependent input, but the system supports no higher than the first order, an affine function based on the values ​​at the start and end of the macrostep can be used.

[0060] When a first or second-order polynomial function according to this method can be injected as a time-dependent input, but the system supports no higher than order 0, a constant function based on the value at the end of the macro step can be used.

[0061] In traditional cosimulation, the dynamic characteristics of coupled variables can be lost (e.g., when using a zero-order predictor model (constant) to maintain the step size input). To avoid this, the input can be computed as a time-dependent variable, preferably a polynomial function, preferably of order 0, 1, 2, or higher. The order of the next step is determined by comparing the absolute error obtained from our attempt to predict the most recently acquired value with predictions of orders 0, 1, and 2. This alpha-posterior criterion determines the order to be applied to the time-dependent input connected to the output, based on which previous computations are performed. This process can be implemented individually for each output variable of each subsystem. This means that different outputs of the same subsystem can have different polynomial orders, and this also applies to inputs from outputs connected to it.

[0062] In co-simulation between subsystems, exchanges can typically be performed at fixed time intervals. Users can usually select a time interval (often called a macro time step) that adjusts the pace of exchanges between different parts of the overall system simulation. This approach is widely used in industry. The challenge may lie in defining the optimal macro time step at which exchanges may occur.

[0063] According to a preferred embodiment of the present invention, the method may include the following additional steps:

[0064] - The error is determined by comparing the digital data calculated by the data prediction model based at least on the steps preceding the latest subsystem step output with the latest digital data of the subsystem step output at the same point in time when the subsystem is being transmitted (preferably: the relative error is calculated from the absolute error).

[0065] - Adjust the subsystem time step of the transmitting subsystem according to a predetermined relationship between the relative error and the subsystem time step change (expand: increase, or contract: decrease).

[0066] This advantageous enhancement enables a better and more dynamic approximation of the optimal time step. The subsystem time step of the transmitting subsystem to be adjusted can be understood as the last time step used by that subsystem, or the "old time step." This last used time step of the subsystem can change dynamically, and it may not be inherent to the model, and it may be different for each subsystem (asynchronicity).

[0067] According to a preferred embodiment of the present invention, the predetermined relationship between the error (preferably: the relative error calculated from the absolute error) and the change in the subsystem time step is a continuous function. More preferably, the predetermined relationship between the error and the subsystem time step is a decreasing function.

[0068] According to a preferred embodiment of the present invention, the predetermined relationship between the error (ERD) and the subsystem time step (SMP) is defined as follows:

[0069] Adjusted (SMP) = Previous (SMP) * BETA * (RTTO / ERD) ∧ (n+1)

[0070] in:

[0071] n: The polynomial order of the data prediction model (DEM)

[0072] RTTO: Relative Tolerance

[0073] ERD: Error (preferably using relative error, which can be referred to as NERR: Normalized Absolute Error (ERD))

[0074] BETA: Safety factor [0.5, 1.0], preferably 0.9.

[0075] According to a preferred embodiment of the present invention, the delay time is suitable for delaying the transmission of digital data until a predetermined time point when the receiving subsystem is ready to receive the digital data.

[0076] This "adjusting subsystem time step" phase can be referred to as time stepping, and the system module that performs the time stepping can be called a "time stepper." The time stepper determines an expansion coefficient on the subsystem that provides the subsystem step output (referred to as "output"). This expansion coefficient is multiplied by the latest co-simulation step size to obtain the upcoming co-simulation step size. Therefore, a coefficient greater than 1.0 will result in an expansion of the step size, while a coefficient less than 1 will result in a contraction of the step size. Subsystems without outputs will set the upcoming co-simulation step size to the difference between the arrival time and the final time. The scheduler can then adjust the step size based on the difference to control desynchronization. At the end of the co-simulation step for a system with at least one output, the value of the output can be retrieved. Since the data prediction model (e.g., a polynomial function) is known, the data prediction model can be evaluated at the end of the most recent co-simulation step (the so-called "predictor") and compared with the value obtained by simulating the upcoming step (the so-called "corrector"). If the data prediction model (e.g., a polynomial function) is of order n, then the error is of order n+1. This means that, at a fixed co-simulation step size, the logarithm of the error should decrease by order n+1 faster than the size of the co-simulation step. By normalizing this error (to eliminate the influence of orders of magnitude) and providing this normalized error (i.e., the relative error) to a "predetermined relationship between the error and the change in the subsystem's time step," which can be called an expansion heuristic, an expansion coefficient can be obtained. The expansion heuristic has one parameter: "relative tolerance." This acts as a threshold: when the relative error is less than the relative tolerance, the expansion coefficient will be greater than 1, and vice versa. The result is that the system may take increasingly larger step sizes when the error on its output is small, and increasingly smaller step sizes otherwise. The β coefficient serves as a safety or stability factor. It can be arbitrarily fixed at 0.9 to ensure that the step size does not increase too rapidly.

[0077] Error normalization can be accomplished as follows:

[0078] Regarding the order of magnitude,

[0079] • Regarding the magnitude observed in the relevant outputs at the start of the co-simulation, or

[0080] • Regarding the magnitude observed in the relevant output from the start of the co-simulation, which we decay at a certain rate (e.g., 5% per second) to ensure that large jumps have no perpetual effect.

[0081] • A process identical to the one described above is used, but a restart is added when an event is detected (forgetting past peaks). This event could be a critical point (derivative annulation), detected by a change in the sign of the slope on the output.

[0082] • The gradually calculated standard deviation of the output of interest, around the gradually calculated mean.

