TECHNICAL FIELD

[0001] The present disclosure is directed, in general, to systems and methods for process analysis and optimization.

BACKGROUND OF THE DISCLOSURE

[0002] A“digital twin” refers to a virtual representation of a physical product or process, used to understand and predict the performance characteristics of the physical counterpart (the“physical twin”). Digital twins are used throughout the product lifecycle to simulate, predict, and optimize the product and production system before investing in physical prototypes and assets. The digital twin uses real-time or historical data and other sources to enable learning, reasoning, and dynamically recalibrating for improved decision making and operation of the corresponding physical twin. Improved systems are desirable.

SUMMARY OF THE DISCLOSURE

[0003] Various disclosed embodiments include methods for simulating and optimizing operation of a physical system and corresponding systems and computer-readable mediums. A method includes receiving, by a data processing system, operational data for a physical system. The method includes inserting the operational data into a model, wherein the model represents a digital twin of the physical system. The method includes extracting ranges from the model for each of a plurality of input parameters. The method includes performing a sensitivity analysis using the predicted operational output, the input parameters and ranges, and/or the model, to produce sensitivity indices. The method includes inserting the sensitivity indices into the model. The method includes simulating the operation of the physical system using the model.

[0004] Some embodiments include updating parameters of the physical system using the model and operating the physical system using the updated parameters. In some embodiments, performing the sensitivity analysis includes generating parameter sets by the data processing system, based on the extracted ranges, using a Sobol sequence; applying the parameter sets to the model by the data processing system; calculating Sobol indices by the data processing system; and determining total, first-order, and second- order sensitivity indices by the data processing system.

[0005] In some embodiments, the model is implemented using a knowledge graph. In some embodiments, the operational data is received as a comma-separated-values file or a spreadsheet file. Some embodiments include encoding the operational data for insertion in the model. Some embodiments include estimating parameters based on differences between the model and the physical system. Some embodiments include predicting an operational output using a neural network based on the input parameters and the model.

[0006] Other embodiments include a data processing system having a processor and an accessible memory, wherein the system is configured to perform processes as described herein. Other embodiments include a non-transitory computer-readable medium storing executable instructions that, when executed, cause a data processing system to perform processes as disclosed herein. [0007] The foregoing has outlined rather broadly the features and technical advantages of the present disclosure so that those skilled in the art may better understand the detailed description that follows. Additional features and advantages of the disclosure will be described hereinafter that form the subject of the claims. Those skilled in the art will appreciate that they may readily use the conception and the specific embodiment disclosed as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. Those skilled in the art will also realize that such equivalent constructions do not depart from the spirit and scope of the disclosure in its broadest form.

[0008] Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words or phrases used throughout this patent document: the terms“include” and“comprise,” as well as derivatives thereof, mean inclusion without limitation; the term“or” is inclusive, meaning and/or; the phrases “associated with” and“associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and the term “controller” means any device, system or part thereof that controls at least one operation, whether such a device is implemented in hardware, firmware, software or some combination of at least two of the same. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. Definitions for certain words and phrases are provided throughout this patent document, and those of ordinary skill in the art will understand that such definitions apply in many, if not most, instances to prior as well as future uses of such defined words and phrases. While some terms may include a wide variety of embodiments, the appended claims may expressly limit these terms to specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] For a more complete understanding of the present disclosure, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, wherein like numbers designate like objects, and in which:

[0010] Figure 1 illustrates an example of a system in accordance with disclosed embodiments;

[0011] Figure 2 illustrates a process in accordance with disclosed embodiments to perform sensitivity analysis;

[0012] Figure 3 illustrates a process in accordance with disclosed embodiments; and

[0013] Figure 4 illustrates a block diagram of a data processing system in which an embodiment can be implemented.

DETAILED DESCRIPTION

[0014] The Figures discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged device. The numerous innovative teachings of the present application will be described with reference to exemplary non-limiting embodiments.

[0015]“Sensitivity analysis” refers to the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input. Sensitivity analysis is used in fields such as risk assessment, economics, and engineering and has become instrumental in the understanding and development of a complex model. The application of sensitivity analysis can be summarized as: (1) understanding the input-output relationship, (2) determining to what extent uncertainty in structural model parameters contribute to the overall variability in the model output, (3) identifying the important and influential parameters that drive model outputs and magnitudes, and (4) guiding future experimental designs. For model builders and users, it is also a useful tool to check the model structure and uncertainty around the input parameters, and feedback into the model refinement to gain additional confidence in the model. In complex models, the results of sensitivity analysis can help the model builders to focus on the critical parameters that determine the model output.

