Multipoint Measurements Research Articles

Instantaneous nondestructive evaluation of elastic modulus by using knocking ball test on sedimentary and metasedimentary rock slope

The elastic modulus of rock masses is a critical parameter for many engineering applications. However, in situ measurement of the elastic modulus can be challenging and time-consuming. This study established a new in situ method to measure the elastic modulus of rock masses, enhancing prior technology using Hertz's theory. The method involves using a knocking ball, which strikes the rock surface with a spherical steel hammer, providing an instantaneous measurement. The knocking ball method was tested on a variety of rock types, and the results showed a significant correlation (R2 > 0.8) between the elastic modulus of the knocking ball (Ekb) and the in situ uniaxial compressive strength (UCS-Schmidt). The knocking ball method overcomes the limitations of the Schmidt hammer by offering rapid, direct, and multipoint measurements. The knocking ball method is non-destructive, handheld, and easy to use, making it ideal for use in field applications.

Multipoint surface electromyography measurement using bull’s-eye electrodes for wide-area topographic analysis

BackgroundSurface electromyography (sEMG) is primarily used to analyze individual and neighboring muscle activity. However, using a broader approach can enable simultaneous measurement of multiple muscles, which is essential for understanding muscular coordination. Using the “bull’s-eye electrode,” which allows bipolar derivation without directional dependence, enables wide-area multipoint sEMG measurements. This study aims to establish a multipoint measurement system and demonstrate its effectiveness and evaluates forearm fatigue and created topographic maps during a grasping task.MethodsNine healthy adults with no recent arm injuries or illnesses participated in this study. They performed grasping tasks using their dominant hand, while bull’s-eye electrodes recorded their muscle activity. To validate the effectiveness of the system, we calculated the root mean squares of muscle activity and entropy, an indicator of muscle activity distribution, and compared them over time.ResultsThe entropy analysis demonstrated a significant time-course effect with increased entropy over time, suggesting increased forearm muscle uniformity, which is possibly indicative of fatigue. Topographic maps visually displayed muscle activity, revealing notable intersubject variations.DiscussionBull’s-eye electrodes facilitated the capture of nine homogeneous muscle activity points, enabling the creation of topographic images. The entropy increased progressively, suggesting an adaptive muscle coordination response to fatigue. Despite some limitations, such as inadequate measurement of the forearm muscles’ belly, the system is an unconventional measurement method.ConclusionThis study established a robust system for wide-area multipoint sEMG measurements using a bull’s-eye electrode setup. This system effectively evaluates muscle fatigue and provides a comprehensive topographic view of muscle activity. These results mark a significant step towards developing a future multichannel sEMG system with enhanced measurement points and improved wearability.Trial registrationThis study was approved by the Ethics Committee of Chiba University Graduate School of Engineering (acceptance number: R4-12, Acceptance date: November 04, 2022).

Arrays of glass wedges for multi-dimensional optical diagnostics.

There is a common need in the advancement of optical diagnostic techniques to increase the dimensionality of measurements. For example, point measurements could be improved to multi-point, line, planar, volumetric, or time-resolved volumetric measurements. In this work, a unique optical element is presented to enable multi-dimensional measurements, namely, an array of glass wedges. A light source is passed through the wedges, and different portions of the illumination are refracted by different amounts depending on the glass wedge angle. Subsequent optics can be used to focus the light to multiple points, lines, or planes. Basic characterization of a glass wedge array is presented. Additional wedge-array configurations are discussed, including the use of a periodic intensity mask for multi-planar measurements via structured illumination. The utility of this optical element is briefly demonstrated in (a)multi-planar flame particulate measurements, (b)multi-point femtosecond-laser electronic excitation tagging for flow velocimetry, and (c)multi-line nitric oxide molecular tagging velocimetry in a hypersonic shock-tunnel. One significant advantage of this optical component is its compatibility with high-energy laser sources, which may be a limiting factor with other beam-splitting or beam-forming elements such as some diffractive optics. Additionally, an array of glass wedges is simple and easily customizable compared to other methods for forming multiple closely spaced illumination patterns. Suggestions for further development and applications are discussed.

