A Real-Time Thermodynamic Prediction Method for SLM Based on Tensor Computation and Artificial Intelligence

Abstract

This invention relates to the field of additive manufacturing technology and discloses a real-time thermodynamic prediction method for SLM (Synthetic Manufacturing Process) based on tensor computation and artificial intelligence. The method collects historical thermodynamic data within a preset time period of the SLM manufacturing process to construct a historical thermodynamic tensor; performs tensor decomposition on the historical thermodynamic tensor to separate core feature components and generate a dynamic evolution tensor accordingly; defines a multidimensional thermodynamic state space using the dynamic evolution tensor, and selects a set of thermodynamic early warning indicators by evaluating the degree of aggregation of historical abnormal events in this space; extracts real-time feature components from real-time monitoring data to form a real-time state tensor, and performs tensor similarity measurement with the early warning indicator set in the multidimensional thermodynamic state space to derive a real-time risk value; finally, establishes a thermodynamic prediction model based on the real-time risk value, core feature components, and dynamic evolution tensor, outputs the thermodynamic state prediction results of the SLM process in real time, and generates operation adjustment commands.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, specifically to a real-time thermodynamic prediction method for SLM based on tensor computation and artificial intelligence. Background Technology

[0002] Selective laser melting (SLM) technology, as an important branch of additive manufacturing, has been increasingly widely used in high-end manufacturing fields such as aerospace, medical devices, and automotive manufacturing due to its ability to directly form complex geometries, high material utilization, and high forming precision. This technology selectively melts metal powder layer by layer using a laser beam, ultimately depositing it to form a three-dimensional solid part. Its manufacturing process involves a series of complex physicochemical processes, including laser-material interaction, heat conduction, molten pool flow, and solidification phase transformation.

[0003] In SLM manufacturing, thermodynamic behavior has a significant impact on the quality of molded parts. Thermodynamic factors such as the distribution and variation of the molten pool temperature, the generation and accumulation of thermal stress, and differences in cooling rates directly affect whether defects such as deformation, cracking, porosity, and incomplete fusion will occur in the parts. For example, when the temperature in a local area is too high or the heating rate is too fast, it may lead to accelerated material evaporation and the formation of porosity defects; while an excessively large temperature gradient can easily induce large thermal stresses, which can cause deformation or even cracking of the parts. Therefore, accurate monitoring and prediction of the thermodynamic state during the SLM process is a key prerequisite for ensuring molding quality.

[0004] Methods for predicting the thermodynamic state of SLM (Self-Modulating Lamp) mainly include numerical simulation methods and empirical methods based on sensor monitoring. Numerical simulation methods establish physical models such as heat conduction and fluid dynamics to perform numerical calculations on the SLM process, thereby predicting thermodynamic parameters such as temperature and stress fields. However, these methods often require precise setting of numerous boundary conditions and material parameters, making the calculation process complex and time-consuming, which is difficult to meet the needs of real-time monitoring and prediction. Especially when dealing with the manufacturing of complex structural parts, their computational efficiency is even lower, significantly limiting their practicality.

[0005] Empirical methods based on sensor monitoring involve deploying temperature sensors, infrared cameras, and other monitoring devices on manufacturing equipment to collect thermodynamic data such as temperature in real time, and then combining this data with historical experience or simple statistical models for prediction. However, this type of method has significant limitations: on the one hand, the number and location of sensors are limited by the equipment structure, making it difficult to comprehensively capture the thermodynamic information of the entire molding area, and easily leading to monitoring blind spots; on the other hand, simple statistical models are unable to characterize the complex spatiotemporal relationships between thermodynamic parameters, and their predictive effect on nonlinear and dynamically changing thermodynamic behavior is poor, making it difficult to identify potential quality risks in advance.

[0006] With the development of artificial intelligence technology, some studies have attempted to apply machine learning algorithms to the thermodynamic prediction of SLM (Sequencing Molding Machine), using data-driven models to predict parameters such as temperature. However, existing methods often process data in vector or matrix form, failing to fully consider the multi-dimensional and spatiotemporal coupling characteristics of thermodynamic data during SLM, resulting in insufficient model representation of complex thermodynamic evolution laws. Furthermore, existing methods lack a systematic approach to anomaly identification and early warning indicator selection, making it difficult to effectively distinguish between normal fluctuations and abnormal risks, thus requiring improvement in the reliability and practicality of the prediction results. Therefore, developing a method capable of real-time and accurate prediction of the thermodynamic state of SLM is of significant practical importance for improving the quality of SLM molding. Summary of the Invention

[0007] The purpose of this invention is to provide a real-time thermodynamic prediction method for SLM based on tensor computation and artificial intelligence, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, this invention provides a real-time SLM thermodynamic prediction method based on tensor computation and artificial intelligence, the method comprising:

[0009] Collect historical thermodynamic data of the SLM manufacturing process within a preset time period, and construct a historical thermodynamic tensor based on the historical thermodynamic data;

[0010] Tensor decomposition is performed on the historical thermodynamic tensor to separate the core feature components, and a dynamic evolution tensor is generated based on the evolution of the core feature components over time.

[0011] A multidimensional thermodynamic state space is defined using a dynamic evolution tensor, and the degree of aggregation of historical anomalous events in the multidimensional thermodynamic state space is evaluated. A set of thermodynamic early warning indicators is selected based on the aggregation results.

[0012] Real-time feature components are extracted from the real-time monitoring data of the SLM process to form a real-time state tensor. Tensor similarity measurement is performed with the thermodynamic early warning index set in the multidimensional thermodynamic state space to derive the real-time risk value.

[0013] Based on real-time risk values, core feature components, and dynamic evolution tensors, a thermodynamic prediction model is established to output the thermodynamic state prediction results of the SLM process in real time and generate operation adjustment commands.

