A real-time calculation method and edge device for dynamics of crank-connecting rod shafting under discontinuous excitation

Abstract

The application discloses a real-time calculation method and an edge device for crank connecting rod shaft system dynamics under discontinuous excitation, and the method comprises the following steps: synchronously collecting cylinder pressure and crank angle signals under different steady-state working conditions through a test bench; mapping from the cylinder pressure to the excitation torque of the crank node is constructed based on engine parameters, and transient simulation is performed in combination with a multi-degree-of-freedom dynamic model of the crank established by using the lumped mass method to generate paired training data sets of the excitation torque and angular displacement response; a PIC-FNO network model is constructed, the model fuses the global modeling capability of Fourier transform and the time series processing capability of causal convolution, and the dynamic model is introduced into a loss function as a constraint in the training process, and the training is performed through a normalized loss weighting strategy. In actual application, the excitation torque converted from the real-time collected cylinder pressure signal is input into the trained PIC-FNO model, and the torsional vibration response of the crank system can be predicted.

Description

Technical Field

[0001] This invention relates to the field of cross-technical technology of dynamic modeling, intelligent simulation and real-time monitoring of power machinery, and specifically to a real-time calculation method and edge device for the dynamics of crank-connecting rod shaft system under discontinuous excitation. Background Technology

[0002] As the core rotating component for power output in an internal combustion engine, the crankshaft's torsional vibration characteristics directly determine the smoothness of engine and powertrain operation, structural durability, and human comfort. In actual operation, when encountering combustion degradation (such as misfires or knocking), bearing wear, or damper performance degradation, the crankshaft and connecting rod shaft system may experience high-amplitude, nonlinear abnormal torsional vibration. This not only significantly reduces the overall vehicle's NVH performance but may also induce coupling fatigue fracture, accelerated main bearing wear, and even low-cycle fatigue failure of the crankshaft itself, leading to serious safety accidents. Therefore, developing a real-time simulation technology capable of predicting crankshaft torsional vibration response with high precision, low latency, and strong generalization is of significant engineering value for achieving engine health management and active vibration control.

[0003] CN112380649A discloses a "method, device, equipment, and storage medium for optimizing engine crankshaft torsional vibration dampers." This technology establishes a multibody dynamics model of the crankshaft, uses the Newmark-β method for numerical integration to solve the torsional vibration response, and then optimizes the damper parameters. This method is based on numerical simulation of multibody dynamics (MBD) or finite element method (FEA). A typical process includes: first, discretizing the continuous crankshaft into several lumped mass nodes and establishing a multi-degree-of-freedom (MDOF) dynamic equation containing a stiffness matrix K, a damping matrix C, and an inertia matrix J; then, using external torque (mainly derived from crankpin excitation converted from combustion pressure in each cylinder) as input, and employing time-domain integration algorithms such as the Newmark-β method and the Runge-Kutta method to solve step by step.

[0004] To overcome the limitations of traditional numerical methods, researchers have recently attempted to introduce data-driven deep learning methods into dynamic simulations. Among them, Physical-Informed Neural Networks (PINNs) have made progress in areas such as flow field reconstruction, solid mechanics, and gear fatigue by embedding control partial differential equations (PDEs) or ordinary differential equations (ODEs) as soft constraints into the loss function. However, PINNs are essentially designed for problems with fixed initial and boundary values, and their network weights are strongly coupled to specific operating conditions (such as rotational speed and load). Once the operating conditions change, the model fails and needs to be retrained, exhibiting poor generalization ability across operating conditions.

[0005] Another class of methods, neural operators, aims to learn a mapping G:u(·) from one function space to another. v(·) inherently possesses the ability to handle different input functions (such as varying boundary conditions or source terms). Representative architectures such as DeepONet and Fourier Neural Operator (FNO) have demonstrated superiority in tasks such as climate simulation, multiphase flow, and material response. FNO is particularly suitable for handling physical fields with smoothness and periodicity. Its core idea is to use Fourier transform to diagonalize the convolution operator and achieve global interaction in the frequency domain through learnable spectral multipliers.

[0006] Nevertheless, directly using FNO for internal combustion engine dynamics simulation still faces two key challenges:

[0007] First, it lacks temporal causality: Standard FNO was originally designed to handle spatial domain PDEs (such as the Navier-Stokes equations), whose inputs / outputs are defined on non-directional spatial coordinates. When forcibly applied to time-domain problems (such as predicting integer-cycle responses with integer-cycle excitations), its underlying Fourier transform treats time as a cyclic dimension, failing to distinguish between "past" and "future." That is, the system's current state is determined only by current and past inputs, without any awareness of future excitations. This lack of causality leads the model to learn spurious physical correlations, making the predictions physically unreliable.

