Parameter Fitting Method Research Articles

Study of a semi-data-driven high-precision spatial load spectrum fitting method for pantograph design

The frequent failures of the pantograph pose a significant risk to the reliable operation of the pantograph-catenary systems (PCS). However, pantograph failures have not received sufficient attention in PCS research, where studies typically focus on system interactions rather than on the pantograph itself. Moreover, high precision load spectrum fitting is also one of the focuses of load spectrum research, therefore, a semi-data-driven high-precision spatial load spectrum fitting method for the pantograph is proposed in this paper. First, a PCS model with a rigid-flexible hybrid pantograph was established and validated to obtain the spatial load at the hinge of the upper arm. Second, an improved parametric load spectrum fitting method was proposed based on single-function estimation methods and chi-square test, while Gaussian kernel density estimation (GKDE) was also employed for fitting and subjected to the chi-square test. Third, the goodness-of-fit for all methods was evaluated using multiple indicators, followed by a comprehensive ranking to identify the optimal fitting method. Finally, a process for determining the optimal load spectrum fitting method was summarized from the above procedures. The results indicate that single functions exhibit poor adaptability to the data due to the limitations of prior knowledge, the improved method proposed in this paper overcomes this problem and enhances the accuracy of individual fittings. Furthermore, compared to the GKDE method, the fitting accuracy was improved by more than 30%, with a maximum improvement of 69.13%, this provides an effective data processing approach for fatigue assessment and life prediction.

Reliability analysis of the vehicle door system EDCU based on Weibull distribution

The paper established a two-parameter Weibull distribution model to analyze the failure law of key components of metro vehicles and employed the least squares method to fit the parameters of the Weibull function. The paper provided a detailed introduction of the model's parameter fitting method based on actual historical failure data. Taking the EDCU (Electrical Door Control Unit) as an example, the failure rate, cumulative failure rate, and reliability of EDCU for 3 different vehicle models were calculated, and the calculation results were verified to conform to the Weibull distribution through Q-Q diagrams. The results show that although the designed service life of EDCU of vehicle door system is 15 years, the reliability of the EDCU decreases significantly around 10 years. The EDCU reliability of the three vehicle models declines by 22%, 4.2%, 10.6% and the failure rates are 2.7%, 0.57%, 1.13%. Based on the reliability of EDCU mentioned above, while ensuring the reliability of components, the maintenance methods of components can be optimized to reduce maintenance costs.

Comparison of terrestrial exospheric hydrogen 3D distributions at solar minimum and maximum using TWINS Lyman-α observations

Remote sensing observations of far-ultraviolet (FUV) emissions have been used to estimate 3D neutral hydrogen (H) density models of the terrestrial exosphere under solar minimum (2008) and solar maximum (2013 and 2015) conditions. Specifically, we used Lyman-alpha (Lyman-α, FUV at 121.6 nm) radiance data acquired by the Lyman-alpha detectors (LADs) onboard NASA’s TWINS satellites, collected over several days for each of the 3 years to provide sufficient coverage of the exospheric region. The datasets included Lyman-α measurements taken only above Earth radii (Re) of 3.75, assumed to be the optically thin region of the exosphere, where the measured Lyman-α intensity along a line of sight (LOS) is linearly proportional to the atomic hydrogen column density. Based on the calibration using multiple UV-bright stars, a significant decrease in TWINS1 LAD1/2 sensitivities was found for 2013 (LAD2 ∼1/2, LAD ∼1/3) and 2015 (LAD2 ∼1/3, LAD ∼1/7) compared to 2008. The calibration uncertainty was derived to be, on average, 5%. We estimated the 3D global hydrogen density distributions from these radiance data using two different tomographic inversion methods: first, a parametric fitting method based on a spherical harmonic function of order 3 and second, a high degree-of-freedom retrieval approach to validate our retrievals of H density. Both inversion methods consistently incorporate the effects of Lyman-α absorption within the exosphere and Lyman-α re-emission from Earth’s albedo. Our results reveal that H densities during solar maximum conditions are, on average, 30%–40% higher than those during solar minimum. All models showed a high concentration of atomic H on the dayside and nightside near the Sun–Earth line, which determines a nose/geotail structure consistent with theoretical effects from the solar radiation pressure. Furthermore, we identified that H-density enhancements during solar maximum with respect to solar minimum conditions occur at mid-to-high latitudes, particularly on the dusk side, while no significant enhancement seems to occur near the dayside nose.

