Balance Method Research Articles

Dynamic Analysis of a Double-Cable-Stayed Shallow Arch Model Under Multi-Frequency Excitation by IHB Method

To reveal the dynamic properties of cable-stayed bridges under complex external excitations, a double-cable-stayed shallow arch model induced by multi-frequency harmonic excitations is established. The cable and shallow arch exhibit primary or subharmonic resonances by sweeping excitations simultaneously and asynchronously. Galerkin method, one/two time scales Incremental Harmonic Balance (IHB) method, and Runge–Kutta (RK) method are applied to explore the nonlinear dynamic responses. Research results demonstrate that both the cables and shallow arch present soft and hard spring properties, despite the very weak hard spring of the shallow arch; one-way dynamic interaction among the cables and the shallow arch is discovered when sweeping excitations asynchronously.

NVW-YOLOv8s: An improved YOLOv8s network for real-time detection and segmentation of tomato fruits at different ripeness stages

Tomato yield estimation relies significantly on the accurate detection of fruit quantity and size. And object detection and semantic segmentation of fruits emerge as efficacious methodologies for the realization of fruit counting and size detection. To address challenges associated with the detection and segmentation of tomato fruits in complex environments such as sample imbalance of different classes, small targets, and susceptibility to occlusion at varying stages of ripeness, this study proposed a foreground-foreground class balance method and an improved YOLOv8s network, NVW-YOLOv8s, for detecting and segmenting tomato fruits simultaneously. The foreground-foreground class balance method initially performed pixel-wise extraction on fruit samples with fewer instances. Subsequently, it synthesized them with original images containing a limited number of samples from the class, thereby augmenting the overall quantity of this specific category of fruit samples. In the NVW-YOLOv8s network, a C2f-N module, founded on the normalization-based attention module (NAM), was specifically crafted for residual feature learning. This design serves to augment the network's proficiency in extracting and integrating feature information pertaining to tomato fruits within intricate environments. Additionally, a variable focal loss (VFL) was introduced as the classification loss function to address the issue of positive and negative sample imbalance, and a regression loss function based on Wise-IoU (WIoU) was incorporated to tackle challenges related to fruit small targets and susceptibility to occlusion. The YOLOv8s models trained with the augmented balanced dataset revealed that the model's detection and segmentation performance, as indicated by mAP@0.5, improved by 4.8 % and 5.4 %, respectively, compared with the model trained with the augmented original training dataset. The test results on the augmented balanced dataset indicated that the proposed NVW-YOLOv8s network achieved a detection mAP@0.5 of 91.4 %, an F1-Score of 85.4 %, a segmentation mAP@0.5 of 90.7 %, and an F1-Score of 84.8 %. These results surpass the baseline YOLOv8s network by 4.3 % and 5.5 % for detection, 4.1 % and 5.0 % for segmentation, respectively. Additionally, the processing for concurrent detection and segmentation was measured at a speed of 60.2 FPS. Therefore, the proposed method has successfully met the precision and real-time requirements for intelligent yield estimation in horticultural crops.

Exogenous Organic Matter Improves Potato Yield by Regulating the Microbiological Fertility Index

