Current Estimation Method Research Articles

A High-Bandwidth Current Estimator With Self Tunning for Digital Buck Controller

In order to solve the low-cost problem of high-speed current sampling in digital buck controllers, a current estimation method based on the direct current resistance (DCR) current detection principle is proposed in this paper. The inductor current including direct current (DC) and alternating current (AC) is obtained by performing high-frequency digital filtering on the voltage across the inductor ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_L</i> ). Quantitative analysis of various factors affecting the accuracy of current estimation is carried out. For improving the estimated current accuracy, the multi-phase interleaved clock sampling technique and the algorithm of the average duty cycle in the filter cycle are proposed to improve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_L</i> accuracy in each filter cycle. Meanwhile, considering the completeness of the current estimation algorithm, a calibration mechanism with a known current sink to adjust filter parameters online is adopted for the change of the inductance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ) and its equivalent impedance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i> ) due to process and aging. The proposed algorithm is verified in a buck prototyping board. Experimental results are presented to show that the proposed method is effective in both fixed frequency and variable frequency control modes. The DC and AC accuracy of estimated current reach 5% and 2%, respectively. The estimated inductor current delay is within 100 ns.

Applicability of deep learning optical flow estimation for PIV methods

Recently, there have been some attempts to introduce the method of deep learning-based optical flow(DL-based OF) into PIV measurements. These attempts have made it possible to estimate the flow field with higher accuracy and higher spatial resolution. The current mainstream deep-learning optical flow estimation method often requires a training set whose data distribution is closer to the real sample when completing the target task. However, there is a certain difference between the rigid body motion dataset commonly used in the field of computer vision and the fluid motion dataset in PIV measurements. Whether networks trained with rigid-body data can be directly applied to fluids has not been fully discussed. However, in existing attempts to introduce the DL-based OF method into the field of PIV measurement, the influence of the characteristics of the PIV particle image on the calculation results of the deep learning optical flow estimation (DL-based OF) has not been fully discussed. Therefore, the boundary conditions of the learning method for PIV calculation cannot be fully demonstrated. In this study, we selected the Flownet2 network, which is a classical baseline model on rigid body datasets, as a representative deep learning optical flow estimation method for experiments. Based on the characteristics of various particle images, this study generates a dataset with a wide range of parameters, such as particle density, particle diameter, sheet thickness, and maximum displacement, which are key to the generation of PIV simulation images and discusses the sensitivity of DL-based OF methods under extreme parameter conditions. This study compares (1) the model parameters trained using rigid body datasets such as Sintel, (2) the model parameters trained using synthetic PIV images, (3) the PIV-WIDIM method, and (4) the Optical Flow-Farneback method. The results reveal that the DL-based OF methods in (1) and (2) have a higher spatial resolution and estimation accuracy than the traditional methods in (3)] and (4). Training with the synthetic fluid dataset results in a smoother flow field in method (2)] compared with training with the rigid body dataset in method (1). In the case of limited training set parameters, Flownet2 can still be suitable for extreme conditions, such as small particle concentration, small particle diameter, insufficient particle brightness, or small particle displacement.

A Nonintrusive Digital Current Sensing Method for DC–DC Converters With Wide Load Range

Current estimators for dc-dc converters reduce the requirement of current transducers (e.g. sense resistor, Hall sensor) which may be either expensive, invasive, and (or) require additional signal conditioning circuits. High-frequency inductor currents within dc-dc converters can be estimated instantaneously using voltage measurements taken at its terminals. The voltage measurement at the switching terminal of the inductor is assisted by a comparator, whose output state is related to the corresponding voltage magnitude. This paper presents a novel unified current estimation method in which a single comparator is required to detect the switch node status both in continuous and discontinuous modes of operation. The other measurements required for this method include sensing dc voltage magnitudes, which are essential measurements for a regulated dc-dc converter system; hence the proposed methodology can be easily integrated into existing digital control schemes. The proposed approach has been applied to first-order dc-dc converters and has been validated using a laboratory prototype of a digitally controlled boost converter system using an FPGA.