[0008] Secondly, the mapping relationship between time-varying excitation and steady-state response is complex: the external excitation source of an internal combustion engine, the in-cylinder pressure, is a highly nonlinear and strongly time-varying signal. The "time-to-time" mapping framework of the FNO (Functional Noise Generation) system struggles to directly learn the global, non-local mapping relationship between a time-varying excitation from one complete cycle to the steady-state response of another. Because the same set of excitations, under different transient initial conditions, will produce an infinite number of transient trajectories, and the steady-state periodic solution is only a special case, this increases the difficulty and uncertainty of model fitting. Currently, internal combustion engine dynamics simulation methods for real-time monitoring suffer from the following problems:

[0009] 1. Traditional numerical methods rely on time-series iterations, which introduces time delays;

[0010] 2. PINNs and neural operator methods rely on the convergence process of time series sequences, resulting in wasted computational resources and delays;

[0011] 3. PINNs and neural operator methods are difficult to adapt to time-varying source term problems in the time domain and have limited generalization ability across operating conditions.

[0012] Due to the aforementioned shortcomings of existing technologies, there is a need for an internal combustion engine dynamics simulation method that can balance real-time computation and generalization capabilities. Summary of the Invention

[0013] To address the problems existing in the prior art, this invention proposes a real-time calculation method and edge device for crank-connecting rod shaft dynamics under discontinuous excitation, in order to solve the core problems of slow calculation speed, large simulation delay and weak generalization ability across working conditions in the prior art.

[0014] The first aspect of this invention is to provide a real-time calculation method for the dynamics of a crank-connecting rod shaft system under discontinuous excitation, comprising:

[0015] Step 1: Under various preset steady-state operating conditions, synchronously acquire cylinder pressure signals and crankshaft speed signals using cylinder pressure sensors and photoelectric encoders;

[0016] Step 2: Based on engine geometry and mass parameters, construct a mapping model from discontinuous in-cylinder combustion excitation to crankshaft node excitation torque, and convert the collected cylinder pressure signal into crankpin torque acting on the crankshaft; use the lumped mass method to construct a multi-degree-of-freedom dynamic model of the crankshaft system, in which the crankshaft excitation torque acting on each node is the sum of the crankpin torque, the output end load torque, and the gear train torque;

[0017] The established dynamic model was subjected to transient simulation using the numerical integration method. After the simulation reached a steady state, the angular displacement response data of each node of the crankshaft were obtained and paired with the crankshaft excitation torque to construct a paired training dataset of excitation torque and angular displacement response.

[0018] Step 3: Construct a Physical Causal Fourier Neural Operator (PIC-FNO) network model, taking the crankshaft excitation torque as input and the torsional angular displacement vector at the corresponding crankshaft node as output; input the paired training dataset constructed in Step 2 into the network model for training;

[0019] The PIC-FNO network model contains at least three Fourier layers. Each Fourier layer performs the following operations: performs a Fourier transform on the input signal to the frequency domain, performs a linear transform on the frequency domain coefficients, and performs an inverse Fourier transform back to the time domain; in parallel with the frequency domain operations, a circular causal convolution operation is used, and the result is summed with the frequency domain transformation result.

[0020] During training, the dynamic model established in step two is used as a constraint to introduce the loss function. The angular displacement predicted by the network model is substituted into the dynamic model to calculate the residual. The time derivative of the dynamic model is discretized using the central difference scheme. The network model is trained using a normalized loss weighting strategy to obtain a trained PIC-FNO model based on physical information constraints.

[0021] Step 4: During actual operation, the cylinder pressure sensor and the photoelectric encoder are used to synchronously and in real time acquire the cylinder pressure signal and crankshaft speed signal of the engine under test;

[0022] Using the constructed mapping model and dynamic model from discontinuous excitation to crankshaft node excitation torque, the crankshaft excitation torque acting on the crankshaft by each cylinder is obtained; the crankshaft excitation torque is input into the PIC-FNO model trained in step three, and the predicted crankshaft angular displacement is output in real time.

[0023] Furthermore, step two specifically includes:

[0024] S21: Based on engine geometry and mass parameters, and using cylinder pressure data under each operating condition, a mapping model from discontinuous excitation to crankshaft node excitation torque is constructed according to the kinematics and dynamics principles of the crank-connecting rod mechanism to obtain the crank pin torque.

[0025] The crankpin torque of each cylinder T Pin for:

[0026] ;

[0027] in, F t This is the tangential force acting on the crank pin from the large end of the connecting rod. F Rod The connecting rod force is r, and the crank radius is r. α It is the crankshaft angle. β It is the link angle;

[0028] S22: A multi-degree-of-freedom torsional vibration dynamic model of the crankshaft is established using the lumped mass method. The parameters of the dynamic model include the lumped mass inertia matrix J, stiffness matrix K, and damping matrix C, determined through finite element analysis or empirical formulas. The established dynamic model is as follows:

[0029] ;

[0030] The damping matrix C includes internal damping and external damping, which respectively simulate the internal friction dissipation of the shaft segment material and the friction dissipation of the piston connecting rod; T is the applied torque vector at each node, θ is the displacement vector at each node, and the applied torque at each node is... T (That is, in the classic model simulation, an instantaneous excitation force T is input at each node at each time step) which is the crank pin torque. T Pin Output load torque and gear train torque T Gear sum:

[0031] ;

[0032] Among them, the output end load torque T Load The torque is a measured or calculated value corresponding to the system's operating state; the gear train torque T Gear Determined by a PID controller;

[0033] The established dynamic model is subjected to long-term transient simulation using the numerical integration method. The angular displacement data after reaching the steady state is extracted as labels and paired with the corresponding excitation torque to form a training dataset.