The nutrient availability of carbon (C), nitrogen (N), and phosphorus (P) has been decreasing due to a decline in the biological function of yellow soil, limiting potato yield (PY). Increasing biochar or organic fertilizer input is an effective way to improve soil microbiological fertility. However, indexes to regulate soil microbiological fertility using biochar and organic fertilizer individually or in combination and these indexes’ associations with PY remain unclear. In this study, four fertilization strategies were developed using the nutrient balance method: CK (recommended NPK fertilization), BC (NPK + biochar), OF (NPK + organic fertilizer), and BF (NPK + 1/2 biochar + 1/2 organic fertilizer). Using different fertilization strategies, the eco-stoichiometry characteristics of the soil microbial biomass and enzyme activity; the bioavailability of C, N, and P; and the differences in PY were investigated, and the direct and indirect effects of these factors on PY were determined over a two-year period. The results showed that exogenous organic matter input could considerably affect the stoichiometric ratios of soil microbial biomass; C; N; P; the stoichiometric ratios of C-converting, N-converting, and P-converting enzyme activities (expressed as BG+CBH, NAG+LAP, and AP, respectively); and the integrated enzyme index (IEI). The IEI was the highest in BF, followed by OF, BC, and CK. A significant positive correlation was found between the microbial biomass C, N, and P and their corresponding converting enzyme activities (p < 0.05). The ln(BG+CBH):ln(NAG+LAP), ln(BG+CBH):lnAP, and ln(NAG+LAP):lnAP ratios were all higher than 1:1, but they approached 1:1 in the order of CK-BC-OF-BF. Compared to soil C and N, P-converting enzyme activity was the primary limiting factor for soil nutrient conversion in the study area. BF was less restricted by P and more balanced in its nutrient ratio. The microbial biomass C:N:P could affect PY in eight ways. (1) Microbial biomass C:N directly decreased PY, and microbial biomass C:P indirectly increased PY. (2) It could decrease C-converting enzyme activity, (3) decrease N availability to increase C-converting enzyme activity, (4) decrease P availability, or (5) decrease P availability to decrease the soil C:P-converting enzyme activity ratio. Microbial biomass N:P indirectly increased PY (6) by increasing the soil C:P-converting enzyme activity ratio, (7) by increasing C-converting enzyme activity, or (8) by increasing N availability to increase C-converting enzyme activity. Thus, BF is an effective strategy for regulating the soil microbiological fertility index; enhancing C, N, and P nutrient conversion; and increasing PY. The input of exogenous organic matter can alter the stoichiometric ratios of soil microbial biomass C, N, and P; the stoichiometric ratios of C-converting, N-converting, and P-converting enzyme activities; and nutrient availability, thus regulating PY. Microbial biomass N:P and soil C:P-converting enzyme activity ratios influence PY the most.

$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming

$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming

Construction of optical solitary wave solutions and their propagation for Kuralay system using tanh-coth and energy balance method

In this article, we study the complex coupled Kuralay system (CKS), which have many applications in different field such as ferromagnetic material and fiber optics. We implement an analytical method, namely, the tanh–coth method to considered system to formulate a system of algebraic equations. Solving the obtained system, we acquire different traveling wave solutions that are expressed in term of hyperbolic tangent functions and hyperbolic cotangent functions. Also, we employ the energy balance technique to the selected model to sort out the behavior of traveling wave solutions. By this method, we obtain periodic wave solution that are expressed in term of cosine function. In order to show the graphical presentation of the acquired solitary waves solutions, 3D and 2D curve are created by selecting well-suited parametric values via Mathematica.

Research Progress and the Prospect of Damping Magnesium Alloys.

As the lightest structural metal material, magnesium alloys possess good casting properties, high electrical and thermal conductivity, high electromagnetic shielding, and excellent damping properties. With the increasing demand for lightweight, high-strength, and high-damping structural materials in aviation, automobiles, rail transit, and other industries with serious vibration and noise, damping magnesium alloy materials are becoming one of the important development directions of magnesium alloys. A comprehensive review of the progress in this field is conducive to the development of damping magnesium alloys. This review not only looks back on the traditional damping magnesium alloys represented by Mg-Zr alloys, Mg-Cu-Mn alloys, etc. but also introduces the new damping magnesium materials, such as magnesium matrix composites and porous magnesium. But up to now, there have still been some problems in the research of damping magnesium materials. The effect of spiral dislocation on damping is still unknown and needs to be studied; the contradiction between damping performance and mechanical properties still lacks a good balance method. In the future, the introduction of more diversified damping regulating methods, such as adding other elements and reinforcements, optimizing the manufacturing method of damping magnesium alloy, etc., to solve these issues, will be the development trend of damping magnesium materials.