Animal Movement Prediction based on the Corroboration of Object Detection and Pose Estimation

With the development of automated driving, driving safety has become a hot topic in the field of automated driving. However, the existing methods mainly define living objects as obstacle handling and mostly focus on the safety of pedestrians, thus ignoring the safety of animal movement in automatic driving. In this paper, we propose an animal movement prediction model with the corroboration of object detection and pose estimation, which aims, to help the autopilot perception system judge animal pose more accurately. First of all, we preprocess the datasets, use a Convolutional Neural Network based object detection method to detect animal images, and then use the current mainstream 2D animal pose estimation method to obtain the key points of animal images, and divide the resulting data set into three categories: running, walking and waiting. After preprocessing, we use Resnet and MLP models to classify the pose. For Resnet model, we will evaluate the accuracy of the model on the test set during training and compare the accuracy of the last model to determine the model with the highest training accuracy. The final model has achieved an accuracy of up to 75% for running evaluation. For MLP model, we tend to use the rank of 13 specific bone points’ angles as the standard of pose classification. Three types of test sets will be put into three trained MLPRegressor model for training to get the classification we want. Finally, the accuracy of all three poses is more than 80%. Finally, we choose the model with the highest accuracy as our classification method. This work is expected to apply animal pose estimation and animal and pose classification to automated driving to improve driving safety.

Multiparameter Estimation of IPMSMs Using Core Loss Current Calculations in dq-Axis Equivalent Circuit Model

Accurate parameter estimation is critical for high-performance modeling and control of interior permanent magnet synchronous machines (IPMSMs). Core loss effects affect the accuracy of the parameter estimation, especially in high loading conditions with saturated cores. Existing research on parameter estimation considering core loss effects generally focuses on the core loss equivalent resistance estimation; however, they require either accurate core loss experimental data or finite element analysis (FEA) model. The core loss equivalent resistance is dependent on the loading conditions, harmonics, frequency, and temperature, which increases the difficulty of accurately estimating the resistance. This article firstly proposes a direct core loss equivalent current estimation method for multiparameter estimation purposes without estimating the core loss equivalent resistance. Based on the estimated core loss equivalent currents, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis inductances equivalent currents are calculated to perform the multiparameter estimation. The proposed approach can improve the precision of the parameter estimation and the computation efficiency by calculating the core loss equivalent resistance currents without having the core loss data. The effectiveness of the proposed multiparameter estimation method is evaluated by comparing the calculated and measured torques of a laboratory 4.5 kW IPMSM in various operating conditions. The improved accuracy of the proposed method is verified by comparing it with two existing online parameter estimation methods and FEA-based offline parameter estimation results.

FineFDR: Fine-grained Taxonomy-specific False Discovery Rates Control in Metaproteomics.

Microbial community proteomics, also termed metaproteomics, investigates all proteins expressed by a microbiota. Tandem mass spectrometry (MS/MS) is the typical method for identifying proteins in metaproteomics, which involves searching the mass spectra against a protein sequence database. A major post-analysis step is controlling the false discovery rate (FDR), i.e., the ratio of false positives to the total number of annotations. The current popular target-decoy FDR estimation method treats all the peptides and proteins equally and overlooks that they could have varied probabilities of being identified. In this study, we report FineFDR, a framework for FDR assessment at fine-grained levels with taxonomy information considered. FineFDR groups the identified peptide-spectrum matches, peptides, and proteins from different taxonomic units and estimates the FDR in each group separately. Empirical experiments on the simulated and real-world data sets demonstrate that our FineFDR achieved higher precision and more peptide and protein identifications when compared to the state-of-the-art methods, such as Comet, Percolator, TIDD, and Tailor. FineFDR is freely available under the GNU GPL license at https://github.com/Biocomputing-Research-Group/FDR.

