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At least 181 records · Page 10

Transfer learning for probabilistic localization of hidden cracks in concrete structures

Abstract The utility of discriminative supervised learning models built using multiple training-data sources is investigated for hidden crack localization in concrete. Feed-forward neural network (FFNN) is chosen as the model architecture, and transfer learning is used to assimilate the information obtained from different sources (computational physics simulations and laboratory experiments). The labeled training data consists of values of a damage index and the known locations of hidden cracks. The classification models need to learn how the presence of damage (hidden cracks) affects the damage index at different sensors for different test conditions. To this end, diagnostic FFNN models are built by sequentially adding and training new hidden layers to assimilate labeled information from computer models (different model geometries, test conditions, crack lengths, crack locations) and laboratory experiments on a plain cement slab. These transfer learning-based models are then used to localize damage in concrete specimens that reflect real-world conditions (i.e., specimens with steel reinforcement and randomly distributed aggregate). The actual damage state in these specimens is determined by extracting cores and performing petrographic studies on the extracted cores. The damage probability estimated by transfer learning-based models is compared with the petrographic damage rating index (DRI) to identify the most suitable approach to train the diagnostic models. The transfer learning-based diagnostic methodology shows promise and could be used in various structural health monitoring applications, where sufficient labeled data are typically not available from a single data source.

Miele, S.↗

Distributed strain sensing using Bi-metallic coated fiber optic sensors embedded in stainless steel

Silica fiber optic sensors are resistant to corrosive environments and high temperatures, making them attractive candidates for harsh conditions found in nuclear and aerospace industries. Moreover, fibers can be deployed remotely for continuous measuring of spatially distributed temperatures and strains. Here, this study investigated embedding a Ni/Cu bi-metallic coated fiber in a stainless-steel 316 (SS316) matrix using laser powder bed fusion towards functionalizing metal components for site-specific health monitoring. The embedded fiber was continuously interrogated during controlled heating to 1000°C. The measured fiber strains were similar to the expected differential thermal strains between the fiber and the SS316 matrix, until divergent behavior was observed at temperatures >500°C. No debonding at the matrix–coating–fiber interfaces was observed during microscopy, but significant interactions between the coatings and matrix resulted in diffusion-driven chemistry variations and Kirkendall void formation. Applying the strain-lag theory revealed plastic behavior in the Ni coating at temperatures >500°C, limiting the strain transfer to the fiber at higher temperatures. It was estimated that the elastic modulus in the Ni coating had decreased from ~200 GPa at room temperature to below 40 GPa, starting at 600°C. The low elastic modulus above 600°C is within the margin of what the tangent modulus would be in the case of bilinear isotropic hardening. Regardless of the divergent strain transfer at higher temperatures, the fiber was exposed to the equivalent of 1.9 % engineering strain at 1000°C, but measured only a 0.7 % engineering strain due to the poor strain transfer. Although compensating for the plastic behavior of Ni proved challenging, the bonding of a brittle silica fiber to a metal matrix surviving to 1000°C invites potential iterations on coating material for future application. For example, the embedded fiber is sufficient for acoustic energy transfer, realizing high temperature distributed acoustic sensing.

36 MATERIALS SCIENCE↗

A surrogate-model-based approach for estimating the first and second-order moments of offshore wind power

