Homogeneous sensor array data fusion method for digital twinning

Abstract

The application discloses a homogeneous sensor array data fusion method for digital twinning, and belongs to the technical field of digital twinning and intelligent manufacturing, and the method comprises the following steps: synchronously collecting data by using a homogeneous sensor array; generating a sample point set by sampling a state space; predicting and constructing a dynamic confidence interval by using a physical motion constraint model; mapping to a measurement space to obtain a reference prediction value; calculating a new information and a covariance to perform space consistency analysis, and quantifying the deviation of each sensor; dynamically judging and physically blocking abnormal data, recombining a pure observation data stream, and calculating a data purity index; in an online fusion stage, the purity index is used to correct observation noise covariance, and the contribution weight of observation data is adjusted. The application can realize physical blocking of sensor fault pollution and joint adaptive adjustment of observation weight, and ensures that the data stream input into digital twinning has high purity and strong robustness.

Description

Technical Field

[0001] This invention relates to the field of digital twin and intelligent manufacturing technology, and in particular to a method for data fusion of homogeneous sensor arrays for digital twins. Background Technology

[0002] Complex manufacturing systems are dynamic production systems composed of various types of equipment, technological processes, control logic, and operating environments. They are characterized by a large number of devices, strong structural coupling, complex operating states, and frequent changes in operating conditions. Digital twins, by constructing high-fidelity virtual models that are mapped, interacted with, and synchronized with the physical system in real time, provide crucial support for the operation monitoring, performance analysis, state prediction, and optimized control of complex manufacturing systems. The operational effectiveness of a digital twin system largely depends on the accuracy, real-time performance, and stability of the underlying sensing data, especially the quality of state data from key equipment and components, which directly affects the mapping accuracy and operational fidelity of the digital twin model.

[0003] In complex manufacturing systems, to improve the reliability of monitoring critical physical quantities, homogeneous sensor arrays are typically used to redundantly acquire data on the same target physical quantity. These homogeneous sensor arrays can improve sensing coverage and measurement reliability to a certain extent, and provide a foundation for subsequent data fusion. By fusing the output data from multiple similar sensors, the influence of random noise can be reduced, and the accuracy and robustness of the measurement results can be improved. Therefore, homogeneous sensor array data fusion has become one of the important fundamental technologies supporting the high-fidelity operation of digital twins.

[0004] In existing technologies, Kalman filtering and its extended forms are commonly used for state estimation in data fusion of homogeneous sensor arrays. Among them, the Unscented Kalman Filter (UKF) can effectively handle state estimation problems in nonlinear systems and has good application value in industrial scenarios. Meanwhile, with the development of data-driven methods, fusion methods combining neural networks and Kalman filtering are also gradually being applied. These methods utilize neural networks to learn the nonlinear dynamic laws of complex systems, and then combine them with filters to achieve state estimation, thereby improving the modeling ability and fusion accuracy of complex systems to a certain extent.

[0005] However, existing data fusion methods still have significant shortcomings in real-world, complex industrial environments. Firstly, when some sensors in a homogeneous sensor array malfunction, the faulty sensors output abnormal data that deviates significantly from the true values. If these abnormal sensors directly participate in the fusion process, the fusion results will be contaminated, and in severe cases, the overall state estimation may even fail. Secondly, industrial systems are affected by factors such as changes in operating conditions, equipment aging, and changes in the operating environment during long-term operation, causing changes in the system's dynamic patterns. Data fusion methods based on fixed models or offline trained models typically lack online adaptive capabilities and struggle to continuously adapt to the system's time-varying characteristics, thus leading to a decrease in fusion accuracy. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of the prior art and provide a data fusion method for homogeneous sensor arrays for digital twins.

[0007] The objective of this invention is achieved through the following technical solution: a method for data fusion of homogeneous sensor arrays for digital twins, comprising the following steps: By using a homogeneous sensor array to synchronously acquire the same target physical quantity of the target physical system, the original sensor measurement data can be obtained. The state space of the target physical system is sampled and initialized to generate a set of sampling points representing the probability distribution information of the system state. Using the physical motion constraint model of the target physical system, a priori state prediction is performed on the sampling point set, and a dynamic priori confidence interval is constructed to characterize the uncertainty of system evolution by combining process noise; Based on the pre-defined observation model, the predicted set of sampling points is mapped to a measurement space with the same dimension as the homogeneous sensor array, and the reference predicted value of the measurement domain of the homogeneous sensor array is determined. Based on the original sensor data and the baseline prediction values ​​of the measurement domain, the innovation sequence and innovation covariance matrix are calculated. Spatial consistency measurement analysis is performed using the innovation flow characteristics and the innovation covariance matrix to quantify the degree of deviation of each sensor measurement value from the baseline. The degree of deviation is judged based on the dynamically adjusted confidence threshold. If the degree of deviation is greater than the confidence threshold, a physical blocking operation is performed, and the remaining valid sensor data is dynamically reassembled to output a clean observation data stream. The ratio of the number of valid sensor data to the total number of sensor arrays is calculated as a data purity index. The clean observation data stream and data purity index are input into the online data fusion stage to perform data fusion processing: the observation noise covariance is dynamically corrected using the data purity index, the data purity is inversely proportional to the observation noise amplification factor, and the contribution weight of each observation data in the state fusion estimation is adjusted according to the corrected observation noise covariance, so as to realize the adaptive adjustment of the sensor array health to the data fusion result.

[0008] In one example, the sampling initialization of the state space of the target physical system to generate a set of sampling points representing the probability distribution information of the system state includes: Determine the state vector describing the target physical system and the corresponding error covariance matrix, and set the sampling scaling factor, non-negative parameters and state distribution parameters in combination with the redundancy distribution characteristics of the homogeneous sensor array; Calculate the composite scaling parameter and the mean weight and covariance weight of the sampling points; Perform Cholesky decomposition on the error covariance matrix to obtain the square root of the matrix, generating a set of sampling points containing the center point and the symmetric point.

[0009] In one example, the process of using a physical motion constraint model of the target physical system to perform prior state prediction on the sample point set and constructing a dynamic prior confidence interval to characterize the uncertainty of system evolution, combined with process noise, includes: Input the set of sampling points into the state transition equation of the target physical system, and calculate the set of prior projection points of each sampling point at the next time step; The weighted summation of the projected sampling point set yields the mean of the prior state estimate, which serves as a virtual reference benchmark for measuring the deviation of data from each sensor in the homogeneous array. The prior error covariance matrix is ​​calculated using covariance weighting coefficients, and the system process noise covariance matrix is ​​introduced to compensate for the uncertainty of the physical model. Based on the prior error covariance matrix, the dynamic prior confidence interval at the current moment is established.

[0010] In one example, the step of calculating the innovation sequence and innovation covariance matrix based on the original sensor data and the measurement domain baseline prediction, and performing spatial consistency measurement analysis using innovation flow characteristics and the innovation covariance matrix, includes: The difference between the original sensor data and the baseline prediction value in the measurement domain is calculated as the innovation sequence. The innovation covariance matrix is ​​calculated using covariance weights, and the sensor's inherent measurement noise covariance matrix is ​​introduced for correction. Using the innovation sequence and innovation covariance matrix, the normalized squared innovation statistical distance between the measured value of each sensor in the homogeneous sensor array and the baseline predicted value of the measurement domain is calculated. The normalized squared innovation statistical distance is used as a spatial consistency measure of the degree to which each sensor deviates from the collective expectation of the homogeneous sensor array.