[0014] Preferably, historical thermodynamic data of the SLM manufacturing process are collected within a preset time period, and a historical thermodynamic tensor is constructed based on the historical thermodynamic data, specifically as follows:

[0015] Obtain temperature, pressure, and laser energy parameters during the SLM manufacturing process within a preset time period;

[0016] Outlier removal and standardization transformation of temperature, pressure, and laser energy parameters;

[0017] The standardized temperature, pressure, and laser energy parameters are integrated into a three-dimensional array structure according to time series and spatial location. This three-dimensional array structure constitutes the historical thermodynamic tensor.

[0018] Preferably, a tensor decomposition operation is performed on the historical thermodynamic tensor to separate the core characteristic components, specifically:

[0019] A high-order singular value decomposition algorithm is used to process the historical thermodynamic tensor, which is decomposed into multiple core tensors.

[0020] Representative feature elements are extracted from the core tensor, and these representative feature elements constitute the core feature components.

[0021] Preferably, a dynamic evolution tensor is generated based on the evolution of core feature components over time, specifically as follows:

[0022] Analyze the numerical changes of core feature components over continuous time intervals, calculate the gradient of change, and integrate the gradient sequence.

[0023] Dynamic evolution tensors are formed based on changing gradient sequences.

[0024] Preferably, a multidimensional thermodynamic state space is defined using a dynamic evolution tensor, specifically as follows:

[0025] The coordinate axes of the multidimensional thermodynamic state space are set according to the number of dimensions of the dynamic evolution tensor. Each coordinate axis corresponds to a thermodynamic characteristic attribute, and the position in the multidimensional thermodynamic state space is determined by the characteristic attribute value.

[0026] Preferably, the degree of aggregation of historical anomalous events in the multidimensional thermodynamic state space is assessed, specifically as follows:

[0027] Locate the corresponding coordinate points of historical anomalous events in the multidimensional thermodynamic state space, measure the distribution density of the coordinate points, and use the distribution density value as the result of the degree of aggregation.

[0028] Preferably, a set of thermodynamic early warning indicators is selected based on the aggregation degree results, specifically as follows:

[0029] Set a clustering threshold, and filter out coordinate points whose clustering results exceed the clustering threshold. The feature attributes associated with these coordinate points constitute a set of thermodynamic early warning indicators.

[0030] Preferably, real-time feature components are extracted from the real-time monitoring data of the SLM process to form a real-time state tensor, specifically as follows:

[0031] Sensor readings during the SLM manufacturing process are captured in real time, converted into tensor format, feature dimensionality reduction is performed on the tensor format, and real-time feature components are output. The real-time feature components are combined into a real-time state tensor.

[0032] Preferably, a tensor similarity measure is performed with the thermodynamic early warning index set in the multidimensional thermodynamic state space to derive the real-time risk value, specifically as follows:

[0033] The real-time state tensor is projected onto a multidimensional thermodynamic state space. The tensor norm distance between the real-time state tensor and each point in the thermodynamic early warning index set is calculated. A similarity score is generated based on the tensor norm distance, and the similarity score is converted into a real-time risk value.

[0034] Preferably, a thermodynamic prediction model is established based on real-time risk values, core feature components, and dynamic evolution tensors, specifically as follows:

[0035] The real-time risk value is integrated with the core feature components and used as the input to the thermodynamic prediction model;

[0036] A thermodynamic prediction model is trained using a deep learning framework, and the thermodynamic prediction model learns the pattern of a dynamic evolution tensor.

[0037] The thermodynamic prediction model outputs thermodynamic state prediction results, which are then mapped into operational adjustment commands.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] This method, by integrating tensor computation and artificial intelligence technologies, provides a novel technical approach for real-time thermodynamic prediction of the SLM manufacturing process, demonstrating significant advantages in multiple aspects.

[0040] At the data processing level, by collecting historical thermodynamic data and constructing historical thermodynamic tensors, it is possible to fully preserve multi-dimensional information in the data, including temperature distribution at different locations in the spatial dimension, dynamic changes in the temporal dimension, and thermodynamic responses under the influence of different process parameters. This complete preservation of multi-dimensional information overcomes the limitations of information simplification in traditional vector or matrix data processing, laying the foundation for accurate extraction of core features.

[0041] By performing tensor decomposition on the historical thermodynamic tensor to separate core feature components, redundant data and noise interference can be removed while retaining key information. The extraction of core feature components focuses on the key factors influencing the thermodynamic behavior of SLM, such as the thermodynamic characteristics corresponding to factors like laser power fluctuations, scanning speed variations, and powder layer thickness inhomogeneity, making the analysis of thermodynamic processes more accurate and efficient. Based on the evolution of the core feature components over time, a dynamic evolution tensor is generated, which can intuitively reflect the dynamic changes in the thermodynamic state, capture the correlation characteristics of thermodynamic behavior at different stages, and provide a clear perspective for understanding the thermodynamic evolution mechanism in the SLM process.

[0042] By defining a multidimensional thermodynamic state space using a dynamic evolution tensor, complex thermodynamic behaviors are mapped onto a structured space, allowing for the quantitative characterization of differences and correlations between different thermodynamic states. Selecting a set of thermodynamic early warning indicators by assessing the clustering degree of historical anomalies within this space ensures a high correlation between the selected indicators and actual quality risks. This method of selecting early warning indicators based on the inherent patterns in the data avoids the subjectivity and limitations of traditional experience-based indicator selection, making risk identification more closely aligned with actual manufacturing processes.

[0043] By extracting real-time feature components from real-time monitoring data to form a real-time state tensor, and performing tensor similarity measurement with the set of early warning indicators in a multi-dimensional thermodynamic state space, real-time risk values ​​can be quickly and accurately derived. This tensor similarity-based measurement method fully utilizes the matching advantages of multi-dimensional information. Compared with traditional comparisons of single or few parameters, it can more comprehensively reflect the degree of proximity between the current thermodynamic state and the abnormal state, thereby enabling timely perception of potential risks.