Power curve, the functional relationship that governs the process of converting a set of weather variables experienced by a wind turbine into electric power, is widely used in the wind industry to estimate power output for planning and operational purposes. Existing methods for power curve estimation have three main limitations: (i) they mostly rely on wind speed as the sole input, thus ignoring the secondary, yet possibly significant effects of other environmental factors, (ii) they largely overlook the complex marine environment in which offshore turbines operate, potentially compromising their value in offshore wind energy applications, and (ii) they solely focus on the first-order properties of wind power, with little (or null) information about the variation around the mean behavior, which is important for ensuring reliable grid integration, asset health monitoring, and energy storage, among others. In light of that, this study investigates the impact of several wind-and wave-related factors on offshore wind power variability, with the ultimate goal of accurately predicting its first two moments. Further, our approach couples OpenFAST—a multi-physics wind turbine simulator—with Gaussian Process (GP) regression to reveal the underlying relationships governing offshore weather-to-power conversion. We first find that a multi-input power curve which captures the combined impact of wind speed, direction, and air density, can provide double-digit improvements, in terms of prediction accuracy, relative to univariate methods which rely on wind speed as the sole explanatory variable (e.g. the standard method of bins). Wave-related variables are found not important for predicting the average power output, but interestingly, appear to be extremely relevant in describing the fluctuation of the offshore power around its mean. Tested on real-world data collected at the New York/New Jersey bight, our proposed multi-input models demonstrate a high explanatory power in predicting the first two moments of offshore wind generation, testifying their potential value to the offshore wind industry.

17 WIND ENERGY↗

Effects of fiber dosage, loading orientation and stress on frequency response of enhanced Carbon Nano-Fiber Aggregates

Nanomaterial additives have been broadly used in cement and concrete-based sensors to measure the stress and strain in the structure. Most of the studies focused on measuring the resistivity of sensors with Direct Current (DC) or relatively low-frequency. Here in this work, the impedance responses of enhanced Carbon Nano-Fiber Aggregates (CNFAs) at different frequencies are rigorously studied and utilized as a tool for real-time structural health monitoring (SHM). The CNFA impedance measurements at different measurement frequencies provide an extra dimension (frequency dimension) to allow the characterization of different phenomena and multimodal measurements simultaneously. First, a comprehensive physical model is established to understand the frequency responses of the CNFA impedance. Second, COMSOL Multiphysics is used to simulate the frequency responses of the CNFA impedance, which provides more insights into the electric field and current density distribution. The impedance of CNFAs decreased with the increased dosage of carbon nanofibers (CNFs). Third, experimental studies are reported in detail. The electrical impedance variation (EZV) of the CNFA in parallel orientation is 151% higher than that of perpendicular orientation at the frequency of 2612 Hz and uniaxial compression stress of 4.65 MPa. The strain-EZV curve obtained from the response spectrum is linear for frequencies ranging from 98 Hz to 463.9 kHz. The strain-EZV curve for 5625 Hz has a linear fit with the gauge factor of 147.78. At 1000 Hz, the CNFA exhibited a repeatable behavior up to 9.35 MPa and detection limit up to the stress of 18.62 MPa.

36 MATERIALS SCIENCE↗

Deep neural operators can predict the real-time response of floating offshore structures under irregular waves

The use of neural operators in a digital twin model of an offshore floating structure holds the potential for a significant shift in the prediction of structural responses and health monitoring, offering valuable real-time control insights. In this work, we investigate the effectiveness of three neural operators, namely the deep operator network (DeepONet), the Fourier neural operator (FNO), and the Wavelet neural operator (WNO), to accurately capture the responses of a floating structure under six different sea state codes (3 − 8) based on the wave characteristics described by the World Meteorological Organization (WMO). To further enhance the accuracy of the vanilla architecture of the neural operators, novel extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed in this paper. The results demonstrate that these high-precision neural operators can deliver structural responses more efficiently, up to two orders of magnitude faster than a dynamic analysis using conventional numerical solvers. Additionally, compared to gated recurrent units (GRUs), a commonly used recurrent neural network for time-series estimation, neural operators are both more accurate and efficient, especially in situations with limited data availability. Taken together, our study shows that FNO outperforms all other operators for approximating the mapping of one input functional space to the output space as well as for responses that have small bandwidth of the frequency spectrum. Conversely, DeepONet, with historical states, proves most accurate in learning the mapping of multiple input functions to the output space and capturing responses within a broad frequency spectrum.

97 MATHEMATICS AND COMPUTING↗

Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system

Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.