[0034] Specifically, in step two, the output torque under load is fed back by a dynamometer on the test bench, and in step four, the output torque under load is the current operating torque calculated by the ECU during actual vehicle operation.

[0035] Furthermore, in step three, the PIC-FNO network model includes:

[0036] The input and dimensionality enhancement layer is used to receive the time series of applied torque at each node. T(t) And mapping the input signal to a high-dimensional latent space;

[0037] At least three cascaded Fourier layers, each performing frequency domain linear transformation and cyclic causal convolution operations in parallel, and then summing the results;

[0038] The dimension matching and output layer is used to map high-dimensional features back to physical quantity dimensions and output the torsional displacement vector of the crankshaft nodes.

[0039] A second aspect of the present invention provides a real-time calculation system for the dynamics of a crank-connecting rod shaft system under discontinuous excitation, comprising:

[0040] The data acquisition and paired training dataset construction module synchronously acquires cylinder pressure signals and crankshaft speed signals from the test frame using cylinder pressure sensors and photoelectric encoders under various preset steady-state operating conditions; and

[0041] Based on engine geometry and mass parameters, a mapping model from discontinuous excitation to crankshaft node excitation torque is constructed, converting the collected cylinder pressure signal into crank pin torque acting on the crankshaft. A multi-degree-of-freedom dynamic model of the crankshaft system is constructed using the lumped mass method. The established dynamic model is subjected to transient simulation using the numerical integration method. After the simulation reaches a steady state, the angular displacement response data of each node of the crankshaft are obtained and paired with the crankshaft excitation torque to generate a paired training dataset.

[0042] The PIC-FNO network model construction and training module constructs a Physical Causal Fourier Neural Operator (PIC-FNO) network model, taking the crankshaft excitation torque as input and the torsional angular displacement vector at the corresponding crankshaft node as output; the paired training dataset constructed by the data acquisition and paired training dataset construction module is input into the network model for training;

[0043] The PIC-FNO network model contains at least three Fourier layers. Each Fourier layer performs the following operations: performs a Fourier transform on the input signal to the frequency domain, performs a linear transform on the frequency domain coefficients, and performs an inverse Fourier transform back to the time domain; in parallel with the frequency domain operations, a circular causal convolution operation is used, and the result is summed with the frequency domain transformation result.

[0044] During training, the dynamic model established in the data acquisition and paired training dataset construction module is used as a constraint to introduce the loss function. The angular displacement predicted by the network model is substituted into the dynamic model to calculate the residual. The time derivative of the dynamic model is discretized using the central difference scheme. The network model is trained using a normalized loss weighting strategy to obtain a trained PIC-FNO model based on physical information constraints.

[0045] The actual operation module is used to synchronously and in real time acquire the cylinder pressure signal and crankshaft speed signal of the engine under test using a cylinder pressure sensor and a photoelectric encoder during actual operation;

[0046] The mapping model and dynamic model from discontinuous excitation to crankshaft node excitation torque are constructed using the data acquisition and paired training dataset construction module to obtain the crankshaft excitation torque of each cylinder acting on the crankshaft; the crankshaft excitation torque is input into the PIC-FNO network model construction and training module trained by the physical information constraint PIC-FNO model, and the predicted crankshaft angular displacement is output in real time.

[0047] A third aspect of the present invention is to provide a dynamic real-time computing edge device, wherein the edge computing device includes a data acquisition card, a microcomputer and a display screen;

[0048] The data acquisition card is electrically connected to the photoelectric encoder and the cylinder pressure sensor respectively, and is used to acquire cylinder pressure signals and crankshaft speed signals;

[0049] A microcomputer, electrically connected to the data acquisition card, has a PIC-FNO model trained by the above method deployed inside it. This model is used to receive the acquired cylinder pressure signal and crankshaft speed signal and to calculate and output the crankshaft angular displacement in real time.

[0050] The display screen is electrically connected to the microcomputer and is used to display real-time calculation results.

[0051] Furthermore, the data acquisition card is electrically connected to the cylinder pressure sensor installed on the engine cylinder head and the photoelectric encoder installed on the shock absorber housing;

[0052] The PIC-FNO model deployed by the microcomputer includes a physical pre-computation layer for calculating the crankpin excitation torque based on the real-time collected cylinder pressure signal.

[0053] The display screen is used to display the predicted crankshaft angular displacement and its derivatives for real-time torsional vibration amplitude monitoring.

[0054] Preferably, the derived quantities include angular velocity, angular acceleration, and shaft segment torque.

[0055] The beneficial effects of this invention are as follows:

[0056] The real-time calculation method for crank-connecting rod shaft dynamics under discontinuous excitation described in this invention transforms the solution of complex multibody dynamic differential equations into an efficient feedforward neural network inference process through a hybrid modeling framework of "physical pre-processing + intelligent core". The trained PIC-FNO network model can accurately and efficiently complete the torsional vibration prediction of a working cycle on an edge computing device, achieving "real-time accurate prediction" and meeting the stringent requirements of online monitoring and active control for computational speed.

