A complex equipment system visualization simulation method and system based on digital twinning

Abstract

The application discloses a kind of complex equipment system visual simulation method and system based on digital twinning, comprising: S1, obtains multi-source observation data and control data;S2, constructs digital twinning mechanism model, establishes state mapping relationship;S3, constraint perception hash addressing mechanism is introduced by Instant-NGP algorithm, and multi-resolution hash coding is executed;S4, state deviation is calculated;S5, input improved 4DGS model, introduce mechanism residual error gate projection mechanism, and execute gate projection;S6, based on SDS constraint algorithm, introduce feasible region constraint calculation of distillation gradient, and execute gradient update;S7, execute consistency determination, and output visual simulation result.The application realizes the high consistency, high stability and high real-time visual simulation output of complex equipment system under complex working condition, strong interference and multiple constraint conditions.

Description

Technical Field

[0001] This invention relates to the field of digital twin and visualization simulation technology, and in particular to a visualization simulation method and system for complex equipment systems based on digital twins. Background Technology

[0002] With the continuous improvement of the intelligence, networking, and visualization levels of high-end equipment, the demand for operational status perception, behavior prediction, and virtual simulation of complex equipment systems in fields such as aerospace, high-end manufacturing, and energy equipment is increasing. Digital twin technology, by constructing a two-way mapping relationship between physical entities and virtual models, has become an important technical path for the operational analysis and visualization simulation of complex equipment systems. Existing visualization simulation methods for complex equipment are mostly based on static geometric models or simple kinematic driving methods, primarily relying on offline modeling and rule-driven rendering to achieve virtual display. However, in practical applications, they generally suffer from the following problems: Complex equipment systems involve multi-source observation data, control data, and mechanistic state data during operation. The data sources are heterogeneous and the time scales are inconsistent. Existing methods are difficult to achieve high-precision alignment and joint modeling of multi-source data in a unified state space, resulting in significant deviations between virtual simulation results and actual operating conditions. Traditional digital twin models focus on structural and motion mechanism descriptions and lack an effective fusion mechanism for observation uncertainties and dynamic residuals. When the equipment state changes rapidly or is disturbed by external factors, the model's predicted state is prone to cumulative errors compared to the actual state. Existing visualization simulations mostly use rule-based animation or rendering methods based on a single perspective, which are difficult to stably express the true form and motion details of key components under complex occlusion, non-rigid changes, and high-dimensional temporal motion conditions, affecting the consistency and credibility of simulation results.

[0003] Therefore, how to provide a visualization simulation method and system for complex equipment systems based on digital twins is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] One objective of this invention is to propose a visualization simulation method and system for complex equipment systems based on digital twins. This invention constructs a digital twin mechanism model, combines multi-source observation data and control data to form a real equipment state sequence, introduces a constraint-aware hash addressing mechanism based on the mechanism-predicted state and state constraint set to generate an observation feature field, and introduces a mechanism residual gated projection mechanism and feasible region constraint calculation of distillation gradient in the improved 4DGS model to complete the updating and consistency determination of the spatiotemporal representation results. It can output visualization simulation results consistent with the mechanism-predicted state, and has the advantages of strong state constraint consistency, high spatiotemporal representation stability, and high dynamic visualization accuracy of complex equipment systems.

[0005] A visualization simulation method for complex equipment systems based on digital twins according to an embodiment of the present invention includes the following steps: S1. Acquire multi-source observation and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. S2. Construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. S3. By introducing a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, multi-resolution hash encoding is performed on the multi-source observation data. The state constraint set is introduced during the hash addressing process to constrain the index space of the hash features and generate an observation feature field. S4. Based on the predicted state and the observed characteristic field, calculate the state deviation to obtain the state residual; S5. Improve the 4DGS model by inputting the structural geometry, key component pose parameters and state residuals of complex equipment systems. Introduce a mechanism residual gated projection mechanism in the temporal motion parameter update process of Gaussian elements, perform gated projection, and generate spatiotemporal representation results. S6. Based on the set of state constraints, calculate the feasible region constraint of the distillation gradient introduced by the SDS constraint algorithm, perform gradient update on the spatiotemporal representation result, and generate an updated spatiotemporal representation result. S7. Perform a consistency determination on the updated spatiotemporal representation result and output a visual simulation result that is consistent with the mechanism prediction state.

[0006] Optionally, S1 specifically includes: Acquire multi-source observation data during the operation of complex equipment systems. The multi-source observation data includes continuous image frame data, depth data, point cloud data, and sensor status data. Acquire control data during the operation of complex equipment systems. The control data includes actuator control command data and operating mode identification data. Timestamp information is extracted from multi-source observation data and control data respectively, and resampling is performed according to a unified time reference to obtain time-aligned data sequences; Perform dimensional unification, amplitude standardization, and outlier removal on the time-aligned data sequence to obtain a state-standardized data sequence. A real equipment state sequence is constructed based on the state-standardized data sequence. The real equipment state sequence includes the observation state vector sequence and the control state vector sequence.

[0007] Optionally, S2 specifically includes: Obtain structural parameters, kinematic parameters, and constraint parameters of complex equipment systems. Structural parameters include component topology parameters and dimensional parameters. Kinematic parameters include joint type parameters and degree of freedom parameters. Constraint parameters include joint travel range parameters and assembly constraint parameters. A digital twin mechanism model is established based on structural parameters, motion mechanism parameters, and constraint parameters. The digital twin mechanism model includes a set of state variables and a set of state constraints. The observed state vector sequence and control state vector sequence from the real equipment state sequence are input into the digital twin mechanism model, and the state variable set is updated to obtain the mechanism prediction state; the mechanism prediction state includes the pose state vector of key components and the velocity state vector of key components. Constraint verification is performed based on the set of state variables and the set of state constraints during the state update process to obtain the set of state constraints. A state mapping relationship is constructed between the actual equipment state sequence and the mechanism prediction state to obtain the state mapping relationship between the actual equipment state sequence and the mechanism prediction state.

[0008] Optionally, S3 specifically includes: Camera intrinsic parameter calibration correction is performed on continuous image frame data, scale consistency correction is performed on depth data, and coordinate system transformation is performed on point cloud data to obtain a unified coordinate system observation data sequence. Multi-resolution hash encoding is performed on the observation data sequence in a unified coordinate system. Hash indexes are calculated on the spatial coordinates in the observation data sequence at different resolution levels to obtain a multi-level hash index sequence. The constraint variables in the state constraint set are mapped to index constraint parameters, and index space constraint processing is performed on the multi-level hash index sequence to obtain the constrained hash index sequence. Perform hash feature read and write processing under a constrained hash index sequence to obtain a multi-resolution hash feature sequence; Feature fusion processing is performed on the multi-resolution hash feature sequence to obtain the observation feature field.

[0009] Optionally, S4 specifically includes: The observation feature field is subjected to state decoding processing to obtain the observation state estimation result; the observation state estimation result includes the pose estimation vector of the key component and the velocity estimation vector of the key component; A differential calculation is performed based on the pose state vector and the pose estimation vector of the key component to obtain the pose deviation vector; a differential calculation is performed based on the velocity state vector and the velocity estimation vector of the key component to obtain the velocity deviation vector. The pose deviation vector and velocity deviation vector are subjected to residual fusion processing to obtain the state residual.