42 ENGINEERING↗

Implantable photoelectronic charging (I-PEC) for medical implants

Medical implants with functionalities such as sensing, health monitoring, stimulation, diagnosis, and physiological treatment are rapidly growing. With the increasing functional sophistication and addition of modules such as data transmission, on-chip processing, and data storage, energy demand of the implantable system is also growing. Using implantable energy harvester either to recharge or ultimately replace hazardous battery is essential to provide a long-term sustainable solution. Furthermore, energy harvesting techniques using piezoelectric, thermoelectric, radio frequency power transmission, biofuel, and photoelectronic (or sometimes termed as “photovoltaic” in terms of solar light harvesting, i.e., PV) conversion, have been attempted for the implantable, but these methods are currently limited by insufficient power output, large footprint, and low efficiency. Nevertheless, the planar PV with potential of lighter weight, higher energy density, and higher efficiency, provides promising power solution for in-body medical implants. In this short review, we will discuss the potential opportunities and challenges associated with PV's for medical implants, covering materials, to devices, and to system level requirements.

60 APPLIED LIFE SCIENCES↗

Post-hazard condition assessment of nuclear piping-equipment systems: Novel approach to feature extraction and deep learning

Over the past decade, the use of artificial intelligence techniques in the field of health-monitoring has gained significant interest, especially for structures such as building and bridges. However, applications to industrial systems such as equipment-piping systems in nuclear plants have not been explored. Here, in this paper, it is shown that the existing techniques developed for buildings and bridges cannot be extended directly to equipment-piping systems as the response of such systems is governed by multiple localized modes unlike that in buildings and bridges. This paper proposes a new approach that consists of three key aspects: (i) a novel vector of degradation-sensitive features extracted from measured data, (ii) using a deep Artificial Neural Network (ANN) for diagnosis of degradation location and degradation severity, and (iii) consideration of uncertainty in degradation severity when training the ANN. Degradation in piping-equipment systems can occur due to flow-accelerated erosion and corrosion. These locations can potentially exhibit damage such as localized yielding or initiation of cracking due to an external event such as an earthquake. Moreover, such locations can at times go undetected by current inspection techniques. Therefore, a robust framework is needed for detection of degradation after a seismic event. This manuscript proposes a proof-of-concept framework, which utilizes data collected from sensors to generate a deep ANN database for predicting degraded locations and severity in a piping-equipment system. Degradation severity is classified as minor, moderate, and severe. In the suggested methodology, a novel vector of degradation-sensitive features is extracted from the sensor data to train the ANN. A simple piping-equipment system is selected to demonstrate feature extraction as a means to simplify pattern recognition, explore the design and parameters of an ANN, and develop a sensor placement strategy. The effectiveness of the proposed framework is demonstrated on a realistic primary safety system of a two-loop nuclear reactor. It is shown that the proposed post-hazard condition assessment framework is able to detect degraded locations along with the severity levels, including minor degradation, with considerably higher accuracy.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Electrochemo-mechanics unlocks hidden dynamics of lithium plating under stacking pressure

Understanding and mitigating lithium plating remains one of the most pressing challenges in advancing the safety and longevity of lithium-ion batteries (LIBs). Here, we present a novel integrative framework that combines in-operando swelling force measurements with a physics-based electro-chemo-mechanical model to uncover previously inaccessible insights into lithium plating dynamics under mechanical constraints. Unlike existing approaches that focus primarily on electrochemical signatures, our approach captures the coupled mechanical responses of commercial pouch cells during cycling, revealing how mechanical constraints fundamentally alter degradation pathways. We demonstrate that the use of a moderate stacking pressure suppresses lithium plating and enhances lithium stripping. This mechanically driven structural effect, coupled with the electrochemical process, significantly extends the linear aging regime in LIBs. Intriguingly, intermittent capacity recovery events that were observed during the battery cycling suggest dynamic lithium reactivation, a phenomenon rarely captured in real-time. This study pioneers a stress-aware methodology for diagnosing and managing lithium plating, establishing a new paradigm for real-time battery health monitoring. The findings offer transformative implications for the design of durable, high-performance LIB systems, opening new avenues for intelligent control strategies in battery management systems.