[0057] Furthermore, the PIC-FNO network model of this invention, by introducing physical information constraint loss and embedding the dynamic model as a physical constraint into the loss function, forces the model's prediction results not only to fit the data but also to comply with basic physical laws; thus, when the model faces new rotational speeds or loads not seen in the training set, the prediction results still maintain physical rationality, significantly enhancing the generalization ability. Attached Figure Description

[0058] Figure 1 This is a flowchart of the real-time calculation method for the dynamics of the crank-connecting rod shaft system under discontinuous excitation as described in this invention;

[0059] Figure 2 This is a schematic diagram of the dynamic real-time calculation edge device described in this invention;

[0060] Figure 3 This is a schematic diagram of the PIC-FNO network constructed in step three of the real-time dynamics calculation method described in this invention;

[0061] Figure 4 To adopt Newmark- β A comparison of the torsional displacement curves of each crank pin obtained in step four, based on simulations using the traditional FNO model and the PIC-FNO model described in this invention.

[0062] Wherein, 1: first cylinder; 2: second cylinder; 3: third cylinder; 4: fourth cylinder; 5: fifth cylinder; 6: sixth cylinder; 7: cylinder head; 8: cylinder pressure sensor; 9: shock absorber housing; 10: photoelectric encoder; 11: data acquisition card; 12: microcomputer; 13: display screen. Detailed Implementation

[0063] To make the objectives, technical solutions, beneficial effects, and significant advancements of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings provided in the examples of the present invention. Obviously, all the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] In the description of this application, unless otherwise expressly specified and limited, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more; unless otherwise specified or explained, the terms "connected," "fixed," etc., should be interpreted broadly. For example, "connected" can be a fixed connection, a detachable connection, an integral connection, or an electrical connection; "connected" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0065] like Figure 1 As shown, a real-time calculation method for the dynamics of a crank-connecting rod shaft system under discontinuous excitation is presented. This method employs a "physical pre-processing + intelligent core" technical framework, specifically including:

[0066] Step 1: System Parameter Calibration and Data Acquisition

[0067] like Figure 2 As shown, a cylinder pressure sensor, a photoelectric encoder 10, and a dynamic real-time edge computing device are installed on a test bench. The edge computing device includes a data acquisition card 11, a microcomputer 12, and a front-end display screen 13. The data acquisition card 11 is electrically connected to the microcomputer 12, and the microcomputer 12 is electrically connected to the display screen 13. The display screen is capable of performing touch operations and displaying information.

[0068] The data acquisition card 11 is electrically connected to the photoelectric encoder 10 and the cylinder pressure sensor 8, respectively. A high-precision cylinder pressure sensor 8 and photoelectric encoder 10 are installed on a test bench, which is a multi-cylinder piston engine, including a first cylinder 1, a second cylinder 2, a third cylinder 3, a fourth cylinder 4, a fifth cylinder 5, a sixth cylinder 6, a cylinder block, and a cylinder head 7. The cylinder pressure sensor 8 is located on the cylinder head 7 and close to the fifth cylinder 5. The position of the cylinder pressure sensor is not limited here; since the consistency of each cylinder in a diesel engine is usually good, it can be placed on the cylinder head of any cylinder. A shock absorber housing 9 is fixedly connected to the cylinder wall on one side and connected to the photoelectric encoder 10 on the other side. The photoelectric encoder 10 is used to acquire the crankshaft rotation angle of the engine.

[0069] Under various preset steady-state conditions (such as idle speed – rated speed, 0 – 100% load), cylinder pressure signals and crankshaft speed signals are acquired synchronously.

[0070] Obtain the geometric and mass parameters of the engine crankshaft and connecting rod mechanism components: cylinder bore, crank radius, connecting rod length, piston mass, connecting rod mass and its center of mass position.

[0071] Step 2: Training Dataset Construction

[0072] (1) Modeling of excitation force of piston connecting rod

[0073] For the cylinder pressure data under each working condition, based on the kinematics and dynamics principles of the crank-connecting rod mechanism, a mapping model from discontinuous excitation to crankshaft node excitation torque is constructed, and the crank pin torque of each cylinder is calculated point by point.

[0074] The resultant force acting on the piston F by gas force F g With inertial force F a composition:

[0075] (1)

[0076] Gas force is generated by cylinder pressure p The calculation shows that:

[0077] (2)

[0078] in, d It refers to the cylinder diameter.

[0079] The inertial force is calculated using the equivalent mass of the piston mass and the small end mass of the connecting rod. The connecting rod mass is divided into the translational mass of the small end as follows: m 1 and large end rotational mass m 2:

[0080] (3)

[0081] in, l It is the center distance between the large and small ends of the connecting rod. l 1 and l 2 represents the distance from the center of mass of the connecting rod to the center of the small end and the center of the large end of the connecting rod, respectively, in meters. Rod It is the mass of the connecting rod.

[0082] Inertial force can be expressed as:

[0083] (4)

[0084] in, m Piston It is the piston mass. This is the piston acceleration.

[0085] Based on the geometric relationships of the planar mechanism, the piston acceleration can be expressed as:

[0086] (5)

[0087] in, r It is the crank radius. ω e It is the average angular velocity under the current operating conditions. α It is the crankshaft angle. β It is the link angle.