[0010] Optionally, the improved 4DGS model specifically includes a Gaussian primitive initialization layer, a temporal motion modeling layer, a mechanistic residual gated projection layer, and a spatiotemporal representation update layer; The Gaussian initialization layer is based on the structural geometric parameters and key component pose parameters of the complex equipment system. It performs spatial coordinate parameterization on the structural geometric parameters and pose vector expansion on the key component pose parameters. Based on the spatial coordinate parameters and pose vectors, it constructs a Gaussian initial parameter set. The Gaussian initial parameter set includes a Gaussian center parameter set, a Gaussian covariance parameter set, and a Gaussian scale parameter set. The temporal motion modeling layer is based on the Gaussian initial parameter set and the pose and velocity state vectors of key components in the mechanism prediction state. It performs temporal displacement modeling on the Gaussian center parameter set, temporal rotation modeling on the Gaussian covariance parameter set, and temporal scale change modeling on the Gaussian scale parameter set to obtain a set of temporal motion parameter update quantities. The aforementioned mechanism residual gated projection layer introduces a mechanism residual gated projection mechanism, representing the state residual as a joint residual vector composed of the pose deviation vector and the velocity deviation vector of the key components. The joint residual vector is formed by concatenating each dimension component of the pose deviation vector and each dimension component of the velocity deviation vector according to their corresponding dimensions. The square operation is performed on each dimension component of the joint residual vector and then summed. The square root operation is then performed on the summation result to obtain the residual amplitude. Each dimension component of the joint residual vector is divided by the residual amplitude to obtain the residual direction. A set of gated weight parameters is generated based on the residual amplitude and residual direction. The weight components in the set of gated weight parameters are obtained by multiplying the residual amplitude by the corresponding dimension component in the residual direction. The center parameter update, covariance parameter update, and scale parameter update in the set of time-series motion parameter updates are respectively subjected to gated modulation processing. The gated and modulated center parameter update, covariance parameter update, and scale parameter update are then concatenated in the order of center parameter update first, covariance parameter update in the middle, and scale parameter update last to form a set of gated update quantities. Each parameter component in the set of gated update quantities is subject to constraint interval judgment. When the parameter component exceeds the allowable range corresponding to the state constraint set, the parameter component is replaced with the boundary value of the allowable range. When the parameter component is within the allowable range, its original value is retained. The spatiotemporal representation update layer performs parameter update processing on the Gaussian central parameter set, Gaussian covariance parameter set, and Gaussian scale parameter set based on the Gaussian initial parameter set and the constrained parameter update set, to obtain the spatiotemporal representation result; the spatiotemporal representation result includes the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set.

[0011] Optionally, the gating modulation processing is performed on the center parameter update, covariance parameter update, and scale parameter update in the time-series motion parameter update set, specifically as follows: Each component of the center parameter update is multiplied by the weight component of the corresponding center parameter in the set of gated weight parameters to obtain the center parameter update after gate modulation. The covariance parameter update is expanded into a main axis direction parameter vector and a scale expansion parameter vector. Each component of the expanded covariance parameter is then multiplied by the weight component of the corresponding covariance parameter in the gating weight parameter set to obtain the gating modulated covariance parameter update. Each component of the scale parameter update is multiplied by the weight component of the corresponding scale parameter in the gating weight parameter set to obtain the scale parameter update after gating modulation.

[0012] Optionally, S6 specifically includes: The constraint variables in the set of state constraints are converted into feasible region boundary parameters, which include a lower bound vector and an upper bound vector. Distillation gradient vectors are constructed based on the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set. The distillation gradient vectors include the central parameter distillation gradient vector, the covariance parameter distillation gradient vector, and the scale parameter distillation gradient vector. Based on the lower bound vector and upper bound vector of the parameters, the feasible region projection process is performed on the distillation gradient vector of the center parameter, the feasible region projection process is performed on the distillation gradient vector of the covariance parameter, and the feasible region projection process is performed on the distillation gradient vector of the scale parameter to obtain the feasible region constrained distillation gradient vector. Based on the feasible region constraint, the gradient update process is performed on the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set to obtain the updated spatiotemporal representation result.

[0013] Optionally, S7 specifically includes: The updated spatiotemporal representation result is subjected to state decoding processing to obtain the visualized state estimation result; the visualized state estimation result includes the visualized key component pose estimation vector and the visualized key component velocity estimation vector. A differential calculation is performed based on the pose state vector of key components and the pose estimation vector of visualized key components to obtain the pose consistency error vector. A speed consistency error vector is obtained by performing differential calculation based on the speed state vector of key components and the speed estimation vector of visualized key components. Perform consistency determination on the pose consistency error vector and velocity consistency error vector, and output a visual simulation result that is consistent with the mechanism prediction state.

[0014] Optionally, a visualization simulation system for complex equipment systems based on digital twins includes the following modules: The data processing module is used to acquire multi-source observation data and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. The mechanism modeling module is used to construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. The feature construction module is used to introduce a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, perform multi-resolution hash encoding on the multi-source observation data, introduce the state constraint set during the hash addressing process, constrain the index space of the hash features, and generate an observation feature field. The spatiotemporal modeling module is used to calculate the state deviation based on the mechanism-predicted state and the observed feature field to obtain the state residual. The structural geometry, key component pose parameters and state residual of the complex equipment system are input into the improved 4DGS model. The mechanism residual gated projection mechanism is introduced to perform gated projection and generate spatiotemporal representation results. The simulation output module is used to calculate the feasible region constraint of the distillation gradient based on the SDS constraint algorithm according to the set of state constraints, perform gradient update on the spatiotemporal representation result, generate updated spatiotemporal representation result, perform consistency judgment, and output a visual simulation result consistent with the mechanism prediction state.

[0015] The beneficial effects of this invention are: (1) By constructing a digital twin mechanism model and introducing the state mapping relationship between the real equipment state sequence and the mechanism prediction state, the multi-source observation data and control data are uniformly constrained into the state variable set and the state constraint set, thereby improving the state consistency expression capability of complex equipment systems under dynamic operating conditions and effectively reducing the systematic deviation between the mechanism prediction state and the real equipment state. (2) In the Instant-NGP algorithm, a constraint-aware hash addressing mechanism is introduced, which directly applies the set of state constraints to the index space of the multi-resolution hash encoding, suppresses the participation of observation features that do not conform to the mechanism constraints in the modeling process, and improves the stability and reliability of the observation feature field under complex working conditions and multi-source noise conditions. (3) In the improved 4DGS model, a mechanism residual gated projection mechanism is introduced. The state residual is used to gate and modulate the update of the temporal motion parameters of the Gaussian element, and constrain the projection. This allows the temporal evolution of the Gaussian element center parameter, covariance parameter and scale parameter to be guided by mechanism constraints, thereby enhancing the ability of the spatiotemporal representation results to fit the actual motion mechanism of the equipment. (4) Based on the SDS constraint algorithm, the feasible region constraint calculation of the distillation gradient is introduced, the set of state constraints is transformed into feasible region boundary parameters, and the distillation gradient vector is updated by projection constraint. This effectively avoids parameter drift of the spatiotemporal representation results during the optimization process and improves the long-term stability and consistency of the visualization simulation results of complex equipment systems. Attached Figure Description