Multimodal Resonance Response of Incompressible Hyperelastic Moderately Thick Cylindrical Shells

Based on the modified third-order shear deformation theory, the harmonic balance method, and the pseudo-arclength continuation method with two-point prediction, the nonlinear forced vibration response of incompressible hyperelastic moderately thick cylindrical shells subjected to a concentrated harmonic load at mid-span and simply supported boundary conditions at both ends is investigated. The algorithmic procedure for solving steady-state periodic solutions of strongly nonlinear systems of differential equations is presented. The structural response characteristics of shells under different excitation amplitudes and structural parameters are analyzed. The numerical results indicate that the aspect ratio of moderately thick hyperelastic cylindrical shells has a significant effect on the natural frequency ratio. Different frequency ratios lead to varying nonlinear mode coupling effects. The coupling effects among modes result in complex nonlinear behavior in the vibration response of each mode, leading to abundant multi-valued phenomena in the response curve.

ANALISIS STRATEGI E-COMMERCE PADA PT. SPADA INOVASI DIGITAL MENGGUNAKAN METODE IT BALANCED SCORECARD

The use of information systems is one of the IS/IT investments in a company. Information systems can certainly improve company performance, but many information systems have not been implemented optimally, and do not meet the company's vision, mission and goals. This research was conducted with the aim of making strategic planning for the implementation of the E-Commerce information system at PT. Beware of Digital Innovation. The strategic plan was developed based on the IT Balanced method. Data collection was carried out through interviews, then the data obtained was subjected to SWOT analysis, then mapped into the IT Balanced Scorecard. This research produces strategic recommendations that companies can implement, including: 1) from an operational excellence perspective, companies need to determine IS/IT employees and regular maintenance; 2) user orientation perspective, companies need to adjust the interface design according to customer wishes and provider manuals as a template for system use; 3) future orientation perspective, companies need to recruit employees which can be done with background checks; 4) from a business contribution perspective, companies need to maintain and improve service quality. It is hoped that the results of this research can improve the quality of PT Waspada Innovation Digital's e-commerce.

Robotic-assisted Total Knee Arthroplasty Technology Provides a Repeatable and Reproducible Method of Assessing Soft Tissue Balance.

Soft-tissue balancing is an important factor in primary total knee arthroplasty (TKA), with 30 to 50% of TKA revisions attributed to technical operative factors including soft-tissue balancing. Robotic-assisted TKA (RATKA) offers opportunities for improved soft-tissue balancing methods. This study aimed to evaluate the repeatability and reproducibility of ligamentous laxity assessments during RATKA using a digital tensioner.Three experienced RATKA surgeons assessed preresection and trialing phases of 12 human cadaveric knees with varying degrees of arthritis. Ligamentous laxity was assessed with manual varus and valgus stresses in extension and flexion, with a digital tensioner providing feedback on the change of laxity displacement. Intraclass correlation coefficient (ICC) analyses were used to determine the repeatability within a single surgeon and reproducibility between the three surgeons.The results showed excellent repeatability and reproducibility in ligamentous laxity assessment during RATKA. Surgeons had excellent repeatability for preresection and trialing assessments, with median ICC values representing excellent reproducibility between surgeons. Surgeons were repeatable within 1 or 1.5 mm for preresection and trialing assessments. On average, the variation within a surgeon was 0.33 ± 0.26 mm during preresection and 0.29 ± 0.28 mm during trialing. When comparing surgeons to each other, they were reproducible within an average of 0.69 ± 0.33 mm for preresection and 0.65 ± 0.31 mm for trialing.This study demonstrated the reliability of robotic-assisted soft-tissue balancing techniques, providing control over ligamentous laxity assessments, and potentially leading to better patient outcomes. The digital tensioner used in this study provided excellent repeatability and reproducibility in ligamentous laxity assessment during RATKA, highlighting the potential benefits of incorporating robotics in TKA procedures.

Convergence and stability of the balanced Euler method for stochastic pantograph differential equations with Markovian switching

In this paper, we concern the strong convergence and stability of the balanced Euler method for stochastic pantograph differential equations with Markovian switching (SPDEs-MS). We present the balanced Euler method of SPDEs-MS and consider its moment boundedness under polynomial growth condition plus Khasminskii-type condition. We also study its strong convergence order and its mean-square stability. Two numerical examples are given to illustrate the theoretical results.