[0088] After obtaining the gas force and inertial force, the connecting rod force F Rod and crank pin torque T Pin It can be calculated that:

[0089] (6)

[0090] (7)

[0091] in, F Rod The connecting rod force is r, and the crank radius is r. α It is the crankshaft angle. β It is the link angle.

[0092] (2) Multi-degree-of-freedom dynamic modeling of crankshaft system

[0093] To address torsional vibration, the crankshaft is considered a flexible body. A simplified model of the crankshaft is constructed using the lumped mass method. Specifically, the crankshaft body is divided into several segments along the axial direction. The moment of inertia of each segment is distributed in a 1:1 ratio between its two adjacent nodes. The stiffness is calculated using finite element analysis software, and the torsional stiffness between the segments is also calculated using finite element analysis software.

[0094] Frictional dissipation of the piston is modeled as six external dampers, while material deformation dissipation within the shaft segment is modeled as internal dampers. c In i and external damping c Ex i The calculation method is as follows:

[0095] (8)

[0096] in, ω e It is the crankshaft's time-averaged speed. i and ξ i These are the internal damping coefficient and the external damping coefficient, respectively. Due to the uniformity of the structure, the internal damping coefficient of each crank is taken to be the same, and the external damping coefficient of each crank is taken to be the same.

[0097] The belt-driven transmission structure at the engine's front end is simplified to a single node at the free end. The internal damping between this node and the crankshaft's front end node simulates the belt's vibration reduction effect. Based on the established lumped mass model and the internal and external damping parameters, a dynamic model is established:

[0098] (9)

[0099] Where J is the inertia matrix, K is the stiffness matrix, and C is the damping matrix. T It is the crankshaft excitation torque (i.e., the external torque vector at each node of the crankshaft). θ These are the displacement vectors of each node.

[0100] The damping matrix C includes internal damping and external damping, comprehensively simulating damping effects such as internal friction dissipation of the shaft segment material and friction dissipation of the piston and connecting rod; crankshaft excitation torque T Crank pin torque T Pin Output torque under load T Load and gear system torque T Gear sum:

[0101] (10)

[0102] Among them, the output end load torqueT Load This is due to the negative torque applied to the crankshaft by the output load. T Pin It refers to the excitation torque of each crankpin and the torque of the gear system. T Gear The gear-assisted mechanical load-carrying torque is a negative torque. The output load-carrying torque is fed back by a dynamometer on the test bench, and the current operating condition output torque calculated in the ECU is taken during actual vehicle operation in subsequent step four. The gear system torque is determined by a PID controller. The PID controller is driven by the difference between the average simulated speed and the actual speed. The PID controller minimizes this tracking error by adjusting its output value (i.e., gear system torque), thereby achieving accurate tracking.

[0103] The Newmark-β numerical integration method was used to perform transient simulations of the established dynamic model (Equation 9) over 500 engine working cycles. The simulation results were used for subsequent dataset construction and model validation. After the simulation stabilized, the nodal angular displacement data of the last one to two converged stable cycles were extracted as torsional vibration label data output. The torsional vibration label data was paired with the corresponding excitation inputs (including in-cylinder pressure, load, etc.) to form a data sample. This process was repeated, and by changing the operating parameters (such as speed, load), a paired training dataset covering a wide range of operating conditions could be constructed.

[0104] Step 3: Construction and Training of the PIC-FNO Model Based on Physical Information Constraints

[0105] S31: Construct a Physical Causal Fourier Neural Operator (PIC-FNO) network model, which can achieve end-to-end prediction of engine crankshaft torsional vibration (torsional vibration) with high accuracy and efficiency.

[0106] The input to the network model is the time series of the applied torque at each node, which varies over time. T(t) The model output is a sequence of torsional angular displacement vectors at each node of the crankshaft, corresponding to the input excitation. θ(t) .

[0107] like Figure 3 As shown, the PIC-FNO network is a deep neural network whose core architecture includes, in sequence: an input layer, a dimension boosting layer, multiple cascaded Fourier layers, a dimension matching network, and an output layer.

[0108] Input and Dimension Boosting Layer: Time series of external torque at each node of the input T(t) First, the input signal enters a dimension-enhancing layer consisting of linear layers, which maps the 18-dimensional input signal to a 36-dimensional latent space. This operation transforms the input features into a high-dimensional representation.

[0109] Fourier Layers: This layer comprises three sequentially connected Fourier layers. Each layer performs a Fast Fourier Transform (FFT) on the high-dimensional features in both the Fourier space (frequency domain) and physical space (time domain), converting the time domain to the frequency domain. After filtering, the filtered frequency domain signal undergoes an Inverse Fast Fourier Transform (IFT). Parallel to the frequency domain transformation, a "cyclic causal convolution" operation is performed, and the convolution result is summed with the frequency domain operation result. This ensures that when processing time series data, the output at the current moment depends only on the current and past inputs, conforming to the causality of the physical system. Within each Fourier layer, "cyclic causal convolution" replaces the standard convolution operation, ensuring the model possesses correct inductive bias.

