To minimize omission and commission errors due to the lack of adequate utilization of forest structure information, this paper presents a tree delineation approach by combining trunk detection with canopy segmentation. First, all potential tree trunk points are detected and detached from leaf-off data by analyzing the points’ vertical histogram, and the obtained points are then clustered using the method based on DBSCAN (Density-Based Spatial Clustering of Application with Noise). Meanwhile, the canopy-based segmentation is implemented using leaf-on data within the same plot. The detected trunks and delineated crown segments are then combined using the matching rules. Finally, single trees are isolated from point clouds, and tree-level structure information is estimated. The novelty of this approach lies in that the trunk detection results and the canopy segmentation results serve as mutual references for final individual tree delineation. Experimental results in a canopy-closed deciduous natural forest show that the presented method can identify 84.0% of trees, 90.7% of the identified trees are correct, and the total segmentation accuracy is 87.2%. The determination coefficient R2 of tree height is 0.96, and the mean difference of tree position is 76 cm. The results imply that the presented approach has good potential for isolating single trees from airborne LiDAR point clouds and estimating tree-level structural parameters in deciduous forests.

The development of new approaches to tree-level parameter extraction for forest resource inventory and management is an important area of ongoing research, which puts forward high requirements for the capabilities of single-tree segmentation and detection methods. Conventional methods implement segmenting routine with same resolution threshold for overstory and understory, ignoring that their lidar point densities are different, which leads to over-segmentation of the understory trees. To improve the segmentation accuracy of understory trees, this paper presents a multi-threshold segmentation approach for tree-level parameter extraction using small-footprint airborne LiDAR (Light Detection And Ranging) data. First, the point clouds are pre-processed and encoded to canopy layers according to the lidar return number, and multi-threshold segmentation using DSM-based (Digital Surface Model) method is implemented for each layer; tree segments are then combined across layers by merging criteria. Finally, individual trees are delineated, and tree parameters are extracted. The novelty of this method lies in its application of multi-resolution threshold segmentation strategy according to the variation of LiDAR point density in different canopy layers. We applied this approach to 271 permanent sample plots of the University of Kentucky’s Robinson Forest, a deciduous canopy-closed forest with complex terrain and vegetation conditions. Experimental results show that a combination of multi-resolution threshold segmentation based on stratification and cross-layer tree segments merging method can provide a significant performance improvement in individual tree-level forest measurement. Compared with DSM-based method, the proposed multi-threshold segmentation approach strongly improved the average detection rate (from 52.3% to 73.4%) and average overall accuracy (from 65.2% to 76.9%) for understory trees. The overall accuracy increased from 75.1% to 82.6% for all trees, with an increase of the coefficient of determination R² by 20 percentage points. The improvement of tree detection method brings the estimation of structural parameters for single trees up to an accuracy level: For tree height, R² increased by 5.0 percentage points from 90% to 95%; and for tree location, the mean difference decreased by 23 cm from 105 cm to 82 cm.

This paper proposes a convex optimization digital twin (CODT) framework for fault diagnosis of intelligent manufacturing equipment, aiming to address the limitations of insufficient labeled samples, poor model interpretability, and low environmental adaptability in traditional data‐driven diagnostic methods. The CODT method integrates convex optimization into a digital twin architecture to realize collaborative data fusion, physical constraint modeling, and adaptive decision‐making. Multisource virtual–physical data are fused to construct high‐dimensional fault features, and the fault diagnosis task is formulated as a constrained convex optimization problem. By combining cross‐entropy loss with L ₂ regularization and adopting a hybrid interior‐point–gradient descent algorithm, globally optimal diagnostic solutions are obtained through dynamic virtual model updating. Experimental results on industrial gearbox datasets validate the performance of the proposed CODT framework. The method achieves a diagnostic accuracy of 98.5% and an F1 score of 98.2%, enabling early fault warning up to 50 time steps ahead. Comparative experiments with SVM, random forest, KNN, and GMM demonstrate that CODT provides more stable diagnostic confidence and lower detection latency. Robustness tests under noisy interference, cross‐device scenarios, and complex operating conditions confirm the framework’s favorable generalization ability. Specifically, the accuracy degradation is only 2.5% under high‐intensity noise, and the cross‐scene accuracy fluctuation remains within 1%. Despite higher training overhead caused by convex optimization iterations and virtual–physical mapping, CODT improves diagnostic stability, interpretability, and proactive warning capability, offering a practical solution for industrial equipment health monitoring.