[0044] The thermodynamic prediction model, based on real-time risk values, core characteristic components, and dynamic evolution tensors, integrates historical patterns, real-time states, and dynamic evolution trends, enabling it to output accurate real-time thermodynamic state prediction results. Simultaneously, it generates operational adjustment commands based on the prediction results, achieving a closed-loop response from state monitoring and prediction to process adjustment. This allows for timely intervention in thermodynamic anomalies that may lead to quality defects, thereby improving the quality stability of SLM-molded parts. Attached Figure Description

[0045] Figure 1 This is a time series diagram of the SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence described in this invention.

[0046] Figure 2 The flowchart for constructing the historical thermodynamic tensor. Detailed Implementation

[0047] The technical solutions of the embodiments 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.

[0048] Please see Figure 1 This invention provides a real-time prediction method for SLM thermodynamics based on tensor computation and artificial intelligence, the method comprising:

[0049] By constructing a multidimensional thermodynamic state space and establishing a dynamic evolution model, real-time monitoring and prediction of the thermodynamic state in the selective laser melting (SLM) manufacturing process are achieved. This method first collects historical thermodynamic data to construct a three-dimensional tensor structure, extracts core feature components through high-order tensor decomposition, and establishes a dynamic evolution model. The aggregation characteristics of abnormal events are analyzed in the multidimensional state space to form a set of early warning indicators. Real-time monitoring data, after feature extraction, is matched with the early warning indicators based on similarity, outputting risk values ​​and driving the prediction model to generate operational commands. The entire process forms a closed-loop control system, achieving optimization of the thermodynamic stability of the manufacturing process.

[0050] Example 1: See Figure 2 The process of acquiring historical thermodynamic data and constructing tensors, as well as the method for extracting core feature components, was described. The entire implementation process began with data acquisition from the manufacturing site, employing a high-precision distributed sensor network to cover the entire processing area. Temperature monitoring utilized a combination of an infrared thermal imager array and embedded thermocouples, achieving a spatial resolution of 50 micrometers and a temperature measurement range covering 200℃ to 3000℃. The pressure sensing system consisted of multiple piezoelectric dynamic pressure sensors, positioned at key locations within the processing chamber, with a sampling frequency set to 10kHz to capture instantaneous pressure fluctuations. Laser energy monitoring was achieved through a combination of a beam splitter and photodiodes, recording laser power fluctuations and energy distribution characteristics in real time.

[0051] During raw data acquisition, all sensor nodes maintain strict time alignment via a time synchronization protocol, with timestamp accuracy controlled at the microsecond level. The acquisition system uses a circular buffer to store the most recent 30 seconds of raw data; when the buffer reaches its predetermined capacity, the data processing flow is triggered. The data preprocessing stage first performs spatial interpolation on the temperature field data, converting irregularly distributed temperature measurement points into uniform grid data. Pressure data undergoes low-pass filtering to eliminate high-frequency noise, with the cutoff frequency dynamically adjusted based on material properties. Laser energy data requires optical path compensation calculations to eliminate measurement deviations caused by optical component attenuation.

[0052] Data standardization employs a dynamic range adjustment method, calculating statistical characteristics within a sliding window for different physical quantities. Temperature data is normalized based on the material's melting point, pressure data undergoes relative value conversion with reference to ambient atmospheric pressure, and laser energy data is scaled proportionally according to theoretical design values. The standardized data is organized into a three-dimensional array structure, with the time dimension divided at 1-millisecond intervals, the spatial dimension using a Cartesian coordinate grid, and the parameter dimension including processed temperature, pressure, and energy data. This three-dimensional structure fully preserves the spatiotemporal evolution characteristics of thermodynamic parameters during the manufacturing process.

[0053] The construction of historical thermodynamic tensors employs a hierarchical storage strategy, storing tensor slices of consecutive time periods in a distributed file system. Each tensor slice contains data from 1000 consecutive time points, corresponding to one second of the manufacturing process. A cache of recently used tensor slices is maintained in memory, and the least recently used algorithm is used for cache replacement. Tensor data is stored in a compressed format, applying lossy compression to temperature field data and lossless compression to key parameters, achieving a balance between storage efficiency and data accuracy.

[0054] The tensor decomposition algorithm is implemented in parallel, dividing a large tensor into multiple sub-blocks and distributing them to a computing cluster for processing. The decomposition process first performs local eigenvalue decomposition on each sub-block, then iteratively merges the local results to obtain the global decomposition. The core tensor is computed using alternating least squares, with a maximum number of iterations and a convergence threshold controlling computational accuracy. In each iteration, the factor matrices of each dimension are optimized sequentially, while keeping other dimensions constant. The effective rank of the tensor is automatically determined during the decomposition process to avoid overfitting or underfitting.

[0055] When extracting feature components from the core tensor, the significance indices of the factor matrices in each dimension are analyzed. Statistical tests are used to identify the feature combinations that have the greatest impact on system behavior. Temperature-related features mainly reflect the stability of the molten pool, pressure-related features reflect the disturbance of the processing environment, and energy-related features characterize the interaction efficiency between the laser and the material. These feature components are arranged in chronological order to form physically meaningful feature curves.

[0056] Post-processing of the feature components includes outlier detection and smoothing. Robust statistical methods are used to identify outliers in the feature curves, which are then corrected using linear interpolation. Smoothing employs an adaptive window-width moving average algorithm to eliminate high-frequency noise while preserving key features. The processed feature components are stored in a time-series database, supporting efficient historical queries and real-time comparisons.

[0057] The entire implementation process involves the collaborative work of various hardware devices, including sensor networks, data acquisition cards, time synchronization devices, and computing servers. The software system adopts a microservice architecture, comprising data acquisition services, preprocessing services, tensor computation services, and feature management services. These services communicate asynchronously via message queues to ensure system scalability and fault tolerance. The monitoring system tracks the operational status of each stage in real time, triggering alarms and automatic recovery mechanisms in the event of anomalies.

[0058] The data processing pipeline is designed with real-time requirements in mind, controlling end-to-end latency from data acquisition to feature extraction to the millisecond level. System resource allocation employs a dynamic adjustment strategy, automatically expanding or shrinking computing nodes based on load. For data security, strict access control is implemented, and all data transmission is encrypted. System logs record the complete data processing process, supporting post-processing analysis and problem tracing.