[0083] • The average deviation of the output calculated gradually around the average value calculated step by step.

[0084] • The safest process among all the previously described processes, that is, the process that causes the smallest expansion coefficient.

[0085] The choice of this normalization method is essentially equivalent and can be applied to each output variable at each time step. The step size evolution should remain under control when the expansion coefficient is too small (which may occur for "very" large errors) or too large (which may occur for temporary constant output variables that produce zero error). For this purpose, as a preferred embodiment, a minimum and a maximum value for the expansion coefficient can be selected. When the coefficient is less than the boundary minimum, the coefficient is set to the minimum value, and correspondingly, when the coefficient is greater than the maximum value, the coefficient is assigned.

[0086] Another preferred embodiment may provide that if the scheduler has reduced the previous (“old”) steps, the minimum and maximum limits of the expansion ratio can be corrected such that the new step is greater than the original minimum expansion ratio multiplied by the original previous step (determined by the time stepper, without correcting the scheduler) and also less than the original maximum expansion ratio multiplied by the original previous step size.

[0087] As a preferred embodiment

[0088] - The system can adjust its step size based on the smallest expansion ratio among those produced by each of its outputs (this is safe, but usually slow), or

[0089] - The step size is set based on the average of the expansion ratios produced by each of its outputs (usually faster because the step size is expected to be larger, but less safe).

[0090] According to a preferred embodiment, the method may include an additional step (or stage) that limits the time step of an upcoming subsystem, such that it corresponds to the end time of the first upcoming step of any subsystem having an output connected to the input of the subsystem to be time-stepped.

[0091] A subsystem can limit its upcoming step size to correspond to the end time of the first upcoming step of any subsystem with an output connected to its input: this is an "input-based constraint". Doing this on each subsystem (starting with the subsystem with the most recent upcoming communication time) ensures that no subsystem uses the data predictor at a time greater than the time when the predictor is considered valid with respect to the applied relative tolerance.

[0092] Applying this step (phase) preferably to each subsystem (preferably starting with the subsystem with the smallest impending communication time) ensures that no subsystem uses the data predictor for a time longer than the time during which the predictor is considered effective with respect to the applied relative tolerance.

[0093] Special attention must be paid to the order of the subsystem being analyzed. In fact, restricting the subsystem to an incorrect order can lead to suboptimal results. According to a preferred embodiment, the order can be adjusted according to the following process:

[0094] - A subsystem with a second most recent next communication time can be provided with different time steps and thus different communication times, where the new value will replace the old value for the remainder of the process.

[0095] Other subsystems can repeat the time step adjustment method steps according to the order of the next most recent communication time.

[0096] In other words, the order of the input-based constraints can be subsystems ordered according to their next communication time, sorted in ascending order of communication time. "Communication time" is equal to the time it takes for the corresponding previous simulation step to end and for the subsystem to prepare to exchange data before the start of the next simulation step.

[0097] According to another preferred embodiment, the same process as described above can be applied, but it should be assumed that each subsystem is connected to every other subsystem (even if this is not the case). This assumption synchronizes the exchange time, provided that each subsystem supports variable step size. This synchronization is useful even in systems that are not specifically composed of subsystems with variable step size capabilities, thus the process results in “more synchronized” co-simulation and reduces the number of idle subsystems waiting for other subsystems.

[0098] The first input-based constraint strategy can be called "causal synchronization." Users can choose to apply "forced synchronization," which proceeds in the same way, but as if each subsystem were connected to every other subsystem. This helps address the problem of insecure constraints when two subsystems have close communication times (this can allow for a very small step size for one of them). Input-based constraints should occur after insensitivity-based extensions; otherwise, the latter would break the guarantees provided by input-based constraints.

[0099] Some subsystems can generate outputs that are connected to the inputs of other subsystems with applied step sizes. These fixed-step receiving subunits will be unable to continue processing data until the next upcoming communication time. If all outputs of a given system are connected to such inputs (belonging to a fixed-step system), and if the system is unconstrained by its inputs (such as input-based constraints), its step size can be expanded.

[0100] According to a preferred embodiment, referred to as "output-based extension," the method may include the following additional steps (stages):

[0101] - Select only the subsystems that have subsystem step size outputs connected to the subsystem step size inputs of subsystems that do not support variable subsystem time steps.

[0102] - Extend the upcoming subsystem time step of the selected subsystem until the next step of the subsystem with subsystem step inputs connected to its subsystem step output ends.

[0103] In practice, these subsystems cannot handle the limitations of changing the time step. Therefore, increasing the time step will not change the outcome, but will instead produce a speedup, which may reduce costs by decreasing elapsed time.

[0104] According to a preferred embodiment of the method, the subsystem has no output (sub-model step output), and the time step can be set to the remaining time until the simulation ends. If such a subsystem without output has sub-model step input, then according to the process described in claim (see Input-Based Constraints), the upcoming time step will be constrained to a more reasonable time step.

[0105] According to a preferred embodiment, additional method steps (stages) may be provided after the time stepper, which defines the time step size for each subsystem and, in other words, the next communication time (in other words, the "meeting" time), can be provided. These method steps (stages) may be provided to correct the time step size according to the I / O limitations of each subsystem.

[0106] Therefore, the scheduling module, or so-called scheduler, can adjust the time step size on each system, thereby defining active and idle subsystems / systems.

[0107] Each time a co-simulation (which may be a coordination module or communication manager (also referred to as the "coordinator")) triggers a subsystem to perform a co-simulation step, some subsystems may be idle (the coordinator does not trigger the system to do anything): these will be the "idle" subsystems. Conversely, the subsystems that are triggered to perform co-simulation steps can be referred to as the "active" systems.