An Assessment of the Residual Stress of Pipelines Subjected to Localized Large Deformations

Subsea pipelines subjected to impacts are prone to generating significant deformations and residual stresses, which could reduce their structural integrity and increase the risk of failure. This paper introduces analytical and numerical frameworks aimed at predicting residual stress behavior induced by subsea pipeline impacts. An empirical formula to regulate residual stress levels in extensively deformed submarine pipelines is derived through a parameter-fitting method. This formula enables the swift and accurate computation of the residual stress magnitudes in such pipelines. Abaqus is employed to simulate the residual stresses in large-deformation submarine pipelines. The results of the finite element analysis are validated through experimental work. A comprehensive database is constructed via the finite element method to fit an empirical formula for residual stresses in large-deformation submarine pipelines. The empirical formula places particular emphasis on the influence of the diameter-to-thickness ratio and dent depth on the residual stresses. It is crucial for pipeline design and maintenance.

Fretting fatigue life prediction of full-scale dovetail joints using the theory of critical distances with mesh control

Fretting fatigue life prediction of full-scale dovetail joints using the theory of critical distances with mesh control

Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid (17-HDHA, a metabolite of docosahexaenoic acid (DHA)), is significantly associated with OA pain. The aim of this multidisciplinary work is to develop a mathematical model to describe the contributions of enzymatic pathways (and the genes that encode them) to the metabolism of DHA by monocytes and to the levels of the down-stream metabolites, 17-HDHA and 14-hydroxydocasahexaenoic acid (14-HDHA), motivated by novel clinical data from a study involving 30 participants with OA. The data include measurements of oxylipin levels, mRNA levels, measures of OA severity and self-reported pain scores. We propose a system of ordinary differential equations to characterise associations between the different datasets, in order to determine the homeostatic concentrations of DHA, 17-HDHA and 14-HDHA, dependent upon the gene expression of the associated metabolic enzymes. Using parameter-fitting methods, local sensitivity and uncertainty analysis, the model is shown to fit well qualitatively to experimental data. The model suggests that up-regulation of some ALOX genes may lead to the down-regulation of 17-HDHA and that dosing with 17-HDHA increases the production of resolvins, which helps to down-regulate the inflammatory response. More generally, we explore the challenges and limitations of modelling real data, in particular individual variability, and also discuss the value of gathering additional experimental data motivated by the modelling insights.

Numerical analysis of the local damage of RC beams under close‐in explosions based on the calibrated Karagozian & Case (K&C) concrete model

AbstractLimited research has been carried out to investigate the local damage features of reinforced concrete (RC) beams under close‐in explosions. To better capture the local damage features of rectangular cross‐sectional RC beams, a numerical study on the RC beams subjected to close‐in explosions based on the calibrated Karagozian & Case (K&C) concrete model was conducted in LSDYNA. First, a systematic calibration of the K&C model for concrete was performed in the single‐element numerical analysis. Calibration of the K&C model consists of parameter determination for the new strength surfaces, modification of the damage function to better feature the tensile behavior of concrete, elimination of the element size effect by introducing an element size factor and determination of the scaled damage factors. The new strength surfaces are verified and determined through both the approximation calculation method and the parameter fitting method. And the damage function was modified by reducing the termination of λ to better characterize the brittleness of concrete and feature the tensile failure. A comparison between the numerical results and the corresponding experimental results demonstrates that the calibrated K&C model and established FEM model of RC beams subjected to close‐in explosions can well characterize the local damage features of RC beams. On this basis, a further parameter analysis on the factors influencing the local damage response of RC beams was conducted by considering reinforcement details (stirrup spacing and longitudinal reinforcement diameter) and charge details (charge mass and aspect ratio). Results show that the close‐in explosions destroyed the concrete corners in the blast surface with shear stress first and the side shear failure of concrete corners weakens the concrete core strength and contributes to the greater loss of concrete core. Rear spalling damage was initially caused by the bond failure between the tensile longitudinal reinforcement and the surrounding concrete. Furthermore, increasing stirrup spacing, tensile longitudinal reinforcement diameter, and charge mass contribute to the increase in local damage sizes.