[0059] The visualization interface for the characteristic components offers a variety of analysis tools, supporting multi-dimensional data comparison and interactive exploration. Users can browse historical characteristic changes via a timeline or focus on specific time periods for detailed analysis. The system automatically generates characteristic evolution reports to help understand key thermodynamic behavior patterns in the manufacturing process.

[0060] Example 2: Technical process covering dynamic evolution modeling of core feature components and construction of multidimensional thermodynamic state space. This implementation loads historical core feature component data from the storage system, including three independent time series data streams: temperature field stability sequence, pressure fluctuation intensity sequence, and energy absorption efficiency sequence. Each sequence contains equally spaced sampling points, with a time resolution consistent with the original data acquisition frequency. The data processing system allocates dedicated computing nodes to process different feature sequences, establishing a parallel computing pipeline.

[0061] The generation process of the dynamic evolution tensor employs a time window segmentation strategy. A fixed-length time window slides along the feature sequence, with a window width set to 200 consecutive sampling points. Each slide increments by 50 sampling points, forming an overlapping window structure. A Hamming window function is applied to the window boundaries to reduce spectral leakage effects. Within a single window, three independent calculations are performed: the second-order difference derivative of the temperature field stability sequence is obtained using a fifth-order precision central difference scheme; the rate of change of the standard deviation within the window is calculated for the pressure fluctuation intensity sequence, and the slope change is analyzed through linear regression; the energy absorption efficiency sequence undergoes piecewise window fitting, with the slope change value at the inflection point as the feature. The three calculation results form a feature evolution vector, corresponding to the system dynamic characteristics of a specific time segment.

[0062] After generating a two-dimensional evolution matrix through time window processing, a high-dimensional data structure is constructed using a tensor expansion algorithm. This expansion process considers four dimensions: the time dimension records the position of the window center point, the feature dimension contains three derived feature values, the change intensity dimension is graded according to statistical distribution, and the spatial correlation dimension calculates the correlation between the feature vector and the neighboring region. Spatial correlation analysis uses the mutual information algorithm to calculate the statistical correlation between the current window data and the eight adjacent spatial grid data blocks. The expanded tensor is represented by a fourth-order array, with the tensor dimensions being, in order, the number of sliding windows, the type of dynamic feature, the level of change intensity, and the spatial correlation index.

[0063] The multidimensional thermodynamic state space is constructed based on the dimensional characteristics of the evolution tensor. The coordinate system design employs the principle of orthogonal projection: the X-axis maps the temperature field stability index, with a scale range of a normalized continuous range of 0 to 1; increasing the value indicates enhanced molten pool stability. The Y-axis corresponds to the pressure fluctuation intensity coefficient, covering a range from -2 to +2, with zero representing the normal fluctuation range. The Z-axis represents the energy absorption efficiency ratio, with a baseline value set at 1.0 and an allowable fluctuation range of 50% or less. The fourth dimension uses a colorimetric coding scheme, with cool colors representing low spatial correlation and warm colors representing high spatial correlation. The measurement units of the spatial coordinate system adopt a uniform scale method, with each coordinate axis divided into scales at 0.05 unit intervals.

[0064] The topological structure of the state space is realized as a three-dimensional entity through a discrete mesh. The spatial domain is divided into a regular voxel array: 40 cells along the X-axis, 80 cells along the Y-axis, and 20 cells along the Z-axis, totaling 64,000 voxels. Each voxel stores the state vector corresponding to its coordinates, and the vector contains four elements: temperature stability gradient, pressure fluctuation trend, energy absorption rate of change, and spatial correlation weight. The formula for calculating the magnitude of the state vector combines these four parameters, and the calculation result reflects the system stability level of the current state. The spatial structure design supports fast spatial retrieval, and the establishment of a three-dimensional spatial index structure accelerates nearest neighbor search.

[0065] The storage of dynamically evolving tensors employs a hierarchical encoding strategy. The base layer stores the original feature evolution matrix, the incremental layer records spatial expansion data, and the metadata layer stores time alignment information. Data compression utilizes a lossy encoding scheme, applying principal component reduction to the feature dimension, difference encoding to the time dimension, and run-length compression to the spatial correlation dimension. The compressed tensor data is stored in a distributed key-value database, supporting time range retrieval and feature-based conditional queries.

[0066] The computing system implements a multi-level caching architecture. Raw feature sequences are stored in an in-memory database, providing microsecond-level access latency; evolution matrix calculation results are stored in a solid-state drive array; and the complete four-dimensional tensor is persistently stored in a pool of mechanical hard drives. A computing task scheduler dynamically balances the load, prioritizing computing resources for real-time feature processing tasks and assigning lower priority to background analysis tasks. A system resource monitoring module tracks CPU, memory, and storage I / O usage, triggering resource reallocation when thresholds are exceeded.

[0067] The state space visualization system employs volume rendering technology. The user interface supports interactive operations: rotating to view the spatial distribution, cutting to display cross-sectional structures, and filtering data points within specific coordinate ranges. Display parameters are dynamically adjustable: coordinate axis scaling, color mapping scheme, and mesh transparency settings, etc. Automatically generated isosurfaces display high-density state regions, and semi-transparent particle clouds display the distribution of anomalous events.

[0068] Feature verification mechanisms are implemented throughout the entire process. Data generated at each computation stage undergoes an automated verification process: input / output dimension matching checks, numerical range validity verification, and data statistical characteristic review. The system is equipped with an outlier interceptor to block outlier data and recalculate previous results. Historical feature datasets are periodically fully validated to detect data drift or distortion.

[0069] The system's fault-tolerant design incorporates multiple protection mechanisms. Data processing nodes employ a primary-backup redundant configuration, synchronizing computational status in real time; persistent storage implements triple mirror backup; critical computation results are digitally signed; an automatic checkpoint mechanism saves the system state every five minutes; and a breakpoint resume function restores the computation process after unexpected interruptions. The monitoring system tracks the heartbeat signals of each module, triggering failover in case of anomalies.

