Measurement Uncertainty Research Articles

Research on Size Measurement Method of Underwater Parts Based on Machine Vision

Abstract In order to measure the deformed parts under pressure, a size measurement method of underwater parts based on machine vision is proposed, whereas the relative position between the camera and target parts remains basically unchanged. Firstly, the imaging theory of the underwater camera is analyzed, and the mathematical relationship between the size of the target object and the number of pixels is established; Then, the underwater parts measurement system based on machine vision is built, and the image processing algorithm is studied to extract the target size; Thirdly, the genetic algorithm is studied to calibrate the camera measurement system; Finally, the relevant experiment is conducted on the underwater parts measurement system. Through the analysis of the results, the measurement uncertainty of the system is 0.0355mm, and the relative error is 0.1%. The underwater parts measurement system has practical value.

Enhancing Thomson scattering polychromator performance with multi-pass spectral filters.

In photon-deficient, noncollective Thomson scattering diagnostics, filter polychromators are typically employed in the spectral analysis of Thomson-scattered signals to achieve acceptable signal-to-noise performance. Currently, the most common polychromator filter configuration employs a set of single-passband optical filters that define individual spectral channels. Here, we introduce a new spectral analysis method for Thomson scattering based on spectral filters with multiple passbands, referred to as Thomson scattering spectral multiplexing. Implementing multi-bandpass spectral filters on polychromators increases the achievable range of electron temperature measurement for a given number of filters employed. In addition, Thomson scattering spectral multiplexing reduces systematic measurement uncertainty, with fewer required spectral channels, thereby decreasing light loss from reduced optical element interactions. A multi-bandpass filter set, optimized by a genetic algorithm, has been successfully installed and tested on the Helically Symmetric eXperiment (HSX), demonstrating the benefits of the Thomson scattering spectral multiplexing method.

Analytic Parameterization of Longwave Optical Properties of Bulk Vegetation Layer Permitting Non‐Zero Leaf Reflectivity and Its Implementation in CLM5

AbstractFor modern land surface models (LSMs) representing a singular bulk vegetation layer, the longwave optical properties (i.e., emissivity, reflectivity, and transmittivity) of vegetation layer are derived with a simplified constraint of assuming zero leaf reflectivity. This constraint is necessary, for instance, to the Beer–Lambert (B–L) law to establish a relationship between the optical properties and leaf area index. However, the simplified constraint leads to an overestimation of land surface emissivity in the vegetated regions. In this study, we introduce a new scheme considering realistic leaf reflectivity values rather than assuming zero. This new scheme is based on the relationship derived from the B–L law, but it is statistically augmented to consider the effects of leaf reflections. It is designed to emulate a multi‐vegetation‐layer numerical model known as the Norman model, which is capable of numerical calculations of multi‐reflections among leaves. This new method consists of only a couple of simple equations; despite its simplicity, it very closely mimics the Norman model; The discrepancy of the results between the new method and the Norman model is less than measurement uncertainties for any combination of input parameters. When the new scheme is implemented in the Community Land Model version 5 (CLM5), the land surface emissivity values are simulated much more consistently with global measurements, resulting in significant alterations of land surface energy budget. The enhanced realism through our new scheme is poised to contribute to more accurate numerical weather and climate simulations.

Evaluation of Measurement Uncertainty Using the Monte Carlo Method in Steady-State Power Measurement of Household Refrigerator Based on IEC 62552:2015

Evaluation of Measurement Uncertainty Using the Monte Carlo Method in Steady-State Power Measurement of Household Refrigerator Based on IEC 62552:2015

GGR Handbook of Rock and Mineral Analysis Chapter 1 (Part 1) Geoanalytical Metrology