[0011] In one example, based on a pre-defined observation model, the predicted set of sampling points is mapped to a measurement space with the same dimension as the homogeneous sensor array, determining the baseline prediction value of the measurement domain for the homogeneous sensor array, including: Input the set of sampling points into the preset observation model and calculate the set of projection points corresponding to each sampling point in the measurement space; By applying the mean weight to the mapped projection point set, the baseline prediction value of the homogeneous array in the measurement domain at the current time is calculated.

[0012] In one example, before judging the degree of bias based on a dynamically adjusted confidence threshold, the following steps are also included: The initial significance level is set according to the real-time high-fidelity accuracy requirements of the digital twin system. The initial confidence threshold is determined by chi-square distribution in combination with the degrees of freedom of the sensor observation space. During the system operation, the value of the significance level is dynamically adjusted according to the spatial consistency analysis results. Furthermore, the confidence threshold is dynamically adjusted according to the data fluctuation amplitude under real-time industrial conditions.

[0013] In one example, the step of inputting the clean observation data stream and data purity index into the online data fusion stage to perform data fusion processing includes: The pure observation data stream is input into the adaptive fusion architecture based on interactive multi-model. The model interaction operation is performed according to the posterior probability of each filter expert model at the previous time step and the preset model transition probability matrix to obtain the interactive initial state and initial covariance input to each filter expert model. Multiple filtering expert models are run in parallel. Each filtering expert model uses a long short-term memory network as a process evolution operator to perform nonlinear temporal feature mapping on the interactive initial state and generate preliminary prior state prediction values ​​based on historical information. The residual features between the predicted trajectory and the intrinsic evolution law of the physical system are extracted online using long short-term memory networks, and the preliminary prior state prediction values ​​are compensated and corrected in real time using the residual features. The compensated and corrected prior state predictions are mapped to the measurement space to obtain the predicted observations. The observation noise covariance is dynamically corrected using the data purity index. The Kalman gain is calculated based on the corrected noise covariance. Based on the real-time clean observation data stream, the compensated and corrected prior state predictions are recursively updated using the Kalman gain. The consistency between the predicted measurement values ​​output by each filter expert model and the actual observation values ​​is calculated simultaneously to generate the measurement likelihood. The trust weights of each filter expert model are dynamically updated based on the measured likelihood, and the posterior state estimation results of each path are weighted and fused according to the updated weights to output the optimal state estimate.

[0014] In one example, performing model interaction operations includes: Two heterogeneous filtering expert branches are preset, including at least a stationary filtering expert model with a first process noise covariance configured for the system's steady operating condition and a rapidly changing filtering expert model with a second process noise covariance configured for the system's dynamic and rapidly changing operating condition. The first process noise covariance is smaller than the second process noise covariance. A model transition probability matrix is ​​set, and based on the posterior probabilities of each filtering expert model at the previous time step, the posterior state estimates and posterior error covariance of each expert at the previous time step are weighted and mixed according to the model transition probability matrix to calculate the interactive initial state and initial covariance input to each expert at the current time step.

[0015] In one example, multiple filter expert models are run in parallel. Each filter expert model uses a long short-term memory network as a process evolution operator to perform nonlinear temporal feature mapping on the initial interactive state and generate preliminary prior state predictions based on the historical state sequence, including: For each filtering expert model, the interaction initial state and the historical state estimation sequence are concatenated to construct a multi-dimensional time-series input vector sequence; Input the multidimensional temporal input vector sequence into the pre-trained long short-term memory network and calculate the hidden layer state; A nonlinear mapping from the feature space to the physical state space is performed on the hidden layer state to obtain the preliminary prior state predictions of each filter expert model at the current time.

[0016] In one example, the method of utilizing the residual features extracted online from the predicted trajectory of the Long Short-Term Memory network and the intrinsic evolutionary laws of the physical system, and using the residual features to perform real-time compensation and correction on the preliminary prior state predictions, includes: For each filtered expert model, the preliminary prior state prediction is compared with the reference trajectory calculated based on physical motion constraints, and the residual feature vector characterizing the degree of model mismatch is extracted. An adaptive calibration operator based on neuron activation weights is constructed, and the calibration gain matrix for correcting prediction bias is calculated using dynamic prior confidence interval information and residual feature vectors. The preliminary prior state prediction values ​​are weighted and compensated in real time using the calibration gain matrix to generate calibrated prior state prediction values.

[0017] It should be further noted that the technical features corresponding to the above examples can be combined or replaced to form new technical solutions.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. By leveraging the spatial redundancy of a homogeneous sensor array, a baseline prediction value for the measurement domain is constructed and spatial consistency measurement analysis is performed, enabling precise quantification of the degree to which each sensor deviates from the collective expectation of the array. Physical blocking operations are performed using dynamically adjusted confidence thresholds, and the number of effective sensors is counted to generate a data purity index. This index is then fed back to the online fusion stage to dynamically correct the observation noise covariance (data purity is inversely proportional to the noise amplification factor). The contribution weight of observation data in state fusion estimation can be adaptively adjusted according to the health of the sensor array. Ultimately, the joint adaptive adjustment of the physical blocking of sensor fault contamination and the contribution weight of observation data is achieved, ensuring that the data stream input to the digital twin has high purity and strong robustness.

[0019] 2. In the online fusion phase, a long short-term memory network is used to generate preliminary predictions, and the residuals between these predictions and physical laws are extracted for real-time compensation to solve the model drift problem. A data purity index is introduced to dynamically adjust the observation noise covariance, ensuring that the observation weights are automatically reduced when sensors fail. Furthermore, the model weights are updated based on the Bayesian criterion and the fusion output is fused, forming a deep linkage between the perceived environmental quality and the model competition mechanism. This effectively eliminates the mismatch between the offline model and the online reality, and adaptively adjusts the fusion weights according to the health of the sensor array, thereby outputting the optimal state estimate that drives the digital twin. This ensures that the digital twin system can achieve real-time and accurate mapping of physical entities throughout its entire lifecycle. Attached Figure Description

[0020] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. The accompanying drawings are provided to provide a further understanding of the present application and constitute a part of the present application. The same reference numerals are used in these drawings to denote the same or similar parts. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application.

[0021] Figure 1 This is a flowchart of a method provided in an embodiment of the present invention; Figure 2 This is a flowchart of a preferred embodiment of the present invention; Figure 3 This is a flowchart of the data preprocessing stage when the method of the present invention is applied to the temperature monitoring scenario of large lithium batteries; Figure 4 This is a flowchart of the online adaptive fusion stage in the application of the method of the present invention to the temperature monitoring scenario of large lithium batteries. Detailed Implementation

[0022] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, 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.

[0023] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0024] In one embodiment, such as Figure 1 As shown, a data fusion method for homogeneous sensor arrays for digital twins includes the following steps: S1: Use a homogeneous sensor array to synchronously acquire the same target physical quantity of the target physical system to obtain the original sensor measurement data.