Evaluation of Model Predictions of the Unsteady Tidal Stream Resource and Turbine Fatigue Loads Relative to Multi-Point Flow Measurements at Raz Blanchard

The next stage of development of the tidal stream industry will see a focus on the deployment of tidal turbines in arrays of increasing device numbers and rated power. Successful array development requires a thorough understanding of the resource within potential deployment sites. This is predictable in terms of flow speeds, based upon tidal constituents. However, the operating environment for the turbine is more complex than the turbine experiencing a uniform flow, with turbulence, shear and wave conditions all affecting the loading on the turbine components. This study establishes the accuracy with which several alternative modelling tools predict the resource characteristics which define unsteady loading—velocity shear, turbulence and waves—and assesses the impact of the model choice on predicted damage equivalent loads. In addition, the predictions of turbulence are compared to a higher fidelity model and the occurrence of flow speeds to a Delft3D model for currents and waves. These models have been run for a specific tidal site, the Raz Blanchard, one of the major tidal stream sites in European waters. The measured resource and predicted loading are established using data collected in a recent deployment of acoustic Doppler current profilers (ADCPs) as part of the Interreg TIGER project. The conditions are measured at three locations across the site, with transverse spacing of 145.7 m and 59.3 m between each device. Turbine fatigue loading is assessed using measurements and model predictions based on an unsteady blade element momentum model applied to near-surface and near-bed deployment positions. As well as across-site spatial variation of loading, the through life loading over a 5-year period results in an 8% difference to measured loads for a near-surface turbine, using conditions purely defined from a resource model and to within 3% when using a combination of modelled shear with measured turbulence characteristics.

Multi-Point Optical Fiber Fabry-Perot Curvature Sensor Based on Microwave Photonics

This article reports a multi-point curvature sensor system based on multiplexed optical fiber Fabry-Perot interferometric (FPI) sensor devices and a microwave photonics interrogation technique. The FPI sensor is fabricated with the assistance of a capillary tube, where a short section of the capillary is sandwiched between two single-mode fibers, forming the air-gap Fabry-Perot cavity. Bending of the FPI device leads to changes in the fringe contrast of its reflection spectrum. Based on the microwave photonics filtering technique, variations of the fringe contrast are encoded into the changes in the peak magnitude of the passband in the frequency response of the FPI device. By multiplexing such FPI devices with different cavity lengths, multi-point measurements of curvature can be realized by tracking changes in corresponding passbands in the frequency response of the system. The FPI curvature sensor is easy-to-manufacture and cost-effective, and the microwave photonics-based system provides an alternative and robust solution to interrogating the multiplexed FPI sensors for multi-point curvature sensing that could be desired in structural health monitoring, human-machine interface sensing, and other related fields.

Interaction phenomena of electrically coupled cells under local reactant starvation in automotive PEMFC stacks

The local current density distribution of polymer electrolyte membrane fuel cells (PEMFCs) can be distorted by various error states. Differences in current density distributions (CDDs) of adjacent cells in a stack are equilibrized by in-plane currents within the sandwiched bipolar plates. Degradation stressors such as detrimental differences in local cell voltage and current density maxima can thus be generated. A novel method was therefore developed to intentionally manipulate CDD profiles by integrating local artificial starvation into only one fuel cell in an assembly. This technique is applied to automotive-sized PEMFCs single cells as well as in 20 cell short-stack to analyze such voltage and current redistribution phenomena. A drastic distortion of local cell voltage is only observed for stacks, which is explained by a supplementary simulation. The local voltage distribution of an electrically coupled fuel cell is therefore calculated by combining CDD measurements with a spatially resolved polarization curve model. The capabilities and limits of a multipoint cell voltage monitoring measurement device are discussed on this basis. The inspected correlation between these two independent online measurement techniques allows to localize such error states with considerable accuracy during operation of automotive sized PEMFC stacks.

On the surface flow patterns and associated aerodynamics of an asymmetrical flat-box section

