Computer-based device implementing a physical model and a data-driven model of a machine

Abstract

The innovative computer-based device (100) serves for generating a device output signal (101) based on a plurality of device input signals (102); the device output signal (101) corresponds to a physical parameter of an industrial machine (10); the device input signals (102) correspond to physical quantities of the industrial machine (10). The device (100) comprises: a first section (110) being a physics-based section, a second section (120) being a data-based section, and a signal combiner (130). The first section (110) is configured to receive at least a first portion of the plurality of device input signals (102), and to generate a first section output (111) signal by applying a mathematical processing to values of the first portion of the plurality of input signals (102), wherein the mathematical processing relates to a physical model of the industrial machine or part of the industrial machine. The second section (120) is configured to receive at least a second portion of the plurality of device input signals (102), and to generate a second section output signal (121) by applying a neural processing to values of the second portion of the plurality of device input signals (102), wherein the neural processing relates to a data-driven model of the industrial machine or part of the industrial machine. The signal combiner (130) is configured to generate a combination of the first section output signal (111) and the second section output signal (121); the device output signal (101) corresponds to this combination. The device (100) is configured to adjust parameters of the mathematical processing and parameters of the neural processing during a training period of the device preceding an operating period of the device.

Description

TITLEComputer-based device implementing a physical model and a data-driven model of a machineDESCRIPTIONTECHNICAL FIELD

[0001] The subject matter disclosed herein relates to computer-based devices for generating signals to be used for example as output signals of so-called “virtual sensors” in industrial machines or as output signals of control systems for industrial machines. Such devices implement both a physical model and a data-driven model of the machine or part of the machine.BACKGROUND ART

[0002] Therefore, the subject matter disclosed herein relates to applications of the so-called Artificial Intelligence (usually abbreviated as “Al”).

[0003] It is known to develop physical models of machines and, more in general, systems. A physical model of a machine or system corresponds to a set of equations that relate physical entities of the machine or system and that describes mathematically the physical phenomena occurring within the machine or system. This is the traditional approach followed by engineers.

[0004] It is known to develop data-driven models of machines and, more in general, systems. This is a relatively new approach followed by engineers and is often used when it is difficult to develop a physical model due to, for example, lack of knowledge and / or understanding of the machine or system. Adata-driven model is often implemented through a so-called Artificial Neural Network (usually abbreviated as “ANN”). As known, an ANN is “trained” using available data; in other words, the values of its internal parameters, called “weights”, are determined so that the output(s) computed by the ANN correspond(s) at best to the data collected from the real world.

[0005] It is also known, even if not common, to combine a traditional physical model and a data-driven model for example from the article by M. L. Thompson and M. A. Kramer entitled “Modelling Chemical Processes Using Prior Knowledge and Neural Networks” published in the AIChE Journal, August 1994, Vol. 40, No. 8, pages 1328-1340.

[0006] As this article describes, there are many possibilities; all of them work relatively well. A possibility is the so-called “semiparametric parallel approach”. According to this possibility, the physical model corresponds to the idealized behavior of a system and the neural network is used to determine the deviation (called “residual” in this article) of the real system from the ideal system that cannot be predicted using the physical model.

[0007] The Applicant has realized that this “semi parametric parallel approach” works quite well when used for predicting a physical parameter of an industrial machine the physics of which is quite well known or is considered to be quite well known. However, if very high accuracy is desired, this “semi parametric parallel approach” is still insufficient. One possible reason of inaccuracy is that the data used for training the ANN may derive not from a machine (e.g. slightly) different from the machine to be subject of prediction, for example it may be a prototype machine, or from an identical machine but in (e.g. slightly) different operating conditions. Another possible reason of inaccuracy is the (idealized) physical model does not take into account some phenomena in the system and / or some details of the system.

[0008] It is known that an autonomous machine has sensors generating input data, while the controller includes two or more neural networks that infer using the input data and generate output data, as described in the patent document n°US2023019834. However this controller is only able to compare two neural networks, but does not allow them to be combined.

[0009] Also, it is known a scientific publication titled “Unifyng Model-Based and Neural Network Feedforward:Physics-Guided Neural Networks with Linear Autoregressive Dynamics” Kon Johan at Al. presented at 2022 IEEE 61 st CONFERENCE ON DECISION AND CONTROL (CDC) 6 December 2022. This document describes an approach that incorporates physical laws directly into the loss function of the neural network. The loss function is what the network tries to minimize during training. By including physics in the loss function, it ensures that the network’s predictions adhere to physical laws.

[0010] Instead, the approach of applicant’s invention is to integrate physical laws into the architecture of the neural network itself. This means that the structure of the network (e.g., how neurons are connected and the activation functions used) is designed to respect the mathematical formulas that describe physical laws. This can make the network more efficient and accurate, as the network’s structure is built to model physical behavior.

[0011] In other words, the approach described in the scientific publication uses physics as a constraint during training, while the approach of applicant’ s invention incorporates it directly into the network’s design.SUMMARY

[0012] Therefore, it would be desirable to provide even better predictions.