[0025] Before executing step S1, a homogeneous sensor array is deployed. Specifically, an array consisting of N homogeneous sensors with the same performance parameters is deployed at the key monitoring parts of the target physical system. For example, an array consisting of 10 homogeneous angular velocity sensors is deployed at the joint of the end effector of an industrial robot to perform redundant and high-density monitoring of the same target physical quantity, such as the joint rotational angular velocity.

[0026] S2: Based on the redundancy distribution characteristics of the homogeneous sensor array, the state space of the target physical system is sampled and initialized to generate a set of sampling points representing the probability distribution information of the system state.

[0027] In step S2, the system state probability distribution information is the probability distribution characteristic that the target physical system's true state (such as temperature value and its rate of change) at a certain moment follows. Specifically, it includes the mean (expected value) and covariance matrix (degree of uncertainty) of the state vector. Within the theoretical framework of unscented Kalman filtering, the sampling point set, i.e., the Sigma point set, is a set of discrete sample points used to approximately characterize the system state probability distribution information. Each sample point contains the specific value of the state vector and the corresponding weight coefficient. The weighted sum and weighted covariance of all sample points can accurately match the mean and covariance of the original state distribution.

[0028] S3: Utilize the physical motion constraint model of the target physical system to perform prior state prediction on the sample point set, and combine it with process noise to construct a dynamic prior confidence interval to characterize the uncertainty of system evolution.

[0029] In step S3, the physical motion constraint model is a mathematical model used to describe the physical laws (such as dynamic equations, kinematic relationships, or thermodynamic laws) that the target physical system follows during its evolution over time. This mathematical model imposes constraint boundaries based on physical principles on the trajectory of the system's state change.

[0030] S4: Based on the preset observation model, the predicted sampling point set is mapped to the measurement space with the same dimension as the homogeneous sensor array, and the measurement domain benchmark prediction value of the homogeneous sensor array used to evaluate the rationality of the original sensor data is determined.

[0031] In step S4, the observation model is a mathematical model used to describe the mapping relationship between the implicit state of the target physical system and the measurement output of the homogeneous sensor array. This model converts the internal state vector of the system (such as temperature value, angular velocity) into the measurement value (such as voltage signal) that the sensor can directly collect.

[0032] S5: Calculate the innovation sequence and innovation covariance matrix based on the original sensor data and the baseline prediction value of the measurement domain, and perform spatial consistency measurement analysis using the innovation flow characteristics and innovation covariance matrix to quantify the degree of deviation of each sensor measurement value from the baseline.

[0033] In step S5, the innovation sequence is a sequence of differences between the actual sensor measurements and the measurement benchmark predicted based on the physical model. It characterizes the degree of deviation of the actual observed data from the model's expected value. In this embodiment, the spatial redundancy characteristics of a homogeneous sensor array can be used to perform a spatial consistency measure, calculating the Mahalanobis distance between each sensor's measurement and the array's collective expected benchmark. This quantifies the degree to which each sensor's data deviates from the overall consistent distribution of the array, accurately identifying outliers generated by faulty sensors. This ensures that valid data conforming to spatial consistency enters the subsequent data fusion stage, guaranteeing data purity.

[0034] S6: Determine the degree of deviation based on the dynamically adjusted confidence threshold. If the degree of deviation is greater than the confidence threshold, perform a physical blocking operation and dynamically reassemble the remaining valid sensor data to output a clean observation data stream; calculate the ratio of the number of valid sensor data to the total number of sensor arrays as the data purity index.

[0035] Furthermore, the clean observation data stream and data purity index are input into the online data fusion stage to perform data fusion processing: the observation noise covariance is dynamically corrected using the data purity index. Data purity is inversely proportional to the observation noise amplification factor, that is, the lower the purity, the higher the observation noise amplification factor, so as to reduce the trust weight of observation data when the sensor array health is insufficient; the contribution weight of each observation data in the state fusion estimation is adjusted according to the corrected observation noise covariance, so as to realize the adaptive adjustment of the sensor array health to the data fusion result, and obtain the final fused data.

[0036] In step S6, during system operation, the confidence threshold can be dynamically adjusted based on the spatial consistency analysis results to achieve adaptive coverage of data fluctuation amplitude under complex industrial conditions. Furthermore, when the deviation exceeds the confidence threshold, the sensor's measurement data is abnormal. By executing a physical blocking operation, a clean observation data stream that meets high-fidelity operation requirements can be output.

[0037] This invention fully utilizes the spatial distribution characteristics of homogeneous sensor arrays, using the prior state estimate generated by unscented Kalman filtering as a virtual reference benchmark. Spatial consistency analysis is performed on the measurements of each sensor, and the Mahalanobis distance of each measurement relative to the benchmark is calculated as a deviation quantification index. The degree of deviation is judged based on a dynamically adjusted confidence threshold. Abnormal data exceeding the threshold is physically blocked, and the retained valid data is dynamically reconstructed to output a clean observation data stream. This mechanism overcomes the limitation of traditional methods that can only suppress outliers but not purify them, significantly improving the immunity of digital twin drivers to sensor failures and data purity, and solving the problem of data contamination caused by sensor failures in complex industrial environments.

[0038] In one embodiment, step S1 further includes: S11: Define the system state-space model.

[0039] Setting the system k The true state vector at time t is Assuming the system follows a random walk model in a short time, its process model is... Represented as: in, It is process noise and follows a Gaussian distribution. , Let be the covariance of the process noise.

[0040] S12: Real-time readings of the target physical quantity are acquired synchronously through various sensors to obtain... k Raw sensor measurement vector at time .

[0041] S13: Construct the observation model.

[0042] Establish the mapping relationship between the actual state of the system and the measurement vector, and the observation model. Represented as: in, For transpose; To measure the noise vector, it must satisfy a Gaussian distribution. , To measure the covariance of noise.

[0043] In one embodiment, step S2 initializes the state space of the target physical system by sampling, generating a set of sampling points representing the probability distribution information of the system state, including: S21: Determine the initial state distribution and sampling parameters of the target physical system.

[0044] First, determine the description of the target physical system. n dimensional state vector and the corresponding error covariance matrix ; Based on the redundant distribution characteristics of homogeneous sensor arrays observing the same physical quantity, a sampling scaling factor is set to control the distribution distance of Sigma points. nonnegative parameters and parameters used to reflect state distribution information This ensures that the sampling points can accurately capture the nonlinear characteristics of the system.

[0045] S22: Calculate the sampling scaling parameters and weighting coefficients.

[0046] Calculate the composite scaling parameter using the given sampling parameters and the mean weights of each sampling point Covariance weights The specific calculation formula is as follows: In the formula, and These are the mean and covariance weights of the central sampling points, respectively. and These are the weighting coefficients for the remaining symmetrical sampling points.

[0047] S23: Generate a Sigma point set representing the statistical properties of the array.

[0048] Using unscented transformation, by adjusting the error covariance matrix Performing Cholesky decomposition to obtain the square roots of the matrix generates a set of common roots. A Sigma point set representing the probability distribution information of the current state of the system The calculation formula is as follows: In the formula, The first root of the matrix represents the square root of the matrix. This step generates a point cloud that fully preserves the high-order moments of the state distribution, laying a high-precision data foundation for constructing a virtual reference benchmark for a homogeneous array.