[0108] In a preferred embodiment, the subsystem can be set to idle to wait for the latest input value.

[0109] According to a preferred embodiment, the subsystem can be set to active or idle based on additional (triggering) steps according to the following rules:

[0110] - A first subsystem is active only if the next end time of all other subsystems assigned to send their outputs as inputs to the first subsystem is strictly greater than the current time of the first subsystem.

[0111] This feature, known as "causal synchronization," improves the method by preventing the subsystem from starting a co-simulation step if it can receive a more recent input value to begin its next co-simulation step, and by preventing the subsystem from running with input values ​​from too long ago (preferably no larger than the step size of the subunit that sent the input data). In short, it improves accuracy.

[0112] According to another embodiment, the selection of idle and active subsystems can be accomplished as if each subsystem were connected to the others. This can be referred to as “forced synchronization.” In this way, systems can be idle, where they will be activated along with previous processing, and any potential asynchrony is controlled. In practice, even if the input-based constraint embodiment reduces asynchrony, it may still occur. For example, when multiple fixed-step subsystems exist, input-based constraints cannot significantly reduce asynchrony. Embodiments that include trigger (active) and stop (idle) subsystems avoid the need to store all output data in a history containing output data generated by subsystems with larger current times and subsystems with smaller current times, as if they were all connected to each other.

[0113] According to a preferred embodiment, the time step size of the subsystem (the difference between the next (planned) communication time and the current arrival time) can be set based on a minimum step size and a maximum step size. This can preferably be done after other method steps change the corresponding step size of the subsystem, or preferably at the final step size change step (phase) of the method. At the end of at least one step size change method step, at least one, several, or each subsystem may have a redefined step size as follows:

[0114] -If the step size is smaller than the smallest, it can be replaced by the smallest.

[0115] -If the step size is greater than the largest, it can be replaced by the largest.

[0116] - If the step size is between the minimum and the maximum, nothing needs to be done.

[0117] Here, the minimum step size is smaller than the maximum step size. To disable this step size adjustment, the minimum step size can be defined as 0, and the maximum step size can be defined as +∞. A subsystem with the applied step size can function without any (including) time step size change steps (stages).

[0118] Another preferred embodiment specifies that the simulation of the system is non-iterative, such that the simulation subsystems interact with each other specifically rather than iteratively.

[0119] Another preferred embodiment specifies that the simulation of the system is iterative, such that at least one of the simulation subsystems interacts iteratively with at least one other simulation subsystem, wherein these subsystems are iterative subsystems.

[0120] For a system in which at least one iterative subsystem can be configured as a manifold model, it is at least a dual model comprising a master model and at least one surrogate model, wherein the surrogate model is capable of repeating at least a single time step, preferably multiple time steps, and wherein the surrogate model includes subsystem step output parameters and subsystem step input parameters that are at least partially identical to those of the master model.

[0121] The method includes additional steps assigned to the defined subsystem time step:

[0122] a) The proxy model receives subsystem step inputs that are at least partially derived from at least one other input-providing subsystem.

[0123] b) The proxy model calculates the subsystem step outputs based on subsystem step inputs that are at least partially derived from at least one subsystem.

[0124] c) At least one other input provides the subsystem computation subsystem step output, including at least a portion of the input to be provided to the next iteration loop of the surrogate model.

[0125] d) Repeat steps a)-c) until the mutual convergence criteria of the input-providing subsystem and the surrogate model's subsystem step outputs are met.

[0126] e) Provide at least a portion of the converged subsystem step output to the main model as at least a part of the subsystem step input.

[0127] f) The master model calculates the subsystem step output based on the subsystem step input and the defined subsystem time step.

[0128] Preferably, the surrogate model can be at least a partial linear approximation of the main model.

[0129] Another preferred embodiment specifies that the converged subsystem step output only covers a portion of the subsystem step input of the main model, wherein the method further includes the following additional steps (stages):

[0130] - The remaining portion of the subsystem input of the master model according to step (e) of claim 1, wherein the master model is the receiving subsystem.

[0131] The present invention also relates to a computer system for simulating a system by applying a computer-implemented method according to at least one of claims 1-12 or a computer-implemented method according to preferred embodiments of the methods described above, comprising:

[0132] - At least two simulation subsystems for simulating the sub-units of the system, wherein each subsystem is designed such that the simulation includes the stepwise and iterative generation of subsystem step outputs based on the subsystem step inputs.

[0133] -Communication Manager

[0134] - The communication channel between the connection subsystem and the communication manager.

[0135] - At least one of the subsystems is designed to send connection interface variables to the communication manager via a communication channel as a transmitting subsystem, and the connection interface variables include at least one of the following:

[0136] -Digital data,

[0137] - At least the parameters of the data prediction model for digital data,

[0138] - Data prediction models assigned to digital data provided by the sending subsystem

[0139] - Wherein the digital data belongs to the subsystem step output of the transmitting subsystem, including details of at least one piece of information about the transmitting subsystem to be sent to at least one receiving subsystem.

[0140] The communication manager is designed to delay the forwarding of received connection interface variables by a delay time, where the delay time is suitable for delaying the transmission of digital data until a predetermined time point.

[0141] -The communication manager or receiving subsystem is designed to predict digital data within a delay time using a data prediction model, in order to obtain the predicted digital data provided by the transmitting subsystem.

[0142] -The receiving subsystem is designed to initiate the next simulation step, which generates the output of the next subsystem step based on the subsystem step input, where the subsystem step input includes predicted digital data.