This chapter (Geoanalytical Metrology) is a contribution to the Geostandards and Geoanalytical Research Handbook of Rock and Mineral Analysis – an online textbook that is a fully revised and updated edition of Handbook of Silicate Rock Analysis, which was written by Philip J. Potts and published in 1987 by Blackie and Son (Glasgow). This second edition comprises chapters, written by prominent research scientists, designed to provide comprehensive overviews of the relevant techniques for the elemental characterisation of rocks and minerals. Chapters are designed to allow new practitioners to the field (including research students) to attain a comprehensive understanding of the theory, practice and capabilities of each technique, as well as being of benefit to established research geoanalysts. In addition to the content, chapter titles have been revised where appropriate to reflect progress in this field.Chapter 1, Part 1 (from Section 1 of the handbook dealing with fundamentals of measurement and instrument design) first sets out the overarching conventions that operate in analytical chemistry, including a description of the international organisations and systems that regulate the standards governing the discipline. This is followed by coverage of the statistical basis on which geoanalytical data sets are treated, analysed and interpreted, which summarises most of the relevant tests and terminology employed in this field. The methods by which the calibration of measured signals from instrumental techniques is tackled, followed by method validation, which covers aspects including measurement uncertainty, bias, precision and trueness. Sections detailing metrological traceability and quality management conclude this chapter.

A novel method for measuring electrolytic conductivity with a polarization impedance control function

The article presents an idealized model of the differential method utilized in conductometry to measure electrolytic conductivity (EC). It identifies the main drawback of the widely used differential method: the inability to control the influence of polarization impedance on EC measurement results. A criterion for the absence of error caused by polarization effects is proposed, involving equality between the ratios of resistance differences and cell constant differences. A novel method for EC measurement, termed the double differential method, is introduced. This method relies on repeated differential impedance measurements and incorporates an additional third impedance measurement of a virtual liquid column. The new approach enables the identification of polarization impedance influence on EC measurements and the calculation of measurement errors for correction. A 3 times lower type A measurement uncertainty value can be achieved by averaging the corrected results.

Single-star Warm-Jupiter Systems Tend to Be Aligned, Even around Hot Stellar Hosts: No T eff–λ Dependency* *This Letter includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.

The stellar obliquity distribution of warm-Jupiter systems is crucial for constraining the dynamical history of Jovian exoplanets, as the warm Jupiters’ tidal detachment likely preserves their primordial obliquity. However, the sample size of warm-Jupiter systems with measured stellar obliquities has historically been limited compared to that of hot Jupiters, particularly in hot-star systems. In this work, we present newly obtained sky-projected stellar obliquity measurements for the warm-Jupiter systems TOI-559, TOI-2025, TOI-2031, TOI-2485, TOI-2524, and TOI-3972, derived from the Rossiter–McLaughlin effect, and show that all six systems display alignment with a median measurement uncertainty of 13°. Combining these new measurements with the set of previously reported stellar obliquity measurements, our analysis reveals that single-star warm-Jupiter systems tend to be aligned, even around hot stellar hosts. This alignment exhibits a 3.4σ deviation from the T eff–λ dependency observed in hot-Jupiter systems, where planets around cool stars tend to be aligned, while those orbiting hot stars show considerable misalignment. The current distribution of spin–orbit measurements for Jovian exoplanets indicates that misalignments are neither universal nor primordial phenomena affecting all types of planets. The absence of misalignments in single-star warm-Jupiter systems further implies that many hot Jupiters, by contrast, have experienced a dynamically violent history.

MEMPSEP‐I. Forecasting the Probability of Solar Energetic Particle Event Occurrence Using a Multivariate Ensemble of Convolutional Neural Networks

AbstractThe Sun continuously affects the interplanetary environment through a host of interconnected and dynamic physical processes. Solar flares, Coronal Mass Ejections (CMEs), and Solar Energetic Particles (SEPs) are among the key drivers of space weather in the near‐Earth environment and beyond. While some CMEs and flares are associated with intense SEPs, some show little to no SEP association. To date, robust long‐term (hours‐days) forecasting of SEP occurrence and associated properties (e.g., onset, peak intensities) does not effectively exist and the search for such development continues. Through an Operations‐2‐Research support, we developed a self‐contained model that utilizes a comprehensive data set and provides a probabilistic forecast for SEP event occurrence and its properties. The model is named Multivariate Ensemble of Models for Probabilistic Forecast of Solar Energetic Particles (MEMPSEP). MEMPSEP workhorse is an ensemble of Convolutional Neural Networks that ingests a comprehensive data set (MEMPSEP‐III by Moreland et al. (2024, https://doi.org/10.1029/2023SW003765)) of full‐disc magnetogram‐sequences and in situ data from different sources to forecast the occurrence (MEMPSEP‐I—this work) and properties (MEMPSEP‐II by Dayeh et al. (2024, https://doi.org/10.1029/2023SW003697)) of a SEP event. This work focuses on estimating true SEP occurrence probabilities achieving a 2.5% improvement in reliability and a Brier score of 0.14. The outcome provides flexibility for the end‐users to determine their own acceptable level of risk, rather than imposing a detection threshold that optimizes an arbitrary binary classification metric. Furthermore, the model‐ensemble, trained to utilize the large class‐imbalance between events and non‐events, provides a clear measure of uncertainty in our forecast.