[0070] A dedicated maintenance interface is provided for system configuration. Administrators can view the computation pipeline status, adjust time window parameters, manage storage resource allocation, and set coordinate mapping rules. Operation logs record the start time, resource consumption, and completion status of each computation task in detail. An audit trail system records all configuration changes and data processing activities.

[0071] Example 3: Location analysis of historical anomaly events in a multidimensional thermodynamic state space and the generation process of a thermodynamic early warning index set. This implementation imports historical anomaly event records from a manufacturing process quality inspection database, including the timestamps and spatial location information of three typical defects: splashing, spheroidization, and lack of fusion. In the data preprocessing stage, discrete event records are aligned with the state space coordinate system, establishing a time-space dual mapping relationship. The event location engine employs a distributed computing framework to process large amounts of historical event data in parallel.

[0072] The coordinate transformation process of abnormal events in the state space considers spatiotemporal correlation. Each event record contains a time stamp accurate to the millisecond level and spatial coordinates accurate to the sub-millimeter level. The corresponding state vector is quickly retrieved through a spatiotemporal index. The transformation algorithm is as follows:

[0073] ;

[0074] in: Represents the projected coordinates of the abnormal event in the state space. Spatiotemporal proximity weighting factor, Representative moment Location The state vector at that point, This refers to the number of neighboring states considered. Weighting factor. It is inversely proportional to the spatiotemporal distance, and the distance calculation uses the Mahalanobis distance metric, taking into account the dimensional differences of different physical quantities. The projection process retains the type labels and severity information of the original events, forming a labeled set of state space points.

[0075] The density field calculation employs an adaptive kernel density estimation method. Kernel function bandwidth parameter. The density is dynamically adjusted based on the local characteristics of the event distribution, increasing bandwidth in sparse regions and decreasing bandwidth in dense regions. Density calculations are performed in a 3D state space subspace, ignoring the chroma encoding dimension. The base resolution of the grid cells is set to 0.1 state units, and the calculation process is accelerated using octree space partitioning. For density field visualization, a moving cube algorithm is used to generate isosurfaces, revealing the topological structure of high-density regions.

[0076] Cluster detection employs a multi-scale analysis strategy. The first round of detection uses a fixed threshold to filter for clearly clustered regions; the threshold is set to the 85th percentile of the overall spatial density distribution. The second round of analysis performs hierarchical clustering within the candidate regions, setting a cutoff distance. The state unit merges neighboring density peaks. The final output cluster region contains descriptive information in three aspects: geometric center coordinates, spatial extent, and density distribution characteristics.

[0077] The generation process of the early warning indicator set undergoes rigorous quality control. Each candidate early warning point must meet two conditions: it must be located within a density cluster and associated with an actual abnormal event. Event type analysis statistically analyzes the distribution of defect categories within each cluster and calculates the type purity index. The early warning point screening algorithm prioritizes the center points of clusters with a purity higher than 80%, and creates composite early warning points when multiple event types are mixed. Each early warning point records a complete feature combination pattern, including the main feature threshold and the range of variation of auxiliary features.

[0078] The data structure for the early warning indicators is designed as a hierarchical tensor format. The top-level tensor records the spatial distribution of early warning points, the middle-level tensors store feature combination patterns, and the bottom-level tensors store historical event statistics. The tensor dimensions are three directions: early warning point number, feature type, and statistical indicator. The storage format employs sparse matrix compression technology and optimizes the processing of zero-value elements.

[0079] The warning level classification considers both density value and event severity. Density value is converted into a standardized score, and event severity is graded according to process standards. The two are weighted and summed to obtain a comprehensive warning score. Weighting coefficients are set based on the experience of process experts; for splash-type events, density value is emphasized, while for non-fusion-type events, severity is emphasized. The final warning level is divided into three levels: Attention, Warning, and Severe, corresponding to different response strategies.

[0080] A verification mechanism is implemented throughout the entire process of generating early warning indicators. The spatial projection stage checks the conservatism of coordinate transformation to ensure no positional bias is introduced. Density calculations undergo cross-validation to compare the stability of results under different bandwidth parameters. Cluster boundary verification employs a combination of manual review and automated detection. The effectiveness of early warning indicators is evaluated through backtesting with historical data, calculating early warning hit rate and false alarm rate.

[0081] In terms of system implementation, the early warning generation module is deployed independently using a microservice architecture. Computing resources are dynamically allocated, and computing nodes are automatically expanded during peak periods. A memory database caches commonly used early warning modes to accelerate real-time comparison and querying. Persistent storage uses a time-series database to record the complete evolution history of early warning indicators. The access interface supports conditional queries and batch export functions, facilitating integration with other systems.

[0082] The visualization subsystem provides interactive analysis tools. A 3D scatter plot displays the distribution of anomalous events, a semi-transparent surface represents density isosurfaces, and warning points are highlighted with special markers. Users can rotate to observe the spatial structure, cut to view cross-sectional distribution, and filter for specific event types. Auxiliary views simultaneously display parallel coordinate plots of feature combinations and pie charts of event statistics.

[0083] The maintenance and management functions include version control and change auditing for early warning indicators. Each indicator update generates a new version, while historical versions are retained for retrospective analysis. Modification logs detail the adjustments, the personnel involved, and the reasons for the changes. Regular indicator effectiveness reports are generated to analyze trends in early warning accuracy and response timeliness.

[0084] The anomaly handling process is designed with a closed-loop feedback mechanism. Real-time system-triggered early warning events record processing results, and successfully handled cases are used to optimize early warning thresholds. Newly occurring anomalies automatically trigger indicator reassessment to maintain the adaptability of the early warning system. An expert knowledge base stores handling solutions for typical events, supporting case-based reasoning and decision-making.

[0085] The calculation process employs multiple fault-tolerant protections. Input data undergoes range checks and logical validation, intermediate results are subject to reasonableness constraints, and the final output is cross-validated. The system monitors computing resource usage and automatically triggers recovery procedures in case of anomalies. A complete early warning indicator database is backed up regularly, enabling rapid system reconstruction during disaster recovery.