In this study, wind tunnel experiments were carried out in smooth flow to examine the nexus between flow patterns around a flat-box section and its aerodynamics with the variation of the wind angle of incidence (α). The model cross section closely represents the overall asymmetric geometry and attendant aerodynamics of a class of flat-box decks frequently employed in long-span bridges. To explore the flow around and associated aerodynamic properties of this model that are distinct from a typical symmetric section (e.g., rectangular), detailed wind tunnel tests involving smoke-wire based flow visualizations and synchronous multipoint pressure measurements were carried out. Experimental results were analyzed to identify flow patterns, pressure distributions and associated Strouhal numbers, power spectral densities, aerodynamic force coefficients, proper orthogonal decomposition (POD) analyses, and span-wise correlation. Three typical flow patterns previously observed around symmetric bluff bodies with varying α were also observed in the asymmetric cross section, i.e., the trailing-edge vortex shedding (TEVS), the impinging leading-edge vortices (ILEV), and the alternate-edge vortex shedding (AEVS). However, due to the chordwise asymmetry of the section, the three flow patterns identified are distinct from the classical ones associated with symmetric sections in terms of flow separation points, the static “stall” angle of the section, and characteristics of leading-edge vortices. The roles played by these flow patterns in the aerodynamics of the flat-box section have been identified. It is observed that, if the ILEV or AEVS governs the flow topology, the aerodynamic force coefficients vary nonlinearly with the increase in α, in contrast with the linear variation in the TEVS-dominant case. For cases in which the TEVS dominates, the POD mode participation factors of the fluctuating pressure field display energy in higher modes. In this case, the reconstruction process requires that higher POD modes are retained. Finally, in the TEVS flow pattern, a weaker spanwise correlation of the fluctuating forces is noted as compared to the ILEV and AEVS-type flows. This study is limited to the fundamental examination of asymmetric section aerodynamics in smooth flows, which should be extended in case the influences of turbulence and aeroelastic effect are of interest.

Velocity of magnetic holes in the solar wind from Cluster multipoint measurements

Abstract. We present the first statistical study on the velocity of magnetic holes (MHs) in the solar wind. Magnetic holes are localized depressions of the magnetic field, often divided into two classes: rotational and linear MHs. We have conducted a timing analysis of observations of MHs from the Cluster mission in the first quarter of 2005. In total, 69 events were used; out of these, there were 40 linear and 29 rotational MHs, where the limit of magnetic field rotation was set to 50∘. The resulting median velocity was 7.4 ± 45 and 25 ± 42 km s−1 for linear and rotational MHs, respectively. For both classes, around 70 % of the events had a velocity in the solar wind frame that was lower than the Alfvén velocity. Therefore, we conclude that within the observational uncertainties, both linear and rotational MHs are convected with the solar wind.

Magnetospheric Multiscale measurements of turbulent electric fields in earth's magnetosheath: How do plasma conditions influence the balance of terms in generalized Ohm's law?

Turbulence is ubiquitous within space plasmas, where it is associated with numerous nonlinear interactions. Magnetospheric Multiscale (MMS) provides the unique opportunity to decompose the electric field (E) dynamics into contributions from different linear and nonlinear processes via direct measurements of the terms in generalized Ohm's law. Using high-resolution multipoint measurements, we compute the magnetohydrodynamic (EMHD), Hall (EHall), electron pressure (EPe), and electron inertia (Einertia) terms for 60 turbulent magnetosheath intervals, to uncover the varying contributions to the dynamics as a function of scale for different plasma conditions. We identify key spectral characteristics of the Ohm's law terms: the Hall scale, kHall, where EHall becomes dominant over EMHD; the relative amplitude of EPe to EHall, which is constant in the sub-ion range; and the relative scaling of the nonlinear and linear components of EMHD and of EHall, which are independent of scale. We find expressions for the characteristics as a function of plasma conditions. The underlying relationship between turbulent fluctuation amplitudes and ambient plasma conditions is discussed. Depending on the interval, we observe that EMHD and EHall can be dominated by either nonlinear or linear dynamics. We find that EPe is dominated by its linear contributions, with a tendency for electron temperature fluctuations to dominate at small scales. The findings are not consistent with existing linear kinetic Alfvén wave theory for isothermal fluctuations. Our work shows how contributions to turbulent dynamics change in different plasma conditions, which may provide insight into other turbulent plasma environments.

A Mobile Laboratory Robot for Various and Precise Measurements of Crops and Soil in Agricultural Fields: Development and Pilot Study

Localized management based on multipoint measurements of crops and soil is expected to improve agricultural productivity. The difficulties with this process are as follows: it is time-consuming due to the many measurement points; it requires various sensors for various measurements; it can lead to unstable measurements due to sunlight and wind. To solve the above issues, the system we propose has the advantages of efficient measurements performed by a robot, various measurements performed through exchangeable sensor units, and stable measurements through protecting the crop from sunlight and wind. As a pilot study for the system, we conducted an experiment to simultaneously measure the crops and soil in a cabbage field. The robot achieved mobility in the field, >4 h of operation time, and the ability to obtain soil electrical conductivity measurements and crop imaging at 100 points. Furthermore, the stability of the measurement conditions within the sensor unit during the experiment was evaluated. Compared to the case without the covering, the illuminance became 280-fold stabler (standard deviation = 0.4 lx), and the wind-induced crop shaking became 20-fold lower (root mean square error of the image pixels = 0.5%). The potential impacts of this research include high reproducibility because of the shareable sensor unit and the expectation of new discoveries using precise indoor sensors.