[0143] -The transmitting subsystem and the receiving subsystem are each a subsystem.

[0144] -The computer system is prepared to initiate the next simulation step of the receiving subsystem to generate the next subsystem step output based on the subsystem step input, wherein the subsystem step input includes digital data.

[0145] The communication manager can be designed to provide the receiving subsystem with either predicted digital data or a data prediction model. If the latter, the receiving subsystem will be designed to predict the digital data within a delay time using the data prediction model to obtain the predicted digital data for the next step.

[0146] Regarding the surrogate model set as a linear approximation, the preferred embodiment specifies that the subsystem can be designed to provide a linear approximation of its internal dynamic characteristics (a so-called "matrix of state-space representation"), and use it to estimate the output values ​​at the end of the upcoming co-simulation step for different input values. In other words, the output numerical data for any time-dependent input at the end of the co-simulation step can be generated by the surrogate model provided by the respective subsystem itself. Once the iterative method for estimating the equations of the surrogate model converges, the subsystem assigned to the respective surrogate model can perform the co-simulation step.

[0147] Generating the output value of the proxy model based on the input value can be accomplished in the following ways:

[0148] • Inject these equations into the solver, or via

[0149] • Calculate the correlation matrix in the Laplace domain and use an algorithm (e.g., Gaver-Stehfest, Fourier, Euler) to compute the latter using the relationship between the obtained input and output.

[0150] According to a preferred embodiment, the second option can be implemented as follows (see claim 17):

[0151] The corresponding subsystems, at least partially represented by surrogate models, can be described by ODE (ordinary differential equation) systems:

[0152]

[0153]

[0154]

[0155]

[0156] t∈[t init , t end [

[0157] in:

[0158] x: State variable (internal to the system). Dimension: n st

[0159] u: Input variable (system requirement). Dimension: n in

[0160] y: Output variable (generated by the system). Dimension: n out

[0161] Linearized ODE system (state-space representation):

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] Control section

[0169] y C =y - (Cx + Du)

[0170]

[0171] Make

[0172] y = y L +y C

[0173] Various symbols

[0174]

[0175]

[0176]

[0177] Control part estimation

[0178] (Reconstruction of polynomial functions with flexible orders, as previously described)

[0179] Linear Part Estimation

[0180] δt [N] :=t [N+1] -t [N]

[0181] Define variable changes on the vector polynomial input function u:

[0182]

[0183]

[0184]

[0185] By switching l and k in the above equation, we obtain The expression for the coefficient:

[0186]

[0187]

[0188]

[0189] in,

[0190] Laplace transform

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197] G can be calculated in the following way:

[0198] Misra P. and Patel RV, “Calculation of the transfer function matrix of a linear multivariable system”, Automatica, Vol. 23, No. 5, pp. 635-640, 1987.

[0199] By considering n out :=n st B:=I (identity matrix) and D:=0 (zero matrix) can be used to calculate P in a similar way.

[0200] Y = GU + Px [N]

[0201]

[0202]

[0203] The estimator itself:

[0204]

[0205] Where Γ is a third-order tensor:

[0206]

[0207] The product of tensor matrices is defined as follows:

[0208]

[0209]

[0210]

[0211] In this way, iteration is costless because each new multidimensional input signal will only change the Ξ matrix, and through the linearity of the inverse Laplace transform, a new output signal can be generated almost instantly.

[0212] A single tensor matrix product is required.

[0213] One of the biggest problems in co-simulation is the long execution time caused by solver restarts within the system. These solver restarts are due to discontinuities in the input variables during communication.

[0214] According to a preferred embodiment of the method of the present invention, the inputs to the receiving subsystem can be transformed such that they are continuous and have continuous time derivatives. In other words, the subsystem receives the C1 interface.

[0215] According to a preferred embodiment, this continuity / smoothness can be achieved by Hermite interpolation at the start and end times of the upcoming step.

[0216] Since the polynomial input formula is known for every input to each subsystem, it is possible to evaluate it and its time derivative in order to obtain these values ​​and derivatives at the upcoming communication time. For the current communication time, the method can reuse the applied values ​​and the time derivative from the previous step—making the data conform to C1.

[0217] When all subsystems are manifolds, iterative solutions can be performed immediately for each surrogate system in a single iteration, where linear systems are constructed as follows:

[0218] - A linear relationship between the inputs and outputs of all subsystem steps, represented by the agent subsystem.

[0219] - A linear relationship between the predicted data and the known value of the upcoming subsystem time step, represented by a multinomial data prediction model, is set to be the same for each subsystem because solving once for the complete set of subsystems makes it create a proxy for the complete system.

[0220] - The remaining portion (which cannot be described using a surrogate model) is treated as a constant term (independent of the input to the next subsystem step expected at the end of the subsystem time step), and

[0221] - The connection information between the subsystem step outputs and the subsystem step inputs of all subsystems can be viewed as an extension of the permutation concept, which allows subsystem step outputs to be unconnected, connected to one or more subsystem step inputs, and this relationship is linear.

[0222] The key advantages of this invention and its preferred embodiments are:

[0223] Robustness and Flexibility: This invention enables co-simulation of models with limited knowledge: the method automatically adjusts the communication step size and selects the order used. A default parameter set is provided. Furthermore, the method allows for any type of co-simulation configuration (accepting systems with applied step sizes mixed with variable-step systems). Regarding the surrogate model, it provides a workaround for systems without rollback that can undergo iterative processes: robustness also rejects systems with no (or fewer) rollback due to the capabilities of the sub-units.

[0224] In terms of the significance of collaborative simulation configuration.