[0016] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a visualization simulation method for complex equipment systems based on digital twins proposed in this invention; Figure 2 This is a schematic diagram of the structure of the improved 4DGS model proposed in this invention; Figure 3 This is a schematic diagram of a visualization simulation system for complex equipment systems based on digital twins, as proposed in this invention. Detailed Implementation

[0017] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0018] refer to Figures 1-2 A visualization simulation method for complex equipment systems based on digital twins includes the following steps: S1. Acquire multi-source observation and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. S2. Construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. S3. By introducing a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, multi-resolution hash encoding is performed on multi-source observation data. A set of state constraints is introduced during the hash addressing process to constrain the index space of the hash features and generate an observation feature field. S4. Based on the mechanism-predicted state and observed characteristic field, calculate the state deviation and obtain the state residual; S5. Improve the 4DGS model by inputting the structural geometry, key component pose parameters and state residuals of complex equipment systems. Introduce a mechanism residual gated projection mechanism in the temporal motion parameter update process of Gaussian elements, perform gated projection, and generate spatiotemporal representation results. S6. Based on the set of state constraints, the feasible region constraint of the distillation gradient is calculated using the SDS constraint algorithm. Gradient update is performed on the spatiotemporal representation result to generate the updated spatiotemporal representation result. S7. Perform a consistency check on the updated spatiotemporal representation results and output a visual simulation result that is consistent with the mechanism prediction state.

[0019] In this embodiment, S1 specifically refers to: Acquire multi-source observation data during the operation of complex equipment systems. The multi-source observation data includes continuous image frame data, depth data, point cloud data, and sensor status data. Acquire control data during the operation of complex equipment systems. The control data includes actuator control command data and operating mode identification data. Timestamp information is extracted from multi-source observation data and control data respectively, and resampling is performed according to a unified time reference to obtain time-aligned data sequences; Perform dimensional unification, amplitude standardization, and outlier removal on the time-aligned data sequence to obtain a state-standardized data sequence. A real equipment state sequence is constructed based on the state-standardized data sequence. The real equipment state sequence includes the observation state vector sequence and the control state vector sequence.

[0020] In this embodiment, S2 specifically refers to: Obtain structural parameters, motion mechanism parameters, and constraint parameters of complex equipment systems. Structural parameters include component topology parameters and dimensional parameters. Component topology parameters describe the connection relationships between components in the form of a node connection matrix. Dimensional parameters describe the spatial scale relationships of components in the form of length, radius, and relative installation offset. Motion mechanism parameters include joint type parameters and degree of freedom parameters. Joint type parameters are used to distinguish between rotational joints and translational joints. Degree of freedom parameters are used to limit the number of independent motion dimensions allowed for each joint. Constraint parameters include joint travel range parameters and assembly constraint parameters. Joint travel range parameters limit the range of joint variables through minimum and maximum allowable values. Assembly constraint parameters limit the relative motion relationships between components through fixed axial constraints and planar constraints. A digital twin mechanism model is established based on structural parameters, motion mechanism parameters, and constraint parameters. The digital twin mechanism model includes a set of state variables and a set of state constraints. The set of state variables includes the pose state variables and velocity state variables of key components. The pose state variables of key components are represented by a concatenation of position vectors and attitude vectors, with the position vector components arranged first and the attitude vector components arranged second. The velocity state variables of key components are represented by a concatenation of linear velocity vectors and angular velocity vectors, with the linear velocity vector components arranged first and the angular velocity vector components arranged second. The set of state constraints is formed by mapping joint travel range parameters and assembly constraint parameters, and is used to limit the allowable value range of each dimension component in the set of state variables. The observed state vector sequence and control state vector sequence from the real equipment state sequence are input into the digital twin mechanism model. The state variable set is updated by adding the state variable set of the previous moment to the corresponding control quantity in the control state vector. The predicted position vector is obtained by multiplying the position vector and velocity vector of the previous moment by the time step and then adding them together. The predicted velocity vector is obtained by multiplying the velocity vector of the previous moment by the corresponding acceleration component in the control state vector and then adding them together. The time step is determined by the difference between adjacent timestamps after time alignment. The mechanism prediction state is formed, which includes the pose state vector of the key component and the velocity state vector of the key component. Constraint verification is performed based on the set of state variables and the set of state constraints during the state update process. The constraint verification is completed by determining whether each component in the set of state variables is within the allowable range defined by the corresponding joint travel range parameter and assembly constraint parameter. When the state variable component exceeds the allowable range, the state variable component is replaced with the nearest range boundary value. When the state variable component is within the allowable range, the original value is maintained. The set of state constraints is updated synchronously with the valid constraint information corresponding to the set of state variables. A state mapping relationship is constructed between the actual equipment state sequence and the mechanism prediction state. The state mapping relationship is completed by matching the observed state vector sequence in the actual equipment state sequence with the pose state vector and velocity state vector of key components in the mechanism prediction state in the time dimension. The time correspondence is established based on the timestamp index after time alignment, thus obtaining the state mapping relationship between the actual equipment state sequence and the mechanism prediction state.

[0021] In this embodiment, S3 specifically refers to: Camera intrinsic calibration parameters are corrected for continuous image frame data. The camera intrinsic calibration parameters include focal length parameters, principal point offset parameters, and distortion parameters. The correction process involves linearly transforming the pixel coordinates according to the focal length parameters and principal point offset parameters, and then performing reverse correction on the radial distortion components and tangential distortion components based on the distortion parameters to obtain the corrected image space coordinates. Scale consistency correction is performed on the depth data. This process involves multiplying each depth value in the depth data by the sensor calibration scale factor at the corresponding timestamp to ensure that the depth values ​​are consistent with a uniform spatial scale. The point cloud data undergoes coordinate system transformation. This transformation is achieved by multiplying the point cloud coordinate vector with the external parameter rotation matrix and adding it to the external parameter translation vector, thereby transforming the point cloud coordinates from the sensor coordinate system to a unified reference coordinate system. The corrected image spatial coordinates, scale-consistent depth data, and point cloud data that have undergone coordinate system transformation are combined in time stamp order. The combination method is to stitch the image spatial coordinates, corresponding depth values, and point cloud 3D coordinates according to spatial dimensions at the same time stamp to form a unified coordinate system observation data sequence. Multi-resolution hash coding is performed on the observation data sequence of the unified coordinate system. Multi-resolution hash coding is performed by performing grid quantization on the three-dimensional spatial coordinates in the observation data sequence of the unified coordinate system under multiple preset spatial resolution levels. Grid quantization is completed by dividing the spatial coordinates by the grid scale of the corresponding resolution level and rounding it down. At each resolution level, the quantized spatial coordinates are mapped to a fixed-length integer index vector. The integer index vector is generated by linearly combining the quantized coordinate components and taking the modulo operation. The linear combination method is to multiply the different dimensional components of the spatial coordinates by preset prime number weights, sum them up, and then take the modulo of the summation result to form a multi-level hash index sequence. The constraint variables in the state constraint set are mapped to index constraint parameters. The index constraint parameters consist of the allowed range of spatial location and the allowed range of motion state. The allowed range of spatial location limits the spatial region corresponding to the hash index by the minimum and maximum spatial boundary values. The allowed range of motion state limits the effective access range of the hash index by the allowed interval of the state variables. Index space constraint processing is performed on the multi-level hash index sequence based on index constraint parameters. The index space constraint processing is completed by determining whether the spatial position corresponding to the hash index falls within the allowed range of spatial position. When the position corresponding to the hash index exceeds the allowed range, the hash index is mapped to the nearest valid index position. When the position corresponding to the hash index is within the allowed range, the original index value is maintained, thus forming a constrained hash index sequence. Hash feature read / write processing is carried out under the constrained hash index sequence. The hash feature read / write processing accesses the hash feature table by using the constrained hash index sequence as the address. The feature vector stored at the corresponding index position is read and associated with the current observation data. The feature vector dimension is determined by the preset feature dimension parameter to form a multi-resolution hash feature sequence. Feature fusion processing is performed on multi-resolution hash feature sequences. The feature fusion processing involves concatenating hash feature vectors at different resolution levels in order of increasing resolution, with low-resolution feature vector components arranged first and high-resolution feature vector components arranged last. The concatenated fused feature vector is used as the observation feature field.