A differential miniaturized thickness measurement calibration system based on laser triangulation sensors

Steel plate thickness inspection is important in high-precision steel processing and manufacturing. Traditional inspection methods use manual contact measurement, which has low inspection efficiency and large human error, so we proposed a differential non-contact thickness measurement system based on laser triangulation sensors. Firstly, we designed a differential measurement structure by placing the laser triangulation sensors on the top and bottom of the steel plate to be measured, so that the data from the top and bottom sensors can be sampled and the steel plate thickness can be calculated simultaneously. Secondly, based on the principle of error averaging effect, we proposed a multi-point measurement averaging method to take multiple points on the surface of the steel plate and calculate the average value as the thickness of the steel plate. Further, to improve the measurement system’s long-term stability, the temperature drift is corrected by the polynomial fitting method. Finally, the experiment proves that the repeatability accuracy of our proposed measurement system can reach ±0.5um and the measurement drift is better than ±0.1% of the steel plate thickness.

Acoustic Field Imaging of Pipeline Turbulence for Noninvasive and Distributed Gas Flow Measurement

Precise control and measurement of the flow are essential for pipeline safety monitoring and economic accounting. Nowadays, the measurement of pipeline flow relies on point measurement schemes such as mechanical flowmeters, which invade the pipeline and can irreversibly damage the fluid pressure, especially when multipoint measurements are required. To overcome these problems, we have explored a novel technique in which the acoustic field properties of pipeline turbulence are reflected by distributed backscattering light field, from which the flow can be measured via acoustic field imaging. The acoustic field information is recorded by a helical deployment scheme using backscattering-enhanced optical fiber (BEOF) encapsulated in the polyethylene anticorrosive layer, thereby achieving highly sensitive, noninvasive, and distributed online monitoring of gas flows. We obtained 24-h flow fluctuation distributions with only one sensing fiber for two operating gas pipelines, and the flow measurement accuracy reached higher than 98% within the error range of −15% to 15%. Moreover, the minimum detectable flow is evaluated and it is demonstrated that the proposed scheme is extremely sensitive to weak flows. We successfully demonstrated noninvasive and distributed online measurement of operational pipeline flow, which will exhibit great potential for pipeline integrity management in the future.

Multi-point scattering measurements for effective property extraction from metamaterials with skin effects

Scattering experiments can be leveraged to extract the effective properties of a heterogeneous metamaterial slab based on multi-point measurements in surrounding media. In this technique, two measurements are made in the ambient media on each side of a finite thickness micro-structured slab to decompose incoming and outgoing waves. The method is applied to an example with locally resonant micro-structured inclusions while paying close attention to parameters that influence the extracted material parameters. It is observed that the extracted overall parameters converge to limiting values when the number of unit cells across the slab thickness or ambient media modulus are increased. Dependence of extracted material parameters on the number of cells through thickness or ambient media properties are attributed to the different response of boundary (skin) and interior cells. A method is presented which represents a finite array with different effective properties for the skin regions vs. the interior regions with great success in reproducing the scattering for different slab thicknesses, and through which the interior regions properties become independent of ambient media properties. In stop bands with lower material loss, challenges arise that are associated with extremely small transmission. The assumption of continuity in transmission phase is enforceable to remove phase ambiguity, although in certain cases (associated with nearly lossless specimens) this assumption appears to fail. In such cases, interference from coupled shear modes may lead to apparent higher longitudinal transmission within the stop band. This work provides a proof of concept for the development of an experimental methodology capable of extracting the effective properties and dispersion behavior of heterogeneous mechanical metamaterials without any knowledge of the internal fields.