[0013] The Applicant has realized through research that better results are achieved if during a training period not only the parameters of the data-drivenmodel are adjusted but also the parameters of the (idealized) physical model are adjusted even if the (idealized) physical model is derived from both theoretical studies and practical studies.

[0014] According to a first aspect, the subject matter disclosed herein relates to a computer-based device for generating a device output signal based on a plurality of device input signals; the device output signal corresponds to a physical parameter of an industrial machine; the device input signals correspond to physical quantities of the industrial machine. The innovative device comprises a first section being a physics-based section, a second section being a data-based section, and a combiner that combines output signals from the first section and the second section. The innovative device is configured to adjust parameters of a mathematical processing carried out by the first section and parameters of a neural processing carried out by the second section during a training period of the device preceding an operating period of the device. According to some embodiments, these two sections may be merged into a single module, i.e. a neural module or neural network based module, for optimization purposes.

[0015] The innovative device may be incorporated for example in a so-called “virtual sensor” (i.e. a piece of software that behaves as a normal sensor, i.e. provides measurement data as output) or in a control system and may be used to generate an output of the sensor or of the system.

[0016] According to a second aspect, the subject matter disclosed herein relates to a computer-implemented method for generating an output signal based on a plurality of input signals; the output signal corresponds to a physical parameter of an industrial machine; the input signals correspond to physical quantities of the industrial machine. The innovative method comprises the steps of a) generating a first signal by applying to the input signals a first processing, the first processing corresponding to a physical model of theindustrial machine or of a part of the industrial machine, b) generating a second signal by applying a second processing to the input signals, the second processing corresponding to a data-driven model of the industrial machine or of a part of the industrial machine, c) summing the first signal and the second signal thus producing the output signal. The first processing and the second processing are set during a setting-up period based on theoretical knowledge of the industrial machine. The first processing and the second processing are then adjusted during the training period based on data collected during operation of the industrial machine. The first processing and the second processing may be carried out sequentially, i.e. one after the other, or at least partially parallelly, i.e. contemporaneously.

[0017] The above mentioned adjustment can be performed in a very effective and efficient way, if neural networks are used for implementing not only the data-driven model but also the physical model. How to implement physical models through neural networks will be described in the following.

[0018] According to a third aspect, the subject matter disclosed herein relates to a method to implement physical model, in particular for constructing and initializing a neural network architecture derived directly from an expression tree of the physical model.BRIEF DESCRIPTION OF THE DRAWINGS

[0019] A more complete appreciation of the disclosed embodiments of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:Fig. 1 shows a block diagram of an embodiment of an inventive virtual sensor incorporating an embodiment of an inventive device,Fig. 2 shows a block diagram of an artificial neuron as typically used in artificial neural networks,Fig. 3 shows a block diagram of an exemplary physical model implemented through artificial neural networks,Fig.3A shows a flowchart of an embodiment of an innovative method to implement physical models of Fig. 3,Fig. 3B shows the expression tree associated with the above equation of an example of physical model,Fig. 4 shows a block diagram of an embodiment of an inventive control system incorporating an embodiment of an inventive device, andFig. 5 shows a flowchart of an embodiment of an innovative method.DETAILED DESCRIPTION OF EMBODIMENTS

[0020] According to the subject matter disclosed herein, an innovative computer-based device generates an output signal to be used for example as output signal of a virtual sensor in an industrial machine or as output signal of a control system for an industrial machine. The innovative device implements both a physical model and a data-driven model of the machine (or part of the machine). The two models are used for generating two signals that are then combined, for example summed, so that the output of the innovative device takes into account both theoretical knowledge of the machine and experimental knowledge of the machine. The innovative device is configured to adjust both the physical model and the data-driven model during a training period of the device preceding an operating period of the device.

[0021] The innovative idea has been conceived by focusing on turbomachines. However, it is not to be excluded that it is applicable to othermachines or apparatuses.

[0022] Fig. 1 shows an embodiment of an inventive device 100. According to this specific embodiment device 100 corresponds to a virtual sensor 200. However, device 100 will now be described independently from its possible applications, for example in virtual sensors (see Fig. 1) and in control systems (see Fig. 4).

[0023] The device 100 is computer-based in particular it is implemented through a computer suitably programmed. It is to be expected that such computer may be running other programs at the same time that may interact with the innovative device program; in other words, it is not a piece of hardware dedicated to implementing the innovative device.

[0024] The device is configured to generate a device output signal 101 based on a plurality of device input signals 102; the device output signals might be more than one; according to this embodiment there is only one device output signal. The input signals and / or the output signals may be in analog form or, more typically, in digital form, i.e. as a sequence of digitized signal samples.

[0025] The device output signal 101 corresponds to a physical parameter of an industrial machine 10. The parameter may be a (current or past or future or desired) physical quantity of the industrial machine. Alternatively, the parameter may be an indication of a (current or past or future or desired) performance of the industrial machine, for example an efficiency.