[0086] The dynamic update strategy for early warning indicators takes into account process changes. When material parameters, equipment configurations, or process plans change, the system automatically marks relevant early warning points as requiring reassessment. The update process adopts a gradual adjustment to avoid system instability caused by sudden changes in indicators. Version migration is implemented through canary releases, gradually replacing old indicators.

[0087] The implementation process emphasizes computational efficiency optimization. In the spatial projection stage, kd-trees are used to accelerate nearest neighbor search, a grid approximation method is applied for density calculation, and a disjoint-set data structure is used for cluster detection. Object pooling technology is implemented for memory management to reduce the overhead of dynamic memory allocation. Computational task scheduling considers data locality and reuses intermediate results as much as possible.

[0088] Standardized interfaces are provided for system integration. The real-time monitoring system receives updates to early warning indicators via a message queue, while the historical analysis system queries the complete indicator database via a REST API. Mobile terminals support push notifications of important early warnings, and on-site displays show the current early warning status. All interface communications are encrypted and authenticated to ensure secure data transmission.

[0089] Example 4: Technical process for extracting feature components and assessing risk values ​​from real-time monitoring data of SLM manufacturing process. This implementation uses an actual manufacturing process of a 316L stainless steel gear component as an example to illustrate the specific process of real-time state tensor generation and risk measurement. The manufacturing equipment is equipped with a 16-channel temperature sensor array, 4 dynamic pressure sensors, and a laser energy monitoring system, with a data acquisition interval set to 5 milliseconds. The sensor readings captured by the real-time data acquisition system at t=1.235 seconds are shown in Table 1.

[0090] Table 1: Sensor readings captured by the real-time data acquisition system at t=1.235 seconds.

[0091] Sensor type Channel number Original measurement value Standardized value Spatial coordinates (mm) Temperature sensor T_07 1682℃ 0.842 (12.3,5.7) Temperature sensor T_12 1543℃ 0.723 (14.8,3.2) pressure sensor P_02 103.2 kPa 1.032 (13.5,4.5) Energy monitoring E_01 285J / mm² 0.912 (13.0,4.0)

[0092] The data preprocessing stage begins with spatiotemporal alignment, mapping discrete sensor readings to a unified 10×10 spatial grid. Temperature data is interpolated using inverse distance weighted interpolation, pressure data is averaged regionally, and energy data retains the center value of the light spot. The interpolated data constitute a 20×20×3 original monitoring tensor, with the three channels corresponding to the temperature, pressure, and energy fields, respectively.

[0093] The feature extraction process employs an incremental tensor decomposition algorithm. The computational system maintains a sliding window buffer, storing the monitoring tensors for the most recent 50 time steps. When new data arrives, the buffer is updated and local feature analysis is performed. The decomposition process retains the first three main feature patterns: the first pattern reflects the overall temperature distribution characteristics, the second pattern characterizes the pressure fluctuation pattern, and the third pattern describes energy absorption characteristics. Real-time feature components are output in the form of a 3×3 upper triangular matrix, where the matrix elements represent the coupling strength between each feature pattern.

[0094] The generation of the real-time state tensor includes a feature fusion step. The feature matrix at the current moment is compared with historical baseline features to calculate the relative change. After normalization, the change data is matched against reference patterns in the early warning indicator set. The matching process considers the directional and amplitude similarity of feature vectors, using a combination of angular distance and Euclidean distance as metrics.

[0095] After receiving the real-time state tensor, the risk value calculation module performs a projection operation in the multidimensional thermodynamic state space. The projection algorithm considers the nonlinear characteristics of the state space, using fine-grid interpolation in dense regions and nearest-neighbor approximation in sparse regions. The calculation system maintains a dynamically updated warning index to accelerate the spatial search process. An influence radius is set for each warning point, and gradient weighting is applied within the radius.

[0096] The risk scoring conversion process employs multi-level filtering. The original similarity score first undergoes time smoothing filtering to eliminate instantaneous fluctuations; secondly, spatial consistency is checked to exclude isolated outliers; finally, type-specific adjustments are performed, with different scoring conversion curves applied to different defect types. The final risk value is calculated on an integer scale from 0 to 100, with higher values ​​indicating a greater degree of risk.

[0097] In terms of system implementation, the real-time processing pipeline adopts an event-driven architecture. Data acquisition triggers feature extraction events, feature updates trigger risk calculation events, and risk warnings trigger control command events. Event handlers are configured with priority queues to ensure timely response to critical tasks. Dynamic load balancing is implemented for computing resource allocation, automatically activating backup computing nodes during peak periods.

[0098] The status monitoring interface displays key parameters in real time: current risk value trend chart, feature component radar chart, and state space projection scatter plot. Operators can view detailed feature decomposition results at any given time and trace the risk value calculation process. The system records a complete processing log, including raw sensor data, intermediate feature data, and the final risk score.

[0099] The anomaly handling process employs a multi-level response mechanism. A primary warning is triggered when the risk value exceeds 60, notifying the process engineer for inspection; a secondary response is activated when it exceeds 80, automatically recording process parameters and preparing a pause command; and an emergency stop is executed when the risk value reaches 95, protecting the manufacturing system. The response strategy can be configured based on material type and component criticality.

[0100] The quality control module undergoes closed-loop verification. Actual quality defects are compared and analyzed with system warning records to calculate temporal and spatial overlap indices. The analysis results are used to adjust warning parameters and optimize risk threshold settings. The verification process considers the normal fluctuation range of manufacturing parameters to avoid false alarms caused by oversensitivity.

[0101] In terms of computational optimization, multiple acceleration techniques are employed. The feature extraction process uses approximation algorithms to reduce computational complexity; spatial projection implements pre-computation and caching strategies; and risk scoring uses a lookup table method instead of real-time computation. Memory management implements an object reuse mechanism to reduce garbage collection overhead. The parallel computing framework fully utilizes the acceleration capabilities of multi-core processors and GPUs.