Using Light Polarization to Identify Fiber Orientation in Carbon Fiber Components: Metrological Analysis.

In this work, a method for measuring tow angles in carbon fiber components, based on the use of a polarized camera, is analyzed from a metrological point of view. Carbon fibers alter the direction of the reflected light's electrical field, so that in each point of the surface of a composite piece, the angle of polarization of reflected light matches the fiber orientation. A statistical analysis of the angle of linear polarization (AoLP) in each pixel of each examined area allows to evaluate the average winding angle. An evaluation of the measurement uncertainty of the method on a cylinder obtained by a filament winding process is carried out, and the result appears adequate for the study of the distribution of angles along the surface of the piece, in order to optimize the process.

Risk assessment of karst water inrush in tunnel engineering based on improved game theory and uncertainty measure theory

The sudden inrush of water poses a serious threat to the safety of workers during tunnel construction in the karst region of southwest China. To mitigate this risk, a model is proposed to assess the risk of water surge through a tunnel by combining improved game theory with uncertainty measure theory. Eight indicators of risk were extracted based on the solubility of rock, its geological structure, capacity for surface catchment, and hydrogeological factors, and were incorporated into the proposed model. The subjective weights of these indicators were obtained using the analytic hierarchy process, while their objective weights were calculated through the entropy weighting method and the criteria importance through intercriteria correlation method. An improved game theory-based method of combinatorial weighting was then used to construct the corresponding weight vectors. Single-indicator measurement functions and multi-indicator measurement matrices were utilized to classify and evaluate the indicators of the risk of a surge in water level based on a confidence criterion. The proposed method was applied to five typical karst sections of the Yanjin Tunnel of the Chongqing–Kunming High-speed Railway Project, and the method was validated by comparing the recorded and estimated inflow volume ranges during the project’s construction, showing consistency with the actual evaluation results. This proposed model thus offers a practical tool for assessing the risk of water inrush in karst tunnels.

Time-varying risk aversion and international stock returns

We estimate aggregate, time-varying risk aversion inferred from options, stock returns and macroeconomic data for a panel of 8 countries. We document that, for most countries, the estimated risk aversion measure is counter-cyclical. Moreover, we show that estimated risk aversion forecasts monthly stock index returns up to 12 months ahead. This effect is statistically significant in panel regressions, and it survives the inclusion of additional control variables, such as an estimated of the variance risk premium, an investors’ sentiment index, and a measure of economic uncertainty. Finally, we show that risk aversion provides useful information to an investor who aims at timing the market. An investment strategy that uses the estimated time-varying risk aversion measure to solve a mean–variance asset allocation problem, delivers significantly positive returns.

Relativistic generalized uncertainty principle for a test particle in four-dimensional spacetime

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, [Formula: see text], becomes uncertain. There exists a specific range of coordinates where the accessibility to [Formula: see text] is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value [Formula: see text]. This expectation value is dependent on [Formula: see text], which is itself limited by a minimum measurable length [Formula: see text]. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between [Formula: see text] and [Formula: see text] is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between [Formula: see text] and the Planck length [Formula: see text] is established with a proportionality factor of [Formula: see text], where [Formula: see text] denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction [Formula: see text], leading to an unrealistic [Formula: see text]. It is also noted that the lower limit of [Formula: see text] is directly proportional to the fundamental tensor.