[0016] A related practice is“uncertainty analysis,” which focuses rather on quantifying uncertainty in model output. Ideally, uncertainty and sensitivity analyses should be run in tandem, with uncertainty analysis preceding sensitivity analysis.

[0017] Variance-based sensitivity analysis (or“Sobol sensitivity analysis”) is a form of global sensitivity analysis that decomposes the variance of the output of the model or system into fractions which can be attributed to inputs or sets of inputs. Sobol sensitivity analysis is used, for example, in economic analyses. Such techniques are described, for example, in Sobol, I.M. (2001),“Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates”, hereby incorporated by reference.

[0018] Disclosed embodiments can apply Sobol sensitivity analysis techniques to digital twin knowledge graphs. As disclosed herein, sensitivity analysis enables the system to identify the parameter or set of parameters that have the greatest influence on the model output. This analysis consequently identifies which model input contributes most to the variability of the model output.

[0019] According to disclosed embodiments, local sensitivity analysis is used to evaluate changes in the model outputs with respect to variations in a single parameter input. The input parameters are changed one at a time in relatively small increments, in some processes, and the effect of this individual parameter perturbation on the model output is calculated using local sensitivity indices. In a global sensitivity analysis, all parameters can be varied simultaneously over the entire parameter space, which allows the system to simultaneously evaluate the relative contributions of each individual parameter as well as the interactions between parameters to the model output variance.

[0020] Figure 1 illustrates an example of a system 100 in accordance with disclosed embodiments. System 100 includes a physical system 110 (the“physical twin” to be analyzed) that interacts with a digital twin 120 (a formal system) that is implemented using one or more data processing systems as disclosed herein. The data processing systems can implement a generative design framework that provides a back-end for knowledge graph databases with support for numerous simulations, analysis, and machine-learning plugins. Non-limiting examples of physical systems that can be controlled as disclosed herein include printed circuit board (PCB) design systems, large gas turbines, and automotive suspension parts and systems.

[0021] The state, operations, and other input data 124 of physical system 110 are encoded and received by digital twin 120. Digital twin 120 inserts this data into model 122, which can be implemented as a knowledge graph. In specific embodiments, operational input data 124 is received as a comma-separated-values or spreadsheet file. The input data 124 can include input parameters, ranges, or other data input to model 122 or digital twin 120. “Receiving,” as used herein, can include loading from storage, receiving from another device or process, receiving via an interaction with a user, and otherwise. The digital twin system (or the data processing systems) can encode this input data 124 by processing through a series of distillers and data processing programs to ensure a normalized data set that can be imported to model 122. The cleaned-up input data 124 is imported into model 122, preferably as part of a knowledge graph database.

[0022] Once in model 122, the digital twin system 120 operates on this data to perform analyses to extract or generate knowledge. Digital twin system 120 can use a variety of estimation and analysis tools known to those of skill in the art. This analysis produces observations and parameters 126 estimated from model 122 and input data 124. Estimations can take different courses. In some embodiments, the estimation includes minimizing, e.g., by least squares, some measure of distance or error between the model 122 and the input data 124, showing differences between the digital twin 120 and the actual physical system 110. After estimation, the best estimated parameters 126 as well as their errors are known. The best estimated parameters can then be decoded to operational parameters and use to operate physical system 110.

[0023] The system performing uncertainty and sensitivity analysis 130. This can be performed by the same data processing system(s) that implement digital twin 120, or by another data processing system system(s) in interaction with digital twin 120. For sensitivity analysis, in some embodiments, the system uses Sobol sensitivity analysis, including decomposition of the model output variance into summands of variances of the input parameters in increasing dimensionality. In particular, the system can concentrate on x-hop neighbors of a particular node of the knowledge graph in case of local analysis. For global analysis, the system can consider the entire graph.

[0024] In some cases, the sensitivity analysis can include sampling values within the given range and calculating the system response using a physics-based simulation method. However, preferred embodiments replace this simulation with an ensemble of surrogate neural-network-based models trained on the data and saved in the knowledge graph of model 122. This enables the sensitivity analysis 130 to run much faster (since the model is already trained) than in other approaches, and the ensemble method ensures better accuracy.

[0025] Figure 2 illustrates a process 200 in accordance with disclosed embodiments that can be performed in a system as described above, referred to generically as the“system” below, to perform sensitivity analysis 130 as disclosed herein. The process illustrated in Fig. 2 can be combined with or implemented in conjunction with any other processes or devices as described herein.

[0026] The system defines upper and/or lower bounds or ranges for parameters (202).

[0027] The system generates parameter sets, based on the defined bounds/ranges, using a Sobol sequence (204). These parameter sets can be stored as or with estimated parameters 126.