[0102] The system integration takes into account the needs of industrial sites. It connects to the manufacturing equipment control system via an OPCUA interface, supporting mainstream PLC data exchange protocols. The safety design complies with industrial network security standards, implementing encrypted data transmission and operator authentication. The hardware configuration meets industrial environmental requirements, possessing dustproof and electromagnetic interference resistance characteristics.

[0103] Maintenance features include automatic calibration and diagnostic tools. Sensor zero-point calibration is performed periodically to verify data acquisition accuracy. A system self-test program checks the health status of each stage of the computational pipeline and initiates a recovery process upon detecting anomalies. The maintenance log records all calibration and diagnostic operations, supporting audit trails.

[0104] Version management employs a strict control process. Algorithm updates undergo simulation testing, are first verified on experimental equipment, and then gradually rolled out to the production system. Older version configurations retain rollback capabilities to ensure system reliability. Change logs detail the modifications and their impact.

[0105] The data persistence solution is designed to balance real-time performance and data integrity. The latest data is stored in an in-memory database for fast access, while historical data is periodically archived to a time-series database. Compression algorithms are optimized for feature-based data, reducing storage space while maintaining accuracy. The backup system implements an off-site disaster recovery plan to prevent data loss.

[0106] The user interface design adheres to ergonomic principles. Risk status is displayed intuitively using color coding, and trend warning lines are set for important parameters. Operation controls differentiate between permission levels, and critical functions require double confirmation. A knowledge base is integrated into the system, providing solutions to common problems and troubleshooting guides.

[0107] Example 5: Establishment and Application Mechanism of the Thermodynamic Prediction Model. This prediction system adopts a multi-source heterogeneous data fusion architecture, integrating a real-time risk analysis module, a historical feature database, and a dynamic evolution model for collaborative operation. The input layer is configured with a dedicated data interface to receive three signals: a risk index stream output by the real-time risk analysis engine (sampling frequency 10Hz); historical core feature components provided by the feature management system, including three major indicators: temperature stability, pressure fluctuation, and energy absorption rate; and a four-dimensional tensor sequence generated by the dynamic evolution modeling system. All input data are strictly synchronized through a timestamp alignment mechanism, with time deviation controlled within 5 milliseconds.

[0108] The main structure of the prediction model implements a neural network architecture. The temporal feature extraction branch uses a deep bidirectional LSTM structure with four hidden layers, each containing 128 neurons, and a time window span of 500 milliseconds. This branch processes real-time risk value sequences and their historical trend changes, extracting evolution patterns over time. The static feature analysis branch uses a three-dimensional convolutional neural network with a kernel size of 3×3×2 and a stride of 1×1×1, extracting spatial correlation features through two convolutional layers. The dynamic evolution branch implements a graph neural network structure, transforming the four-dimensional tensor into an attribute graph structure: nodes represent state space units, and edges represent spatiotemporal adjacency relationships. A graph attention mechanism calculates the interaction weights between nodes, aggregating information from neighboring regions. The three branches use tensor connection operations in the fusion layer to integrate and form a joint feature representation space.

[0109] The model training phase employs a distributed data parallelism strategy. The training dataset contains over 2000 hours of manufacturing process records, divided into 80% training set, 15% validation set, and 5% test set based on time series. The optimization algorithm chosen is the AdamW variant with adaptive gradient clipping, with an initial learning rate of 0.001, decaying by 0.95 per training epoch. The loss function combination design includes: a weighted mean squared error criterion for thermodynamic state prediction, the Huber loss function for operation command generation, and L2 norm constraints for model regularization. The computing hardware configuration utilizes eight accelerator cards for parallel training, implementing a synchronous gradient update strategy during data sharding. An early stopping strategy is implemented during training, terminating training if the validation loss shows no improvement after 30 consecutive epochs.

[0110] The prediction output layer employs a dual-stream processing architecture. The state prediction stream outputs a field distribution tensor for future time series, with a temporal resolution of 10 milliseconds and a time span of 500 milliseconds. The spatial scope covers key processing areas, and the output tensor dimensions are designed as time step × X grid × Y grid × physical quantity (50 × 15 × 15 × 3). The physical quantity channels include temperature field correction values, pressure field compensation values, and energy field offset rates, with values ​​normalized to the [-1, 1] interval. The operation command stream contains four control variables: a continuous adjustment command for laser power adjustment within a ±50W range, with a resolution of 0.1W; a scanning speed change rate setting with a ±10% adjustment range and a step accuracy of 0.1%; a substrate preheating temperature correction value within a ±5℃ range, with a resolution of 0.1℃; and a protective gas flow rate adjustment range within a ±15% range, with an adjustment step size of 0.5%. All control commands are accompanied by confidence scores, calculated from the probability distribution of the model output.

[0111] The command transmission system implements an industrial-grade real-time communication protocol. Control signals are encapsulated into structured data frames and transmitted to the device controller via Gigabit Ethernet. The transmission protocol employs a triple-protection mechanism: data verification uses CRC32 cyclic redundancy check code, channel redundancy design includes dual-link hot backup transmission, and time-sensitive network scheduling strategy ensures timing. Control command execution records are returned to the prediction system in real time, forming a closed-loop feedback. When the execution deviation exceeds a preset threshold, a model self-calibration process is triggered, fine-tuning the model parameters through incremental learning. The self-calibration process is executed asynchronously in the background, without affecting the real-time prediction function.

[0112] The system employs a multi-level monitoring mechanism for runtime management. A resource monitor tracks model computation latency, controlling it to within 150 milliseconds throughout the entire process; a data quality inspection module detects input anomalies and discards sensor readings exceeding reasonable limits; and a sliding window standard deviation calculation is used for prediction result stability analysis, automatically switching to a backup model when fluctuations exceed limits. The system status panel displays key operational indicators such as computational load, memory usage, and communication latency in real time.