Quantification of the Uncertainty in Ultrasonic Wave Speed in Concrete: Application to Temperature Monitoring with Embedded Transducers.

This article presents an overall examination of how small temperature fluctuations affect P-wave velocity (Vp) measurements and their uncertainties in concrete using embedded piezoelectric transducers. This study highlights the fabrication of custom transducers tailored for long-term concrete monitoring. Accurate and reliable estimation of ultrasonic wave velocities is challenging, since they can be impacted by multiple experimental and environmental factors. In this work, a reliable methodology incorporating correction models is introduced for the quantification of uncertainties in ultrasonic absolute and relative velocity measurements. The study identifies significant influence quantities and suggests uncertainty estimation laws, enhancing measurement accuracy. Determining the onset time of the signal is very time-consuming if the onset is picked manually. After testing various methods to pinpoint the onset time, we selected the Akaike Information Criterion (AIC) due to its ability to produce sufficiently reliable results. Then, signal correlation was used to determine the influence of temperature (20 °C to 40 °C) on Vp in different concrete samples. This technique proved effective in evaluating velocity changes, revealing a persistent velocity decrease with temperature increases for various concrete compositions. The study demonstrated the capability of ultrasonic measurements to detect small variations in the state of concrete under the influence of environmental variables like temperature, underlining the importance of incorporating all influencing factors.

Indirect optical geometry measurements with a stream of particles as micro probes

The manufacturing of micro-structured components with varying geometries and materials requires precise and versatile applicable geometry measurement techniques. Optical measurement approaches enable high-precision measurements, but they rely on cooperative surfaces. To overcome the dependency on the optical surface response, the surface of a measured object is determined indirectly using an aerosol flow with fluorescent particles and a confocal fluorescence microscope. To precisely extract the surface position from the scanned fluorescence signal of the particles in the surrounding air, a model-based signal processing is proposed. To assess the measurement capabilities and the influence of the aerosol supply flow, geometry and flow measurements are performed on a flat plate geometry and a step geometry. As a result, a measurement uncertainty of ▪ with no systematic error was achieved for the flat plate experiment, despite the different boundary layer flows at the different measurement positions. In contrast to this, a significant systematic measurement error occurred in the wake flow region of the step geometry because of flow separation and, thus, no detectable particles directly behind the step. In summary, the findings clarify an in principle achievable sub-micrometre resolution with improved optics and a large number of detected particles, but also emphasise the necessity of a sufficient particle supply for enabling indirect optical geometry measurements.

Optimizing the uncertainty of measurements on a coordinate measuring machine when controlling complex geometric surfaces

The object of this study is the process of optimizing measurement uncertainty on a coordinate measuring machine (CMM) when inspecting complex geometric surfaces. The problem addressed was insufficient accuracy and efficiency of measurements of complex parts on CMMs under production conditions. A method for optimizing measurement uncertainty has been devised, which includes a mathematical model of the measurement process and an adaptive algorithm for optimizing the control strategy, based on the Monte Carlo method. The model takes into account the geometry of surfaces and CMM characteristics, while the algorithm dynamically adjusts measurement parameters. The results demonstrate a reduction in measurement uncertainty by 15–20 % and a reduction in inspection time by 10–12 % compared to conventional methods. This is achieved by taking into account the specificity of complex surface geometry and an adaptive approach. The uniqueness of the developed method is the ability to automatically adapt to different types of CMMs and measured objects, optimizing the number and location of measurement points, the speed of probe movement, and its contact force with the surface. The method takes into account not only the geometric parameters of objects but also the characteristics of the CMM itself, which allows for high accuracy. The method is particularly effective for parts with complex geometry, in which conventional methods often lead to significant errors. Practical application is possible at machine-building enterprises for quality control of complex parts, especially in serial production. The implementation of the developed method allows for improving product quality and reducing production costs by 8–10 % due to optimization of the control process and reduction of defects