[0110] Dimensional Matching and Output Layer: High-dimensional features processed by multiple Fourier layers are fed into a dimensional matching network to map the high-dimensional features back to the final physical quantity, outputting the torsional displacement vector of the crankshaft nodes. θ(t) .

[0111] Unlike traditional neural networks that process fixed-dimensional inputs, FNO learns an operator. G : u v This operator will be defined in the continuous domain. x Input function on ∈Ω u ( x Mapping (e.g., initial conditions or boundary conditions) to the output function v ( x (e.g., solving the field). The core idea of ​​FNO stems from a key theory: linear operators can be diagonalized in the Fourier domain. Specifically, for a translation-invariant linear operator K, its function... u The effect can be represented by convolution operation:

[0112] (11)

[0113] (12)

[0114] Where F represents the Fourier transform, and These are functions u and convolution kernel κ Fourier coefficients.

[0115] FNO replaces the convolution kernel with a learnable spectral multiplier. In practical applications, this architecture first includes a lifting layer that feeds the input function... u ( x )∈R du Mapping to a higher-dimensional representation v 0( x )∈R dvThis is followed by a series of Fourier layers. Each Fourier layer performs the following operation:

[0116] (13)

[0117] in, W l It is a local linear transformation, F and F -1 These represent the Discrete Fourier Transform (DFT) and its inverse transform, respectively. R l (k)∈C dv×dv It is a complex learnable weight matrix, only for low-frequency patterns | k |≤ k max Definition (high-frequency patterns are truncated to reduce computational cost and avoid overfitting). σ It is a non-linear activation function.

[0118] Finally, a projection layer maps the latent representation back to the output dimension.

[0119] The above local linear transformation is implemented using a circular causal convolution. The circular causal convolution is an improvement upon the standard causal convolution, which is as follows:

[0120] (14)

[0121] in, x [ n ] represents the input sequence (e.g., node torque). h [ k ] is a length of K The learnable filter, and when nk Zero-padding is used when the value is less than 0. However, zero-padding only aligns the signal length and lacks corresponding causal information at the beginning of the period, resulting in discontinuous periods. Therefore, to maintain both periodic continuity and temporal causality, a cyclic causal convolution is proposed, replacing zero-padding with periodic extension:

[0122] (15)

[0123] The output of the circular causal convolution is:

[0124] (16)

[0125] Formula (16) formally transforms the index in standard causal convolution. Replace with module Operation. When ≥ hour,( ) mod = The behavior is consistent with standard causal convolution; when < hour,( ) mod = +( This means that the historical stimulus is automatically traced back to the end of the previous cycle.

[0126] S32: The loss function is designed using a weighted strategy of physical information loss and dynamic normalization loss.

[0127] To enhance the physical consistency of the model, the dynamic model shown in equation (9) is introduced as a constraint into the loss function. However, FNO takes whole-cycle torque as input and whole-cycle displacement as output, and has no explicit time query mechanism, so it cannot directly use automatic differentiation to calculate the continuous-time derivative. Therefore, a second-order central difference scheme is used to discretize the time derivative:

[0128] (17)

[0129] Based on this, the residuals of the dynamic model are directly calculated at discrete time points. The original equations of motion for the multi-degree-of-freedom system are:

[0130] (18)

[0131] in, For steady-state angular velocity, 01 This represents the cumulative angular displacement after long-term transient simulation and periodic convergence. 02 This represents the average relative angle offset between nodes. T Mean and T Flu These represent the mean and fluctuation components of the cylinder pressure excitation, respectively. To reduce training difficulty, the dynamics are decomposed into steady-state and fluctuation components. Under periodic steady-state conditions, the system is in mechanical equilibrium: all nodes move at the same angular velocity. Rotation, no relative motion, therefore the damping term C =0; simultaneously, static displacement 01 satisfy K 01 =0, because ω e t This does not result in a relative displacement of 0. Therefore, the dynamic model can be simplified to:

[0132] (19)

[0133] To preserve the relative poses between nodes, during detrending, the same time-based mean is subtracted from all nodes simultaneously, rather than subtracting the mean from each node individually, ensuring... 02 Information is stored in Flu In the displacement term. Furthermore, due to the extremely high stiffness of the crankshaft system, even a small displacement error can lead to a drastic amplification of the residuals, causing the loss function to be ill-conditioned. Therefore, we rewrite the physical constraints in explicit displacement form:

[0134] (20)

[0135] And define the physical residual:

[0136] (twenty one)

[0137] Both data fidelity loss and physical information loss are expressed using mean squared error (MSE):

[0138] (twenty two)

[0139] (twenty three)

[0140] Since both have the same unit (radians), their magnitudes are naturally comparable. To dynamically balance their contributions, a joint training strategy using the Adam optimizer and a dynamic normalization weighting strategy is employed.

[0141] (twenty four)

[0142] Where l is the moving average of the two types of losses in recent training iterations. >0 is used for numerical stability. Thanks to dimensional alignment and dynamic normalization, the weight hyperparameter can be kept within a reasonable range (e.g., 0.01 ≤ 0.01). It can be flexibly adjusted within ≤10, without the need for cumbersome magnitude testing, which is significantly better than the loss weighting method in traditional PINNs that relies solely on empirical parameter tuning.