[0022] The existing Instant-NGP algorithm improves spatial representation efficiency through multi-resolution hash encoding, but the hash indexing and feature reading and writing process does not consider equipment operation constraints, and it is easy to generate feature representations in state-unreachable regions. This implementation introduces a set of state constraints into the Instant-NGP framework to participate in hash addressing, maps mechanistic constraints to index constraint parameters, and restricts the hash index space, so that the observed feature field is only constructed within the state space allowed by the mechanism, thereby realizing constraint-aware feature encoding.

[0023] In this embodiment, S4 specifically refers to: State decoding is performed on the observed feature field. This process maps the feature vectors in the observed feature field to the state variable space. The state mapping relationship is formed by multiplying the linear weight matrix with the feature vector and superimposing the bias vector to obtain the observed state estimation result. The observed state estimation result includes the pose estimation vector and the velocity estimation vector of the key component. The pose estimation vector of the key component is formed by concatenating the position estimation vector and the attitude estimation vector, with the position estimation vector components arranged first and the attitude estimation vector components arranged second. The velocity estimation vector of the key component is formed by concatenating the linear velocity estimation vector and the angular velocity estimation vector, with the linear velocity estimation vector components arranged first and the angular velocity estimation vector components arranged second. Align the pose state vector of the key component with the pose estimation vector of the key component in the same dimension, and perform an algebraic difference operation on the corresponding dimensional components. The algebraic difference is obtained by subtracting the corresponding component of the pose estimation vector from the corresponding component in the pose state vector of the key component, thus forming the pose deviation vector. Align the velocity state vector of the key component with the velocity estimation vector of the key component in the same dimension, and perform an algebraic difference operation on the corresponding dimension components. The algebraic difference is obtained by subtracting the corresponding component of the velocity estimation vector of the key component from the corresponding component in the velocity state vector of the key component, thus forming a velocity deviation vector. The pose deviation vector and velocity deviation vector are subjected to residual fusion processing. The residual fusion processing is performed by concatenating the pose deviation vector and the velocity deviation vector in the order of pose deviation vector components first and velocity deviation vector components last. The concatenated joint vector is used as the state residual.

[0024] In this embodiment, the improved 4DGS model specifically includes a Gaussian primitive initialization layer, a temporal motion modeling layer, a mechanism residual gated projection layer, and a spatiotemporal representation update layer; The Gaoski initialization layer performs parameter construction processing based on the structural geometric parameters and key component pose parameters of the complex equipment system. The spatial coordinates in the structural geometric parameters are expanded into a three-dimensional spatial coordinate set by combining the component topological relationship parameters and size parameters. Each coordinate in the three-dimensional spatial coordinate set is obtained by adding the component reference point position and the relative installation offset. The pose parameters of the key components are expanded into a pose vector of uniform length by expanding the position vector and attitude vector. The expansion method is that the position vector components are arranged first and the attitude vector components are arranged second. The initial parameter set of Gaussian elements is constructed based on the set of spatial coordinates and the pose vector. The center parameter set of Gaussian elements is obtained by combining each coordinate in the set of spatial coordinates with the position component in the corresponding pose vector. The covariance parameter set of Gaussian elements is composed of the covariance matrix describing spatial uncertainty, expanded into the main axis direction vector and the axial variance vector. The scale parameter set of Gaussian elements is composed of the scale vector describing the coverage of Gaussian elements, with each dimension component in the scale vector corresponding to the extended scale in the spatial dimension direction. The temporal motion modeling layer performs temporal modeling based on the initial parameter set of Gaussian elements and the pose and velocity state vectors of key components in the mechanism prediction state. The temporal displacement modeling of the central parameter set of Gaussian elements is completed by multiplying the linear velocity component in the velocity state vector of the key component by the time step and adding it to the central parameter. The time step is determined by the difference between adjacent timestamps. The temporal rotation modeling of the Gaussian covariance parameter set is completed by mapping the attitude change components in the pose state vector of the key components to rotation increments and performing a rotation transformation on the covariance principal axis direction vector. The rotation transformation is completed by constructing a rotation matrix through the attitude change components and multiplying it with the principal axis direction vector. The temporal scale change modeling of the Gaussian scale parameter set is completed by mapping the velocity amplitude change in the velocity state vector of key components to a scale change factor and linearly scaling the corresponding components in the scale vector, forming a set of temporal motion parameter update quantities. The set of temporal motion parameter update quantities includes the center parameter update quantity, the covariance parameter update quantity, and the scale parameter update quantity. The mechanism residual gated projection layer introduces a mechanism residual gated projection mechanism, which represents the state residual as a joint residual vector. The joint residual vector is formed by splicing the pose deviation vector and the velocity deviation vector in dimensional order, with the pose deviation vector components arranged first and the velocity deviation vector components arranged last. The residual magnitude is obtained by squaring and summing each component in the joint residual vector, and then taking the square root of the summation result. The residual magnitude represents the magnitude of the joint residual vector in the state space. Divide each component of the joint residual vector by the residual magnitude to obtain the residual direction, which represents the unit direction of the joint residual vector in the state space. A set of gated weight parameters is generated based on the residual magnitude and residual direction. The set of gated weight parameters consists of weight vectors corresponding to the dimensions of the center parameter update, covariance parameter update, and scale parameter update. Each component in the weight vector is obtained by multiplying the residual magnitude by the corresponding dimension component in the residual direction. The update values ​​of the central parameter, covariance parameter, and scale parameter are multiplied by the corresponding weight components in the gating weight parameter set to obtain the gating modulated update values ​​of the central parameter, covariance parameter, and scale parameter. These values ​​are then concatenated in the order of central parameter update value first, covariance parameter update value in the middle, and scale parameter update value last to form a gating update value set. Based on the set of state constraints, interval judgment is performed on each parameter component in the set of gated update quantities. When the parameter component is less than the corresponding lower bound in the set of state constraints, the parameter component is replaced with the lower bound value. When the parameter component is greater than the corresponding upper bound in the set of state constraints, the parameter component is replaced with the upper bound value. When the parameter component is between the upper and lower bounds, the original value is maintained, thus forming a set of constrained parameter update quantities. The spatiotemporal representation update layer performs parameter update processing based on the initial parameter set and the set of constrained parameter update amounts of the Gaussian elements. The central parameter set of the Gaussian elements is updated by adding the updated central parameter amount to the original central parameter. The covariance parameter set of the Gaussian elements is updated by mapping the updated covariance parameter amount back to the covariance matrix space. The scale parameter set of the Gaussian elements is updated by adding the updated scale parameter amount to the original scale parameter, forming the spatiotemporal representation result. The spatiotemporal representation result includes the updated central parameter set, covariance parameter set, and scale parameter set of the Gaussian elements.

