Physical Uncertainties Research Articles

Network analysis of anxiety and depressive symptoms among patients with heart failure.

Anxiety and depressive symptoms are common among patients with heart failure (HF). Physical limitations, lifestyle changes, and uncertainties related to HF can result in the development or exacerbating of anxiety and depressive symptoms. However, the central and bridge symptoms of anxiety and depressive symptoms network among patients with HF remain unclear. Network analysis is a statistical method that can discover and visualize complex relationships between multiple variables. This study aimed to establish a network of anxiety and depressive symptoms and identify the central and bridge symptoms in this network among patients with HF. This study employed a cross-sectional study design and convenience sampling to recruit patients with HF. This study followed the Helsinki Declaration and was approved by the Research Ethics Committee of Hospital. The Generalized Anxiety Disorder-7 (GAD-7) and Patient Health Questionnaire (PHQ-9) were administered to evaluate anxiety and depressive symptoms among patients with HF, respectively. Network analysis of anxiety and depressive symptoms was performed using R. In the anxiety and depressive symptoms network, PHQ2 (feeling down, depressed, or hopeless), PHQ7 (inability to concentrate), and GAD4 (difficulty relaxing) were the most central symptoms. Anxiety and depressive symptoms were linked by PHQ2 (feeling down, depressed, or hopeless), GAD6 (becoming easily annoyed or impatient), GAD5 (unable to sit still because of anxiety), GAD7 (feeling afraid that something terrible is about to happen), and PHQ6 (feeling bad or like a failure, or disappointing oneself or family). This study identified the central and bridge symptoms in a network of anxiety and depressive symptoms. Targeting these symptoms can contribute to interventions for patients with HF at risk of-or suffering from-anxiety and depressive symptoms, which can be effective in reducing the comorbidity of anxiety and depression.

From Envelope Spectra to Bearing Remaining Useful Life: An Intelligent Vibration-Based Prediction Model with Quantified Uncertainty

Bearings are pivotal components of rotating machines where any defects could propagate and trigger systematic failures. Once faults are detected, accurately predicting remaining useful life (RUL) is essential for optimizing predictive maintenance. Although data-driven methods demonstrate promising performance in direct RUL prediction, their robustness and practicability need further improvement regarding physical interpretation and uncertainty quantification. This work leverages variational neural networks to model bearing degradation behind envelope spectra. A convolutional variational autoencoder for regression (CVAER) is developed to probabilistically predict RUL distributions with confidence measures. Enhanced average envelope spectra (AES) are used as network input for its physical robustness in bearing condition assessment and fault detection. The use of the envelope spectrum ensures that it contains only bearing-related information by removing other rotor-related frequencies, hence it improves the RUL prediction. Unlike traditional variational autoencoders, the probabilistic regressor and latent generator are formulated to quantify uncertainty in RUL estimates and learn meaningful latent representations conditioned on specific RUL. Experimental validations are conducted on vibration data collected using multiple accelerometers whose natural frequencies cover bearing resonance ranges to ensure fault detection reliability. Beyond conventional bearing diagnosis, envelope spectra are extended for statistical RUL prediction integrating physical knowledge of actual defect conditions. Comparative and ablation studies are conducted against benchmark models to demonstrate their effectiveness.

Two methods to analyze radial diffusion ensembles: The perils of space- and time-dependent diffusion

Particle dynamics in Earth's outer radiation belt can be modeled using a diffusion framework, where large-scale electron movements are captured by a diffusion equation across a single adiabatic invariant, L*(L). While ensemble models are promoted to represent physical uncertainty, as yet there is no validated method to analyze radiation belt ensembles. Comparisons are complicated by the domain dependent diffusion, since diffusion coefficient DLL is dependent on L. We derive two tools to analyze ensemble members: time to monotonicity tm and mass/energy moment quantities N,E. We find that the Jacobian (1/L2) is necessary for radiation belt error metrics. Components of ∂E/∂t are explicitly calculated to compare the effects of outer and inner boundary conditions, and loss, on the ongoing diffusion. Using tm, N, and E, we find that: (a) different physically motivated choices of outer boundary condition and location result in different final states and different rates of evolution; (b) the gradients of the particle distribution affect evolution more significantly than DLL; (c) the enhancement location, and the amount of initial background particles, are both significant factors determining system evolution; (d) loss from pitch-angle scattering is generally dominant; it mitigates but does not remove the influence of both initial conditions and outer boundary settings, which are due to the L-dependence of DLL. We anticipate that this study will promote renewed focus on the distribution gradients, on the location and nature of the outer boundary in radiation belt modeling, and provide a foundation for systematic ensemble modeling.