[0225] • Performance: When required, the method of this invention can accelerate co-simulation compared to the fixed-step-size zero-order preserving non-iterative Jacobian method due to the following two aspects: 1. Defining the minimum step size as equal to the step size of the non-iterative Jacobian method (i.e., the most basic co-simulation algorithm, widely used) to give acceptable results (therefore, this invention can only use a larger or equal step size); 2. Using the C1 interface of a system with an embedded solver, the solver can be restarted more quickly due to this guarantee after each communication time.

[0226] • Accuracy: Due to the availability of known solvers in the surrogate model, the process is highly flexible and capable of achieving accurate solutions. In fact, iterative methods (known to be more accurate than non-iterative methods) are possible in configurations with systems that cannot be rolled back. Furthermore, time stepping allows the method to take small steps around the rigid parts of the simulation, which helps increase accuracy.

[0227] The time stepper adjusts the step size when frequent communication is not required. The scheduling defined above avoids unnecessary but costly communication, and the interface can be smoothed to avoid interfering with the solver in the system. Attached Figure Description

[0228] Embodiments of the invention will now be described by way of example only with reference to the accompanying drawings, in which:

[0229] Figure 1A flowchart of the method according to the present invention is shown;

[0230] Figure 2 A flowchart of option (f) of the method step according to a preferred embodiment of the present invention is shown;

[0231] Figure 3 A simplified schematic diagram of a computer system is shown for simulating a system using a method implemented by applying a computer.

[0232] The illustrations in the accompanying drawings are schematic. Note that similar or identical elements may have the same reference numerals in different drawings. Detailed Implementation

[0233] Figure 1 A simplified flowchart illustrating a computer implementation method for digital modular simulation of system SYS is shown, including the following steps:

[0234] (a) Decompose the system SYS into at least two sub-units SSY and simulate the subsystem SMN.

[0235] (b) Simulate the corresponding sub-unit SSY by operating n subsystems SMN, wherein the simulation includes progressively and repeatedly generating the subsystem step output MSO based on the subsystem step input MSI (where the subsystem SMN acts as the receiver of the subsystem SMR) during the corresponding subsystem time step SMP (where the subsystem SMN acts as the sender of the subsystem SMS).

[0236] It is characterized by the following additional steps:

[0237] (c) Receive connection interface variable TRD from the transmitting subsystem SMS, which includes at least one of the following:

[0238] -Digital Data (DTA)

[0239] -At least the parameters of the data prediction model DEM for digital data DTA,

[0240] - Data prediction models DEM assigned to digital data DTA,

[0241] The digital data DTA belongs to the subsystem step output MSO of the transmitting subsystem SMS, including details of at least one piece of information about the transmitting subsystem SMS to be sent to at least one receiving subsystem SMR.

[0242] The functions of the transmitting subsystem (SMS) and the receiving subsystem (SMR) are respectively performed by the subsystem (SMN).

[0243] (d) Delay the forwarding of the received connection interface variable TRD by a delay time DLT.

[0244] (e) The digital data DTA is extrapolated from the data prediction model DEM within the delay time DLT to obtain the predicted digital data EDT of the digital data DTA, which can preferably be calculated in the corresponding receiver subsystem SMR.

[0245] (f) Start the next simulation step of subsystem SMN, and generate the next subsystem step output MSO based on the subsystem step input MSI, where the subsystem step input MSI includes the predicted digital data EDT.

[0246] Step (c) above may include the following additional steps:

[0247] (c1) The data prediction model DEM is determined by selecting the data prediction model type DET from a set of predetermined functions, and

[0248] (c2) Calibrate the data prediction model DEM by transmitting the SMS digital data DTA from the corresponding sending subsystem of the MSO from the previous subsystem steps 1, 2, 3 or more, including the latest MSO. lst .

[0249] Step (f) above may include the following additional steps:

[0250] (f1) By comparing the numerical data DTA calculated by the data prediction model DEM based at least on the steps prior to the output MSO of the latest subsystem step. prd (In this case, the predicted data EDT) corresponds to the latest subsystem step output MSO at the same time point PIT as the sending subsystem SMS. lst Digital Data DTA rel Determine the error ERD.

[0251] (f2) Adjust the subsystem time step SMP of the transmitting subsystem SMS according to the predetermined relationship between the error ERD and the subsystem time step SMP. The predetermined relationship between the error ERD and the subsystem time step SMP can be defined as:

[0252] The adjusted SMP will be referred to as SMP adj The previous SMP will be called SMP. prv :

[0253] SMP adj =SMP prv *BETA*(RTTO / ERD)∧n+1

[0254] in:

[0255] n: The polynomial order of the data prediction model DEM

[0256] SMP prv SMP of previous co-simulation steps

[0257] RTTO: Relative Tolerance

[0258] ERD: Error, preferably relative error.

[0259] BETA: Safety factor in the range [0.5, 1.0], preferably 0.9.

[0260] Set the delay time DLT to SMP adj The length can be adapted to delay the transmission of digital data (DTA) until a predetermined time point (PIT) when the receiving subsystem (SMR) is ready to receive the digital data DTA.