[0025] Existing 4DGS models achieve continuous spatiotemporal representation through Gaussian elements, but the temporal motion parameter updates mainly rely on observation-driven mechanisms and lack regulation of the mechanistic prediction state and observation bias. This implementation introduces a mechanistic residual gating projection mechanism into the 4DGS structure, transforming the state residual between the mechanistic prediction state and the observed state into gating weights, modulating the temporal update amounts of the Gaussian element center parameters, covariance parameters, and scale parameters, and combining the state constraint set to perform interval projection on the update results, so that the temporal evolution of the Gaussian elements is simultaneously controlled by observation information and mechanistic constraints.

[0026] In this embodiment, gating modulation processing is performed on the center parameter update, covariance parameter update, and scale parameter update in the time-series motion parameter update set, specifically as follows: The set of temporal motion parameter updates is divided into center parameter updates, covariance parameter updates, and scale parameter updates. The center parameter updates represent the incremental vector of the Gaussian element center in the spatial coordinate dimension, the covariance parameter updates represent the incremental change of the spatial uncertainty structure of the Gaussian element, and the scale parameter updates represent the incremental change of the scale of the Gaussian element coverage. The set of gating weight parameters is divided into central parameter weight vector, covariance parameter weight vector and scale parameter weight vector according to parameter type. The dimension of the weight vector is consistent with the dimension of the corresponding parameter update. The value of each component in the weight vector is limited to between 0 and 1. The weight component is obtained by multiplying the residual amplitude with the corresponding dimension component in the residual direction, which is used to characterize the modulation intensity of the state residual in the corresponding parameter dimension. Each component of the central parameter update quantity is multiplied with the weight component of the corresponding dimension in the central parameter weight vector. The product is used as the effective update component of the central parameter update quantity in the corresponding dimension. The effective update components of all dimensions are arranged in the original dimension order to form the central parameter update quantity after gating modulation. The covariance parameter update is expanded into a principal axis direction parameter vector and a scale expansion parameter vector. The principal axis direction parameter vector is used to describe the rotational change of the covariance in the principal axis direction, and the scale expansion parameter vector is used to describe the expansion change of the covariance in the principal axis direction. The expansion method is to arrange the principal axis direction parameter vector components first and the scale expansion parameter vector components second. Multiply each component of the expanded principal axis direction parameter vector with the corresponding weight component of the covariance parameter weight vector to obtain the modulated principal axis direction update component. Multiply each component of the expanded scale expansion parameter vector with the corresponding weight component of the covariance parameter weight vector to obtain the modulated scale expansion update component. Concatenate the modulated principal axis direction update component and the modulated scale expansion update component in the order of principal axis direction first and scale expansion last to form the gated modulated covariance parameter update quantity. Each dimension component of the scale parameter update quantity is multiplied by the corresponding dimension weight component in the scale parameter weight vector. The product is taken as the effective update component of the scale parameter update quantity in the corresponding dimension. The effective update components of all dimensions are arranged in the original dimension order to form the scale parameter update quantity after gating modulation.

[0027] In this embodiment, S6 specifically refers to: The constraint variables in the state constraint set are mapped to feasible region boundary parameters. The feasible region boundary parameters consist of a lower bound vector and an upper bound vector. Each component of the lower bound vector corresponds to the minimum allowable value of the corresponding parameter component in the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set. Each component of the upper bound vector corresponds to the maximum allowable value of the corresponding parameter component in the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set. The lower bound vector and the upper bound vector maintain a one-to-one correspondence with the parameter set in the parameter dimension. Distillation gradient vectors are constructed based on the Gaussian central parameter set, Gaussian covariance parameter set, and Gaussian scale parameter set. The distillation gradient vector is formed by concatenating the central parameter distillation gradient vector, the covariance parameter distillation gradient vector, and the scale parameter distillation gradient vector. The concatenation method is as follows: the central parameter distillation gradient vector components are arranged first, the covariance parameter distillation gradient vector components are in the middle, and the scale parameter distillation gradient vector components are arranged last. The central parameter distillation gradient vector represents the gradient direction of the Gaussian central parameter set at the current time, the covariance parameter distillation gradient vector represents the gradient direction of the Gaussian covariance parameter set at the current time, and the scale parameter distillation gradient vector represents the gradient direction of the Gaussian scale parameter set at the current time. Based on the lower and upper bound vectors of the parameters, feasible region projection processing is performed on the central parameter distillation gradient vector. The feasible region projection processing is completed by gradient step combination of the central parameter distillation gradient vector and the corresponding component of the central parameter set. Gradient step combination is obtained by subtracting the product of the corresponding component of the central parameter distillation gradient vector and the step size parameter from the corresponding component in the central parameter set to obtain the candidate update component. When the candidate update component is less than the corresponding component in the lower bound vector, the candidate update component is replaced with the corresponding component in the lower bound vector. When the candidate update component is greater than the corresponding component in the upper bound vector, the candidate update component is replaced with the corresponding component in the upper bound vector. When the candidate update component is between the lower and upper bound vectors of the parameters, the candidate update component remains unchanged. The constrained central parameter distillation gradient component is obtained by back-calculating the difference between the candidate update component and the corresponding component in the original central parameter set. Based on the lower bound vector and upper bound vector of the parameters, the feasible region projection process is carried out on the distillation gradient vector of the covariance parameters. Each component in the distillation gradient vector of the covariance parameters is combined with the corresponding component in the covariance parameter set through gradient step to generate candidate update components. The candidate update components are then subjected to interval pruning process by the lower bound vector and upper bound vector of the parameters. The constrained distillation gradient components of the covariance parameters are obtained by back-calculating the difference between the pruned candidate update components and the corresponding components in the original covariance parameter set. Based on the lower bound vector and upper bound vector of the parameters, the feasible region projection process is carried out on the scale parameter distillation gradient vector. Each component in the scale parameter distillation gradient vector and the corresponding component in the scale parameter set are combined by gradient step to generate candidate update components. The candidate update components are then subjected to interval pruning process by the lower bound vector and upper bound vector of the parameters. The constrained scale parameter distillation gradient components are obtained by back-calculating the difference between the pruned candidate update components and the corresponding components in the original scale parameter set. The constrained central parameter distillation gradient vector, the constrained covariance parameter distillation gradient vector, and the constrained scale parameter distillation gradient vector are concatenated in the order of central parameter first, covariance parameter in the middle, and scale parameter last to form the feasible region constrained distillation gradient vector. Gradient update processing is performed on the Gaussian meta-central parameter set based on the feasible region-constrained distillation gradient vector. The gradient update processing is completed by subtracting the product of the corresponding central parameter component in the feasible region-constrained distillation gradient vector and the step size parameter from the corresponding component in the central parameter set. Gradient update processing is performed on the Gaussian covariance parameter set based on the feasible region-constrained distillation gradient vector. The gradient update processing is completed by subtracting the product of the corresponding covariance parameter component in the feasible region-constrained distillation gradient vector and the step size parameter from the corresponding component in the covariance parameter set. The gradient update process is performed on the Gaussian scale parameter set based on the feasible region-constrained distillation gradient vector. The gradient update process is completed by subtracting the product of the corresponding scale parameter component and the step size parameter in the feasible region-constrained distillation gradient vector from the corresponding component in the scale parameter set, and thus obtaining the updated spatiotemporal representation result.