A new real-time hole cleaning monitoring method based on downhole multi-point pressure measurement and data driven approach

During the construction of long horizontal wells and extended reach wells, inadequate hole cleaning can lead to a series of drilling problems. Traditional hole cleaning analysis is simply based on theoretical models or surface vibrating screen data, and cannot accurately assess downhole cuttings distribution and existing problems. This paper introduces a novel research idea that combines the traditional drilling hydraulic model with the artificial intelligence method. A downhole true cuttings distribution technology based on measurement data, the inversion of flow characteristics from pressure in the hole cleaning field, and a new method for quantitatively evaluating the dynamic distribution of downhole cuttings using along-string measurement (ASM) data were proposed. The results depict that, the relationship between hole cleanliness and annular pressure loss in different hole sections under different working conditions is proportional. Second, under given flow conditions, a pressure-driven hole-cleaning model exerted a reverse pressure drop by inferring the effect of cuttings on the borehole. Third, downhole multipoint measurement indicated an accurate evaluation of the hole cleaning condition and provide detailed downhole information that avoided and solve inadequate hole cleaning of long horizontal wells and extended reach wells. In conclusion, the combination of these methods can overcome the defects of traditional hole cleaning analysis. The integrated approach is helpful in improving the practical technique in hole cleaning and promotes the large-scale application in the oil and gas industry.

Uncovering the fracture behavior of metallic cylindrical shells under internal explosive loadings via careful design of densely-arranged multi-point photon Doppler velocimetry measurements

While the expanding process of cylindrical shells under internal explosive loadings is fundamental and ubiquitous in engineering applications, the comprehensive understanding of the underlying mechanism is still a challenge due to the limitation of the spatial resolution on the current diagnostic techniques. To address this issue, an improved densely-arranged multi-point photon Doppler velocimetry (DMPDV) technique with enough spatial resolution to capture the local dynamical evolution was carefully designed. The DMPDV technique was then applied to investigate the expanding behavior of an explosively driven 304 L stainless steel cylindrical shell. As a step beyond the coarse understanding of the overall dynamical response, the expanding process can then be demonstrated comprehensively with more exact concentrations on one fragment. By the combination of DMPDV and high-speed photography, we uncovered the evolution of the expanding process which can be divided into three stages: (1) In the beginning, due to the symmetries of the specimen and the loading, the cylinder expands uniformly and all the velocity-time curves at different hoop positions are coincide with each other. (2) after the emergence of cracks at the outer surface of the cylinder, the velocity-time curves start to separate from each other and are regularly arranged according to their test positions. (3) following the penetration of the crack through the thickness of the cylinder, there is a reverse in the velocity-time curves and the fragments begin to rotate, the rotation angle can be estimated using the velocity difference. The hidden mechanism is then revealed with the help of unloading wave theory and rigid body dynamics. Here the second stage is dominated by unloading wave while the last stage is controlled by the denotation products. These experimental results provide deep insight into the detailed fracture behavior of expanding cylindrical shell and are further validated by the Mott wave models as well as numerical simulations, respectively.

Data-driven Uncertainty Quantification of the Wave Telescope Technique: General Equations and Demonstration Using HelioSwarm

The upcoming NASA mission HelioSwarm will use nine spacecraft to make the first simultaneous multipoint measurements of space plasmas spanning multiple scales. Using the wave telescope technique, HelioSwarm’s measurements will allow for both the calculation of the power in wavevector and frequency space and the characterization of the associated dispersion relations of waves present in the plasma at MHD and ion-kinetic scales. This technique has been applied to the four-spacecraft Cluster and Magnetospheric Multiscale missions, and its effectiveness has previously been characterized in a handful of case studies. We expand this uncertainty quantification analysis to arbitrary configurations of four through nine spacecraft for three-dimensional plane waves. We use Bayesian inference to learn equations that approximate the error in reconstructing the wavevector as a function of relative wavevector magnitude, spacecraft configuration shape, and number of spacecraft. We demonstrate the application of these equations to data drawn from a nine-spacecraft configuration to both improve the accuracy of the technique, as well as expand the magnitudes of wavevectors that can be characterized.

A laser absorption spectroscopy chamber system based on closed dynamic chamber method for multi-point synchronous monitoring ammonia emissions

This study reports on the field testing of a newly and originally designed laser absorption spectroscopy chamber (LASC) system based on closed dynamic chamber method, which is well suited for multi-point synchronous measurement of ammonia emissions in field multiple plot experiment. Main design feature of the LASC system is individual multi-reflection cells for each chamber, achieving the synchronous in-situ monitoring ammonia emissions of all the chambers. Two movable covers for automated opening and closing of the chamber, and the highly transparent chamber walls made of acrylic plate minimize the disturbance of the chamber deployment on the ammonia transport process in the chamber. Controlled field assessment experiment was conducted to evaluate the applicability and reliability of the LASC system. The results indicated that the optimum time length of chamber closure for monitoring ammonia emission is 3 min, and the appropriate time length of chamber ventilation is 17 to 37 min. The LASC system has higher accuracy for measuring ammonia emission rate and reliability for comparatively measuring ammonia emissions from different treatments than the traditional chamber methods.