Online Short-Circuit Current Estimation of Permanent Magnet Motors

In this article, online short-circuit estimation of permanent magnet synchronous motors (PMSMs) are presented, which is essential for postfault ac drive operations. For this purpose, initially, the PMSM model with interturn short-circuit fault (ITSC) is extended to cover motors with saliency. By utilizing ITSC model voltage equations and voltage reference equations, the amplitude and phase relationship between short-circuit current and the phase reference voltage is established. In the next step, second harmonics in the reference voltage and feedback current are used to extract the short-circuit current information. In order to efficiently use ac drive microcontroller bandwidth, the proposed short-circuit current estimation method is executed after the ITSC fault is detected, not continuously. Instead of running the proposed short-circuit current estimation continuously, it is reasonable to run it after an ITSC fault detection to efficiently use ac drive microcontroller bandwidth. Therefore, two intermediate steps, a simple ITSC fault detection and severity estimation algorithms are proposed as well. The proposed technique can estimate the fault current and severity without the knowledge of fault location and valid for all PM motors. The findings are experimentally tested using two PMSMs to demonstrate the effectiveness and practicability of the proposed estimation technique.

Current estimation of switched reluctance motor based on piecewise model and iteration calculation

SummaryTo reduce the number of current sensors in the switched reluctance motor (SRM) system, a current estimation method of the SRM is proposed. There is only one current sensor needed to measure the sum of phase currents. Current estimation model consists of two equations, one is equation of the sum of phase currents and another is mechanical equation of the SRM. Torque, a variable in the mechanical equation, has complex nonlinear relation with phase currents. This makes it difficult to solve the current estimation model online. To deal with the problem, a piecewise modeling method is used to establish a simple analytical torque model. Accuracy of the established torque model is better than that of traditional torque models after comparisons. A parameter of speed and acceleration is defined to compensate errors of the torque model and avoid identifications of moment of inertia and friction coefficient. On the basis of features of the current estimation model and phase currents of the SRM, Newton's method is chosen to solve the current estimation model and a practical stop condition of iteration is given. Realization process of online computation is illustrated. Finally, the proposed current estimation method is validated by experiments.

Phase Current Reconstruction Method With an Improved Direct Torque Control of SRM Drive for Electric Transportation Applications

Acquisition of the accurate phase currents is indispensable for the control and protection of switched reluctance motor (SRM) drives for electric transportation applications. Existing phase current reconstruction techniques for SRM are implemented under the current control techniques, which generate large torque pulsations. Therefore, the direct torque control (DTC) method can be adopted to minimize torque pulsations and to enhance transient performance in electrified vehicles. However, the existing current estimation methods cannot be applied to DTC strategies due to the simultaneous conduction of all phases at any switching instant. Furthermore, it offers a lower torque per ampere ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T/A$</tex-math></inline-formula> ) ratio and draws a high source current. This article addresses the aforementioned concerns by proposing a cost-effective phase current reconstruction method with an improved DTC strategy for a 4-kW four-phase SRM drive. This method employs a 16-sector partition method with a new voltage vector selection by detecting zero-current regions of each phase. As a result, the long-tail currents can be avoided, thereby limiting the simultaneous conduction of all phases. The simulation and test results show that the proposed DTC has minimal torque pulsations, high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T/A$</tex-math></inline-formula> ratio, low converter losses, and lower source current ripple in comparison to the existing DTC schemes under various operating conditions. Also, the proposed phase current estimation method effectively reconstructs the phase currents under both steady-state and transient operating conditions.

Interaction force measurement of parallel robots based on structure-integrated force sensors using interpretable linear neural networks

The parallel robot in this research is mainly designed for the human-machine collaboration, which has two working modes: follow-up mode and pressing mode. In order to better realize these two functions, the measurement of the interaction force is mainly concerned. In the arrangement of the hardware, different from the six-dimensional force sensor method and current estimation method commonly used in industry, the structure-integrated force sensors (SIFS) measurement method is used. In the calculation method, a back propagation neural networks (BPNN) method is introduced to calculate the interaction force. Then, based on the prior knowledge of physics, a new interpretable linear neural networks (ILNN) method is proposed. The details of the ILNN algorithm and its differences from the classic neural network methods are given. Finally, the experimental results of the direct Newton–Euler method, the least square method, the BPNN method, and the ILNN method are compared. Experimental results show that the inference accuracy of the ILNN method is slightly better than the direct Newton–Euler method and the least square method, and its generalization ability is much better than the BPNN method. The use of the ILNN method based on the FIFS arrangement makes the measurement of the interaction force more accurate and reliable.