Nonlinear vibrations of porous-hyperelastic cylindrical shell under harmonic force using harmonic balance and pseudo-arc length continuation methods

The resonant responses are investigated for the porous-hyperelastic Mooney–Rivlin cylindrical shell subjected to a radial harmonic excitation. Considering the higher-order shear deformation theory (HSDT), fourth-order strain-displacement relations are derived, which include the radial geometric imperfections varying along the thickness direction. Using the porous-hyperelastic Mooney–Rivlin constitution relation and Lagrange equation, the differential governing equations of motion are obtained for the porous-hyperelastic cylindrical shells. The resonant conditions are presented and the accuracy of the mathematical models is verified. The harmonic balance and pseudo-arc length continuation methods are used to obtain the amplitude-frequency and forced-amplitude curves. The stability of the solutions is analyzed by Floquet theory. The effects of the external excitation amplitudes, structure parameters and porosity infill parameters on the linear frequencies, amplitude-frequency responses and force-amplitude responses are discussed for the imperfect porous-hyperelastic cylindrical shells. The results show that the linear frequencies of the porous-hyperelastic cylindrical shells increase obviously as the uniform and sigmoid function porosity parameters reach the certain values. The increase of the structure parameters enhances the response amplitudes of the first-order mode and minified response amplitudes of the second-order mode. The decreasing porosity ratios weaken the softening nonlinear behaviors of the porous-hyperelastic cylindrical shells. With the changes of the external excitation amplitudes and structure parameters, the motion of the porous-hyperelastic cylindrical shell indicates that the synchronous vibrations occur with the period and chaotic vibrations alternately.

Advancing battery energy storage system: State‐of‐health aware state‐of‐charge balancing in multilevel inverters for electric transportation

AbstractThis research presents an innovative methodology for enhancing battery energy storage systems for electrically powered transportation, utilizing a distinctive cascaded H‐bridge multilevel inverter design, termed P‐CHBMI. Central to this work is the development of a state‐of‐health aware state‐of‐charge (SoH‐aware‐SoC) balancing technique, which leverages an advanced algorithm integrated with a Proportional‐Integral (PI) controller technique to efficiently balance battery cells according to their state‐of health (SoH). This technique significantly improves operational efficiency and extends the lifespan of battery systems by intelligently optimizing cell discharge processes. Moreover, this research work delivers a wide range of simulations for the generation of a streamlined control algorithms for the development of the symmetric and asymmetric configuration of the P‐CHBMI. Similarly, recommended topology is proficient of equal voltage discharge across battery cells, which is an exclusive property of the conventional cascaded H‐bridge topology. The study includes extensive MATLAB/Simulink simulations to validate the superiority of the P‐CHBMI and the SoH‐aware‐SoC balancing method over conventional systems, highlighting substantial enhancements in switch count efficiency, operational flexibility, and battery durability. Further, the practical applicability of the proposed topology is evidenced through a hardware implementation of a symmetric 5‐level inverter. This study plays a significant role in the development of the inverter technology particularly in off‐grid scenarios such as electric vehicle and aircrafts, keeping the battery efficiency and reliability as a most important factor.

Hybrid IFDMB/4D-Var inverse modeling to constrain the spatiotemporal distribution of CO and NO2 emissions using the CMAQ adjoint model

We performed a hybrid approach that combines the iterative finite difference mass balance (IFDMB) and four-dimensional variational data assimilation (4D-Var) methods to effectively constrain the spatiotemporal distribution of emissions. To quantitatively compare the performance of inverse modeling in constraining CO and NO2 emissions in South Korea spatiotemporally, we conducted a model-based twin experiment for three inverse modeling methods: IFDMB, 4D-Var, and hybrid inversions. We performed numerical modeling using the Community Multi-scale Air Quality (CMAQ) and its adjoints to calculate the values required for inverse modeling. As a result, the IFDMB inversion can effectively constrain the average spatial distribution of emissions. Meanwhile, the 4D-Var inversion can help estimate temporal variations in emissions, but it is not effective in regions with large prior emission errors. The hybrid inversion showed the best performance in constraining the spatiotemporal distribution of emissions because it combined the strengths of the two aforementioned methods. Furthermore, to compare the performance of the inverse modeling of pollutants with different chemical properties, we conducted additional inverse modeling for highly reactive NO2. After the application of inverse modeling, the emission errors of NO2 (18.339%) were larger than those of CO (10.593%). This difference in inverse modeling errors was due to the greater nonlinear relationship between emissions and concentrations in the inverse modeling process for NO2, which is more reactive compared to CO. In this study, the ideal modeling tests were performed to quantitatively assess the performance of inverse modeling. In future studies, we expect to apply the hybrid inversion approach used in this study to inverse modeling using actual observations.