[0049] In one embodiment, step S3 utilizes the physical motion constraint model of the target physical system to perform prior state prediction on the sampling point set, and combines process noise to construct a dynamic prior confidence interval for characterizing the uncertainty of system evolution, including: S31: Perform time-domain projection of the sample point set based on the system dynamics equations.

[0050] The Sigma point set representing the current distribution characteristics of the system generated in step S23 is used to... Input the preset target physical system state transition equation Calculate and obtain the prior projection point set of each sampling point at the next time step. The calculation formula is as follows: In the formula, For the system in Time-based control input, This represents the process noise term. This step uses a physical motion constraint model to predict the expected physical position of the homogeneous array during its time-domain evolution before observation information is introduced.

[0051] S32: Calculate the mean of the prior state estimates for the homogeneous array.

[0052] Using the mean weighting coefficients determined in step S22 By performing a weighted summation on the projected prior sample point set, a prior state estimate that can characterize the overall evolution trend of the homogeneous array is obtained. The specific calculation formula is as follows: The prior state estimate This serves as a virtual reference benchmark for measuring the data deviation of each sensor in the homogeneous array in subsequent steps.

[0053] S33: Construct dynamic prior confidence intervals to represent the uncertainty of evolution.

[0054] Using covariance weighting coefficients Calculate the prior error covariance matrix And introduce the system process noise covariance matrix. The formula for compensating for uncertainties in the physical model is as follows: Based on the prior error covariance matrix Establish a dynamic prior confidence interval for the current moment. This interval defines the reasonable fluctuation range of homogeneous array data under the current operating conditions, providing a dynamic search boundary for subsequent identification of outlier sensor data contaminated by faults.

[0055] In one embodiment, step S4 maps the predicted sampling point set to a measurement space consistent with the dimension of the homogeneous sensor array based on a preset observation model, and determines the measurement domain benchmark prediction value of the homogeneous sensor array used to evaluate the rationality of the original sensor data, including: S41: Perform spatial mapping of sampling points based on observation operators.

[0056] The prior sampling point set obtained in step S31 Input the preset observation model Calculate and obtain the set of projection points corresponding to each sampling point in the measurement space. The calculation formula is as follows: The above formula will The system state is projected onto a physical dimension space consistent with the measurement dimension of the sensor array, realizing the transformation from the implicit state space to the sensing measurement space.

[0057] S42: Determine the reference prediction value for the measurement domain of the homogeneous array.

[0058] Using the mean weighting coefficients determined in step S22 For the mapped projection point set After weighting, the reference prediction value of the homogeneous array in the measurement domain at the current time is calculated. The specific calculation formula is as follows: The baseline prediction value of this measurement domain This represents the theoretical expected value that each sensor in the homogeneous array should observe under the constraints of current physical evolution laws. This value serves as a global comparison reference for evaluating whether there is fault contamination in the original sampling data of each sensor in subsequent steps.

[0059] In one embodiment, step S5 calculates the innovation sequence and innovation covariance matrix based on the original sensor data and the measurement domain baseline prediction value, and performs spatial consistency measurement analysis using the innovation flow characteristics and the innovation covariance matrix, including: S51: Calculate the innovation flow characteristics and covariance matrix of a homogeneous array.

[0060] Combined with the raw sensor measurement data collected in step S1 Compared with the measurement domain reference prediction value determined in step S42 The innovation sequence reflecting the real-time fluctuation characteristics of the array is calculated. The calculation formula is as follows: Simultaneously, the covariance weighting coefficients determined in step S22 are used. Calculate the new information covariance matrix And introduce the sensor's inherent measurement noise covariance matrix. The correction is made, and the calculation formula is as follows: In the formula, This is the set of sampling points in the measurement space. This step involves introducing the measurement noise covariance matrix. This ensures that the deviation quantification process can take into account the random measurement errors of the sensor itself, providing an accurate statistical characteristic benchmark for spatial consistency analysis.

[0061] S52: Perform spatial consistency measurement and deviation quantification based on Mahalanobis distance.

[0062] Using the aforementioned information sequence With the new covariance matrix For the first homogeneous sensor array One sensor ( ), calculate its normalized innovation squared statistical distance relative to the virtual benchmark. The Mahalanobis distance (MD) is calculated using the following formula: In the formula, For the first Measurement deviation of each sensor This represents the corresponding covariance component. This statistical distance... This constitutes a quantitative indicator for measuring the spatial consistency of a homogeneous array, and its value directly reflects the degree to which the measurements of each sensor deviate from the collective expectation of the array.

[0063] In one embodiment, step S6 determines the degree of deviation based on a dynamically adjusted confidence threshold. If the degree of deviation exceeds the confidence threshold, a physical blocking operation is performed, and the remaining valid sensor data is dynamically reassembled to output a clean observation data stream. The ratio of the number of valid sensor data points to the total number of sensor array points is calculated as a data purity index, including: S61: Determine the dynamic discrimination criteria and confidence threshold.

[0064] Based on the real-time, high-fidelity accuracy requirements of digital twin systems, a saliency level is set. And combined with the degrees of freedom of the sensor observation space The initial confidence threshold was determined by consulting the chi-square distribution table. The calculation formula is: During system operation, the significance level is dynamically adjusted based on the spatial consistency analysis results of the homogeneous array obtained in step S5. The value of is used to achieve the confidence threshold. Adaptive coverage of data fluctuation amplitude under complex industrial operating conditions.

[0065] S62: Online identification and physical blocking of abnormal contamination data.

[0066] The normalized innovation squared statistical distances of each sensor calculated in step S52 are used to calculate the normalized innovation squared statistical distances. With the confidence threshold Perform a step-by-step comparison and execute the following judgment logic: like Then determine the first The measurement data from each sensor is valid data; like Then determine the first If the measurement data of a sensor is contaminated by a fault or exhibits significant anomalies, a physical blocking operation is performed to prevent the abnormal data from entering the subsequent computing link, thereby eliminating the negative impact of the contamination source on the operating accuracy of the digital twin model.

[0067] S63: Dynamic reorganization and purity index output of effective observation data streams.

[0068] The number of sensors deemed valid in a homogeneous array. Furthermore, the retained valid measurement data are dynamically reorganized in dimensions to construct a clean observation data vector. .

[0069] At the same time, calculate the data purity index P at the current moment. k =M / N, representing the pure observation data vector Along with data purity index The data is then output to the online fusion stage. This step, through real-time reconstruction of the observation space, ensures that the data stream at the input backend possesses both physical authenticity and carries complete information about the perceived environment.

[0070] In one embodiment, the pure observation data vector Along with data purity index The data is then output to the online fusion stage for processing, including: S7: Input the clean observation data stream into the adaptive fusion architecture based on interactive multi-model. Based on the posterior probability of each filter expert model at the previous time step and the preset model transition probability matrix, perform model interaction operation to calculate the interactive initial state and initial covariance input to each heterogeneous filter expert model.

[0071] In step S7, within the interactive multi-model framework, the model transition probability matrix describes the probabilistic laws governing the switching between different dynamic modes (such as steady-state and rapidly changing conditions) of the system. Each element in the matrix represents the probability of transitioning from one expert model to another. The filtered expert model is a filtering unit specifically designed for a particular dynamic mode (such as steady-state operation or drastic change) of the target physical system. This filtering unit includes complete state prediction, observation update, and error correction functions, enabling optimal estimation of the system state under that specific mode. In this embodiment, the heterogeneous filtered expert model includes at least model branches with different time-domain characteristics set for the system's steady-state and rapidly changing conditions.