A branch current estimation and correction method for a parallel connected battery system based on dual BP neural networks

In the actual use of a parallel battery pack in electric vehicles (EVs), current distribution in each branch will be different due to inconsistence characteristics of each battery cell. If the branch current is approximately calculated by the total current of the battery pack divided by the number of the parallel branches, there will be a large error between the calculated branch current and the real branch current. Adding current sensors to measure each branch current is not practical because of the high cost. Accurate estimation of branch currents can give a safety warning in time when the parallel batteries of EVs are seriously inconsistent. This paper puts forward a method to estimate and correct branch currents based on dual back propagation (BP) neural networks. In the proposed method, one BP neural network is used to estimate branch currents, the other BP neural network is used to reduce the estimation error cause by current pulse excitations. Furthermore, this paper makes discussions on the selection of the best inputs for the dual BP neural networks and the adaptability of the method for different battery capacity and resistence differences. The effectiveness of the proposed method is verified by multiple dynamic conditions of two cells connected in parallel.

A Novel Field Current Estimation Method for Brushless Wound-Field Synchronous Machine

Compared with other electric machines, wound-field synchronous machines (WFSMs) have the advantage of having three control variables (stator <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis currents and rotor current). Determining the optimum combination of field and armature currents is necessary for ensuring the high-performance control of the WFSM. Two methods are usually employed to supply the field winding of the WFSM. The first one uses brushes and slip rings, while the second one uses a brushless excitation system. Concerning the WFSM with a brushless excitation system, a dc field current is provided by a rotating diode bridge rectifier fed by an exciter machine. Therefore, direct measurement of the field current is not possible. As a solution, field current needs to be accurately estimated. Previously, field current estimation methods proposed in the literature have been based on modeling the brushless exciter machine and the rotating rectifier. Using the brushless exciter machine model, these methods estimate electric quantities of the exciter rotor (currents and voltages); then, through the rotating rectifier model, the rectified field current is estimated. Accordingly, any inaccuracy in the models leads to estimation errors. The effectiveness of the techniques relying on the brushless excitation system model is not clearly justified, especially because the nonlinearity of the brushless system has been intensified by the existence of the rotating uncontrolled diode bridge rectifier. This article proposes an accurate online field current estimation method for WFSMs without the need neither to estimate exciter rotor voltages or currents nor to use a rotating rectifier model. The accuracy and effectiveness of the proposed field current estimation method are demonstrated by experimental validation tests.

Calculating economical impact by standard chemical exergy value and environmental impact by life cycle assessment method for desulfurization from Elbistan Lignite with leaching process (H2O2/H2SO4)

In this context, this study aims to reduce the harmful effects of coal combustion and to investigate the possibility of efficient use of Turkish lignite with high sulfur content. In this study, peroxide leaching process and accounts for approximately 35% of lignite reserves in Turkey total sulfur content of the garment was removed from lignite. For this purpose, the effect of H2O2 on 5%, 10%, 20%, and 30% solutions and H2SO4 on the sulfur removal using 0.05 N, 0.1 N, 0.15 N, and 0.2 N solutions separately and together were investigated. According to the results, increasing the H2O2 concentration from 5% to 30%, the total sulfur content of the coal sample was removed by approximately 75%. When 0.1 N H2SO4 and H2O2 were used together, about 93% of sulfur removal was realized. The originality of the study is that scenario 8 of 12 situations is both high standard chemical exergy value used for economic analysis, low CO2 emission value determined according to the life cycle assessment method used for environmental impact assessment, and 20-year operating cost calculated by current value estimation method. The lowest value indicates that 20% of H2SO4 is suitable for the establishment of the desulphurization plant with a yield of 63.2% from 200 kg of coal per hour. The highest exergy efficiency value was calculated as 8,01782E-06 for the 8th scenario. So the 8th scenario should be applied for the establishment of a desulfurization plant for E.L. Due to the results, this study is an economical method of sulfur removal. The addition of H2SO4 to H2O2 has a synergistic effect on sulfur removal. In this study, a new perspective has been developed by using exergy calculation and life cycle methods apart from conventional methods while determining the economy.