Bhowmick, Amit↗

Multi-fidelity physics-informed machine learning for probabilistic damage diagnosis

Machine learning (ML) models are gaining popularity in structural health monitoring (SHM) because of their ability to learn the complex relationship between damage and sensor data. However, the lack of sufficient experimental data for structures with different degrees of damage is a key problem in training ML models for SHM. This problem can be alleviated by using physics-based models to generate the required training data to build physics-informed ML (PIML) models for SHM. However, it takes significant computational effort to perform enough high-fidelity simulations of the diagnostic test. It is thus desirable to know whether the available computational resource budget should be expended on numerous low-fidelity physics simulations, or a small number of high-fidelity simulations, or their combination. In this paper, we investigate this aspect of generating adequate training data for PIML, by constructing multi-fidelity PIML models. We evaluate the performance of several PIML models, trained with different amounts of low-fidelity and high-fidelity data, in locating hidden cracks in concrete structures using a nonlinear dynamics-based diagnosis technique. Here, we find that high-fidelity physics simulations that do not cover the (test and damage) parameter space do not improve the performance of diagnostic PIML models built using data from many low-fidelity physics simulations.

42 ENGINEERING↗

3D Printed Parahydrophobic Surfaces as Multireaction Platforms

We report Parahydrophobic surfaces (PHSs) composed of arrays of cubic μ-pillars with a double scale of roughness and variable wettability were systematically obtained in one step and a widely accessible stereolithographic Formlabs 3D printer. The wettability control was achieved by combining the geometrical parameters (H = height and P = pitch) and the surface modification with fluoroalkyl silane compounds. Homogeneous distribution of F and Si atoms onto the pillars was observed by XPS and SEM-EDAX. A nano-roughness on the heads of the pillars was achieved without any post-treatment. The smallest P values lead to surfaces with static contact angles (CAs) >150° regardless of the H utilized. Interestingly, the relationship 0.6 ≤ H/P ≤ 2.6 obtained here was in good agreement with the H/P values reported for nano- and submicron pillars. Furthermore, experimental CAs, advancing and receding CAs, were consistent with the theoretical prediction from the Cassie–Baxter model. Structures covered with perfluorodecyltriethoxysilane with high H and short P lead to PHSs. Conversely, structures covered with perfluorodecyltrimethoxysilane exhibited a superhydrophobic behavior. Finally, several aqueous reactions, such as precipitation, coordination complex, and nanoparticle synthesis, were carried out by placing the reactive agents as microdroplets on the parahydrophobic pillars, demonstrating the potential application as chemical multi-reaction array platforms for a large variety of relevant fields in microdroplet manipulation, microfluidics systems, and health monitoring, among others.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Size and Structural Control of Mechanoluminescent ZnS:Mn 2+ Nanocrystals for Optogenetic Neuromodulation

Mechanoluminescent materials hold immense potential for various transformative applications, from medical imaging and diagnostics to health monitoring and wearable displays. Conventionally produced as bulk powders or microparticles, they face significant size limitations for advanced applications, particularly in biological systems and microscale devices. Here, this work presents an approach to ZnS:Mn 2+ nanocrystal synthesis that involves self-assembly and subsequent calcination. In addition to effective size control within the nanoscale, this approach promotes the formation of abundant stacking faults, significantly enhancing piezoelectric and mechanoluminescent properties by increasing trap density and reducing trap depth. Unlike mechanoluminescent materials produced using conventional methods, these nanocrystals demonstrate strong mechanoluminescence without requiring UV pre-excitation, and the light emission persists even after mechanical stress is removed. These advantageous properties make them promising candidates for optogenetic neuromodulation, as they can effectively trigger electrical signals in neurons upon ultrasound stimulation both with and without UV pre-excitation. The persistent mechanoluminescence prolongs the duration of neuronal electrical activity, providing an extended temporal window for neuromodulation compared to conventional mechanoluminescent materials. This study provides a scalable method for producing efficient mechanoluminescent nanoparticles and reveals the crucial role of particle size and defect structures in determining their mechanoluminescent behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advanced Microstructured BaTiO 3 -Embedded PVDF–HFP/PEO Film for Enhanced Triboelectric Interface in Self-Sufficient Energy Generation and Sensing