[0261] Step (e) above may include the following additional steps:

[0262] (e1) Select a single data prediction model type DET from the predefined function group (data prediction model type). se1 ,as well as

[0263] (e2) Based on the previous subsystem steps 1, 2, 3 or more, the corresponding sending subsystem SMS digital data DTA (excluding the latest subsystem step output MSO) is generated. 1st ), calibrate the selected data prediction model type DET data prediction model DEM1,...,DEM n ,

[0264] (e3) By using the data prediction model DEM k At least based on the latest subsystem steps, output MSO 1st The previous steps calculated the digital data DTA k The corresponding latest subsystem step output MSO at the same time point as the sending subsystem SMS in the PIT. 1st Latest digital data DTA re1 Compare and determine the DEM for each data prediction model. k Error ERD

[0265] (e4) From the selected data prediction model type DET sel Select the ERD with the smallest absolute error sm1 Data prediction model DEM k The institute selected the DEM data prediction model. se1 =DEM k This is the data prediction model we will be using now.

[0266] like Figure 2As shown, step (f) above may include at least one iterative subsystem ISM, which is provided as a manifold model, at least one dual model TMD, which includes a master model MMD and at least one surrogate model SMD, wherein the surrogate model SMD is capable of repeating at least a single co-simulation step, preferably capable of repeating multiple co-simulation steps, wherein the surrogate model SMD includes subsystem step output MSO parameters and subsystem step input MSI parameters that are at least partially identical to those of the master model MMD.

[0267] The method includes additional steps assigned to the defined subsystem time steps SMP:

[0268] a) The surrogate model SMD receives subsystem step inputs MSI that are at least partially derived from at least one other input providing subsystem SMN.

[0269] b) The surrogate model SMD calculates the subsystem step output based on the subsystem step input and MSI calculation.

[0270] MSO, the subsystem step input MSI is at least partially derived from other inputs provided by the subsystem.

[0271] In an SMN, the computational subsystem step output MSO includes the information to be provided to the agent model.

[0272] At least a portion of the input to the next iteration loop of SMD

[0273] c) Repeat steps a)-b) until the mutual convergence criterion CCT of the subsystem step outputs MSO of the input-providing subsystem SMN and the surrogate model SMD is met.

[0274] d) Use at least part of the converged subsystem step output (MSO) as the subsystem step input.

[0275] At least a portion of the MSI is provided to the main model MMD.

[0276] e) The master model MMD calculates the subsystem step output MSO based on the subsystem step input MSI and the defined subsystem time step SMP.

[0277] Figure 3 A simplified computer system (CPS) is schematically illustrated for simulating a system by applying a computer-implemented method according to the invention, and optionally according to any combination of the mentioned preferred embodiments, the computer system comprising:

[0278] - At least two simulation subsystems SMN for simulating the subunit SSY of the system SYS, wherein the subsystem SMN is designed such that the simulation includes the stepwise and iterative generation of the subsystem step output MSO based on the subsystem step input MSI.

[0279] -Communication Manager (CMM)

[0280] - Communication channel CCH, which connects the subsystem SMN and the communication manager CMM.

[0281] -At least one of the subsystems SMN is designed to transmit a connection interface variable TRD to the communication manager CMM via the communication channel CCH as a transmitting subsystem SMS, the connection interface variable TRD including at least one of the following:

[0282] -Digital Data (DTA)

[0283] -At least the parameters of the data prediction model DEM for digital data DTA,

[0284] - The data prediction model DEM is assigned to the digital data DTA provided by the SMS subsystem.

[0285] - Wherein, the digital data DTA belongs to the subsystem step output MSO of the transmitting subsystem SMS, including details of at least one piece of information about the transmitting subsystem SMS to be sent to at least one receiving subsystem SMS.

[0286] -The Communication Manager (CMM) or Receiver Subsystem (SMR) is designed to predict Digital Data Aspect (DTA) using the Data Prediction Model (DEM) to obtain the Predicted Digital Data Aspect (EDT) of the DTA provided by the Transmitter Subsystem (SMS).

[0287] - The receiving subsystem SMR is designed to initiate the next simulation step, which generates the next subsystem step output MSO within a delay time DLT based on the subsystem step input MSI, where the subsystem step input MSI includes the predicted digital data EDT.

[0288] -The functions of the transmitting subsystem (SMS) and the receiving subsystem (SMR) are performed by the subsystem (SMN).

[0289] -The computer system CPS is prepared to initiate the next simulation step of the receiving subsystem SMR, and generate the next subsystem step output MSO based on the subsystem step input MSI, wherein the subsystem step input MSI includes the predicted digital data EDT.

[0290] Although the invention has been described in detail with reference to preferred embodiments, it should be understood that the invention is not limited to the disclosed examples, and that many additional modifications and variations can be made to it by those skilled in the art without departing from the scope of the invention.

[0291] It should be noted that the use of "a" or "an" throughout this application does not exclude a plurality, and "comprising" does not exclude other steps or elements. Furthermore, elements described in different embodiments may be combined. It should also be noted that reference numerals in the claims should not be construed as limiting the scope of the claims.

Claims

1. A computer-implemented method for digital modular simulation of a system (SYS), comprising: (a) Decompose the system (SYS) into at least two sub-units (SSY) simulation subsystems (SMN). (b) Simulate the corresponding sub-unit (SSY) stepwise and repeatedly during the corresponding subsystem time step (SMP) and generate the subsystem step output (MSO) based on the subsystem step input (MSI). It is characterized by the following additional steps: (c) Send the subsystem step input (MSI) to the receiving subsystem (SMR) and simulate the subsystem (SMN) over the delay time (DLT) before generating the subsystem step output (MSO). (d) Receive a connection interface variable (TRD) from the Sending Subsystem (SMS), the connection interface variable including at least one of the following: - Digital Data (DTA) - At least the parameters of the data prediction model (DEM) for the digital data (DTA), - Data prediction model (DEM) assigned to the digital data (DTA). The digital data (DTA) belongs to the subsystem step output (MSO) of the transmitting subsystem (SMS) and includes details of at least one piece of information about the transmitting subsystem (SMS) to be sent to at least one receiving subsystem (SMR). (e) The digital data (DTA) is predicted by the data prediction model (DEM) over the delay time (DLT) to obtain the predicted digital data (EDT) of the interface variable (TRD) provided by the transmission subsystem (SMS). (f) Start the next simulation step of the receiving subsystem (SMR) and generate the next subsystem step output (MSO) based on the subsystem step input (MSI), wherein the subsystem step input (MSI) includes the predicted digital data (EDT).