A simple rotor current estimation method for predictive control of multi‐phase drives

SummaryPredictive control of stator currents is a model‐based technique needing an estimation of rotor currents, which are normally not measured. These currents affect the evolution of the stator currents and, therefore, also affect the predictions used by the controller. The usual procedure consists in correcting their effect by a simple feedback technique. In this article, the estimation of rotor currents is tackled based in the induction machine equivalent circuit. The proposed estimation procedure aims at improving the predictions with respect to the usual procedure. Simulation and experimental results are provided for the particularly demanding case of a multi‐phase induction machine, showing the superiority of the proposal.

Automated 3D Segmentation of the Aorta and Pulmonary Artery on Non-Contrast-Enhanced Chest Computed Tomography Images in Lung Cancer Patients

Pulmonary hypertension should be preoperatively evaluated for optimal surgical planning to reduce surgical risk in lung cancer patients. Preoperative measurement of vascular diameter in computed tomography (CT) images is a noninvasive prediction method for pulmonary hypertension. However, the current estimation method, 2D manual arterial diameter measurement, may yield inaccurate results owing to low tissue contrast in non-contrast-enhanced CT (NECT). Furthermore, it provides an incomplete evaluation by measuring only the diameter of the arteries rather than the volume. To provide a more complete and accurate estimation, this study proposed a novel two-stage deep learning (DL) model for 3D aortic and pulmonary artery segmentation in NECT. In the first stage, a DL model was constructed to enhance the contrast of NECT; in the second stage, two DL models then applied the enhanced images for aorta and pulmonary artery segmentation. Overall, 179 patients were divided into contrast enhancement model (n = 59), segmentation model (n = 120), and testing (n = 20) groups. The performance of the proposed model was evaluated using Dice similarity coefficient (DSC). The proposed model could achieve 0.97 ± 0.66 and 0.93 ± 0.16 DSC for aortic and pulmonary artery segmentation, respectively. The proposed model may provide 3D diameter information of the arteries before surgery, facilitating the estimation of pulmonary hypertension and supporting preoperative surgical method selection based on the predicted surgical risks.

A Current Sharing State Estimation Method of Redundant Switched-Mode Power Supply Based on LSTM Neural Network

Redundant Switched-mode Power supplies (SMPSs) are commonly used to improve electronic systems’ reliability, and accurate estimation of the current sharing state is significant for evaluating the system’s health. Currently, the current sharing state estimation is mainly realized by using current sensors to detect each branch’s current, and the deployment and maintenance costs are high. In this paper, a method for power supply current sharing state estimation based on LSTM recurrent neural network is proposed. By taking advantage of subtle differences in the inherent spectral characteristics of SMPSs, this method only needs to detect the voltage ripple at the switching frequency of the load terminal to estimate the output current of each power supply branch. The verification experiment on the three-power redundant experimental platform shows that the estimation error is less than 10%. The method has the characteristics of simple structure, non-invasion, convenient deployment and maintenance, so it has high application and promotion value.

A model based balancing system for battery energy storage systems

Battery balancing is considered as one of the most promising solutions for the inconsistency problem of a series-connected battery energy storage system. The passive balancing method (PBM) is widely used since it is low-cost and low-complexity. However, the PBM normally suffers low-power problems, and the balancing speed is usually unsatisfactory. To solve these problems, a model based balancing system (MBBS) is proposed in this paper. A variable and controllable balancing current can be applied to the battery cells with the MBBS. The balancing current can be much higher than the traditional PBM and most active balancing methods. Additionally, the cost of the main circuits of such an MBBS is lower than that of the traditional PBM. The model based balancing current estimation method is proposed to eliminate the balancing current sensors, further reducing system cost. The experimental platform is established, and the proposed MBBS is experimentally verified. The experimental results show that the maximum balancing current of the MBBS can be as large as 10 A, compared to typically 0.1 A for the traditional PBM. Meanwhile, for the 10 A balancing current requirement, the cost of the main circuits of the proposed MBBS is dramatically reduced compared to that of the traditional PBMs, not to mention the active balancing methods.