[0028] The system applies the parameter sets to the model (206). In particular, the system can apply the parameter sets to a knowledge graph of model 122.

[0029] The system calculates Sobol indices (208).

[0030] The system determines and analyzes total, first-order, and second-order sensitivity indices (210).

[0031] The system inserts sensitivity analysis results back into model 122 (212). In particular, the system can insert the sensitivity analysis results into the knowledge graph of model 122. The system can therefore determine how the output variance of the physical twin or digital twin is be attributed to individual input variables. The interaction between each of the input variables, the total-order, first-order, second-order, and higher- order sensitivity indices are calculated to accurately reflect the influence of the individual inputs and the interactions between them.

[0032] Figure 3 illustrates a process 300 in accordance with disclosed embodiments that can be performed in a system as described above, referred to generically as the“system” below, to optimize operation of a physical system as described herein. The process illustrated in Fig. 3 can be combined with or implemented in conjunction with any other processes or devices as described herein.

[0033] The system receives operational data for a physical system (302). This can include receiving operational data from the physical system and/or generating data through simulation of the physical system by the digital twin.

[0034] The system inserts the operational data into a model (304). In various embodiments, this includes placing the operational data into a knowledge graph that represents a digital twin of the physical system.

[0035] The system extracts ranges from the model for each of a plurality of input parameters (306). The system can also determine the number of input variables.

[0036] The system predicts an operational output using a neural network based on the input parameters and the model (308).

[0037] The system performs a sensitivity analysis using the predicted operational output, the input parameters and ranges, and/or the model, to produce sensitivity indices (310). This can include performing a process as in Fig. 2, can include Sobol analysis and/or Morris analysis, or otherwise.

[0038] The system inserts the sensitivity indices into the model (312). This can include inserting the sensitivity indices, the parameters, or any other data into a knowledge graph.

[0039] The system simulates the operation of the physical system using the model (314).

[0040] The system updates the parameters of the physical system using the model (316). The system can thereby operate the physical system using the updated parameters, including the sensitivity indices, the parameters, or any other data in the model or knowledge graph. The system can therefore determine how the output variance of the physical twin or digital twin is be attributed to individual input variables and optimize the operation accordingly. The interaction between each of the input variables, the total- order, first-order, second-order, and higher-order sensitivity indices are calculated to accurately reflect the influence of the individual inputs and the interactions between them.

[0041] Figure 4 illustrates a block diagram of a data processing system in which an embodiment can be implemented, for example as part of a system as described herein, or as a control system as described herein, particularly configured by software or otherwise to perform the processes as described herein, and in particular as each one of a plurality of interconnected and communicating systems as described herein. The data processing system depicted includes a processor 402 connected to a level two cache/bridge 404, which is connected in turn to a local system bus 406. Local system bus 406 may be, for example, a peripheral component interconnect (PCI) architecture bus. Also connected to local system bus in the depicted example are a main memory 408 and a graphics adapter 410. The graphics adapter 410 may be connected to display 411.

[0042] Other peripherals, such as local area network (LAN) / Wide Area Network / Wireless ( e.g . WiFi) adapter 412, may also be connected to local system bus 406. Expansion bus interface 414 connects local system bus 406 to input/output (LO) bus 416. I/O bus 416 is connected to keyboard/mouse adapter 418, disk controller 420, and LO adapter 422. Disk controller 420 can be connected to a storage 426, which can be any suitable machine usable or machine readable storage medium, including but not limited to nonvolatile, hard-coded type mediums such as read only memories (ROMs) or erasable, electrically programmable read only memories (EEPROMs), magnetic tape storage, and user-recordable type mediums such as floppy disks, hard disk drives and compact disk read only memories (CD-ROMs) or digital versatile disks (DVDs), and other known optical, electrical, or magnetic storage devices.

[0043] Storage 426 can store any data or code used for performing processes as described herein, including any executable instructions. For example, storage 426 can store operational data 452, which can include any data related to the physical system or the digital twin. Storage 426 can store parameters 454, which can include any parameters or parameter sets discussed herein. Storage 426 can store model 456 as described herein, including storing a knowledge graph or neural network or any other data related to model 456. Storage 426 can store outputs 458, including any generated or predicted outputs discussed herein. Storage 426 can store inputs 460, which can include any inputs, input data, input parameters, or other information input to the system whether from the physical system, a user, another device or process, or otherwise. Storage 426 can store analysis data 462, which can include any ranges, indices, or other data used in the sensitivity analysis processes described herein.