The global reliance on fossil fuels and natural gas has largely dominated the energy production field, but due to finite resource depletion and escalating greenhouse gas emissions, the immediate exploration of sustainable energy alternatives to mitigate climate change and ensure resource security has been a major concern. There has been extensive research into other more renewable methods of energy production, such as wind and hydropower. Of these current energy generation types, there are many areas of untapped potential from the mechanical movements generated ambiently not only in the large scale of power generation but also on a smaller scale. The piezoelectric and triboelectric effects are phenomena where these ambient mechanical movements can generate electrical energy. Developing a hybrid system that leverages both mechanical stress and surface charges presents an ideal opportunity to exploit these untapped energy sources. Producing a hybrid PVDF–HFP/PEO film with perovskite BaTiO 3 (BTO) enables ambient power harvesting from both mechanical movement and surface charge. The optimized cell produced a potential of up to 15 V and a current of 200 nA with a 68 kΩ resistor, a substantial increase from a base system with an average of 2.1 V and 40 nA. These hybrid TENGs offer significant potential for energy harvesting in small-scale applications, such as health monitoring devices and indicators in electric circuits.

Ybarra, Rigobert [University of Texas Rio Grande V↗

Aerosol jet printed capacitive strain gauge for soft structural materials

Soft structural textiles, or softgoods, are used within the space industry for inflatable habitats, parachutes and decelerator systems. Evaluating the safety and structural integrity of these systems occurs through structural health monitoring systems (SHM), which integrate non-invasive/non-destructive testing methods to detect, diagnose, and locate damage. Strain/load monitoring of these systems is limited while utilizing traditional strain gauges as these gauges are typically stiff, operate at low temperatures, and fail when subjected to high strain that is a result of high loading classifying them as unsuitable for SHM of soft structural textiles. For this work, a capacitance based strain gauge (CSG) was fabricated via aerosol jet printing (AJP) using silver nanoparticle ink on a flexible polymer substrate. Printed strain gauges were then compared to a commercially available high elongation resistance-based strain gauge (HE-RSG) for their ability to monitor strained Kevlar straps having a 26.7?kN (6?klbf) load. Dynamic, static and cyclic loads were used to characterize both types of strain monitoring devices. Printed CSGs demonstrated superior performance for high elongation strain measurements when compared to commonly used HE-RSGs, and were observed to operate with a gauge factor of 5.2 when the electrode arrangement was perpendicular to the direction of strain.

36 MATERIALS SCIENCE↗

Hybrid epoxy–acrylate resins for wavelength-selective multimaterial 3D printing

Structures in nature have evolved to combine hard and soft materials in precise 3D arrangements, which imbues bulk properties and functionality that remain elusive to mimic synthetically. However, the potential for biomimetic analogs to seamlessly interface hard materials with soft surfaces for applications ranging from robotics and sealants to medical devices (e.g., prosthetics and wearable health monitors) has driven the demand for innovative chemistries and manufacturing approaches. Herein, we unveil a liquid resin for rapid, high resolution digital light processing (DLP) 3D printing of multimaterial objects with an unprecedented combination of strength, elasticity, and resistance to aging. Two enabling discoveries are the use of a covalently bound (hybrid) epoxy-acrylate monomer that precludes plasticization of soft domains and a wavelength-selective photosensitizer that accelerates cationic curing for hard domains. Using dual projection for multicolor DLP 3D printing (UV and violet light), several bioinspired metamaterial structures are fabricated, including one with hard springs embedded in a soft cylinder to adjust compressive behavior and a detailed knee joint featuring “bones” and “ligaments” for smooth motion. Lastly, the application of this system to facilitate selective stretching for electronic devices is demonstrated with a proof-of-concept device.