A sound-vibration physical-information fusion constraint-guided deep learning method for rolling bearing fault diagnosis

Although current deep learning models for bearing fault diagnosis have achieved excellent accuracy, the lack of constraint-guided learning of the physical mechanisms of real bearing failures and a physically scientific training paradigm leads to low interpretability and unreliability of intelligent fault diagnosis models. In this study, a sound-vibration physical-information fusion constraint-guided (PFCG) deep learning (DL) method is proposed, aiming at weighted fusion of sound and vibration multi-physical information into a deep learning model, to guide the DL model to learn more realistic physical laws of bearing failure. Firstly, a 15-degree-of-freedom nonlinear dynamics model of multi-stage degraded bearing failure mechanism with sound-vibration response is developed, which considers the evolutionary mechanism of bearing failure from healthy state to different stages, and utilizes a particle filtering algorithm for dynamic calibration of hidden parameters. Moreover, a lightweight DL fault diagnosis model is designed to realize the deep interaction between the physical model and the DL model through the weighted fusion of the cross-entropy loss function, physical consistency loss and uncertainty loss. Moreover, the superior diagnostic performance of the proposed sound and vibration PFCG-DL model is verified by comparing the performance fluctuations and parameter attributes of different DL benchmark models before and after being guided by physical information fusion constraints (PFCG). Eventually, the proposed PFCG-Transformer model achieves a diagnostic accuracy of 99.45% while keeping the number of parameters at only 0.62M, which significantly improves the accuracy and reduces the computational complexity by 81.5% compared to the CAME-Transformer model's 3.24 M number of parameters and 95.00% diagnostic accuracy. In addition, the test time of PFCG-Transformer is reduced to 1.02 s, which is 60.2% less than CAME-Transformer, demonstrating higher computational efficiency and real-time performance. Importantly, in terms of interpretability, the engineering interpretability and credibility of the models are further improved by visualizing the feature learning results of the vibration modal and multimodal fusion models and the sensitivity analyses of the sound-vibration response models with internal and external physical hyperparameters. Therefore, this study proposes a physical information-guided deep learning method with strong interpretability and superior performance, which provides an important reference for further research and application in the field of bearing fault diagnosis.

Fatigue Characteristics Analysis of Carbon Fiber Laminates with Multiple Initial Cracks

In the entire wind turbine system, the blade acts as the central load-bearing element, with its stability and reliability being essential for the safe and effective operation of the wind power unit. Carbon fiber, known for its high strength-to-weight ratio, high modulus, and lightweight characteristics, is extensively utilized in blade manufacturing due to its superior attributes. Despite these advantages, carbon fiber composites are frequently subjected to cyclic loading, which often results in fatigue issues. The presence of internal manufacturing defects further intensifies these fatigue challenges. Considering this, the current study focuses on carbon fiber composites with multiple pre-existing cracks, conducting both static and fatigue experiments by varying the crack length, the angle between cracks, and the distance among them to understand their influence on the fatigue life under various conditions. Furthermore, this study leverages the advantages of Paris theory combined with the Extended Finite Element Method (XFEM) to simulate cracks of arbitrary shapes, introducing a fatigue simulation method for carbon fiber composite laminates with multiple cracks to analyze their fatigue characteristics. Concurrently, the Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal weight configuration, and the Backpropagation neural network (BP) is used to train and adjust the weights and thresholds to minimize network errors. Building on this foundation, a surrogate model for predicting the fatigue life of carbon fiber composite laminates with multiple cracks under conditions of physical parameter uncertainty has been constructed, achieving modeling and assessment of fatigue reliability. This research offers theoretical insights and methodological guidance for the utilization of carbon fiber-reinforced composites in wind turbine blade applications.