[0026] The device input signals 102 correspond to physical quantities of the industrial machine 10. It is to be noted that any of the device input signals may come from a sensor (that may be a physical sensor or a virtual sensor) or from a system (for example a piece of software or a piece of hardware) specifically designed for generating a physical quantity signal based on measurements and / or calculations; in the latter case, the signal may come for example from adata storage device. The above-mentioned sensor and system may be close to the inventive device or remote from the inventive device.

[0027] The device 100 comprises: a first section 110 being a physics-based section, a second section 120 being a data-based section, and a signal combiner 130. Typically, as shown in Fig. 1, there is only one physics-based section and only one data-based section.

[0028] The first section 110 is configured to receive at its section inputs 112 at least a first portion of the plurality of device input signals 102, and to generate at its section output Il l a first section output signal by applying a mathematical processing to values of the first portion of the plurality of input signals 102. The mathematical processing relates to a physical model PHY of the industrial machine 10 or part of the industrial machine 10.

[0029] The second section 120 is configured to receive at its section inputs 122 at least a second portion of the plurality of device input signals 102, and to generate at its section output 121 a second section output signal by applying a neural processing to values of the second portion of the plurality of device input signals 102. The neural processing relates to a data-driven model DAT of the industrial machine 10 or part of the industrial machine 10.

[0030] The signal combiner 130 is configured to generate at its output 131 a combination of the section output signals received at its inputs 132, in particular the first section output signal 111 and the second section output signal 121.

[0031] The device output signal 101 corresponds to said combination; in other words, the output of the signal combiner 130 is coupled to the output of the inventive device 100. Although in the embodiment of Fig. 1 there is a direct connection between output 131 and output 101, it is not to be excluded that, according to alternative embodiments, there may be some e.g. simple signaladaptation, for example amplification, attenuation, delay.

[0032] During an operating period of the device 100, device input signals are received (e.g. repeatedly received) by the sections 110 and 120, section output signals are generated (e.g. repeatedly generated) by the sections 110 and 120 and sent to the signal combiner 130, the signal combiner 130 combines (e.g. repeatedly combines) the section output signals and generates the device output signal 101.

[0033] During a training period of the device 100 that precedes an operating period of the device 100, the device 100 is configured to adjust parameters of the mathematical processing (to be carried out later by the section 110) and the parameters of the neural processing (to be carried out later by the section 120). It is to be noted that a training period may occur only once (or few times), and, afterwards, there is may be for example a plurality of short distinct and separate operating periods or a long operating period. The adjustment of both sets of parameters occur preferably during the same training period, and even more preferably at the same time or even contemporaneously. Adjustment of both sets of parameters is carried preferably based on the same data coming from an industrial machine.

[0034] According to some embodiments, the first section is configured to receive all signals of the plurality of device input signals, as shown in Fig. 1; this means that the physical model takes into account or may take into account all the physical quantities that are made available to the device.

[0035] According to some embodiments, the second section is configured to receive all signals of the plurality of device input signals, as shown in Fig. 1; this means that the data-driven model takes into account or may take into account all the physical quantities that are made available to the device. It is to be noted that in this case, the adjustment during the training period willdetermine the relevance for the data-driven model of each physical quantity available to the device; for example, there may be one or more of them that may have no relevance or almost no relevance.

[0036] The two possibilities described in the above two paragraphs may advantageously be provided in a same embodiment, as shown in Fig. 1.

[0037] According to some embodiments, the signal combiner is configured to carry out a sum or a weighted sum of the first section output signal and the second section output signal, as shown in Fig. 1. This is simple and effective: the output of the innovative device has a first contribution due to the physical model and a second contribution due to the data-driven model.

[0038] Notably, if the input of the signal combiner from the first section is weighted by a first weight and the input of the signal combiner from the second section is weighted by a second weight, the signal combiner may be configured to adjust the first weight and / or the second weight during the training period. This means that thanks to the training during the training period, the innovative device is able to understand (and adapt accordingly) if the relevant machine or part of machine behaves more or less close to an ideal (i.e. corresponding to its physical knowledge) behavior.

[0039] According to some embodiments, both the first section and the second section comprise artificial neural networks. This is particularly effective for the training of the innovative device. In fact, the neural network architecture is designed to allow adjustments of its parameters.

[0040] According to some embodiments, the first section comprises at least one or only one feedforward artificial neural network. This way of implementing a mathematical formula (that describes mathematically the physical phenomena occurring within the machine) is particularly effective for the training of the innovative device. In fact, the neural network architectureis designed to allow adjustments of its parameters.

[0041] Fig. 2 shows a block diagram of an artificial neuron 200 (that may be referred simply as “neuron” in this technical field) as known and typically used in artificial neural networks. Neuron 200 has a number n of inputs xl, x2, x3, ... xn and one output o that may be also called “activation”. Each of the inputs xl, x2, x3, ... xn is multiplied by a corresponding “weight” wl, w2, w3, ... wn, that are parameters of the neuron (as well as parameters of a neural network including this neuron). The results of such multiplications are applied to a so-called “transfer function”; typically, the “transfer function” corresponds simply to an addition operation (see the symbol used in Fig. 2). In general, the “transfer function” may be considered a characteristic of the neuron and may be specifically defined by parameters, that are parameters of the neuron. The output of the “transfer function” is provided, as a “net input”, or simply “net”, to an “activation function” that generates the output o or “activation” of the neuron; typically, the “activation function” is a non-linear function and may correspond for example to a “step function” or a “signum function” or a “ReLU function” or a “sigmoid function” or a “hyperbolic tan function”. In general, the “activation function” may be considered a characteristic of the neuron, and may be specifically defined by parameters, that are parameters of the neuron, typically and exemplarily the “threshold”.