[0072] S8: Run multiple filter expert models in parallel. Each filter expert model uses a long short-term memory network as a process evolution operator to perform nonlinear time-series feature mapping on the interactive initial state and generate preliminary prior state prediction values ​​that can capture the fluctuation trend of complex working conditions based on historical information (historical dynamic laws of the physical system). In step S8, the Long Short-Term Memory Network is used as the core process evolution operator to accurately capture complex nonlinear temporal dependencies, effectively replacing the traditional kinematic model.

[0073] S9: The Adapter adaptive module is activated, which utilizes the residual features extracted online from the Long Short-Term Memory Network to predict the trajectory and the inherent evolution law of the physical system. The residual features are then used to compensate and correct the preliminary prior state prediction values ​​in real time, realizing the deep integration of data-driven prediction and physical mechanism constraints. This eliminates the mismatch between the offline pre-trained model and the online running situation, and improves prediction accuracy and system adaptability.

[0074] S10: Map the compensated and corrected prior state predictions to the measurement space to obtain the predicted observations. Use the data purity index to dynamically correct the observation noise covariance. Calculate the Kalman gain based on the corrected noise covariance. Based on the real-time clean observation data stream, use the Kalman gain to recursively update the compensated and corrected prior state predictions. Simultaneously calculate the consistency between the predicted measurements output by each filter expert model and the actual observations, and generate the measurement likelihood that reflects the model's matching ability.

[0075] S11: Based on the measured likelihood, the trust weights of each filter expert model are dynamically updated using Bayes' rule, and the posterior state estimation results of each path are weighted and fused according to the updated weights to output the optimal state estimate.

[0076] This invention uses a Long Short-Term Memory (LSTM) network as the core process evolution operator of the filtering expert, directly replacing the traditional kinematic model for state prediction. It also introduces an adaptive correction module to extract residual features between the deep learning predicted trajectory and physical laws online, providing real-time compensation and correction for the predicted values. This solves the technical challenge of offline pre-trained models being unable to cope with online device aging and law drift. Simultaneously, the data purity index output from the preprocessing stage is fed back to the online fusion stage to dynamically correct the observation noise covariance. This enables adaptive adjustment of the fusion weights based on the sensor array health, forming a deep linkage between the perceived environmental quality and the model competition mechanism. This ensures that the digital twin system can achieve real-time and accurate mapping of physical entities throughout its entire lifecycle.

[0077] Compared to traditional data fusion methods, this invention focuses on homogeneous sensor data fusion to improve the fidelity of digital twins, employing an interactive multi-model Bayesian framework for online fusion. In this framework, the deep learning model itself acts as a filtering expert in state estimation. Specifically, a long short-term memory network is trained as the system's process evolution operator, replacing the traditional kinematic model for state prediction. To adapt to the dynamic changes of the system under different operating conditions, this invention runs two filtering expert models in parallel, each based on the same long short-term memory network but configured with different process noise covariances. The low-noise expert is suitable for stable operating conditions, while the high-noise expert is suitable for rapidly changing conditions. Each expert model outputs its own measurement likelihood. The system dynamically updates the trust weights of each expert according to Bayesian rules and achieves smooth switching and weighted fusion between expert models through an adaptive multilayer perceptron module, outputting an optimal state estimate with adaptive capabilities to drive the high-fidelity operation of the digital twin system.

[0078] In one embodiment, step S7 inputs the clean observation data stream into an adaptive fusion architecture based on interactive multi-models. Based on the posterior probabilities of each filter expert model at the previous time step and a preset model transition probability matrix, model interaction operations are performed to calculate the initial interactive states and initial covariances input to each heterogeneous filter expert model, including: S71: Calculate the conditional probability and predictive influence between models.

[0079] according to Posterior model probabilities of each filter expert at time step and the preset model transition probability matrix ,calculate Time model Transfer to Time model Predicted conditional probability ,as well as Time model Predicted influence The calculation formulas are as follows: In the formula, This represents the total number of filtering experts operating in parallel. This step achieves logical coupling between different dynamic law models through probability weight allocation.

[0080] S72: Perform interactive initial state estimation and mixed covariance calculation for each filter expert.

[0081] Using predicted conditional probabilities, the posterior state of each filter expert at the previous time step is estimated. and posterior error covariance Perform weighted mixing to determine the input. Initial state of interaction among experts at any given moment with initial covariance The calculation formulas are as follows: The initial interactive state set incorporates the estimated features of all historical models, providing a unified and consistent starting point for the independent evolution of each expert at the current moment.

[0082] S73: Establish the task allocation and model configuration parameters for the heterogeneous filtering expert model.

[0083] To address the dynamic differences of industrial physical systems under various operating conditions, the initial interactive states are assigned to heterogeneous filter expert branches with different time-domain response characteristics: (1) Set expert branch A as a stationary operating model, and its internal process noise covariance Set to a low value to suppress measurement noise and maintain high-precision steady-state mapping; (2) Set expert branch B as a dynamic and drastic change model, and its internal process noise covariance Set to a high value to improve the system's sensitivity to sudden changes in operating conditions.

[0084] This step, through heterogeneous expert task allocation, ensures that the system can achieve optimal logical switching between maintaining accuracy and dynamic response.

[0085] In one embodiment, step S8 runs multiple filtering expert models in parallel. Each filtering expert model uses a long short-term memory network as a process evolution operator to perform nonlinear temporal feature mapping on the initial interactive state and generate preliminary prior state prediction values ​​based on historical information, including: S81: Construct the time-series input sequence of the expert model based on a sliding window.

[0086] For each heterogeneous filtering expert The initial interactive state obtained in step S72 With the preset historical time step length as The state estimation sequences are concatenated to construct a multidimensional time-series input vector sequence. The calculation formula is as follows: This step, through a sliding window mechanism, provides the deep learning model with the historical context information needed for the system's evolution.

[0087] S82: Performs dynamic feature extraction based on LSTM gating mechanism.

[0088] The time-series input sequence Input the data into a pre-trained Long Short-Term Memory (LSTM) network, and pass it through its internal forgetting gate. Input gate and output gate Selective memorization and feature extraction of historical information are performed to calculate the hidden layer state. Its logical evolution formula is: In the formula, This represents the current state of the cell. and These are the weight matrix and bias term for the corresponding gating structure. This step utilizes the iterative capability of LSTM to capture the nonlinear behavior of the physical system caused by operating condition fluctuations or equipment aging.

[0089] S83: Mapping to generate preliminary prior state predictions for heterogeneous experts.

[0090] Extracted hidden layer features The input is a fully connected layer, which performs a nonlinear mapping from the feature space to the physical state space, yielding the results for each expert model. Preliminary prior state prediction at time 1 The calculation formula is: Among them, the preliminary prior state prediction value This forms the data-driven basis for each filtering expert to perform adaptive calibration, providing accurate state evolution guidance when physical laws are missing or mismatched.