36 MATERIALS SCIENCE↗

Advanced Reactor Control and Operations (ARCO): A University Research Facility for Developing Optimized Digital Control Rooms

The Advanced Reactor Control and Operations (ARCO) facility was constructed in January 2018 to serve as a test bed for advanced reactor control rooms and operator support systems. Since then, it has supported human-machine interface user experience research, fault detection and mitigation technology development, control room concept of operations development, and remote operations research. ARCO serves as the control room for the Compact Integral Effects Test (CIET) facility, which replicates the primary-side flow paths and thermal-hydraulic behavior of a fluoride-salt-cooled high-temperature reactor (FHR) using simulant fluids and scaling principles. New reactor designs feature different operating conditions and scenarios than those in existing reactors. ARCO supports the research and development of digital tools for operator communications, intuitive real-time data analysis, online health monitoring and prognostics, and control room cybersecurity. By integrating these different technologies, ARCO acts as a prototypical control system to iteratively develop methods and tools of operation in advanced small modular nuclear reactors. This paper describes the features of and challenges to operating advanced small modular reactors underlying the design basis for ARCO and its operator support systems.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Photonic curing for innovative fabrication of flexible metal oxide optoelectronics

Abstract Flexible optoelectronics, based on non-planar substrates, hold promise for diverse applications such as wearables, health monitors, and displays due to their cost-effective manufacturing methods. Despite the superior properties of metal oxides, the challenge of processing them at high temperatures incompatible with plastic substrates necessitates innovative annealing approaches. Photonic curing, which delivers microsecond to millisecond broadband (200–1500 nm) light pulses on a sample, emerges as a viable solution. Depending on the optical properties, the targeted film absorbs the radiant energy resulting in rapid heating while the transparent substrate absorbs a minimal amount of light and remains at ambient temperature. The light intensity can be high, but since the light pulse is short, the total energy absorbed by the sample remains low and will not damage the plastic substrate. This perspective explores the innovative application of photonic curing to fabricate flexible metal oxide optoelectronics, including thin-film transistors, metal–insulator–metal devices, solar cells, transparent conductors, and Li batteries, emphasizing the conversion of sol–gel precursors to metal oxides. However, this technique was initially developed for sintering metal nanoparticles to conductive patterns and poses intriguing challenges in explaining its mechanism for metal oxide conversion, especially considering the limited absorption of visible light by most sol–gel precursors. The review delves into UV-induced photochemistry, common flexible metal-oxide optoelectronic components, and non-intuitive distinctions between photonic curing and thermal annealing. By elucidating the distinctive role of photonic curing in overcoming temperature-related challenges and advancing the fabrication of flexible metal oxide optoelectronics, this perspective offers valuable insights that could shape the future of flexible optoelectronics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characterizing Canopy Openness in Open Forests: Spherical Densiometer and Canopy Photography Are Equivalent but Less Sensitive than Direct Measurements of Solar Radiation

In forest ecosystems, canopy openness affects understory light availability, plant growth, and tree species recruitment, thus shaping future forest composition, structure, and functional diversity. Foresters must correctly and quickly measure canopy openness to meet their management objectives. To help guide the selection of an appropriate method for measuring canopy openness, we compared three common techniques that vary in cost, complexity, and time required for measurements and data processing: smartphone-based hemispherical photography, spherical densiometer measurements, and direct measurements of solar radiation (using AccuPAR ceptometer). We measured canopy openness using these three methods on 28 permanent forest health monitoring plots in pine-oak forests of the Central Pine Barrens of Long Island in New York State. By analysis of variance and regression analyses, we found the three methods (particularly densiometer and hemispherical photographs) yielded broadly equivalent and strongly positively correlated descriptions of canopy openness. The direct measurements of solar radiation seemed to have a greater potential to detect subtle variation in forest understory light. Forest managers may sufficiently characterize canopy openness using quick and cheap methods (e.g., spherical densiometers) and avoid larger costs of devices for direct light measurements (e.g., ceptometers) and the larger data processing times of hemispherical photography.

54 ENVIRONMENTAL SCIENCES↗