Secondary Side Voltage and Current Estimation of Wireless Power Transfer Systems

This article presents a secondary side voltage and current estimation method in the wireless power transfer (WPT) systems on the basis of load parameter identification. In the application of limited space and weight, it is difficult to arrange sensors to monitor the high-frequency voltages and currents in the WPT secondary side. Compared with the conventional methods, joint estimation of several secondary side voltages and currents is achieved in this article to monitor WPT electrical stress, based on only the RMS value of one primary side measured voltage. First, an equivalent circuit model of the WPT system with the dual-side <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCC</i> compensation networks and rectifier load is established. Then, T-type equivalent circuit of the coils and compensation capacitors is adopted to simplify the model. Moreover, the relationship between the RMS value of the primary side measured voltage and system equivalent load resistance is obtained and simplified for the load parameter identification. Furthermore, the secondary side voltage and current estimation method are proposed based on the identified system equivalent load resistance. Finally, a WPT prototype is developed and the experimental results indicate that the proposed method can achieve high estimation accuracy under the conditions of battery load voltage change, inverter phase-shift angle variation, and coil misalignment.

Fault Current and Voltage Estimation Method in Symmetrical Monopolar MMC-based DC Grids

Symmetrical monopolar configuration is the prevailing scheme configuration for modular multilevel converter based high-voltage direct current (MMC-HVDC) links, in which severe DC overvoltage or overcurrent can be caused by the DC faults. To deal with the possible asymmetry in the DC faults and the coupling effects of the DC lines, this paper analyzes the DC fault characteristics based on the phase-mode transformation. First, the DC grid is decomposed into the common-mode and the differential-mode networks. The equivalent models of the MMCs and DC lines in the two networks are derived, respectively. Then, based on the state matrices, a unified numerical calculation method for the fault voltages and currents at the DC side is proposed. Compared with the time-domain simulations performed on PSCAD/EMTDC, the accuracy of the proposed method is validated. Last, the system parameter analysis shows that the grounding parameters play an important role in reducing the severity of the pole-to-ground faults, whereas the coupling effects of the DC lines should be considered when calculating the DC fault currents associated with the pole-to-pole faults.

Nonscalability of Fractal Dimension to Quantify Canopy Structural Complexity from Individual Trees to Forest Stands

Canopy structural complexity is a critical emergent forest attribute, and light detection and ranging (lidar)-based fractal dimension has been recognized as its powerful measure at the individual tree level. However, the current lidar-based estimation method is highly sensitive to data characteristics, and its scalability from individual trees to forest stands remains unclear. This study proposed an improved method to estimate fractal dimension from lidar data by considering Shannon entropy, and evaluated its scalability from individual trees to forest stands through mathematical derivations. Moreover, a total of 280 forest stand scenes simulated from the terrestrial lidar data of 115 trees spanning large variability in canopy structural complexity were used to evaluate the robustness of the proposed method and the scalability of fractal dimension. The results show that the proposed method can significantly improve the robustness of lidar-derived fractal dimensions. Both mathematical derivations and experimental analyses demonstrate that the fractal dimension of a forest stand is equal to that of the tree with the largest fractal dimension in it, manifesting its nonscalability from individual trees to forest stands. The nonscalability of fractal dimension reveals its limited capability in canopy structural complexity quantification and indicates that the power-law scaling theory of a forest stand underlying fractal geometry is determined by its dominant tree instead of the entire community. Nevertheless, we believe that fractal dimension is still a useful indicator of canopy structural complexity at the individual tree level and might be used along with other stand-level indexes to reflect the “tree-to-stand” correlation of canopy structural complexity.