Recycling the rain: Exploring forest management practices in a western Mediterranean watershed to recouple the atmospheric and terrestrial water cycle

Current knowledge of the role that forests play in recycling rainwater has led to the proposal of forest management practices to mitigate desertification in the western Mediterranean basin. Building upon this hypothesis, we present the Mijares watershed in eastern Spain as a detailed case study. We then perform a scientific literature review in the context of the western Mediterranean basin to identify the physical and biophysical uncertainties associated with forest management practices that aim to strengthen the atmospheric and terrestrial components of the water cycle. The review identified eleven interconnected uncertainties that result from complex vegetation, climate, soil, and water relationships. We discuss the need to deepen our understanding of the atmospheric dynamics of the Mijares by accounting for the role of forests in recycling rainfall and by adopting an adaptive management approach to apply the lessons learned in the territory. Based on these considerations, we propose forest management practices to reinforce the water cycle of the watershed. Our work contributes to understanding the uncertainties arising from forest management practices aimed at mitigating desertification, thereby supporting decision-making. These insights apply to other western Mediterranean coastal watersheds.

Online tree-based planning for active spacecraft fault estimation and collision avoidance.

Autonomous robots operating in uncertain or hazardous environments subject to state safety constraints must be able to identify and isolate faulty components in a time-optimal manner. When the underlying fault is ambiguous and intertwined with the robot's state estimation, motion plans that discriminate between simultaneous actuator and sensor faults are necessary. However, the coupled fault mode and physical state uncertainty creates a constrained optimization problem that is challenging to solve with existing methods. We combined belief-space tree search, marginalized filtering, and concentration inequalities in our method, safe fault estimation via active sensing tree search (s-FEAST), a planner that actively diagnoses system faults by selecting actions that give the most informative observations while simultaneously enforcing probabilistic state constraints. We justify this approach with theoretical analysis showing s-FEAST's convergence to optimal policies. Using our robotic spacecraft simulator, we experimentally validated s-FEAST by safely and successfully performing fault estimation while on a collision course with a model comet. These results were further validated through extensive numerical simulations demonstrating s-FEAST's performance.

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

Transitional Palliative Care for Family Caregivers: Outcomes From a Randomized Controlled Trial

ContextPatients receiving inpatient palliative care often face physical and psychological uncertainties during transitions out of the hospital. Family caregivers often take on responsibilities to ensure patient safety, quality of care, and extend palliative care principles, but often without support or training, potentially compromising their health and well-being. ObjectivesThis study tested an eight-week intervention using video visits between palliative care nurse interventionists and caregivers to assess changes in caregiver outcomes and patient quality of life. MethodsThis randomized controlled trial, conducted from 2018 to 2022, enrolled adult caregivers in rural or medically underserved areas in Minnesota, Wisconsin, and Iowa. Eligible caregivers included those caring for patients who received inpatient palliative care and transitioned out of the hospital. The intervention group received teaching, guidance, and counseling from a palliative care nurse before and for eight weeks after hospital discharge. The control group received monthly phone calls but no intervention. Caregiver outcomes included changes in depression, burden, and quality of life, and patient quality of life, as reported by the caregiver. ResultsOf those consented, 183 completed the intervention, and 184 completed the control arm; 158 participants had complete baseline and eight-week data. In unadjusted analyses, the intervention group and their care recipients showed statistically significant improvements in quality of life compared to the control group. Improvements persisted in adjusted analyses, and depression significantly improved. No differences in caregiver burden were observed. ConclusionAddressing rural caregivers’ needs during transitions in care can enhance caregiver outcomes and improve patient quality of life.

A new atmospheric characterization of the sub-stellar companion HR 2562 B with JWST/MIRI observations