2. The method of claim 1, further comprising the following additional steps: - The data prediction model (DEM) is determined by selecting the data prediction model type (DET) from a set of predefined functions, and - The data prediction model (DEM) is calibrated based on the digital data (DTA) of the corresponding transmission subsystem (SMS) of the subsystem step outputs (MSOs) of previous steps (a), (b), (c) or more, excluding the most recently generated subsystem step outputs (MSOs). lst ).

3. The method according to claim 2, wherein, The data prediction model (DEM) is a polynomial function.

4. The method according to claim 1 or 2, comprising the following steps: The data prediction model (DEM) is selected after the Sending Subsystem (SMS) co-simulation step (SMP). In the corresponding step of the corresponding transmitting subsystem (SMS), before the receiving subsystem (SMR) makes predictions, the selected data prediction model (DEM) is calibrated according to the pre-selected data prediction model type (DET).

5. The method according to claim 3, comprising the following steps: After the Sending Subsystem (SMS) co-simulation step (SMP), the polynomial degree of the Data Prediction Model (DEM) is selected. In the corresponding step of the corresponding transmitting subsystem (SMS), before the receiving subsystem (SMR) makes the prediction, the data prediction model (DEM) is calibrated using the selected polynomial degree according to the pre-selected data prediction model type (DET).

6. The method of claim 3, further comprising the following additional steps: - Select the polynomial order of the data prediction model type (DET). - By comparing the data prediction model (DEM) with the data prediction model based at least on the latest subsystem step output (MSO) 1st The digital data (DTA) calculated by the subsystem step output (MSO) of the previous steps. prd The subsystem step output (MSO) at the same point in time (PIT) as the transmission subsystem (SMS) 1st The latest digital data (DTA) rel ), Determine the error (ERD). - Repeat the following steps at least once: - Choose the order of the polynomial, where... Choose a polynomial order that is different from that in the previous repetitions, and - Determine the associated error (ERD). - The polynomial order of the data prediction model (DEM) is selected as the one with the minimum error (ERD) among the data prediction models (DEMs) selected and determined by error (ERD) during the previous repeated steps. - Use a constant data prediction model (DEM) if all polynomial orders of the data prediction model type produce errors greater than a given threshold (TRS).

7. The method of claim 6, further comprising the additional step of: - extending the polynomial degree of the obtained data prediction model (DEM) by Hermitian interpolation.

8. The method according to any one of claims 1 to 3, comprising the following additional steps: - By comparing the data prediction model (DEM) with the data prediction model based at least on the latest subsystem step output (MSO) 1st The numerical data (DTA) calculated in the previous steps prd The subsystem step output (MSO) at the same point in time (PIT) as the transmission subsystem (SMS) 1st The latest digital data (DTA) rel ), Determine the error (ERD). - Based on the error (ERD) and the previous subsystem time step (SMP) prv The predetermined relationship between the sending subsystem (SMS) and the time step (SMP) of the subsystem is adjusted.

9. The method according to claim 8, wherein, The error (ERD) and the previous subsystem time step (SMP) prv The predetermined relationship between them is a decreasing function.

10. The method according to claim 9, wherein, Adjust the subsystem time step (SMP) adj The error (ERD) and the previous subsystem time step (SMP) prv The associated predetermined relationship is defined as follows: (JUNIOR HIGH SCHOOL adj ) = (Junior High School prv ) BETA (RTTO / ERD) ∧ (n+1) in: n: The polynomial degree of the data prediction model (DEM) RTTO: Relative Tolerance ERD: Error BETA: Safety factor within [0.5, 1.0].

11. The method of claim 8, further comprising the additional step of: - for at least one subsystem (SMS), limiting the upcoming subsystem time step (SMP) such that it corresponds to the end time of the first upcoming step of any subsystem (SMS) having an output connected to the input of the subsystem whose time step is limited.

12. The method of claim 11, further comprising the following additional steps: - Select the subsystem (SMS) whose subsystem step outputs (MSOs) are connected to the subsystem step inputs (MSIs) of the subsystem (SMR) that does not support variable subsystem time steps (SMP). - Expand the upcoming subsystem time step (SMP) size of the selected subsystem (SMS) until the next step of the subsystem (SMR) with the subsystem step input (MSI) connected to the subsystem step output (MSO) ends.

13. The method according to any one of claims 1-3, wherein, When the transmission subsystem (SMR) provides a reliable data prediction model (DEM) with respect to a given relative tolerance (RTTO), the delay time (DLT) is adapted to delay the transmission of the digital data (DTA) until a predetermined point in time (PIT).