[0028] Existing SDS-constrained algorithms guide the optimization process with distillation gradients, but gradient updates are not subject to explicit state boundary constraints, which may cause parameter updates to exceed the feasible range of the equipment. This implementation converts the set of state constraints into parameter lower bound vectors and parameter upper bound vectors, and performs feasible region projection on the distillation gradient vectors of the central parameter, covariance parameter, and scale parameter, respectively, so that the gradient update direction and magnitude are limited to the mechanism-allowed range, thereby forming a constrained gradient optimization process.

[0029] In this embodiment, S7 specifically refers to: The updated spatiotemporal representation results are subjected to state decoding processing. State decoding processing is completed by mapping the updated Gaussian central parameter set, Gaussian covariance parameter set, and Gaussian scale parameter set to the state variable space. The mapping process is completed by weighted summation of the spatial coordinate components in the Gaussian central parameter set to form a position estimation vector, and constructing an attitude estimation vector based on the principal axis direction component and scale component in the Gaussian covariance parameter set. The position estimation vector and attitude estimation vector are concatenated in the order of position component first and attitude component second to form the pose estimation vector of the visualized key component. Based on the changes in the Gaussian metacenter parameter set at adjacent time stamps in the updated spatiotemporal representation results, velocity estimation components are constructed. The changes are obtained by dividing the difference between the center parameter set at the current time stamp and the center parameter set at the previous time stamp by the time step. The linear velocity estimation vector is composed of position change components, and the angular velocity estimation vector is composed of attitude change components. The linear velocity estimation vector and the angular velocity estimation vector are concatenated in the order of linear velocity component first and angular velocity component second to form the velocity estimation vector of the visualized key components. The visualization of the pose estimation vector of key components and the velocity estimation vector of key components are combined to form the visualization state estimation result. Align the pose state vector of the key component with the pose estimation vector of the visualized key component in the same dimension, and perform an algebraic difference operation on the corresponding dimensional components. The algebraic difference is obtained by subtracting the corresponding component of the pose estimation vector of the visualized key component from the corresponding component in the pose state vector of the key component, thus forming a pose consistency error vector. Align the velocity state vector of the key component with the velocity estimation vector of the visualized key component in the same dimension, and perform an algebraic difference operation on the corresponding dimension components. The algebraic difference is obtained by subtracting the corresponding component of the velocity estimation vector of the visualized key component from the corresponding component in the velocity state vector of the key component, thus forming a velocity consistency error vector. The pose consistency error scalar is obtained by squaring and summing each component in the pose consistency error vector, and then taking the square root of the summation result. The pose consistency error scalar represents the degree of deviation between the pose estimation and the mechanism prediction in the state space. The velocity consistency error scalar is obtained by squaring and summing each component in the velocity consistency error vector, and then taking the square root of the summation result. The velocity consistency error scalar represents the degree of deviation between the velocity estimate and the mechanism prediction in the state space. Consistency determination processing is carried out based on pose consistency error scalar and velocity consistency error scalar. The consistency determination processing is completed by comparing pose consistency error scalar with pose consistency threshold and velocity consistency error scalar with velocity consistency threshold. When both pose consistency error scalar and velocity consistency error scalar are not greater than the corresponding consistency threshold, a visual simulation result consistent with the mechanism prediction state is output.

[0030] refer to Figure 3 In this embodiment, a visualization simulation system for complex equipment systems based on digital twins includes the following modules: The data processing module is used to acquire multi-source observation data and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. The mechanism modeling module is used to construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. The feature construction module is used to introduce a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, perform multi-resolution hash encoding on multi-source observation data, introduce a set of state constraints during the hash addressing process, constrain the index space of hash features, and generate an observation feature field. The spatiotemporal modeling module is used to calculate the state deviation based on the mechanism-predicted state and the observed feature field to obtain the state residual. The structural geometry, key component pose parameters and state residual of the complex equipment system are input into the improved 4DGS model. The mechanism residual gated projection mechanism is introduced to perform gated projection and generate spatiotemporal representation results. The simulation output module is used to calculate the feasible region constraint of the distillation gradient based on the SDS constraint algorithm according to the set of state constraints, perform gradient update on the spatiotemporal representation results, generate updated spatiotemporal representation results, perform consistency judgment, and output a visual simulation result that is consistent with the mechanism prediction state.

[0031] Example 1: To verify the feasibility of this invention in practice, it was applied to a visualization simulation scenario of a complex equipment system of a six-degree-of-freedom industrial robot in an automobile assembly workshop. The complex equipment system consists of a robot body, a reducer, a linkage mechanism, and an end effector. Continuous image frame cameras, depth cameras, laser point cloud sensors, and encoders were deployed on-site to collect multi-source observation data. Simultaneously, control command data of the actuators and operation mode identification data from the control data were also collected. On-site, there were welding arcs, obstructions, and vibration impacts. Continuous image frames showed local overexposure and motion blur, the point cloud showed sparseness and missing data, and the encoder showed instantaneous jitter. Traditional visualization simulations based on offline geometric models and rule-based animations exhibited key component pose drift during work condition switching, and the image jitter and inconsistency between reality and virtuality were obvious, making it difficult to meet the online monitoring and reproduction requirements under production cycle conditions.