A novel rotor dynamic balancing method based on blade tip clearance measurement without the once per revolution sensor

The existence of the aeroengine casing, limited monitoring points, and multi-fault characteristics make obtaining the rotor’s vibration transmission characteristics challenging, resulting in difficulties accurately identifying the rotor unbalance. This paper utilizes a high-frequency composite sensor to monitor the engine’s blade tip clearance (BTC) and extracts unbalanced information from BTC signals for rotor dynamic balancing, while avoiding the need for the once per revolution (OPR) sensor. First, the vibration characteristics of the rotor-blade system under multi-fault conditions are investigated. Then, based on BTC measurement, a none OPR method and an unbalance identification method are proposed, in which the radial vibration of the blade tip in the BTC signals at different speeds is extracted and operated in the time domain to obtain the rotor unbalanced vibration, the signal is reconstructed, and cross-correlation analysis is used to accurately identify the magnitude and phase of the unbalanced signal. Finally, a rotor test bench is utilized for experimental verification. The results reveal that the dynamic balancing method based on the BTC signal can more precisely identify the rotor unbalance than the traditional rotor dynamic balancing method. The application of this technique will effectively improve engine health management and fault prediction.

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

The objective of this work is to propose a data-driven Bayesian inference framework to efficiently identify parameters and select models of nonlinear aeroelastic systems. The framework consists of the use of Bayesian theory together with advanced kriging surrogate models to effectively represent the limit cycle oscillation response of nonlinear aeroelastic systems. Three types of sampling methods, namely, Markov chain Monte Carlo, transitional Markov chain Monte Carlo, and the sequential Monte Carlo sampler, are implemented into Bayesian model updating. The framework has been demonstrated using a nonlinear wing flutter test rig. It is modeled by a two-degree-of-freedom aeroelastic system and solved by the harmonic balance methods. The experimental data of the flutter wing is obtained using control-based continuation techniques. The proposed methodology provided up to a 20% improvement in accuracy compared to conventional deterministic methods and significantly increased computational efficiency in the updating and uncertainty quantification processes. Transitional Markov chain Monte Carlo was identified as the optimal choice of sampling method for stochastic model identification. In selecting alternative nonlinear models, multimodal solutions were identified that provided a closer representation of the physical behavior of the complex aeroelastic system than a single solution.

Determination of hydration kinetic of pinto beans: A hyperspectral images application

Hydration is a typical operation applied to legumes before cooking, reducing time and the associated energy cost. To monitor the process, mass balance method is the most used methodology, despite this method is destructive, repetitive, and time-consuming. For that reason. hyperspectral techniques are presented as an alternative for assessing the hydration process since it is a noninvasive method. Therefore, the objective of this work was to evaluate the technique of hyperspectral imaging for studying the hydration kinetics of pinto beans. For this purpose, a sample of pinto beans was hydrated in distilled water, determining moisture content during the process and taking hyperspectral images by reflectance mode, in the range 400 to 800 nm until constant mass. The moisture content was modelled using Peleg and a sigmoidal model. Next, the images were pre-treated and the median spectral profile for each bean was obtained. Then, a regression model was fitted, using the wavelength that maximized the coefficient of determination (R2) and minimized the root mean square error (RMSE). The results show that Peleg model fit experimental data with R2 in the range of 0.974 to 0.989 while sigmoidal model of 0.997 to 0.999. On other hand, mean spectral profiles at 632 nm and sigmoidal model give the higher metrics 0.997 and 38.3 for R2 and RMSE respectively. The results showed that hyperspectral imaging in reflectance mode is a tool capable of measuring the hydration level of beans with higher performance at 632 nm, with a determination coefficient R2 higher than 0.98.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES.