[0042] The neuron 200 of Fig. 2 has a set of parameters that may be adjusted for example during a training period of a neural network including the neuron; there are at least n parameters corresponding to the n weights and there may be one or more other parameters associated to the “transfer function” and / or to the “activation function”.

[0043] Fig. 3 shows a block diagram of an exemplary physical model 300 implemented through only one artificial neural network, in particular only one feedforward artificial neural network. An architecture of this type may be usedfor example as a first section of an innovative device, for example as the first section 110 of an innovative device 100 in Fig. 1.

[0044] In the block diagram of Fig. 3 there are five neurons 310, 320, 330, 340, 350 and one multiplicator 360 which is also a neuron as it will be clear from the following. The neurons 310, 320, 330, 340, 350 have respectively inputs 311, 321, 331, 341, 351 (three for the first neuron 310, one for the second neuron 320, two for the third neuron 330, three for the fourth neuron 340 and three for the fifth neuron 350) and outputs 312, 322, 332, 342, 352 (one for each neuron), The multiplicator has two inputs 361 and one output 362. The neurons 310, 320, 330, 340, 350 apply respectively the functions F 10, F20, F30, F40, F50 to their inputs. The mathematical formula corresponding to the physical model is the following:F40(F10(311),F20(321), F30(331)) * F50(351)

[0045] In Fig. 3, a single artificial neural network of the feedforward type is shown configured according to the so-called “expression tree” corresponding to the above mathematical formula. The network has three layers; neurons 310, 320, 330, and 350 belong to the first layer, neuron 340 belongs to the second layer, and neuron 360 belongs to the third layer. The second network has a single layer; neuron 350 belongs to the single layer. According to the example of Fig. 3, the number of parameters that may be adjusted during a training period is greater than or equal to fourteen, corresponding to all the weights of the neurons.

[0046] The possibility of transforming the expression tree of any mathematical formula into a neural network is based on the possibility of freelychoosing the “transfer function” and / or the “activation function” of each neuron of the neural network. The idea of exploiting such possibility, in particular in order to implement an expression tree of a mathematical formula, is highly innovative. Very often the “transfer function” is a summing function and often the “activation function” is a ReLU function. On the contrary, typically according to the subject matter disclosed herein, these functions of the neurons are different from the summing function and the ReLU function; for example, the “transfer function” of neuron 360 is a multiplying operation and the “activation function” of neuron 360 is a linear function with coefficient equal to one (which corresponds to no “activation function”). In addition, typically according to the subject matter disclosed herein, these functions differ from neuron to neuron.

[0047] Considering the embodiment of Fig. 3, according to a first possibility, neurons 310, 320, 330, 340, 350 and 360 have respective different “transfer functions” and respective different “activation functions”; according to a second possibility, neurons 310, 320, 330, 340, 350 and 360 have respective different “transfer functions” and the same “activation function”; according to a third possibility, neurons 310, 320, 330, 340, 350 and 360 have the same “transfer function” and respective different “activation functions”; of course, other possibilities exist.

[0048] It is to be noted that the physical model embodied in the architecture shown in Fig. 3 is provided only as an exemplification of the possibility of implementing a physical model through an artificial neural network. Such possibility of implementation is advantageous as it facilitates adjustment of the model by adjusting the parameters of the network. For any embodiment, the architecture(s) of the artificial neural network(s) depends on the mathematical formula (s) corresponding to the physical model.

[0049] As explained above with non-limiting reference to Fig.3 the generalmathematical formulaF40(F10(311), F20(321), F30(331)) x F50(351) is usable to construct a neural network through a physical model, which takes the physical model’s input and calculates the output.

[0050] For example, to construct a physical model capable of accurately estimating the amount of NOx emissions from a gas turbine, in particular refer to the release of nitrogen oxides, primarily nitric oxide (NO) and nitrogen dioxide (NO2), during the combustion process emitted by gas turbines, with the ultimate objective of replacing the current analyzer device used for this purpose.

[0051] The NOx formula from Bakken et al. (1995) is a well-known model used to estimate nitrogen oxide emissions from gas turbines.

[0052] This model typically involves a set of equations that describe the formation of NOx based on various factors such as temperature, pressure, and fuel composition.