HR\,2562\,B is a planetary-mass companion at an angular separation of $0.56 ($19$\,au) from the host star, which is also a member of a select number of L/T transitional objects orbiting a young star. This companion gives us a great opportunity to contextualize and understand the evolution of young objects in the L/T transition. However, the main physical properties (e.g., $ T_ eff $ and mass) of this companion have not been well constrained (34<!PCT!> uncertainties on $ T_ eff $, 22<!PCT!> uncertainty for log(g)) using only near-infrared (NIR) observations. We aim to narrow down some of its physical parameters uncertainties (e.g., $ T_ eff $: 1200K-1700K, log(g): 4-5) incorporating new observations in the Rayleigh-Jeans tail with the JWST/MIRI filters at $10.65$, $11.40$, and $15.50\ m$, as well as to understand its context in terms of the L/T transition and chemical composition. We processed the MIRI observations with reference star differential imaging (RDI) and detect the companion at high S/N (around $16$) in the three filters, allowing us to measure its flux and astrometry. We used two atmospheric models ATMO and Exo-REM to fit the spectral energy distribution using different combinations of mid-IR and near-IR datasets. We also studied the color-magnitude diagram using the F1065C and F1140C filters combined with field brown dwarfs to investigate the chemical composition in the atmosphere of HR\,2562\,B, as well as a qualitative comparison with the younger L/T transitional companion VHS\,1256\,b. We improved the precision on the temperature of HR\,2562\,B ($ T_ eff $ = $1255$\,K) by a factor of $6 compared to previous estimates ($ vs $ using ATMO . The precision of its luminosity was also narrowed down to $-4.69 dex. The surface gravity still presents a wider range of values (4.4 to 4.8 dex). While its mass was not narrowed down, we find the most probable values between $8 M_ Jup $ ($3$-sigma lower limit from our atmospheric modeling) and $18.5 M_ Jup $ (from the upper limit provided by astrometric studies). We report a sensitivity to objects of mass ranging between $2-5 M_ Jup $ at $100$\,au, reaching the lower limit at F1550C . We also implemented a few improvements in the pipeline related to the background subtraction and stages 1 and 2. HR\,2562\,B has a mostly (or near) cloud-free atmosphere, with the ATMO model demonstrating a better fit to the observations. From the color-magnitude diagram, the most probable chemical species at MIR wavelengths are silicates (but with a weak absorption feature); however, follow-up spectroscopic observations are necessary to either confirm or reject this finding. The mass of HR\,2562\,B could be better constrained with new observations at $3-4 m$. Although HR\,2562\,B and VHS\,1256\,b have very similar physical properties, both are in different evolutionary states in the L/T transition, which makes HR\,2562\,B an excellent candidate to complement our knowledge of young objects in this transition. Considering the actual range of possible masses, HR\,2562\,B could be considered as a planetary-mass companion; hence, its name then ought to be rephrased as HR\,2562\,b.

To cascade feedback loops, or not?

AbstractLinear time invariant (LTI) block diagrams—and the associated transfer functions—are profoundly inadequate for multi‐loop control system design. A practitioner has to have a thorough understanding of the physical uncertainties—and of their inter‐dependencies—in the different parts of an interconnected system, or in a given block diagram. Lack of attention to, or understanding of, such causal interactions has led to ill‐advised reliance on cascaded control in practice—and to consternation when cascading fails to yield the expected improvement over a single‐loop design.

Are Atmospheric Models Too Cold in the Mountains? The State of Science and Insights from the SAIL Field Campaign

Abstract Mountains play an outsized role in water resource availability, and the amount and timing of water they provide depend strongly on temperature. To that end, we ask the question: How well are atmospheric models capturing mountain temperatures? We synthesize results showing that high-resolution, regionally relevant climate models produce 2-m air temperature (T2m) measurements colder than what is observed (a “cold bias”), particularly in snow-covered midlatitude mountain ranges during winter. We find common cold biases in 44 studies across global mountain ranges, including single-model and multimodel ensembles. We explore the factors driving these biases and examine the physical mechanisms, data limitations, and observational uncertainties behind T2m. Our analysis suggests that the biases are genuine and not due to observation sparsity or resolution mismatches. Cold biases occur primarily on mountain peaks and ridges, whereas valleys are often warm biased. Our literature review suggests that increasing model resolution does not clearly mitigate the bias. By analyzing data from the Surface Atmosphere Integrated Field Laboratory (SAIL) field campaign in the Colorado Rocky Mountains, we test various hypotheses related to cold biases and find that local wind circulations, longwave (LW) radiation, and surface-layer parameterizations contribute to the T2m biases in this particular location. We conclude by emphasizing the value of coordinated model evaluation and development efforts in heavily instrumented mountain locations for addressing the root cause(s) of T2m biases and improving predictive understanding of mountain climates.

Impact of Illness Uncertainty on Health-Related Quality of Life in Patients With Unruptured Intracranial Aneurysms After Coil Embolization.