Curvature envelope area based rapid identification method of bridge distributional element stiffness using microwave interference radar

The bearing capacity of a bridge mainly relies on its own stiffness, while, at present, it remains a challenge to identify the bridge stiffness rapidly. In this paper, a rapid and innovative identification method of bridge distributional element stiffness (BDES) is proposed based on microwave interference radar technology and curvature envelope area (CEA). The main contributions of the work are as follows: (1) Taking advantage of multi-point displacement synchronous measurement, the self-developed microwave inference radar makes possible the acquisition of rotation influence lines (RILs) through the measured multi-point displacement influence lines (DILs). (2) Based on the one-to-one accurate correspondence between CEA, moment envelope area (MEA) and stiffness (“point-to-point” matching), and using the essential relationships among CEA and rotation, the bridge stiffness can be derived by using the DILs and the MEA calculated from the calibrated moving load (“point-to-line” matching). (3) Due to the radar feature of synchronous observation over a large area and referring to the proposed stiffness identification method, the BDES of the monitored area can be further obtained (“line-to-surface” matching). The proposed bridge identification method was applied at a laboratory experiment to identify the BDES of a steel beam for both undamaged and damaged conditions, and the results support the feasibility of the proposed method in BDES identification.

A Wearable Flower-Shaped Sensor Based on Fiber Bragg Grating Technology for In-Vivo Plant Growth Monitoring

One of the biggest challenges facing the world agriculture is feeding a growing population in a sustainable way. Therefore, global food availability is under a severe strain exacerbated by climate changes and biological stresses. Moreover, the content of macro- and micronutrients obtained from in plant-food sources strongly depends on the plant development. An attractive strategy to increase agricultural productivity is the growth monitoring of plants and edible parts by using wearable systems. However, most of these tools measure dimensional changes uniaxially, while an accurate representation of the growth distribution requires multipoint strain measurement especially for plants that show an anisotropic development. Here, we present a stretchable multisensor wearable system highly adaptable to the curvilinear surface of leaves and fruits for multidirectional dimensional monitoring. The proposed sensor consists of six fiber Bragg gratings (FBGs) within a biomimetic flexible substrate with a flower design. FBGs with their miniaturized size, high metrological properties, and multiplexing capacities are well suited to this purpose. A finite-element model (FEM) guides the optimal design and sensors positioning within the flower-shaped matrix to exhibit an adequate strain sensitivity and negligible crosstalk effects among the six sensing elements with a reduced encumbrance. A metrological characterization is first performed followed by the application of the proposed system for in-vivo detection of dimensional changes of a leaf and fruit in both indoor and outdoor scenarios.

Multi-point temperature measurements in packed beds using phosphor thermometry and ray tracing simulations

Packed bed reactors are commonly found in the process industry, for example in flame-assisted calcination for cement production. Understanding the heat transfer inside the bed is essential for process control, product quality and energy efficiency. Here we propose a technique to determine the internal temperature distribution of packed beds based on a combination of lifetime-based phosphor thermometry, ray tracing simulations, and assimilation of temperature data using finite element heat transfer simulations. To establish and validate the technique, we considered a reproducible regular packing of 6 mm diameter aluminum spheres, with one of the spheres in the top layer being electrically heated. If a sphere inside the packing is coated with thermographic phosphors and excitation light is directed towards the packing, luminescence from the coated sphere exits the packed bed after multiple reflection and the sphere's temperature can be determined. Isothermal measurements showed that the temperature obtained by phosphor thermometry is independent of the luminescent sphere location. When imaging the luminescence on a camera, the luminescence distribution in recorded image depended, however, on the position of the sphere. Therefore, in setups with multiple phosphor-coated spheres, their signals can be separated using a least squares fit. We demonstrate the approach using a setup with three luminescent spheres and validated the temperature readings against thermocouple measurements. To obtain the spatial signatures for individual sphere positions required for the least squares fit, ray tracing simulations were used. These provide an efficient alternative to single sphere measurements that are only practical for regular spherical packed beds. Multi-point measurements were used as input to a finite element heat transfer simulations to determine parameters such as particle-to-particle air gap distance. With these, the full temperature distribution inside the bed could be assimilated from the measured values.