[0053] In this case given the general formula of invention:F40(F10(311), F20(321), F30(331)) x F50(351)Each of these functions of this general formula is correlate to the components of the NOx formula:- F40: This function corresponds to the combination of the subexpressions F10(311), F20(321), and F30(331). It represents the overall product of the components in the NOx formula:- Fl 0(311): This function represents the term related to the compressor discharge pressure :- F20(321): This function corresponds to the term involving the fuel / air ratio :- F30(331): This function represents the exponential term related to the combustion discharge temperature:- F50(351): This function corresponds to the constant multiplier in the NOx formula. In this case, it represents the constant:Where x1, x2,x3,x4 are physical inputsPutting all these components together, the general formula:F40(F10(311), F20(321), F30(331)) x F50(351) can be mapped as:

[0054] Additionally, a neural network architecture, derived directly from an expression tree

[0055] 3B the expression tree 700 corresponding to the above mathematical formula mapped as:

[0056] Advantageously, the proposed neural network architecture is derived directly from the expression tree of the physical model. This expression tree encapsulates the mathematical operations, variables, and constants defined by the physical model, allowing for a structured transformation into a neural network. First, the physical model is represented as an expression tree, which includes leaf nodes representing input features (like pressure and temperature) and constants, as well as internal nodes representing mathematical operations such as addition and multiplication.

[0057] In particular each node and connection in the expression tree is then mapped to a corresponding neural network component. Leaf nodes are mapped directly to input neurons in the input layer. Internal nodes, which represent binary and unary operations, are translated into hidden neurons or substructures. Binary operations, such as addition and multiplication, are implemented using neurons or sets of neurons performing these operations, while unary operations, like activation functions, are implemented as activation neurons in appropriate layers. The final computed result is mapped to the output neurons, initially producing outputs identical to the physical model.

[0058] Moreover weights in the neural network are initialized using the coefficients from the physical model to ensure that the network’s initial output replicates the physical model’s output. Before training, the neural network outputs exactly match those of the physical model, as both share the same initial weights derived from the physical model’s coefficients.

[0059] The network undergoes training with actual measured data, where input data consists of measured features (e.g., pressure, temperature) andoutput data consists of actual observed values that the model aims to predict.

[0060] To capture more complex relationships, additional fully connected neurons can be introduced. These neurons start with zero weights to ensure initial output consistency and adjust during training to enhance the model’s adaptability and generalization abilities.

[0061] Advantageously once training is complete, the neural network can be translated back into an optimized mathematical equation, encapsulating the learned relationships and refining the original physical model’s expression for improved predictive performance. This hybrid system combines the robustness of physical models with the flexibility of neural networks, retaining the physical model’s characteristics initially and enhancing prediction accuracy by adapting to new data.

[0062] Furthermore a framework for simulating and validating the neural network model ensures accuracy by comparing neural network outputs with the physical model and empirical data, and ensuring the fidelity and correctness of the transformed model. An optimization algorithm specifically designed to optimize neural network weights while respecting the expression tree structure is used to improve performance, employing gradient-based methods and integrating empirical data to refine and enhance the predictive accuracy of the network

[0063] As explained above with non-limiting reference the flow chart of Fig.3A shows a method 600 to implement physical models in particular for constructing and initializing a neural network architecture, preferably feedforward neural network, derived directly from an expression tree of the physical model. The flow chart includes a BEGIN block 610 and an END block 680 that corresponds conceptually to the begin and end of the innovative method 600, wherein this method comprises the steps ofdefinition 620 of the physical model, in particular definition of a plurality of mathematical operations (e.g. addition, multiplication and other functional forms), a plurality input features (e.g. pressure, temperature), and a plurality constants; representation 630 of the physical model as an expression tree, in particular representation of the mathematical operations with internal nodes, and the input features, and constants with leaf nodes; mapping 640 the expression tree to neural network, each node and connection og the expression tree is mapped to a corresponding neural network component: input layers, hidden layers, and output layers; initialization 650 of weights: weights in the neural network are initialized using the coefficients from the physical model to ensure that the network’s initial output replicates the physical model’s output;- training and optimization 660: choosing the transfer function and or activation function for each neuron of the neural network to suit the specific mathematical operations required. Consequently, each neuron now possesses a distinct transfer function that aligns with the corresponding mathematical operations derived from the physical model; mathematical representation post-training 670: once training is complete, the neural network can be translated back into an optimized mathematical equation, encapsulating the learned relationships and refining the original physical model’s expression for improved predictive performance.

[0064] According to some embodiments, the second section comprises only one or only two or only three neurons organized as a one-layer artificial neural network; the output of each neuron is provided (e.g. in parallel) to the signal combiner to be combined with the output of the first section. Such implementation has turned out to effective even if simple; in fact, the data- driven model may be aimed only “refining” the result from the physical model.The neuron(s) may have an architecture as shown in Fig. 2.

[0065] According to a first simple possibility, the second section may comprise only one neuron with a linear activation function.

[0066] According to a second (still simple) possibility, the second section may comprises only two or only three neurons. One of the neurons may have a linear activation function and at least one of the neurons may have a nonlinear activation function.

[0067] If the second section includes at least a first neuron and a second neuron both with non-linear activation functions, the first activation function and the second activation function are advantageously different.