[0044] Also connected to I/O bus 416 in the example shown is audio adapter 424, to which speakers (not shown) may be connected for playing sounds. Keyboard/mouse adapter 418 provides a connection for a pointing device (not shown), such as a mouse, trackball, trackpointer, touchscreen, etc. I/O adapter 422 can be connected to communicate with or control physical system 428, which can include any physical systems, devices, or other devices that can be simulated, optimized, and controlled as described herein.

[0045] Those of ordinary skill in the art will appreciate that the hardware depicted in Figure 4 may vary for particular implementations. For example, other peripheral devices, such as an optical disk drive and the like, also may be used in addition or in place of the hardware depicted. The depicted example is provided for the purpose of explanation only and is not meant to imply architectural limitations with respect to the present disclosure.

[0046] A data processing system in accordance with an embodiment of the present disclosure includes an operating system employing a graphical user interface. The operating system permits multiple display windows to be presented in the graphical user interface simultaneously, with each display window providing an interface to a different application or to a different instance of the same application. A cursor in the graphical user interface may be manipulated by a user through the pointing device. The position of the cursor may be changed and/or an event, such as clicking a mouse button, generated to actuate a desired response.

[0047] One of various commercial operating systems, such as a version of Microsoft Windows™, a product of Microsoft Corporation located in Redmond, Wash may be employed if suitably modified. The operating system is modified or created in accordance with the present disclosure as described.

[0048] LAN/ WAN/Wireless adapter 412 can be connected to a network 430 (not a part of data processing system 400), which can be any public or private data processing system network or combination of networks, as known to those of skill in the art, including the Internet. Data processing system 400 can communicate over network 430 with server system 440 (such as cloud systems as described herein), which is also not part of data processing system 400, but can be implemented, for example, as a separate data processing system 400.

[0049] Of course, those of skill in the art will recognize that, unless specifically indicated or required by the sequence of operations, certain steps in the processes described above may be omitted, performed concurrently or sequentially, or performed in a different order.

[0050] Those skilled in the art will recognize that, for simplicity and clarity, the full structure and operation of all data processing systems suitable for use with the present disclosure is not being depicted or described herein. Instead, only so much of a data processing system as is unique to the present disclosure or necessary for an understanding of the present disclosure is depicted and described. The remainder of the construction and operation of data processing system 400 may conform to any of the various current implementations and practices known in the art.

[0051] It is important to note that while the disclosure includes a description in the context of a fully functional system, those skilled in the art will appreciate that at least portions of the mechanism of the present disclosure are capable of being distributed in the form of instructions contained within a machine-usable, computer-usable, or computer- readable medium in any of a variety of forms, and that the present disclosure applies equally regardless of the particular type of instruction or signal bearing medium or storage medium utilized to actually carry out the distribution. Examples of machine usable/readable or computer usable/readable mediums include: nonvolatile, hard-coded type mediums such as read only memories (ROMs) or erasable, electrically programmable read only memories (EEPROMs), and user-recordable type mediums such as floppy disks, hard disk drives and compact disk read only memories (CD-ROMs) or digital versatile disks (DVDs).

[0052] Although an exemplary embodiment of the present disclosure has been described in detail, those skilled in the art will understand that various changes, substitutions, variations, and improvements disclosed herein may be made without departing from the spirit and scope of the disclosure in its broadest form.

[0053] Disclosed embodiments provide significant advantages, including that sensitivity information for a knowledge graph can improve the update process for the graph, enabling more knowledge to be extracted at lower input cost. It can also provide confidence in the output of the graph in terms of the confidence in the input parameters.

[0054] For complex systems, physics-based simulation approaches are often slow and far from accurate. Often, it is impossible to measure variables using traditional approaches. Using an ensemble of surrogate models trained on the data to approximate the true function instead of simulation make this approach faster and more accurate.

[0055] The use of a knowledge graph, as in certain embodiments, ensures knowledge extraction at lower cost. The use of models as disclosed herein ensures better expected accuracy and improves execution time.

[0056] The use of techniques as disclosed herein is an improved functionality of the data processing system(s) implementing the digital-twin simulations and results in improved operation of the corresponding physical twin.

[0057] None of the description in the present application should be read as implying that any particular element, step, or function is an essential element which must be included in the claim scope: the scope of patented subject matter is defined only by the allowed claims. Moreover, none of these claims are intended to invoke 35 USC § 112(f) unless the exact words "means for" are followed by a participle. The use of terms such as (but not limited to) “mechanism,” “module,” “device,” “unit,” “component,” “element,” “member,” “apparatus,” “machine,” “system,” “processor,” or“controller,” within a claim is understood and intended to refer to structures known to those skilled in the relevant art, as further modified or enhanced by the features of the claims themselves, and is not intended to invoke 35 U.S.C. §1 12(f).