14. The method according to any one of claims 1-3, further comprising the following additional steps: - Select a single Data Prediction Model Type (DET) from a set of predefined Data Prediction Model Types (DETs), and - Calibrate at least two data prediction models (DEMs) of the selected type according to the digital data (DTA) of the corresponding transmission subsystem (SMS) of the subsystem step outputs (MSOs) of the previous steps (a), (b), (c) or more, excluding the last output (MSO). lst ), - By comparing the data prediction model (DEM) with the data prediction model based at least on the latest subsystem step output (MSO) 1st The numerical data (DTA) calculated in the previous steps prd The subsystem step output (MSO) at the same point in time (PIT) as the transmission subsystem (SMS) 1st The latest digital data (DTA) rel ), and determine the error (ERD) for each of the data prediction models (DEMs). - Select the data prediction model (DEM) with minimum error (ERD) from the data prediction models (DEM) of the selected data prediction model type (DET).

15. The method according to claim 7, wherein, The simulation of the system (SYS) is iterative, such that at least one of the simulation subsystems (SMN) interacts iteratively with at least one other simulation subsystem (SMN), wherein these subsystems are iterative subsystems (ISM).

16. The method according to claim 15, in, At least one of the iterative subsystems (ISM) is provided as a manifold model, at least a dual model (TMD), comprising a master model (MMD) and at least one surrogate model (SMD), wherein the surrogate model (SMD) is capable of repeating at least a single co-simulation step. The surrogate model (SMD) includes subsystem step output (MSO) parameters and subsystem step input (MSI) parameters that are at least partially identical to those in the master model (MMD). The method includes additional steps assigned to a defined subsystem time step (SMP): a) The proxy model (SMD) receives subsystem step inputs (MSI) that are at least partially derived from at least one other input providing subsystem (SMN). b) The surrogate model (SMD) calculates the subsystem step output (MSO) based on the subsystem step input (MSI), wherein the subsystem step input (MSI) is at least partially derived from at least one of the at least one other input-providing subsystems (SMN), and the calculation of the subsystem step output (MSO) includes at least a portion of the input to be provided to the next iteration loop of the surrogate model (SMD). c) Repeat steps a)-b) until the mutual convergence criterion (CCT) of the input providing subsystem (SMN) and the subsystem step output (MSO) of the surrogate model (SMD) is met. d) Provide at least a portion of the convergent subsystem step output (MSO) to the master model (MMD) as at least a portion of the subsystem step input (MSI). e) The master model (MMD) calculates the subsystem step output (MSO) based on the subsystem step input (MSI) for the defined subsystem time step (SMP).

17. The method of claim 16, further comprising the following additional steps: I. Define matrices A, B, C, and D to represent the linearized state-space representation of the model (MMD). II. Calculate the state-space representation of the system by C((sI-A)). -1 The pre-solution matrix is ​​defined by B+D, where -1 This represents finding the inverse of a matrix. III. Calculate the Laplace transform of the monomial basis as filled with 1, t, t ∧ The first single-column matrix of each Laplace transform of 2…, where, t represents time, where the exponent reaches the maximum polynomial degree of the polynomial subsystem step input (MSI). IV. Calculate the Kronecker product of the pre-solution matrix and the first single-column matrix. V. Collect the polynomial coefficients of each subsystem step input (MSI) in the second single-column matrix. VI. Calculate the matrix product of the Kronecker product and the inverse Laplace transform of the second single-column matrix. , VII. Calculate matrix P as C (sI-A) -1 Where I represents an identity matrix of the same size as A, and s represents the variables in the Laplace field. VIII. Calculate the matrix-vector product of the matrix P and the vector containing the state variables of the subsystem at the beginning of the co-simulation step (SMP) corresponding to the end of the previous co-simulation step. IX. Calculate the inverse Laplace transform of the matrix-vector product over the length of the co-simulation step (SMP) corresponding to the delay time (DLT). , X. Calculate the linear part as the product of the matrices. With the inverse Laplace transform the sum of XI. Calculate the control section according to step (e) of claim 1, 2, or 3, wherein the master model (MMD) is the receiving subsystem (SMR). XII. The subsystem step output (MSO) of the agent model (SMD) is calculated as the sum of the linear part and the control part.

18. The method according to claim 16, wherein, The surrogate model (SMD) is at least a partial linear approximation of the master model (MMD).

19. The method according to claim 16, 17 or 18, wherein, The converged subsystem step output (MSO) covers only a portion of the subsystem step input (MSI) of the master model (MMD), and the method includes the following additional step: - calculating the remainder of the subsystem step input (MSI) of the master model (MMD) according to step (e) of claim 1, 2 or 3, wherein the master model (MMD) is the receiving subsystem (SMR).

20. The method according to claim 17 or 18, wherein, All subsystems (SMN) are manifold, and among them, using a linear system constructed from the following, iterative solutions for each surrogate subsystem (SMD) can be completed immediately in a single iteration: - The linear relationship between all subsystem step inputs (SMI) and all subsystem step outputs (SMO) represented by the agent subsystem. - According to any one of claims 3-7, the linear relationship between the predicted data (EDT) and the known value (DATre1) at the upcoming subsystem time step (SMP) represented by the multinomial data prediction model (DEM) is set to be the same for each subsystem when a solution is completed for the entire set of subsystems, thereby creating a proxy for the entire system (SYS). - The remainder described as a constant term in claim 16, and - Connection information between the subsystem step outputs (MSOs) of all subsystems (SMS) and the subsystem step inputs (MSIs) of these subsystems (SMR), which can be viewed as an extended concept of permutations that allow subsystem step outputs (MSOs) to be unconnected, connected to one or more subsystem step inputs (MSIs), and where such relationships are linear.

21. A computer system (CPS) comprising at least one processor, said at least one processor being arranged and configured to perform the steps of the method according to any one of the preceding claims.

22. A computer-readable medium encoded with executable instructions, which, when executed, cause a computer system (CPS) according to claim 21 to perform the method according to any one of claims 1 to 20.

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