MASS PROFILES OF LATE GALAXIES USING A GENETIC ALGORITHM. I - TESTING THE ALGORITHM

The rotation curve of a galaxy contains a wealth of information about its dynamical properties, being the mass distribution one of the most important. The rotation curve fitting procedures used to estimate the mass profiles of disc galaxies have become more sophisticated over the years, providing ever more reliable results. However, the time-cost and data requirements (e.g. high-resolution NIR photometry) necessary to put to use some of them have restricted these kind of studies to small samples of galaxies. We propose a simple procedure that could be used as a good first approximation for the study of large galaxy samples. It is based on a parameter-fitting method along with a recent optimization algorithm, called the Asexual Genetic Algorithm (AGA). With this procedure, we were able to replicate previously published results, within uncertainties, suggesting that it will provide a reliable first estimation, suitable for its application to large galaxy samples.

Realistic 3D Face Reconstruction Method for Single Image

To solve the problem that the 3DMM parameter fitting methods cannot generate realistic 3D face, a single-image realistic 3D face reconstruction method based on deep learning is proposed. Firstly, the RP-Net regression network is constructed, and a dataset containing 50 000 face images is constructed at the same time. The parameters are learned from the input images, and the face model is fitted to generate the 3D face geometry. Secondly, weakly supervised learning is performed by constructing a multi-level loss function, which includes low-level pixel loss, landmark loss, and high-level identity loss. Thirdly, a realistic face texture is generated by means of texture mapping. Finally, two real face data and one generated data are used to compare experiments with recent 3D face reconstruction methods. The factors affecting the reconstruction such as lighting, expression, and steering are used to test proposed method, and quantitatively evaluate the reconstruction by SSIM and PSNR. These results show that proposed method can generate accurate face shapes and realistic face textures. Compared with the recent 3D face reconstruction method, the training time and number of iterations of the proposed method are reduced by 6% and 13%, respectively, the SSIM value is increased by 0.005‒0.010, and the PSNR value is increased by 0.03‒0.08 dB on average.

Experimental Study on the Evolution Law of Coal Mine Underground Reservoir Water Storage Space under the Disturbance and Water—Rock Interaction Effect

The void of the cracked rock mass of the goaf is the main water storage space of underground reservoirs, which is in a time-space dynamic evolution process. Before the formation of the underground reservoir, the water storage space was primarily affected by disturbances. After the safe operation of the coal mine underground reservoir, the water level of the mine rises and falls repeatedly and the water storage space is affected by the water-rock interaction. To study the void evolution law of a cracked rock mass under mining disturbance and the compaction and void deformation characteristics of caving gangue under the effect of the water-rock interaction, a simulation test of a coal mine underground reservoir is conducted. Furthermore, the rupture motion law and movement deformation characteristics of the overburden during coal mining are analyzed. The digital image method and fractal theory are introduced to describe the fractal characteristics of the rock mass void of the caving zone, fracture zone, and entire goaf during the mining process. Five prototype gangue samples with different immersion times are prepared with the same grain size grading as the similar model caving gangue. The influence of the immersion times on the compaction characteristics and evolution law of the void rate of the gangue are also studied. Based on the parameter fitting method, the stress–strain relationship equation of the gangue sample and void rate-stress relationship equation of the cylindrical gangue sample, considering the influence of the immersion times, are constructed. The results show that the overburden of the model is of a “two zone” structure and the entire structure moves and sinks asymmetrically in a “∩” shape. As the advancing distance of the working face increased, the fractal dimensions of the rock mass void of the caving zone and entire goaf increased logarithmically, and the fractal dimension of the rock mass void of the fracture zone first increased rapidly (60–80 cm) and then decreased linearly (80–200 cm). As the immersion time increased, the saturated moisture content and density of the gangue samples increased logarithmically and exponentially, respectively. Under the same stress, the strain of the gangue sample increased gradually, and the void rate decreased gradually (except for the initial loading).