CONCERTO at APEX On-sky performance in continuum

Context. CarbON CII line in post-rEionisation and ReionisaTiOn epoch (CONCERTO) instrument is a low-resolution mapping spectrometer based on lumped element kinetic inductance detector (LEKIDs) technology, operating at 130-310 GHz. It was installed on the 12-metre APEX telescope in Chile in April 2021 and was in operation until May 2023. CONCERTO’s main goals were the observation of [CII]-emission line fluctuations at high redshift and of the Sunyaev–Zel’dovich (SZ) signal from galaxy clusters. Aims. We present the data processing algorithms and the performance of CONCERTO in continuum by analysing the data from the commissioning and scientific observations. Methods. We developed a standard data processing pipeline to proceed from the raw data to continuum maps. Using a large dataset of calibrators (Uranus, Mars, and quasars) acquired in 2021 and 2022 at the APEX telescope across a wide range of atmospheric conditions, we measured the CONCERTO continuum performance and tested its stability against observing conditions. Further, using observations on the COSMOS field and observations targeting a distant sub-millimetre galaxy in the UDS field, we assessed the robustness of the CONCERTO performance on faint sources and compared our measurements with expectations. Results. The beam pattern is characterised by an effective full width at half maximum (FWHM) of 31.9 ± 0.6″ and 34.4 ± 1.0″ for high-frequency (HF) and low-frequency (LF) bands, respectively. The main beam is slightly elongated with a mean eccentricity of 0.46. Two error beams of ~65″ and ~130″ are characterised, allowing us to estimate a main beam efficiency of ~0.52. The field of view is accurately reconstructed and presents coherent distortions between the HF and LF arrays. LEKID parameters were robustly determined for 80% of the read tones. Cross-talks between LEKIDs are the first cause of flagging, followed by an excess of eccentricity for ~10% of the LEKIDs, all located in a given region of the field of view. Of the 44 scans of Uranus selected for the absolute photometric calibration, 72.5% and 78.2% of the LEKIDs were selected as valid detectors with a probability >70%. By comparing the Uranus measurements with a model, we obtain calibration factors of 19.5±0.6 Hz Jy−1 and 25.6±0.9 Hz Jy−1 for HF and LF, respectively. The point-source continuum measurement uncertainties are 3.0% and 3.4% for the HF and LF bands, ignoring the uncertainty in the model (which is <2%). This demonstrates the accuracy of the methods we deployed to process the data. Finally, the RMS of CONCERTO maps is verified to evolve as proportional to the inverse square root of the integration time. The measured noise-equivalent flux densities (NEFDs) for HF and LF are 115±2 mJy beam−1 s1/2 and 95±1 mJy beam−1 s1/2, respectively, obtained using CONCERTO data on the COSMOS field for a mean precipitable water vapour (pwv) and elevation of 0.81 mm and 55.7 deg. Conclusions. CONCERTO has unique capabilities in fast dual-band spectral mapping at ~30 arcsec resolution and with a ~18.5 arcmin instantaneous field of view. CONCERTO’s performance in continuum is perfectly in line with expectations.

Development and validation of a LC-MS method for the quantification of microcystins in fish for their monitoring in environmental and food context

Cyanobacterial blooms in aquatic ecosystems can result in the accumulation of cyanotoxins in other organisms. Fish can potentially accumulate large amounts of cyanotoxins through their direct interaction with contaminated water and the ingestion of cyanobacterial cells. As a human food source, this can result in a potential health risk. Investigating and monitoring this risk requires analytical methods sufficiently robust to be suitable for different fish species. This study, therefore, aimed to optimize and validate an UHPLC-MS/MS method for the quantification of eight microcystin congeners and nodularin in five different fish species. The limits of detection and quantification were 1 and 3 μg kg−1, respectively. The linearity of the method was very good, with calculated R2 values above 0.99. The mean recovery of the method was within the acceptable range of 70.0%–120.0 %, the repeatability was not higher than 12.6 %, and the highest intra-laboratory reproducibility was 18.7 %. The estimated range for the expanded measurement uncertainty was between 29 % and 58 %. Moreover, multiple fish from Flemish waters were analyzed to show the method's applicability. Multiple microcystin congeners were detected (up to 88.3 μg kg−1 sum of analyzed microcystins) in the liver and viscera of perch and sander. Small amounts of MC-LR and MC-YR (up to 6.1 μg kg−1) were also detected in perch muscle tissue.