[0143] The loss function simultaneously calculates the mean square error of the predicted displacement and the actual displacement, as well as the residual of the dynamic model based on the central difference scheme (also expressed as mean square error).

[0144] This allows us to obtain a well-trained PIC-FNO model based on physical information constraints.

[0145] Step 4: Solidify the PIC-FNO model trained in Step 3 and deploy it to the edge computing device.

[0146] During online operation, the cylinder pressure and engine crankshaft angle of the current working cycle are collected and received in real time.

[0147] A fixed "physical pre-computation layer" is embedded in the network front end, that is, the crank pin excitation torque is calculated by using the cylinder pressure according to formula (1)-(7) to achieve end-to-end training.

[0148] The PIC-FNO model automatically completes the full mapping from cylinder pressure excitation to crankshaft torsional vibration, thereby outputting the predicted angular displacement of each node of the crankshaft.

[0149] Based on the prediction results, derivative quantities such as angular velocity, angular acceleration, and shaft segment torque can be further calculated for real-time torsional vibration amplitude monitoring.

[0150] To verify the real-time calculation method for crank-connecting rod shaft dynamics under discontinuous excitation described in this invention, Newmark- β The data obtained in step four are simulated using the traditional FNO model, the PIC-FNO model described in this invention, and other methods. Figure 4 A comparison chart is shown. Figure 4 Figures (a) to (f) show the torsional displacement curves of the first crank pin (crank pin 1) to the sixth crank pin (crank pin 6), respectively. The simulation results calculated by the Newmark-β numerical integration method are used as the true baseline results and compared with the prediction results of the FNO model and the PIC-FNO model. The fitting curves of the prediction results and the error curves calculated by "prediction results minus simulation results" are compared respectively. It is found that the fitting accuracy of PIC-FNO at the extreme points is significantly higher than that of FNO, and PIC-FNO reduces the trend error within one period compared with FNO.

[0151] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style of the specification is merely for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A real-time calculation method for the dynamics of a crank-connecting rod shaft system under discontinuous excitation, characterized in that... include: Step 1: Under various preset steady-state conditions, the cylinder pressure sensor (8) and the photoelectric encoder (10) are used to synchronously collect the cylinder pressure signal and the crankshaft speed signal; Step 2: Based on the engine geometry and mass parameters, construct a mapping model from discontinuous in-cylinder combustion excitation to crankshaft node excitation torque, and convert the collected cylinder pressure signal into crankpin torque acting on the crankshaft; use the lumped mass method to construct a multi-degree-of-freedom dynamic model of the crankshaft system, in which the crankshaft excitation torque acting on each node is the sum of crankpin torque, output end load torque and gear train torque; The established dynamic model was subjected to transient simulation using the numerical integration method. After the simulation reached a steady state, the angular displacement response data of each node of the crankshaft were obtained to construct a paired training dataset of excitation torque and angular displacement response. Step 3: Construct a Physical Causal Fourier Neural Operator (PIC-FNO) network model, with crankshaft excitation torque as input and torsional angular displacement vector at the corresponding crankshaft node as output; input the paired training dataset constructed in Step 2 into the network model for training; The PIC-FNO network model contains at least three Fourier layers. Each Fourier layer performs the following operations: performs a Fourier transform on the input signal to the frequency domain, performs a linear transform on the frequency domain coefficients, and performs an inverse Fourier transform back to the time domain; in parallel with the frequency domain operations, a circular causal convolution operation is used, and the result is summed with the frequency domain transformation result. During training, the dynamic model established in step two is used as a constraint to introduce the loss function. The angular displacement predicted by the network model is substituted into the dynamic model to calculate the residual. The time derivative of the dynamic model is discretized using the central difference scheme. The network model is trained using a normalized loss weighting strategy to obtain a trained PIC-FNO model based on physical information constraints. Step 4: During actual operation, the cylinder pressure sensor (8) and the photoelectric encoder (10) are used to synchronously and in real time collect the cylinder pressure signal and crankshaft speed signal of the engine under test; Using the constructed mapping model and dynamic model from discontinuous excitation to crankshaft node excitation torque, the crankshaft excitation torque acting on the crankshaft by each cylinder is obtained; the crankshaft excitation torque is input into the PIC-FNO model trained in step three, and the predicted crankshaft angular displacement is output in real time.

2. The real-time calculation method for crank-connecting rod shaft dynamics under discontinuous excitation according to claim 1, characterized in that, Step two specifically includes: S21: Based on engine geometry and mass parameters, and using cylinder pressure data under each operating condition, a mapping model from discontinuous excitation to crankshaft node excitation torque is constructed according to the kinematics and dynamics principles of the crank-connecting rod mechanism to obtain the crank pin torque. The crankpin torque of each cylinder T Pin for: ； in, F t This is the tangential force acting on the crank pin from the large end of the connecting rod. F Rod The connecting rod force is r, and the crank radius is r. α It is the crankshaft angle. β It is the link angle; S22: A multi-degree-of-freedom torsional vibration dynamic model of the crankshaft is established using the lumped mass method. The parameters of the dynamic model include the lumped mass inertia matrix J, stiffness matrix K, and damping matrix C, determined through finite element analysis or empirical formulas. The established dynamic model is as follows: ； The damping matrix C includes internal damping and external damping, which respectively simulate the internal friction dissipation of the shaft segment material and the friction dissipation of the piston connecting rod; T is the applied torque at each node, θ is the displacement vector at each node, and the applied torque at each node is... T Crank pin torque T Pin Output load torque and gear train torque T Gear sum: ； Among them, the output end load torque T Load The torque is a measured or calculated value corresponding to the system's operating state; the gear train torque T Gear Determined by a PID controller; The established dynamic model is subjected to long-term transient simulation using the numerical integration method. The angular displacement data after reaching the steady state is extracted as labels and paired with the corresponding excitation torque to form a training dataset.