[0113] The deployment architecture employs a containerized microservice design. The prediction engine is encapsulated as an independent container, connected to data input and command output interfaces via a service mesh. A dynamic configuration center manages model parameters and alert thresholds, supporting non-downtime update strategies. A version control system records complete configuration parameters for each model iteration, enabling rollback of historical versions within seconds in case of failure. An automated testing pipeline performs smoke testing before each deployment to verify the integrity of core functionalities.

[0114] The security mechanism implements a multi-layered protection system. Operation command transmission is encrypted end-to-end with AES-256, access control employs role-based access control, and operation audit logs retain complete timestamps and operator identification tags. Critical control logic is implemented with hardware-level isolation, and an anomaly detection system monitors control command patterns, automatically intervening to protect against abnormal command sequences. An uninterruptible power supply (UPS) ensures persistent storage of critical status data.

[0115] The application interface provides multi-dimensional visualization tools. A 3D heatmap shows future state evolution trends, the control command panel displays current adjustment parameters, and historical prediction curves can be analyzed retrospectively. A diagnostic view marks areas with low confidence to assist human decision-making. The configuration interface allows authorized engineers to adjust the sensitivity of control parameters to adapt to different material processing characteristics. The knowledge base system integrates typical processing cases, providing analogical decision support. User operation trajectories are audited and tracked throughout the process, and key configuration changes require secondary authorization confirmation. The prediction system is deeply integrated with the manufacturing execution system, enabling linked adjustments between prediction results and production plans. Processing quality reports are automatically linked to prediction system records, establishing a complete process traceability chain.

[0116] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0117] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A real-time thermodynamic prediction method for SLM based on tensor computation and artificial intelligence, characterized in that, Includes the following steps: Collect historical thermodynamic data of the SLM manufacturing process within a preset time period, and construct a historical thermodynamic tensor based on the historical thermodynamic data; Tensor decomposition is performed on the historical thermodynamic tensor to separate the core feature components, and a dynamic evolution tensor is generated based on the evolution of the core feature components over time. A multidimensional thermodynamic state space is defined using a dynamic evolution tensor, and the degree of aggregation of historical anomalous events in the multidimensional thermodynamic state space is evaluated. A set of thermodynamic early warning indicators is selected based on the aggregation results. Real-time feature components are extracted from the real-time monitoring data of the SLM process to form a real-time state tensor. Tensor similarity measurement is performed with the thermodynamic early warning index set in the multidimensional thermodynamic state space to derive the real-time risk value. Based on real-time risk values, core feature components, and dynamic evolution tensors, a thermodynamic prediction model is established to output the thermodynamic state prediction results of the SLM process in real time and generate operation adjustment commands.

2. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 1, characterized in that, Historical thermodynamic data of the SLM manufacturing process within a preset time period are collected, and a historical thermodynamic tensor is constructed based on the historical thermodynamic data, specifically as follows: Acquire temperature, pressure, and laser energy parameters during the SLM manufacturing process within a preset time period; Outlier removal and standardization transformation of temperature, pressure, and laser energy parameters; The standardized temperature, pressure, and laser energy parameters are integrated into a three-dimensional array structure according to time series and spatial location. This three-dimensional array structure constitutes the historical thermodynamic tensor.

3. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 2, characterized in that, Perform tensor decomposition on the historical thermodynamic tensor to separate the core eigencomponents, specifically: A high-order singular value decomposition algorithm is used to process the historical thermodynamic tensor, which is decomposed into multiple core tensors. Representative feature elements are extracted from the core tensor, and these representative feature elements constitute the core feature components.

4. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 3, characterized in that, A dynamic evolution tensor is generated based on the evolution of core feature components over time, specifically as follows: Analyze the numerical changes of core feature components over continuous time intervals, calculate the gradient of change, and integrate the gradient sequence. Dynamic evolution tensors are formed based on changing gradient sequences.

5. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 4, characterized in that, The multidimensional thermodynamic state space is defined using the dynamic evolution tensor, specifically as follows: The coordinate axes of the multidimensional thermodynamic state space are set according to the number of dimensions of the dynamic evolution tensor. Each coordinate axis corresponds to a thermodynamic characteristic attribute, and the position in the multidimensional thermodynamic state space is determined by the characteristic attribute value.

6. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 5, characterized in that, The degree of aggregation of historical anomalous events in the multidimensional thermodynamic state space is assessed, specifically as follows: Locate the corresponding coordinate points of historical anomalous events in the multidimensional thermodynamic state space, measure the distribution density of the coordinate points, and use the distribution density value as the result of the degree of aggregation.

7. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 6, characterized in that, The set of thermodynamic early warning indicators is selected based on the aggregation degree results, specifically as follows: Set a clustering threshold, and filter out coordinate points whose clustering results exceed the clustering threshold. The feature attributes associated with these coordinate points constitute a set of thermodynamic early warning indicators.

8. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 7, characterized in that, Real-time feature components are extracted from the real-time monitoring data of the SLM process to form a real-time state tensor, specifically: Sensor readings during the SLM manufacturing process are captured in real time, converted into tensor format, feature dimensionality reduction is performed on the tensor format, and real-time feature components are output. The real-time feature components are combined into a real-time state tensor.

9. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 8, characterized in that, In a multidimensional thermodynamic state space, a tensor similarity measure is performed with the set of thermodynamic early warning indicators to derive the real-time risk value. Specifically: The real-time state tensor is projected onto a multidimensional thermodynamic state space. The tensor norm distance between the real-time state tensor and each point in the thermodynamic early warning index set is calculated. A similarity score is generated based on the tensor norm distance, and the similarity score is converted into a real-time risk value.

10. The SLM thermodynamic real-time prediction method based on tensor computation and artificial intelligence according to claim 9, characterized in that, A thermodynamic prediction model is established based on real-time risk values, core feature components, and dynamic evolution tensors, specifically as follows: The real-time risk value is integrated with the core feature components and used as the input to the thermodynamic prediction model; The thermodynamic prediction model is trained using a deep learning framework based on tensor computation, enabling the model to learn the dynamic evolution pattern of tensors. The thermodynamic prediction model outputs thermodynamic state prediction results, which are then mapped into operational adjustment commands.

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