Uncertainties in measurements of bubbly flows using phase-detection probes

The analysis of bubbly two-phase flows is challenging due to their turbulent nature and the need for intrusive phase-detection probes. However, accurately characterizing these flows is crucial for safely designing critical infrastructure such as dams and their appurtenant structures. The combination of dual-tip intrusive phase-detection probes with advanced signal processing algorithms enables the assessment of pseudo-instantaneous 1-D velocity time series; for which the limitations are not fully fathomed. In this investigation, we theoretically define four major sources of error, which we quantify using synthetically generated turbulent time series, coupled with the simulated response of a phase-detection probe. Based on the analysis of 1010 simulated bubble trajectories, our findings show that typical high-velocity flows in hydraulic structures hold up to 15% error in the mean velocity estimations and up to 35% error in the turbulence intensity estimations for the most critical conditions, typically occurring in the proximity of the wall. Based on thousands of simulations, our study provides a novel data-driven tool for the estimation of these baseline errors (bias and uncertainties) in real-word phase-detection probe measurements of bubbly flows (air concentrations c<40%).

Aeroelastic Influence of Blade-Shaft Coupling in a 1 1/2-Stage Axial Compressor

Abstract The design process of turbomachinery, is often constraint by aeroelastic phenomena. The design choices are limited by possible structural failure, which can be caused by high vibration amplitudes. In particular, damping has an important impact on these phenomena. In the absence of friction, damping is mainly created by aerodynamics. In this paper, additional damping created by the shaft will be investigated. This becomes relevant when blade vibrations with nodal diameters 1 and -1 couple structurally with shaft vibrations. To investigate the blade-shaft coupling, a simulation process is set up based on a full structural dynamic model of the blisk-shaft assembly and a harmonic balance CFD model to account for the aeroelastic effects. In addition, mistuning identification is performed based on an experimental modal analysis at standstill. All results are incorporated into a structural reduced order model that calculates the vibrational behavior of the blading. These results are compared to damping determined during operation using an acoustic excitation system and measured forced frequency responses. The numerical results agree well with the experimental results, i.e. within the measurement uncertainty. Furthermore, the blade-shaft coupling results in significant changes of the eigenfrequencies and damping. As a consequence, damping increases by up to twelve times due to the coupling. This reduces amplitudes by a factor of nine for the mistuned blade responses. Consequently, higher structural safety factors can be achieved by taking the blade-shaft coupling into account so that the remaining potentials in the aerodynamic design could be better exploited.

Adsorption of Selected Herbicides on Activated Carbon from Single- and Multi-Component Systems-Error Analysis in Isotherm Measurements.

The aim of this study is to examine the influence of various factors on the precision and repeatability of the experimental determination of herbicide adsorption isotherms. Studies were conducted for the activated carbon RIB as an adsorbent and three herbicides as adsorbates: 2,4-dichlorophenoxyacetic acid (2,4-D), 4-chlorophenoxyacetic acid (4-CPA), and 3-chlorophenoxypropionic acid (3-CPP). The herbicide adsorption process was carried out in single-component and multi-component modes (the herbicide was adsorbed in the presence of an accompanying substance, i.e., 4-nitroaniline (4-NA)). Due to the significant contribution of the competition phenomenon in the adsorption process, which is important, e.g., in multi-component environmental systems, a qualitative and quantitative analysis of herbicide adsorption in the presence of a competing substance was presented. This work presents, among other things, the influence of adsorbent heterogeneity (grain size) on measurement uncertainties. The spread of standard deviations for solutions requiring dilution during spectrophotometric measurements was discussed, indicating that dilutions contribute to increasing measurement uncertainties. The heterogeneity parameters of the Freundlich equation for the studied adsorption systems were analyzed; the 2,4-D/RIB system was indicated as the most energetically heterogeneous. Differentiation of the experimental conditions (pH, temperature) allowed us to assess their impact on the efficiency and mechanism of adsorption. A high repeatability of experimental isotherms was obtained for the multi-component system. The accuracy of quantitative determination of equilibrium concentrations for the tested two-component systems was assessed based on the measured UV-Vis spectra, and the adsorption of herbicides from single- and multi-component systems was compared.