BACKGROUND: This study aimed to identify the impact of illness uncertainty on physical and mental health-related quality of life (HRQoL) in patients with unruptured intracranial aneurysms (UIAs) after coil embolization. METHODS: A cross-sectional study was conducted and HRQoL was evaluated using the Short Form-12 Health Survey Questionnaire, which assesses physical and mental HRQoL. RESULTS: The participants had a mean age of 56.4 years, and among them, 190 (71.2%) were women. Physical and mental HRQoL were negatively correlated with physical symptoms, anxiety, depression, and illness uncertainty. Mental HRQoL was positively correlated with social support. Physical HRQoL was significantly influenced by depression (β = -0.26, P = .004) and was not influenced by illness uncertainty (β = -0.10, P = .101). Mental HRQoL was significantly influenced by anxiety (β = -0.45, P < .001), depression (β = -0.19, P = .003), social support (β = 0.14, P = .004), and illness uncertainty (β = -0.14, P = .005). The finding that illness uncertainty influences HRQoL suggests a basis for interventions aimed at improving mental HRQoL by reducing illness uncertainty in patients with UIAs. CONCLUSION: The physical and mental HRQoL in patients with UIAs after coil embolization is negatively influenced by depression, whereas mental HRQoL is also affected by anxiety, illness uncertainty, and social support. These results may serve as reference data for the design and development of interventions to improve HRQoL in patients with UIAs after coil embolization.

Data-driven and knowledge-guided denoising diffusion probabilistic model for runoff uncertainty prediction

The existing medium and long-term runoff prediction methods, which are based on data-driven and knowledge-guided methods, are associated with inherent limitations, and chaotic phenomena in runoff prediction models often leads to oscillation in the prediction error, affecting the robustness of the prediction. A knowledge-guided denoising diffusion probabilistic model (DK-RDDPM) that introduces physical theory to guide constraint quantification and obtain effective runoff uncertainty prediction results is therefore proposed in this study. The main advantage of this model is that the physical randomness in the runoff prediction process can be captured and combined with the Saint-Venant process to guide model optimization and realize more accurate medium- and long-term runoff prediction. The main contributions of this study are the establishment of a dynamic runoff probabilistic prediction model with stochastic quantification characteristics that includes the prediction uncertainty over time, and modelling of the physical constraint boundary of runoff prediction from the perspective of partial differentiation. The effectiveness of the DK-RDDPM was verified by predicting runoff in the Qijiang and Tunxi Basins in China. The results show that: 1) Encoding the physical random uncertainty operator in runoff prediction into the network of the denoising diffusion probabilistic model (DDPM) effectively captures the physically complex implicit randomness of the process, thus reducing the error that results from randomness in runoff prediction. 2) The constraint matrix that is formed using the Saint-Venant equation and the prediction matrix are layered and projected, with the fluctuation range of the constraints in each step adjusted in the optimization direction within a certain random threshold range. 3) The DK-RDDPM shows superior performance to the benchmark models, even under the influence of different noise interference factors.

Combining simulation and experimental data via surrogate modelling of continuum dislocation dynamics simulations

Several computational models have been introduced in recent years to yield comprehensive insights into microstructural evolution analyses. However, the identification of the correct input parameters to a simulation that corresponds to a certain experimental result is a major challenge on this length scale. To complement simulation results with experimental data (and vice versa) is not trivial since, e.g. simulation model parameters might lack a physical understanding or uncertainties in the experimental data are neglected. Computational costs are another challenge mesoscale models always have to face, so comprehensive parameter studies can be costly. In this paper, we introduce a surrogate model to circumvent continuum dislocation dynamics simulation by a data-driven linkage between well-defined input parameters and output data and vice versa. We present meaningful results for a forward surrogate formulation that predicts simulation output based on the input parameter space, as well as for the inverse approach that derives the input parameter space based on simulation as well as experimental output quantities. This enables, e.g. a direct derivation of the input parameter space of a continuum dislocation dynamics simulation based on experimentally provided stress–strain data.

Least-cost and 2 °C-compliant mitigation pathways robust to physical uncertainty, economic paradigms, and intergenerational cost distribution

Each run of an integrated assessment models produces a single mitigation pathway consistent with stated objectives (e.g. maximum temperature) and optimizing some objective function (e.g. minimizing total discounted costs of mitigation). Even though models can be run thousands of times, it is unclear how built-in assumptions constrain the final set of pathways. Here we aim at broadly exploring the space of possible mitigation scenarios for a given mitigation target, and at characterizing the sets of pathways that are (near-)optimal, taking uncertainties into account. We produce an extensive set of CO2 emission pathways that stay below 2 °C of warming using a reduced-form climate-carbon model with a 1000 different physical states. We then identify 18 sets of quasi ‘least-cost’ mitigation pathways, under six assumptions about cost functions and three different cost minimization functions embarking different visions of intergenerational cost distribution. A first key outcome is that the absence or presence of inertia in the cost function plays a pivotal role in the resulting set of least-cost pathways. Second, despite inherent structural differences, we find common pathways across the 18 combinations in 96% of the physical states studied. Interpreting these common pathways as robust economically and in terms of intergenerational distribution, we shed light on some of their characteristics, even though these robust pathways differ for each physical state.