[0068] The first section 110 is configured to be subject to training before being used for generating device output signals 101. The training may be carried out based on data coming from the industrial machine 10, in particular data from physical measurements carried out on the industrial machine 10. Alternatively, the data may come from another machine, for example a prototype machine and / or an already-installed machine for example of the same plant or of a different plant.

[0069] The second section 120 is configured to be subject to training before being used for generating device output signals 101. The training may be carried out based on data coming from the industrial machine 10, in particular data from physical measurements carried out on the industrial machine 10. Alternatively, the data may come from another machine, for example a prototype machine and / or an already-installed machine for example of the same plant or of a different plant.

[0070] The training of the first section 110 and the training of the second section 120 may advantageously be carried out at the same time, i.e. during thesame time period. The training of the first section 110 and the training of the second section 120 may advantageously be carried out based on the same data coming from an industrial machine. Preferably, even the signal combiner is involved in such training as the output of the device, i.e. corresponding to the output of the signal combiner is compared with reference data considered to be accurate or expected. Training of the two sections or of the two sections and the combiner may be contemporaneous in the sense that a first set of data are provided to the innovative device and the output data of the components of the innovative device are compared with the accurate or expected data (i.e. belonging to the first set of data) and consequently a first adjustment occurs, then a second set of data is used, and so on.

[0071] According to some embodiments, during a training phase, different learning rates for distinct components within the inventive device are possible for example if a first architecture of e.g. the physical model exhibits partial connectivity while a second architecture of e.g. the data-driven model exhibits full connectivity. In such case, as training progresses, the optimization algorithm assigns greater importance to one of the architectures, in particular the second one, by allocating additional weight and allowing the process to span several epochs; consequently, the influence of the physical model on the device output diminishes over time. In order to address e.g. this challenge, it is possible to adopt a strategy of assigning different learning rates to distinct components (for example sections) of the inventive device. For example, a higher learning rate was applied to the physics-based section with respect to the data-based section.

[0072] Fig. 5 shows a simplified flowchart of an embodiment 500 of an innovative computer-implemented method. The method serves for generating an output signal based on a plurality of input signals; the output signal corresponds to a physical parameter of an industrial machine, while the inputsignals correspond to physical quantities of the industrial machine. The flow chart of Fig. 5 includes an operating period, corresponding to blocks 540 and 550 and 560, but also other activities carried out before the operating period, and does not exclude other activities before and / or after the operating period. The flow chart includes a BEGIN block 510 and an END block 570 that corresponds conceptually to the begin and end of an innovative method.

[0073] During the operating period, there are a generation step 540 of a first signal, a generation step 550 of a second signal and a summing step 560 of these signals. In the flow chart of Fig. 5, step 540 precedes step 550; alternatively, step 550 may precede step 540; still alternatively, step 540 and step 550 may be carried out during the same time period (totally or partially contemporaneously). Clearly, step 560 must be carried out after the end of both step 540 and step 550.

[0074] In the flow chart of Fig. 5, these three steps are repeated cyclically considering that the signals develop along time, i.e. are dynamic and not static. According to typical embodiments, each signal corresponds to a sequence of digitized samples, and any cycle of the loop in Fig. 5 corresponds to the processing of distinct samples.

[0075] At step 540, a first signal is generated by applying to the input signals of said plurality a first processing. The first processing corresponds to a physical model of the industrial machine or of a part of the industrial machine.

[0076] At step 550, a second signal is generated by applying to the input signals of said plurality a second processing. The second processing corresponds to a data-driven model of the industrial machine or of a part of the industrial machine.

[0077] At step 560, the first signal and the second signal are summed thus producing the output signal. Before being summed weights may be applied tothe first signal and the second signal, this means that the sum at step 560 may be a weighted sum.

[0078] The flow chart of Fig. 5 provides the possibility that the steps 540 and 550 and 560 of the operating period may be preceded by one or more other steps, namely step 520 and step 530.

[0079] At step 520, the first processing and the second processing are set during a setting-up period preceding a training period. Setting-up may be based on theoretical knowledge of an industrial machine, in particular but not necessarily the industrial machine to be considered during the operating period. Setting-up may consist in initially setting parameters of neural networks used thereafter for the generation steps 540 and 550.

[0080] At step 530, following step 520, the first processing and the second processing are adjusted during the training period preceding the operating period. Training may be based on data collected during operation of an industrial machine, in particular but not necessarily the industrial machine to be considered during the operating period. Training may consist in initially adjusting parameters of neural networks used thereafter for the generation steps 540 and 550.

[0081] As already anticipated, a first possible application of the innovative device and / or of the innovative method is in so-called “virtual sensors”.

[0082] Fig. 1 shows an embodiment of an innovative virtual sensor 200. According to this embodiment, the virtual sensor 200 corresponds exactly to the innovative device 100, i.e. there is no additional components. Alternatively, there may be one or more minor additional components, for example some simple signal adaptation (amplification, attenuation, delay, etc.) at the inputs 202 and / or some simple signal adaptation (amplification, attenuation, delay, etc.) at the output 201. Still alternatively, there may be one or more substantialadditional components, i.e. components that contribute to the sensing function.