[0091] In one embodiment, step S9 utilizes the residual features extracted online from the predicted trajectory of the Long Short-Term Memory network and the intrinsic evolutionary laws of the physical system, and uses the residual features to perform real-time compensation and correction on the preliminary prior state prediction values, including: S91: Extract the mismatch residuals between deep learning predicted trajectories and physical evolution laws.

[0092] For each heterogeneous filtering expert The preliminary prior state prediction values ​​obtained in step S83 are... By comparing the model with a reference trajectory calculated based on physical motion constraints, a residual vector representing the degree of model mismatch is extracted. This step identifies insufficient capture of nonlinear features caused by drift in operating conditions by quantifying the deviation between the model output driven by data and the theoretical evolution path of the physical system.

[0093] S92: Calculate the adaptive calibration gain of the Adapter module.

[0094] An adaptive calibration operator based on neuron activation weights is constructed, and the Adapter gain matrix for correcting prediction bias is calculated using the dynamic prior confidence interval information generated in step S33. The gain matrix is ​​dynamically adjusted based on the significance of the current residuals, and its calculation formula is as follows: In the formula, This is the adaptive activation function of the Adapter module, used to identify the state components that need to be compensated based on the current system uncertainty (error covariance).

[0095] S93: Perform online residual compensation and correction for prior state predictions.

[0096] Preliminary prior state predictions using the calibration gain matrix Perform real-time weighted compensation to generate calibrated prior state predictions. The calculation formula is: In the formula, This represents the element-wise product operation. Through this step, the system completes online correction of deep learning prediction bias before filter updates, realizing the logical evolution from data-driven prediction to physical-data collaborative perception, and providing accurate prior input for subsequent high-fidelity fusion.

[0097] In one embodiment, step S10 maps the compensated and corrected prior state prediction value to the measurement space to obtain the predicted observation value, dynamically corrects the observation noise covariance using the data purity index, calculates the Kalman gain based on the corrected noise covariance, recursively updates the compensated and corrected prior state prediction value using the Kalman gain according to the real-time clean observation data stream, and simultaneously calculates the consistency between the predicted measurement value output by each filtered expert model and the actual observation value to generate the measurement likelihood, including: S101: Perform the observation space mapping for calibrating the prior states.

[0098] For each heterogeneous filtering expert The calibrated prior state prediction values ​​obtained in step S93 are then processed using an unscented transformation. and its prior error covariance Resampling is performed to generate a predicted Sigma point set; the observation operator is then used. The point set is mapped to the measurement space, and the predicted observations under the filtered expert model are calculated by combining the weighting coefficients. The calculation formula is: This step enabled an equivalent transformation from the corrected data-driven prediction space to the physical perception space.

[0099] S102: Calculate the gain and innovation statistics by combining the data purity index.

[0100] Combined with the clean observation data vector output in step S63 Calculate the innovation vector of each expert model. and the new information covariance matrix During this process, the data purity index output in step S63 is used. observation noise covariance Perform dynamic corrections and calculate the Kalman gain matrix accordingly. The calculation formula is: In the formula, To predict the observed autocovariance, For state-observation cross-covariance. (Through...) The introduction of this technology enables real-time adjustment of the filter gain based on the perceived environmental integrity, ensuring a deep understanding of the effectiveness of the sensor array during the fusion process.

[0101] S103: Complete the post-hoc update of the expert model and the measurement likelihood quantization. Using the Kalman gain matrix The prior states are recursively corrected to obtain the posterior state estimates for each filtered expert model. With posterior error covariance Simultaneously, the degree of agreement between the predicted values ​​output by each filter expert model and the actual observed values ​​is calculated based on the Gaussian probability density function, i.e., the measurement likelihood. The calculation formula is: The likelihood measurement As a quantitative indicator to measure the degree of matching of each expert model under the current working conditions, it provides the core evaluation basis for subsequent dynamic updates of model probabilities.

[0102] In one embodiment, step S11 dynamically updates the trust weights of each filtered expert model based on the measured likelihood using Bayes' rule, and performs weighted fusion of the posterior state estimation results according to the updated weights to output the optimal state estimate, including: S111: Perform dynamic updates of model probabilities based on Bayesian criteria.

[0103] The measurement likelihood of each filter expert model calculated in step S103. and the predicted influence obtained in step S71 The posterior model probability of each filter expert at the current time is calculated using Bayes' theorem. The calculation formula is: The posterior model probability This represents the system's level of confidence in each filter expert model (stationary or rapidly changing) under the current operating conditions; since the measured likelihood has been indexed by data purity... The probability update process has been modified to have adaptive sensing capabilities for the effectiveness of the sensor array.

[0104] S112: Perform weighted fusion of system state estimates based on trust weights.

[0105] Using the posterior model probability as weighting coefficients, the posterior state estimates of each filter expert obtained in step S103 are calculated. By performing a linear combination, the final fusion state estimate of the target physical system is calculated. The specific calculation formula is as follows: This fusion state estimate It combines the predictive advantages of multiple heterogeneous expert models and can simultaneously cover the steady-state operating characteristics and sudden dynamic changes of the system.

[0106] S113: Calculate the fusion error covariance and output high-fidelity running data.

[0107] Based on the posterior error covariance of each expert And the state bias between models, calculate the final fusion error covariance matrix. The calculation formula is: The final fusion state estimate obtained The final fused data is output to the digital twin platform as high-fidelity driving data. This data stream, through preprocessing and elimination and online adaptive fusion, ensures the real-time and accurate mapping of the physical entity by the digital twin system.

[0108] Combining the above embodiments yields preferred embodiments of the present invention, such as... Figure 2 As shown, the method includes the following steps: S1': Use a homogeneous sensor array to synchronously acquire the same target physical quantity of the target physical system to obtain the original sensor measurement data; S2': Based on the redundancy distribution characteristics of the homogeneous sensor array, the state space of the target physical system is sampled and initialized to generate a set of sampling points representing the probability distribution information of the system state; S3': Using the physical motion constraint model of the target physical system, perform prior state prediction on the sampling point set, and combine process noise to construct a dynamic prior confidence interval to characterize the uncertainty of system evolution; S4': Based on the preset observation model, the predicted sampling point set is mapped to the measurement space with the same dimension as the homogeneous sensor array, and the measurement domain benchmark prediction value of the homogeneous sensor array used to evaluate the rationality of the original sensor data is determined. S5': Calculate the innovation sequence and innovation covariance matrix based on the original sensor data and the baseline prediction values ​​of the measurement domain, and perform spatial consistency measurement analysis using the innovation flow characteristics and innovation covariance matrix to quantify the degree of deviation of each sensor measurement value from the baseline. S6': The degree of deviation is judged based on the dynamically adjusted confidence threshold. If the degree of deviation is greater than the confidence threshold, a physical blocking operation is performed, and the remaining valid sensor data is dynamically reassembled to output a clean observation data stream; the ratio of the number of valid sensor data to the total number of sensor arrays is calculated as a data purity index. S7': Input the clean observation data stream into the adaptive fusion architecture based on interactive multi-model. According to the posterior probability of each filter expert model at the previous time step and the preset model transition probability matrix, perform model interaction operation to calculate the interactive initial state and initial covariance input to each heterogeneous filter expert model. S8': Multiple filter expert models run in parallel. Each filter expert model uses a long short-term memory network as a process evolution operator to perform nonlinear temporal feature mapping on the interactive initial state and generate preliminary prior state prediction values ​​based on historical information. S9': Utilizes the residual features between the predicted trajectory and the intrinsic evolution law of the physical system by extracting the long short-term memory network online, and uses the residual features to perform real-time compensation and correction on the preliminary prior state prediction values; S10': Map the compensated and corrected prior state prediction value to the measurement space to obtain the predicted observation value. Use the data purity index to dynamically correct the observation noise covariance. Calculate the Kalman gain based on the corrected noise covariance. Based on the real-time clean observation data stream, use the Kalman gain to recursively update the compensated and corrected prior state prediction value. Simultaneously calculate the consistency between the predicted measurement value output by each filter expert model and the actual observation value to generate the measurement likelihood. S11': Based on the measured likelihood, the trust weights of each filter expert model are dynamically updated using Bayes' rule, and the posterior state estimation results of each path are weighted and fused according to the updated weights to output the optimal state estimate.