3. The real-time calculation method for crank-connecting rod shaft dynamics under discontinuous excitation according to claim 1, characterized in that, In step three, the PIC-FNO network model includes: The input and dimensionality enhancement layer is used to receive the time series of applied torque at each node. T(t) And mapping the input signal to a high-dimensional latent space; At least three cascaded Fourier layers, each performing frequency domain linear transformation and cyclic causal convolution operations in parallel, and then summing the results; The dimension matching and output layer is used to map high-dimensional features back to physical quantity dimensions and output the torsional displacement vector of the crankshaft nodes.

4. A real-time calculation system for the dynamics of a crank-connecting rod shaft system under discontinuous excitation, characterized in that... include: The data acquisition and paired training dataset construction module synchronously acquires the cylinder pressure signal and crankshaft speed signal of the test frame using a cylinder pressure sensor (8) and a photoelectric encoder (10) under various preset steady-state conditions; and Based on engine geometry and mass parameters, a mapping model from discontinuous excitation to crankshaft node excitation torque is constructed, and the collected cylinder pressure signal is converted into crank pin torque acting on the crankshaft. A multi-degree-of-freedom dynamic model of the crankshaft system is constructed using the lumped mass method. The established dynamic model is subjected to transient simulation using the numerical integration method. After the simulation reaches a steady state, the angular displacement response data of each node of the crankshaft are obtained to generate a paired training dataset. The PIC-FNO network model construction and training module constructs a Physical Causal Fourier Neural Operator PIC-FNO network model, taking the crankshaft excitation torque as input and the torsional angular displacement vector at the corresponding crankshaft node as output; the paired training dataset constructed by the data acquisition and paired training dataset construction module is input into the network model for training. The PIC-FNO network model contains at least three Fourier layers. Each Fourier layer performs the following operations: performs a Fourier transform on the input signal to the frequency domain, performs a linear transform on the frequency domain coefficients, and performs an inverse Fourier transform back to the time domain; in parallel with the frequency domain operations, a circular causal convolution operation is used, and the result is summed with the frequency domain transformation result. During training, the dynamic model established in the data acquisition and paired training dataset construction module is used as a constraint to introduce the loss function. The angular displacement predicted by the network model is substituted into the dynamic model to calculate the residual. The time derivative of the dynamic model is discretized using the central difference scheme. The network model is trained using a normalized loss weighting strategy to obtain a trained PIC-FNO model based on physical information constraints. The actual operation module is used to synchronously and in real time collect the cylinder pressure signal and crankshaft speed signal of the engine under test using the cylinder pressure sensor (8) and photoelectric encoder (10) during actual operation; The mapping model and dynamic model from discontinuous excitation to crankshaft node excitation torque are constructed using the data acquisition and paired training dataset construction module to obtain the crankshaft excitation torque of each cylinder acting on the crankshaft; the crankshaft excitation torque is input into the PIC-FNO network model construction and training module trained by the physical information constraint PIC-FNO model, and the predicted crankshaft angular displacement is output in real time.

5. A dynamic real-time computing edge device, comprising a data acquisition card (11), a microcomputer (12), and a display screen (13); characterized in that, The data acquisition card (11) is electrically connected to the photoelectric encoder (10) and the cylinder pressure sensor (8) respectively, and is used to acquire cylinder pressure signal and crankshaft speed signal; A microcomputer (12) is electrically connected to the data acquisition card (11), and has a PIC-FNO model based on physical information constraints, which is trained by the real-time calculation method of crank-connecting rod shaft dynamics under discontinuous excitation as described in any one of claims 1-2. The model is used to receive the acquired cylinder pressure signal and crankshaft speed signal and calculate and output the crankshaft angular displacement in real time. The display screen is electrically connected to the microcomputer (12) and is used to display real-time calculation results.

6. The dynamic real-time calculation edge device according to claim 5, characterized in that, The data acquisition card (11) is electrically connected to the cylinder pressure sensor (8) installed on the engine cylinder head (7) and the photoelectric encoder (10) installed on the shock absorber housing (9); The PIC-FNO model deployed by the microcomputer (12) includes a physical pre-computation layer for calculating the crankpin excitation torque based on the real-time collected cylinder pressure signal. The display screen (13) is used to display the predicted crankshaft angular displacement and its derivatives for real-time torsional amplitude monitoring.

7. The dynamic real-time calculation edge device according to claim 6, characterized in that, The derived quantities include angular velocity, angular acceleration, and shaft torque.

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