[0083] The virtual sensor 200 is configured to output the device output signal 101 as sensor output 201. The virtual sensor 200 is configured to receive as sensor input signals 202 the device input signals 102.

[0084] In Fig. 1, the industrial machine 10 is shown as directly connected to the virtual sensor 200. Alternatively, and more commonly, the device input signals derive from a computer running a program and data collection from the industrial machine 10 is done at a different place and / or at a different time. It is to be noted that the innovative virtual sensor may be coupled in general to a system that may correspond for example to a plant, an apparatus, a machine or a device (that may also be considered a component of a plant, an apparatus or a machine).

[0085] As already anticipated, a second possible application of the innovative device and / or of the innovative method is in control systems sensors.

[0086] Fig. 4 shows an embodiment of an innovative control system 400. According to this embodiment, the control system 400 corresponds almost exactly to the innovative device 100, i.e. there is no additional substantial component with the exception of some simple signal adaptation (amplification, attenuation, delay, etc.) at the inputs 402 and some simple signal adaptation (amplification, attenuation, delay, etc.) at the output 401. Alternatively, there may be one or more substantial additional components, i.e. components that contribute to the control function.

[0087] The control system 400 is configured to output the device output signal 401 as sensor output 401. The control system 400 is configured to receive as system input signals 402 the device input signals 102.

[0088] In Fig. 4, the industrial machine 10 is shown as directly connected tothe control system 400. Alternatively, and more commonly, the device input signals derive from a computer running a program and data collection from the industrial machine 10 is done at a different place and / or at a different time. Alternatively, and more commonly, the device output signal is provided to a computer running a program and data transmission to the industrial machine 10 is done at a different place and / or at a different time. It is to be noted that the innovative virtual sensor may be coupled in general to a system that may correspond for example to a plant, an apparatus, a machine or a device (that may also be considered a component of a plant, an apparatus or a machine).

[0089] From the above description, it is clear that an innovative virtual sensor may be incorporated in an industrial machine or in an industrial plant thus giving rise to an innovative industrial machine or an innovative industrial plant.

[0090] From the above description, it is also clear that an innovative control system may be incorporated in an industrial machine or in an industrial plant thus giving rise to an innovative industrial machine or an innovative industrial plant.

[0091] Embodiments of the innovative system may be incorporated in or associated with a computer-implemented system.

[0092] The subject matter described herein can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structural means disclosed in this specification and structural equivalents thereof, or in combinations of them. The subject matter described herein can be implemented as one or more computer program products, such as one or more computer programs tangibly embodied in an information carrier (e.g., in a machine readable storage device), or embodied in a propagated signal, for execution by, or to control the operation of, data processing apparatus (e.g., aprogrammable processor, a computer, or multiple computers). A computer program (also known as a program, software, software application, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file. A program can be stored in a portion of a file that holds other programs or data, in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.

[0093] The processes and logic flows described in this specification, including the method steps of the subject matter described herein, can be performed by one or more programmable processors executing one or more computer programs to perform functions of the subject matter described herein by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus of the subject matter described herein can be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0094] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processor of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupledto receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, (e.g., EPROM, EEPROM, and flash memory devices); magnetic disks, (e.g., internal hard disks or removable disks); magneto optical disks; and optical disks (e.g., CD and DVD disks). The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0095] To provide for interaction with a user, the subject matter described herein can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, (e.g., a mouse or a trackball), by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well. For example, feedback provided to the user can be any form of sensory feedback, (e.g., visual feedback, auditory feedback, or tactile feedback), and input from the user can be received in any form, including acoustic, speech, or tactile input.

[0096] The techniques described herein can be implemented using one or more modules. As used herein, the term “module” refers to computing software, firmware, hardware, and / or various combinations thereof. At a minimum, however, modules are not to be interpreted as software that is not implemented on hardware, firmware, or recorded on a non-transitory processor readable recordable storage medium (i.e., modules are not software per se). Indeed “module” is to be interpreted to always include at least some physical, non-transitory hardware such as a part of a processor or computer. Two different modules can share the same physical hardware (e.g., two differentmodules can use the same processor and network interface). The modules described herein can be combined, integrated, separated, and / or duplicated to support various applications. Also, a function described herein as being performed at a particular module can be performed at one or more other modules and / or by one or more other devices instead of or in addition to the function performed at the particular module. Further, the modules can be implemented across multiple devices and / or other components local or remote to one another. Additionally, the modules can be moved from one device and added to another device, and / or can be included in both devices.

[0097] The subject matter described herein can be implemented in a computing system that includes a back end component (e.g., a data server), a middleware component (e.g., an application server), or a front end component (e.g., a client computer having a graphical user interface or a web browser through which a user can interact with an implementation of the subject matter described herein), or any combination of such back end, middleware, and front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), e.g., the Internet.

[0098] Although some specific embodiments have been described herein, other embodiments are within the scope and spirit of the subject matter as per the annexed claims.