[0032] When applying this invention, timestamps are first extracted from multi-source observation data and control data, and resampled according to a unified time base. The resampling period is set to 0.02s, and the maximum cross-channel time difference of the time-aligned data sequence is controlled within 0.008s. Dimensional unification, amplitude standardization, and outlier removal are performed on the time-aligned data sequence to construct a realistic equipment state sequence. A digital twin mechanism model is established based on structural parameters, motion mechanism parameters, and constraint parameters. The set of state variables includes the pose state vectors and velocity state vectors of key components, and the set of state constraints includes the allowable intervals corresponding to joint travel range parameters and assembly constraint parameters. The digital twin mechanism model, combined with the realistic equipment state sequence and control data, yields the mechanism prediction state. Multi-resolution hash encoding is performed on the multi-source observation data, and the set of state constraints is introduced during the hash addressing process to form a sense of constraint. A hash addressing mechanism is used to generate an observation feature field. Based on the mechanistic prediction state and the observation feature field, state decoding is completed to obtain the observation state estimation result, and the state deviation is calculated to obtain the state residual. The structural geometry, key component pose parameters, and state residual are input into the improved 4DGS model. A mechanistic residual gated projection mechanism is introduced in the temporal motion parameter update process of Gaussian elements to generate spatiotemporal representation results. Based on the SDS constraint algorithm, feasible region constraint calculation of distillation gradient is introduced. The state constraint set is converted into parameter lower bound vector and parameter upper bound vector. Feasible region projection processing is performed on the distillation gradient vector to complete the gradient update and obtain the updated spatiotemporal representation result. Consistency judgment is performed on the updated spatiotemporal representation result and a visual simulation result consistent with the mechanistic prediction state is output. On-site, it is continuously output at 25fps with a latency stable in the range of 78ms to 96ms.

[0033] The comparative verification uses the same data source and the same digital twin mechanism model parameters. The only difference is that the traditional method does not introduce a constraint-aware hash addressing mechanism, a mechanism residual gating projection mechanism, or a feasible region constraint calculation of the distillation gradient. The statistical indicators are taken from 30 minutes of continuous data, covering four types of working conditions: uniform speed transport, emergency stop and start, end load change, and occlusion interference. The pose error is represented by position error and attitude error, the velocity error is represented by linear velocity error and angular velocity error, and the consistency error is a joint evaluation of the pose consistency error scalar and the velocity consistency error scalar.

[0034] Table 1. Comparison of Consistency Indicators for Complex Equipment Systems

[0035] Table 1 shows that the scalar values ​​of pose consistency error and velocity consistency error of the method of the present invention are significantly lower than those of the traditional method under four types of working conditions. Especially under the conditions of emergency stop and start and load change, the consistency error decreases more significantly. The position error decreases from 8.3mm to 9.1mm to 2.7mm to 3.1mm, and the attitude error decreases from 1.21° to 1.35° to 0.31° to 0.39. This is related to the constraint construction of the observation feature field by the constraint-aware hash addressing mechanism. The observation features are generated in the index space limited by the state constraint set. The deviation between the observation state estimation result obtained by state decoding and the mechanism prediction state is smaller, and the state residuals are more concentrated. The improved 4DGS model modulates and projects the temporal motion parameter update under the mechanism residual gating projection mechanism, which reduces the non-mechanistic drift of Gaussian parameters under disturbance conditions.

[0036] Table 2. Comparison of Visual Stability and Optimization Process Data

[0037] Table 2 shows that while maintaining 25fps output, the inter-frame jitter amplitude decreased from 6.7mm to 1.9mm, the pose drift over 30 minutes decreased from 18.9mm to 4.6mm, the number of parameter out-of-bounds triggers decreased from 47 to 3, and the occlusion recovery time was shortened from 1.12s to 0.34s. These results indicate that the feasible region constraint calculation of the distillation gradient effectively restricts the gradient update direction and magnitude. The lower and upper bound vectors of the parameters provide clear boundaries for the update process of the central parameter set, covariance parameter set, and scale parameter set, improving the stability of the spatiotemporal representation results. Subsequent consistency judgments are more likely to meet the pose consistency threshold and velocity consistency threshold requirements, thus enabling the visualization simulation results to maintain consistency with the mechanism prediction state under complex occlusion and vibration interference conditions.

[0038] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A visualization simulation method for complex equipment systems based on digital twins, characterized in that, Includes the following steps: S1. Acquire multi-source observation and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. S2. Construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. S3. By introducing a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, multi-resolution hash encoding is performed on the multi-source observation data. The state constraint set is introduced during the hash addressing process to constrain the index space of the hash features and generate an observation feature field. S4. Based on the predicted state and the observed characteristic field, calculate the state deviation to obtain the state residual; S5. Improve the 4DGS model by inputting the structural geometry, key component pose parameters and state residuals of complex equipment systems. Introduce a mechanism residual gated projection mechanism in the temporal motion parameter update process of Gaussian elements, perform gated projection, and generate spatiotemporal representation results. S6. Based on the set of state constraints, calculate the feasible region constraint of the distillation gradient introduced by the SDS constraint algorithm, perform gradient update on the spatiotemporal representation result, and generate an updated spatiotemporal representation result. S7. Perform a consistency determination on the updated spatiotemporal representation result and output a visual simulation result that is consistent with the mechanism prediction state.

2. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S1 is: Acquire multi-source observation data during the operation of complex equipment systems. The multi-source observation data includes continuous image frame data, depth data, point cloud data, and sensor status data. Acquire control data during the operation of complex equipment systems. The control data includes actuator control command data and operating mode identification data. Timestamp information is extracted from multi-source observation data and control data respectively, and resampling is performed according to a unified time reference to obtain time-aligned data sequences; Perform dimensional unification, amplitude standardization, and outlier removal on the time-aligned data sequence to obtain a state-standardized data sequence. A real equipment state sequence is constructed based on the state-standardized data sequence. The real equipment state sequence includes the observation state vector sequence and the control state vector sequence.

3. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S2 is: Obtain structural parameters, kinematic parameters, and constraint parameters of complex equipment systems. Structural parameters include component topology parameters and dimensional parameters. Kinematic parameters include joint type parameters and degree of freedom parameters. Constraint parameters include joint travel range parameters and assembly constraint parameters. A digital twin mechanism model is established based on structural parameters, motion mechanism parameters, and constraint parameters. The digital twin mechanism model includes a set of state variables and a set of state constraints. The observed state vector sequence and control state vector sequence from the real equipment state sequence are input into the digital twin mechanism model, and the state variable set is updated to obtain the mechanism prediction state; the mechanism prediction state includes the pose state vector of key components and the velocity state vector of key components. Constraint verification is performed based on the set of state variables and the set of state constraints during the state update process to obtain the set of state constraints. A state mapping relationship is constructed between the actual equipment state sequence and the mechanism prediction state to obtain the state mapping relationship between the actual equipment state sequence and the mechanism prediction state.

4. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S3 is: Camera intrinsic parameter calibration correction is performed on continuous image frame data, scale consistency correction is performed on depth data, and coordinate system transformation is performed on point cloud data to obtain a unified coordinate system observation data sequence. Multi-resolution hash encoding is performed on the observation data sequence in a unified coordinate system. Hash indexes are calculated on the spatial coordinates in the observation data sequence at different resolution levels to obtain a multi-level hash index sequence. The constraint variables in the state constraint set are mapped to index constraint parameters, and index space constraint processing is performed on the multi-level hash index sequence to obtain the constrained hash index sequence. Perform hash feature read and write processing under a constrained hash index sequence to obtain a multi-resolution hash feature sequence; Feature fusion processing is performed on the multi-resolution hash feature sequence to obtain the observation feature field.

5. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S4 is: The observation feature field is subjected to state decoding processing to obtain the observation state estimation result; the observation state estimation result includes the pose estimation vector of the key component and the velocity estimation vector of the key component; A differential calculation is performed based on the pose state vector and the pose estimation vector of the key component to obtain the pose deviation vector; a differential calculation is performed based on the velocity state vector and the velocity estimation vector of the key component to obtain the velocity deviation vector. The pose deviation vector and velocity deviation vector are subjected to residual fusion processing to obtain the state residual.

6. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, The improved 4DGS model specifically includes a Gaussian initialization layer, a temporal motion modeling layer, a mechanism residual gated projection layer, and a spatiotemporal representation update layer; The Gaussian initialization layer is based on the structural geometric parameters and key component pose parameters of the complex equipment system. It performs spatial coordinate parameterization on the structural geometric parameters and pose vector expansion on the key component pose parameters. Based on the spatial coordinate parameters and pose vectors, it constructs a Gaussian initial parameter set. The Gaussian initial parameter set includes a Gaussian center parameter set, a Gaussian covariance parameter set, and a Gaussian scale parameter set. The temporal motion modeling layer is based on the Gaussian initial parameter set and the pose and velocity state vectors of key components in the mechanism prediction state. It performs temporal displacement modeling on the Gaussian center parameter set, temporal rotation modeling on the Gaussian covariance parameter set, and temporal scale change modeling on the Gaussian scale parameter set to obtain a set of temporal motion parameter update quantities. The aforementioned mechanism residual gated projection layer introduces a mechanism residual gated projection mechanism, representing the state residual as a joint residual vector composed of the pose deviation vector and the velocity deviation vector of the key components. The joint residual vector is formed by concatenating each dimension component of the pose deviation vector and each dimension component of the velocity deviation vector according to their corresponding dimensions. The square operation is performed on each dimension component of the joint residual vector and then summed. The square root operation is then performed on the summation result to obtain the residual amplitude. Each dimension component of the joint residual vector is divided by the residual amplitude to obtain the residual direction. A set of gated weight parameters is generated based on the residual amplitude and residual direction. The weight components in the set of gated weight parameters are obtained by multiplying the residual amplitude by the corresponding dimension component in the residual direction. The center parameter update, covariance parameter update, and scale parameter update in the set of time-series motion parameter updates are respectively subjected to gated modulation processing. The gated and modulated center parameter update, covariance parameter update, and scale parameter update are then concatenated in the order of center parameter update first, covariance parameter update in the middle, and scale parameter update last to form a set of gated update quantities. Each parameter component in the set of gated update quantities is subject to constraint interval judgment. When the parameter component exceeds the allowable range corresponding to the state constraint set, the parameter component is replaced with the boundary value of the allowable range. When the parameter component is within the allowable range, it retains its original value, thus forming a set of constrained parameter update quantities. The spatiotemporal representation update layer performs parameter update processing on the Gaussian central parameter set, Gaussian covariance parameter set, and Gaussian scale parameter set based on the Gaussian initial parameter set and the constrained parameter update set, to obtain the spatiotemporal representation result; the spatiotemporal representation result includes the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set.

7. The visualization simulation method for complex equipment systems based on digital twins according to claim 6, characterized in that, The gating modulation processing performed on the center parameter update, covariance parameter update, and scale parameter update in the time-series motion parameter update set is as follows: Each component of the center parameter update is multiplied by the weight component of the corresponding center parameter in the set of gated weight parameters to obtain the center parameter update after gate modulation. The covariance parameter update is expanded into a main axis direction parameter vector and a scale expansion parameter vector. Each component of the expanded covariance parameter is then multiplied by the weight component of the corresponding covariance parameter in the gating weight parameter set to obtain the gating modulated covariance parameter update. Each component of the scale parameter update is multiplied by the weight component of the corresponding scale parameter in the gating weight parameter set to obtain the scale parameter update after gating modulation.

8. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S6 is: The constraint variables in the set of state constraints are converted into feasible region boundary parameters, which include a lower bound vector and an upper bound vector. Distillation gradient vectors are constructed based on the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set. The distillation gradient vectors include the central parameter distillation gradient vector, the covariance parameter distillation gradient vector, and the scale parameter distillation gradient vector. Based on the lower bound vector and upper bound vector of the parameters, the feasible region projection process is performed on the distillation gradient vector of the center parameter, the feasible region projection process is performed on the distillation gradient vector of the covariance parameter, and the feasible region projection process is performed on the distillation gradient vector of the scale parameter to obtain the feasible region constrained distillation gradient vector. Based on the feasible region constraint, the gradient update process is performed on the Gaussian central parameter set, the Gaussian covariance parameter set, and the Gaussian scale parameter set to obtain the updated spatiotemporal representation result.

9. The visualization simulation method for complex equipment systems based on digital twins according to claim 1, characterized in that, Specifically, S7 is: The updated spatiotemporal representation result is subjected to state decoding processing to obtain the visualized state estimation result; the visualized state estimation result includes the visualized key component pose estimation vector and the visualized key component velocity estimation vector. A differential calculation is performed based on the pose state vector of key components and the pose estimation vector of visualized key components to obtain the pose consistency error vector. A speed consistency error vector is obtained by performing differential calculation based on the speed state vector of key components and the speed estimation vector of visualized key components. Consistency determination is performed on the pose consistency error vector and velocity consistency error vector, and a visual simulation result consistent with the mechanism prediction state is output.

10. A visualization simulation system for complex equipment systems based on digital twins, comprising executing the visualization simulation method for complex equipment systems based on digital twins as described in any one of claims 1 to 9, characterized in that, Includes the following modules: The data processing module is used to acquire multi-source observation data and control data of complex equipment systems during operation, perform time alignment and state standardization processing, and form a real equipment state sequence. The mechanism modeling module is used to construct a digital twin mechanism model, calculate the mechanism prediction state and state constraint set based on the real equipment state sequence and control data, and establish the state mapping relationship between the real equipment state sequence and the mechanism prediction state. The feature construction module is used to introduce a constraint-aware hash addressing mechanism through the Instant-NGP algorithm, perform multi-resolution hash encoding on the multi-source observation data, introduce the state constraint set during the hash addressing process, constrain the index space of the hash features, and generate an observation feature field. The spatiotemporal modeling module is used to calculate the state deviation based on the mechanism-predicted state and the observed feature field to obtain the state residual. The structural geometry, key component pose parameters and state residual of the complex equipment system are input into the improved 4DGS model. The mechanism residual gated projection mechanism is introduced to perform gated projection and generate spatiotemporal representation results. The simulation output module is used to calculate the feasible region constraint of the distillation gradient based on the SDS constraint algorithm according to the set of state constraints, perform gradient update on the spatiotemporal representation result, generate updated spatiotemporal representation result, perform consistency judgment, and output a visual simulation result consistent with the mechanism prediction state.

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