[0109] The above preferred embodiment is applied to a temperature monitoring scenario for large lithium batteries, in which an array of N=10 homogeneous temperature sensors is deployed on the battery surface. Due to electromagnetic interference and complex nonlinear dynamic conditions in industrial environments (such as drastic temperature changes caused by start-up and shutdown), this embodiment ensures high fidelity of the data output to the digital twin system through the following steps: like Figure 3 As shown, the data preprocessing stages (S1''-S6'') include: S1'': Data synchronous collection.

[0110] Using 10 homogeneous temperature sensors to simultaneously sample raw temperature data, obtain The original measurement vector at time .

[0111] S2'': State space sampling initialization.

[0112] Define the state dimension of the target physical system (Temperature and its rate of change).

[0113] Set sampling parameters: To control the compact distribution of Sigma points, take To achieve the optimal reconstruction effect under Gaussian distribution, take .

[0114] Calculate composite scaling parameters using sampling parameters and the mean weights of each sampling point Covariance weights And for the covariance matrix Perform Cholesky decomposition to generate A set of Sigma points representing the distribution characteristics of the array. .

[0115] S3'': Prior prediction and dynamic confidence interval construction Substitute the point set into the thermodynamic equations of the actuator and set the sampling period. The prior projection point set is obtained. .

[0116] The mean of the prior state estimate was calculated. As a virtual reference benchmark.

[0117] Define the system process noise covariance matrix $, calculate the prior error covariance This establishes the dynamic prior confidence interval for the current moment.

[0118] S4'': Measurement domain reference transformation.

[0119] Using observation operators Project the prior point set onto the measurement space. For a homogeneous array, the projected point set... .

[0120] Calculate the baseline prediction value of the measurement domain This value serves as the theoretical central value that the 10 sensors should observe under the current physical constraints.

[0121] S5'': Spatial Consistency Analysis and Deviation Quantification Calculate the original measurement Compared with the benchmark The new information sequence between And calculate the innovation covariance matrix based on the covariance weighting coefficients. .

[0122] Setting the inherent measurement noise covariance of the sensor Regarding the first Each sensor calculates its Mahalanobis distance. This quantifies the degree to which it deviates from the overall expected value of the array.

[0123] S6'': Abnormal data identification and removal and data stream reassembly Set significance level Due to the single sensor's degree of freedom of observation Determine the confidence threshold by consulting the chi-square distribution table. .

[0124] Decision logic: If If the sensor is contaminated by a fault (such as a sudden spike), then physical blocking will be performed.

[0125] Count of valid sensors Reconstruct and output a clean observation data vector Output data purity index. .

[0126] 2. For example Figure 4 As shown, the online adaptive fusion phase (S7-S11) includes: S7'': Interaction model initialization.

[0127] Two heterogeneous expert branches are preset: stable expert A and dramatic expert B.

[0128] Set the model transition probability matrix .

[0129] Based on the posterior probability of the previous time step Calculate the initial state of the interaction and initial covariance .

[0130] S8'': Nonlinear state prior prediction Setting the LSTM sliding window length The historical state sequence is input into the pre-trained LSTM model.

[0131] The LSTM structure parameters are set as follows: two hidden layers, each containing 64 hidden units. Preliminary prior predictions for each expert branch are generated through temporal feature mapping. .

[0132] S9'': Recursive observation update and likelihood quantification.

[0133] Using the clean observation data output by S6'' Perform the update.

[0134] Key calibration logic: utilizing data purity index Dynamically correct observation noise. Set the corrected noise covariance. For example, if only 5 valid sensors remain ( If this occurs, the observation noise will increase by a factor of two, reducing the confidence in the observation values.

[0135] Calculate the measurement likelihood This serves as an indicator to measure the degree of matching between the expert model and the current working conditions.

[0136] S10'': Dynamically weighted model probability and high-fidelity output. Updating model probabilities using Bayes' criterion .

[0137] If the system is in a steady state, the probability of expert A will approach 1; if an abnormal increase in the rate of temperature change is detected, the probability of expert B will rise rapidly.

[0138] The final state estimate is output based on the weighted fusion. This drives the digital twin system to achieve high-fidelity mapping of actuator temperature.

[0139] This invention presents a homogeneous sensor data fusion method for high-fidelity operation of digital twins. It constructs a layered and decoupled data fusion architecture comprising two stages: data preprocessing and online fusion. In the data preprocessing stage, an unscented Kalman filter with an embedded innovation gating mechanism is used to identify and remove outliers from faulty sensors in real time by calculating the normalized squared innovation distance. Preliminary fusion of valid data is then performed to reduce the pressure of excessive data volume in the homogeneous array, thus ensuring the purity of the input data. In the online fusion stage, an adaptive dynamic fusion architecture based on interactive multi-models is adopted. A process model trained using a long short-term memory network is used to initially describe the dynamic laws of the system. Multiple unscented Kalman filter expert models configured for different dynamic characteristics are run in parallel to correct the system laws. An adaptive module dynamically adjusts the model probabilities to adapt to different operating conditions, thereby achieving online compensation for model law mismatch caused by changes in operating conditions or equipment aging in the physical system. Through the collaborative work of the data preprocessing and online fusion stages, the high-fidelity and stable operation of the digital twin system is maintained.

[0140] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A method for data fusion of homogeneous sensor arrays for digital twins, characterized in that, Includes the following steps: By using a homogeneous sensor array to synchronously acquire the same target physical quantity of the target physical system, the original sensor measurement data can be obtained. The state space of the target physical system is sampled and initialized to generate a set of sampling points representing the probability distribution information of the system state. Using the physical motion constraint model of the target physical system, a priori state prediction is performed on the sampling point set, and a dynamic priori confidence interval is constructed to characterize the uncertainty of system evolution by combining process noise; Based on the pre-defined observation model, the predicted set of sampling points is mapped to a measurement space with the same dimension as the homogeneous sensor array, and the reference predicted value of the measurement domain of the homogeneous sensor array is determined. Based on the original sensor data and the baseline prediction values ​​of the measurement domain, the innovation sequence and innovation covariance matrix are calculated. Spatial consistency measurement analysis is performed using the innovation flow characteristics and the innovation covariance matrix to quantify the degree of deviation of each sensor measurement value from the baseline. The degree of deviation is judged based on the dynamically adjusted confidence threshold. If the degree of deviation is greater than the confidence threshold, a physical blocking operation is performed, and the remaining valid sensor data is dynamically reassembled to output a clean observation data stream. Calculate the ratio of the number of valid sensor data points to the total number of sensor array points, and use it as a data purity index; The clean observation data stream and data purity index are input into the online data fusion stage to perform data fusion processing: the observation noise covariance is dynamically corrected using the data purity index, the data purity is inversely proportional to the observation noise amplification factor, and the contribution weight of each observation data in the state fusion estimation is adjusted according to the corrected observation noise covariance, so as to realize the adaptive adjustment of the sensor array health to the data fusion result.

2. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 1, characterized in that, The initialization of the state space of the target physical system by sampling to generate a set of sampling points representing the probability distribution information of the system state includes: Determine the state vector describing the target physical system and the corresponding error covariance matrix, and set the sampling scaling factor, non-negative parameters and state distribution parameters in combination with the redundancy distribution characteristics of the homogeneous sensor array; Calculate the composite scaling parameter and the mean weight and covariance weight of the sampling points; Perform Cholesky decomposition on the error covariance matrix to obtain the square root of the matrix, generating a set of sampling points containing the center point and the symmetric point.

3. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 1, characterized in that, The process of using the physical motion constraint model of the target physical system to perform prior state prediction on the sample point set and constructing a dynamic prior confidence interval to characterize the uncertainty of system evolution by combining process noise includes: Input the set of sampling points into the state transition equation of the target physical system, and calculate the set of prior projection points of each sampling point at the next time step; The weighted summation of the projected sampling point set yields the mean of the prior state estimate, which serves as a virtual reference benchmark for measuring the deviation of data from each sensor in the homogeneous array. The prior error covariance matrix is ​​calculated using the covariance weighting coefficients, and the system process noise covariance matrix is ​​introduced to compensate for the uncertainty of the physical model. The dynamic prior confidence interval at the current moment is established based on the prior error covariance matrix. The step of calculating the innovation sequence and innovation covariance matrix based on the original sensor data and the measurement domain baseline prediction value, and performing spatial consistency measurement analysis using innovation flow characteristics and the innovation covariance matrix, includes: The difference between the original sensor data and the baseline prediction value in the measurement domain is calculated as the innovation sequence. The innovation covariance matrix is ​​calculated using covariance weights, and the sensor's inherent measurement noise covariance matrix is ​​introduced for correction. Using the innovation sequence and innovation covariance matrix, the normalized squared innovation statistical distance between the measured value of each sensor in the homogeneous sensor array and the baseline predicted value of the measurement domain is calculated. The normalized squared innovation statistical distance is used as a spatial consistency measure of the degree to which each sensor deviates from the collective expectation of the homogeneous sensor array.

4. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 1, characterized in that, Based on a pre-defined observation model, the predicted set of sampling points is mapped to a measurement space with the same dimension as the homogeneous sensor array, determining the baseline predicted value of the measurement domain for the homogeneous sensor array, including: Input the set of sampling points into the preset observation model and calculate the set of projection points corresponding to each sampling point in the measurement space; By applying the mean weight to the mapped projection point set, the baseline prediction value of the homogeneous array in the measurement domain at the current time is calculated.

5. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 1, characterized in that, Before judging the degree of deviation based on the dynamically adjusted confidence threshold, the following is also included: The initial significance level is set according to the real-time high-fidelity accuracy requirements of the digital twin system. The initial confidence threshold is determined by chi-square distribution in combination with the degrees of freedom of the sensor observation space. During the system operation, the value of the significance level is dynamically adjusted according to the spatial consistency analysis results. Furthermore, the confidence threshold is dynamically adjusted according to the data fluctuation amplitude under real-time industrial conditions.

6. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 1, characterized in that, The process of inputting the clean observation data stream and data purity index into the online data fusion stage and performing data fusion processing includes: The pure observation data stream is input into the adaptive fusion architecture based on interactive multi-model. The model interaction operation is performed according to the posterior probability of each filter expert model at the previous time step and the preset model transition probability matrix to obtain the interactive initial state and initial covariance input to each filter expert model. Multiple filtering expert models are run in parallel. Each filtering expert model uses a long short-term memory network as a process evolution operator to perform nonlinear temporal feature mapping on the interactive initial state and generate preliminary prior state prediction values ​​based on historical information. The residual features between the predicted trajectory and the intrinsic evolution law of the physical system are extracted online using long short-term memory networks, and the preliminary prior state prediction values ​​are compensated and corrected in real time using the residual features. The compensated and corrected prior state predictions are mapped to the measurement space to obtain the predicted observations. The observation noise covariance is dynamically corrected using the data purity index. The Kalman gain is calculated based on the corrected noise covariance. Based on the real-time clean observation data stream, the compensated and corrected prior state predictions are recursively updated using the Kalman gain. The consistency between the predicted measurement values ​​output by each filter expert model and the actual observation values ​​is calculated simultaneously to generate the measurement likelihood. The trust weights of each filter expert model are dynamically updated based on the measured likelihood, and the posterior state estimation results of each path are weighted and fused according to the updated weights to output the optimal state estimate.

7. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 6, characterized in that, The execution model interactive operation includes: Two heterogeneous filtering expert branches are preset, including at least a stationary filtering expert model with a first process noise covariance configured for the system's steady operating condition and a rapidly changing filtering expert model with a second process noise covariance configured for the system's dynamic and rapidly changing operating condition. The first process noise covariance is smaller than the second process noise covariance. A model transition probability matrix is ​​set, and based on the posterior probabilities of each filtering expert model at the previous time step, the posterior state estimates and posterior error covariance of each expert at the previous time step are weighted and mixed according to the model transition probability matrix to calculate the interactive initial state and initial covariance input to each expert at the current time step.

8. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 6, characterized in that, The parallel operation of multiple filtering expert models, each employing a long short-term memory network as the process evolution operator, performs nonlinear temporal feature mapping on the initial interactive state, and generates preliminary prior state predictions based on historical information, including: For each filtering expert model, the interaction initial state and the historical state estimation sequence are concatenated to construct a multi-dimensional time-series input vector sequence; Input the multidimensional temporal input vector sequence into the pre-trained long short-term memory network and calculate the hidden layer state; A nonlinear mapping from the feature space to the physical state space is performed on the hidden layer state to obtain the preliminary prior state predictions of each filter expert model at the current time.

9. The method for data fusion of homogeneous sensor arrays for digital twins according to claim 6, characterized in that, The method of utilizing the residual features extracted online from the predicted trajectory of the Long Short-Term Memory network and the intrinsic evolutionary laws of the physical system, and using these residual features to perform real-time compensation and correction on the preliminary prior state predictions, includes: For each filtered expert model, the preliminary prior state prediction is compared with the reference trajectory calculated based on physical motion constraints, and the residual feature vector characterizing the degree of model mismatch is extracted. An adaptive calibration operator based on neuron activation weights is constructed, and the calibration gain matrix for correcting prediction bias is calculated using dynamic prior confidence interval information and residual feature vectors. The preliminary prior state prediction values ​​are weighted and compensated in real time using the calibration gain matrix to generate calibrated prior state prediction values.

Images