[0099] It is noted that one or more references are incorporated herein. To the extent that any of the incorporated material is inconsistent with the present disclosure, the present disclosure shall control. Furthermore, to the extent necessary, material incorporated by reference herein should be disregarded if necessary to preserve the validity of the claims.

Claims

CLAIMS1. A computer-based device (100) for generating a device output signal (101) based on a plurality of device input signals (102), wherein the device output signal (101) corresponds to a physical parameter of an industrial machine (10), wherein the device input signals (102) correspond to physical quantities of the industrial machine (10), wherein the device (100) comprises: a first section (110) being a physics-based section, comprises at least one or only one feedforward artificial neural network. a second section (120) being a data-based section, and a signal combiner (130); wherein the first section (110) is configured to receive at least a first portion of the plurality of device input signals (102), and to generate a first section output (111) signal by applying a mathematical processing to values of the first portion of the plurality of input signals (102), wherein the mathematical processing relates to a physical model of the industrial machine or part of the industrial machine, wherein the second section (120) is configured to receive at least a second portion of the plurality of device input signals (102), and to generate a second section output signal (121) by applying a neural processing to values of the second portion of the plurality of device input signals (102), wherein the neural processing relates to a data-driven model of the industrial machine or part of the industrial machine, wherein the signal combiner (130) is configured to carry out a sum or a weighted sum of the first section output signal and the second section output signal and to generate a combination of the first section output signal (111) and the second section output signal (121), wherein the device output signal (101) corresponds to said combination, wherein the device (100) is configured to adjust parameters of the mathematical processing and parameters of the neural processing during atraining period of the device preceding an operating period of the device, wherein said only one feedforward artificial neural network is derived directly from an expression tree of the physical model, according to the expression tree corresponding to the mathematical processing.

2. The device (100) of claim 1, wherein said expression tree encapsulates a plurality of mathematical operations, input features, and constants defined by the physical model, allowing for a structured transformation into a neural network.

3. The device (100) of claim 1, wherein both the first section (110) and the second section (120) comprise artificial neural networks.

4. The device (100) of claim 1, wherein the second section (120) consists of only one or only two or only three neurons.

5. The device (100) of claim 1, wherein the first section (110) is configured to be subject to a training before being used for generating a device output signal (101), wherein the training is carried out based on data coming from an industrial machine (10), in particular data from physical measurements carried out on an industrial machine (10).

6. The device (100) of claim 1, wherein the second section (120) is configured to be subject to a training before being used for generating a device output signal (101), wherein the training is carried out based on data coming from an industrial machine (10), in particular data from physical measurements an industrial machine (10).

7. The device (100) of claim 6, being configured so that the training of the first section (110) and the training of the second section (120) are carried out at the same time.

8. The device (100) of claims 6 and 7, being configured so that the training of the first section (110) and the training of the second section (120) are carried out based on same data coming from an industrial machine (10).

9. The device (100) according to any of claims from 1 to 8, wherein the industrial machine (10) is a turbomachine.

10. A method (600) to implement physical models, for constructing and initializing a neural network architecture derived directly from an expression tree of the physical model, wherein said method (600) comprises the steps of- definition (620) of the physical model, preferably definition of a plurality of mathematical operations, a plurality input features, and a plurality constants;- representation (630) of the physical model as an expression tree, preferably representation of the mathematical operations with internal nodes, and the input features, and constants with leaf nodes;- mapping (640) the expression tree to the neural network, each node and connection of the expression tree is mapped to a corresponding neural network components; initialization (650) of weights;- training and optimization (660): choosing the transfer function and or activation function for each neuron of the neural network, to suit the specific mathematical operations required; mathematical representation post-training (670).

11. A computer-implemented method (500) for generating an output signal based on a plurality of input signals during an operating period, wherein the output signal corresponds to a physical parameter of an industrial machine, wherein the input signals correspond to physical quantities of the industrial machine, wherein the method comprises the steps ofa) generating a first signal (540) by applying to the input signals of said plurality a first processing, the first processing corresponding to a physical model of the industrial machine or of a part of the industrial machine, b) generating a second signal (550) by applying to the input signals of said plurality a second processing, the second processing corresponding to a data-driven model of the industrial machine or of a part of the industrial machine, c) summing (560) the first signal and the second signal thus producing the output signal; wherein the first processing and the second processing are set (520) during a setting-up period preceding a training period based on theoretical knowledge of an industrial machine, wherein the first processing and the second processing are adjusted (530) during the training period preceding the operating period based on data collected during operation of an industrial machine.

12. The method of claim 10, wherein: step a) precedes step b), or step b) precedes step a), or step a) and step b) are at least partially contemporaneous.

13. A virtual sensor (200) comprising a device (100) according to any of claims from 1 to 9, wherein the virtual sensor (200) is configured to output the device output signal (101) as sensor output (201).

14. A control system (400) for an industrial machine (10) or an industrial plant comprising a device (100) according to any of claims from 1 to 9, wherein the control system (100) is configured to output the device output signal (101) as control output (401) for the industrial machine (10) or the industrial plant.

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