Study of irrigation aspect in the interconnection system of Telaga Tanjung and Singin Ponds in Tabanan Regency

Interconnection is a channel that links multiple water channel systems with those downstream of a river area. The proposed system will utilize existing canals in Gadungan, Matan, and Unun Irrigation Areas, extending to the Lambuk Reservoir dam system. The problem is that irrigation areas downstream of the Lambuk Reservoir are Lambuk (726 ha), Babakan Anyar (42 ha), and Lanyah (281 ha) experience water shortages (planting intensity of 170% to 200%) during the dry season. The study utilized water balance methods in rice fields, the basic year method for main discharge at weirs, and interconnection channel analysis for water needs calculation. From the water balance analysis, the Singin System cannot make a new interconnection channel to the Lambuk Reservoir because the available water in each reservoir can only irrigate the Matan and Unun Irrigation Areas. From the Telaga Tunjung System, there is still a lot of water available, especially during the rainy season, so that it can supply the reservoir for the Lambuk Reservoir. This means that the interconnection system from this reservoir still needs to be created from the primary channel of the Gadungan Irrigation Area.

An Enhanced Nonlinear Energy Sink for Hybrid Bifurcation Passive Mitigation and Energy Harvesting From Aeroelastic Galloping Phenomena

Abstract Galloping is a self-excited vibration problem that structures immersed in fluid flow can experience. Due to its essential nonlinear phenomena, the structure exhibits limit cycle oscillations (LCOs), which, at high levels, can lead to failure of the systems. This work proposes an investigation of electromagnetic-enhanced nonlinear energy sinks (NES-EH) for the hybrid mitigation of aeroelastic LCOs and energy harvesting. The study focuses on a prismatic bluff body with a linear suspension immersed in the airflow, using classical steady nonlinear modeling for aerodynamic loads. The conventional NES approach is adopted, employing cubic stiffness and linear damping. Additionally, a linear electromagnetic transducer is included in the assembly for the energy harvesting process. By combining the method of multiple scales with the Harmonic Balance Method, analytical solutions are derived to characterize the system's dynamics under the influence of the device. The different response domains and their respective boundaries induced by the NES-EH are characterized based on the bifurcation diagrams. Furthermore, a slow invariant manifold (SIM) characterization is presented for each induced response domain, and its significant features are discussed. Parametric studies are carried out based on bifurcation analyses to assess the effect of NES-EH parameters on the galloping system dynamics, which allows for designing the absorber parameters. The electrical resistance is optimized to maximize the harvested power. The optimal design of NES-EH is then compared with classical energy harvesting solutions for the galloping problem. Additionally, a thorough analysis of the Target Energy Transfer phenomenon is performed.

Comparison of Methods to Determine Nutrient Uptake of Tomato Grown in Free-Draining Perlite Substrate—Key Information for Optimal Fertigation Management

Two methods were compared to determine crop nutrient uptake by tomato crops in free-draining perlite substrate. They were the nutrient balance method (applied minus drained) and the dry matter method (DM) (nutrients in plant material). Uptake of N, P, K, Ca, Mg, and S was determined using both methods, in three consecutive tomato crops planted in the same perlite. Nutrient uptake determined using the balance method was consistently higher than with the DM method. Relative differences (balance minus dry matter, with respect to the DM method) were N: −1 to 16%, P: 27–45%, K: 14–46%, Ca: 17–87%, Mg: 28–111%, and S: 15–65%. There was a clear tendency for the difference between the methods to reduce with successive crops. The differences between the methods were reduced when the measured retention of nutrients in the perlite substrate and estimated nutrient retention in roots (using a model) were included. However, these data did not explain all of the observed differences between the two methods. Various retention and loss processes may explain the differences. The results suggest that the DM matter method estimates nutrient uptake by the crop, and the balance method estimates nutrient consumption by the cropping system.