Estimator-based multi-target tracking of networked robotic systems via predefined-time hierarchical control method

In this paper, we study the multi-target tracking problem of networked robotic systems (NRSs) within predefined time under a directed interaction topology considering disturbances and physical parameter uncertainties. On the basis of non-singular sliding-mode surface, a new predefined-time estimator-based hierarchical control algorithm is put forward so as to address the tracking problem under the case of multiple moving targets. Using the time base generator (TBG), a distributed estimator algorithm is designed to ensure that the followers can estimate different target states within a predefined-time. Certain sufficient conditions of predefined-time multi-target tracking of NRSs are presented using the Lyapunov stability and neighbor information interaction principle. In the end, numerical simulation experiments are offered to indicate the availability and correctness of the theoretical results.

Binocular reconstruction of breaking ship bow waves in circulating water channel

This study conducts an experiment on the bow waves generated by a 1:80 KRISO container ship (KCS) model in a circulating water channel. The Froude numbers (characterized by the length of perpendiculars) reach high conditions of 0.377, 0.424, and 0.471. A binocular imaging system is employed to reconstruct three-dimensional configurations of the bow wave surface. The dynamic characteristics of bow wave fields are investigated by observing the standard deviation and employing the Proper Orthogonal Decomposition (POD) method. The power spectral density function presents a power-law relationship with frequency. A novel technique referred as Stereoscopic Foam Image Velocimetry (SFIV) is developed to extract the instantaneous three-dimensional velocity of the foam in breaking area. The velocity field obtained through SFIV defines the nominal time-averaged velocity and nominal turbulent energy. A correlation mapping from pixel coordinates to world coordinates is established to evaluate the actual physical uncertainty. The results demonstrate the superior spatiotemporal accuracy and resolution of binocular imaging technology in measuring the characteristics of bow waves. This research provides significant experimental data of surface three-dimensional configurations for the bow waves breaking issues at high Froude numbers.

An Intuitive Stability Analysis Method for Single-Parameter Variations in Linear Systems

Analyzing the influence of controller parameters and physical system uncertainty is the premise of system stability design. This letter presents an intuitive analysis method for single-parameter variations in linear systems. Different from the root locus analysis, in the proposed method, the effect of single-parameter full-range variations on the system stability can be clearly visualized by simply plotting one Nyquist curve of reconstructed function at an arbitrary parameter point. Finally, the validity of the proposed method is demonstrated by a case study for the single-phase grid-following inverter.

Tracking solar radio bursts using Bayesian multilateration

Solar radio bursts (SRBs), such as Type IIs and IIIs, are emitted by electrons propagating through the corona and interplanetary space. Tracking such bursts is key to understanding the properties of accelerated electrons and radio wave propagation as well as the local plasma environment that they propagate through. In this work, we present a novel multilateration algorithm called BayEsian LocaLisation Algorithm (BELLA) and validate the algorithm using simulated and observed SRBs. In addition, apparent SRB positions from BELLA are compared with comparable localisation methods and the predictions of solar wind models. BELLA uses Bayesian inference to create probabilistic distributions of source positions and their uncertainties. This facilitates the estimation of algorithmic, instrumental, and physical uncertainties in a quantitative manner. We validated BELLA using simulations and a Type III SRB observed by STEREO A and STEREO B at pm 116 degr from the Sun-Earth line and by Wind at L1. BELLA tracked the Type III source from sim 10--150 $R_ (2--0.15 MHz) along a spiral trajectory. This allowed for an estimate of an apparent solar wind speed of sw 400 km $ and a source longitude of $ 30degr . We compared these results with well-established methods of positioning: Goniopolarimetric (GP), analytical time-difference-of-arrival (TDOA), and Solar radio burst Electron Motion Tracker (SEMP). We found them to be in agreement with the results obtained by BELLA. Additionally, the results aligned with solar wind properties assimilated by the Heliospheric Upwind Extrapolation with time dependence (HUXt) model. We have validated BELLA and used it to identify apparent source positions as well as velocities and densities of the solar wind. Furthermore, we identified higher than expected electron densities, suggesting that the true emission sources were at lower altitudes than those identified by BELLA, an effect that may be due to appreciable scattering of electromagnetic waves by electrons in interplanetary space.