Analysis of CFRP-confined CFST columns reinforced with steel angles under axial compression

To study the axial compression properties of specimens of concrete-filled steel tubes reinforced with steel angles, abbreviated as SRCFST, and of specimens of FRP-confined SRCFST, abbreviated as F-SRCFST, relevant finite element (FE) models were established using ABAQUS software. For verifying the accuracy of the proposed FE models, the axial load carried by each component of the specimen was first analysed and the distribution rules of the contact pressure between the steel tube and concrete as well as between the steel angles and concrete were analysed. In the second phase, the important parameters, such as the yield strength and wall thickness of the steel tube, the yield strength and cross-sectional area of the steel angles, the tensile strength and number of FRP wrapping layers were analysed. The third phase consisted of creating and proposing the design formulas for the SRCFST and F-SRCFST specimens on the basis of parametric analyses and numerical fitting method. The research results indicate that FRP has a minimal effect on the axial carrying capacity of the steel tube and the fundamental effect for the improved ultimate load is the indirect confinement effect by the FRP on the concrete. The proposed design formulas can accurately predict the ultimate load of SRCFST and F-SRCFST specimens, and the calculation error is generally within 10%.

An improved parameter fitting approach of a planar biaxial test including the experimental prestretch

Planar biaxial testing is a popular experimental technique for characterizing and comparing biological soft tissues. A correct identification of the different stress states of the tissue sample is therefore essential. However, the difference between the zero-stress reference state and the sample state prior to the loading cycle caused by the mounting, preconditioning and preloading is often not considered. The importance of this difference, caused by prestretch, is investigated by simulating virtual planar biaxial experiments, either assuming an ideal test with a single deformation gradient or using finite element modeling to simulate a rake-based experiment. Multiple parameter fitting methods are used to estimate the material properties based on the available experimental data. These methods vary based on how they approximate the zero-stress state: either the prestretch is ignored, or the loads are zeroed after the preload has been reached, or the unknown prestretch values are included into the optimization function. The results reveal the high necessity of assessing the stress-free state when analyzing a planar biaxial test. The material fitting including the prestretch outperforms the other methods in terms of correctly describing the mechanical behavior of the tested material. It can be extended to correct for the boundary effects induced by the gripping mechanisms, providing a more accurate, yet more computationally expensive estimate of the material properties.

Research on Analog-to-Digital Converter (ADC) Dynamic Parameter Method Based on the Sinusoidal Test Signal

The acquisition of dynamic analog-to-digital converter (ADC) parameters is becoming increasingly relevant as electronic information develops at a rapid pace. The fundamental challenge of the spectrum test for ADC is that coherent sampling is difficult to achieve, especially because of the high accuracy of the excitation signal necessary for coherent sampling. Therefore, incoherent sampling is certainly unavoidable in the actual test. If the coherent sampling condition is not reached in the test, spectrum leaks from test data after Discrete Fourier Transform (DFT) analysis, resulting in inaccurate parameters. In this study, a new breakdown and reconstruction method was presented using the Ensemble Empirical Mode Decomposition (EEMD); Hilbert transform and parameter fitting method can accurately estimate the incoherent fundamental and harmonic waves, then reconstruct them to obtain accurate ADC dynamic parameters.

Physics-encoded deep learning in identifying battery parameters without direct knowledge of ground truth

We show a method to embed physical laws and on-line observation into machine learning so that irrelevant low-cost battery data can be utilized to identify complex system parameters by machine learning without knowledge of their ground truth as the training data. Lithium diffusivity, a complicated function of lithium concentration, is a crucial parameter for battery performance but difficult to measure directly. We take diffusivity as an example and show that it can be obtained from easily measured sequence of battery voltage over time. In simulations, our results show that this method accurately quantifies not only the diffusivities of both positive and negative electrodes, but also as complex non-linear functions of lithium concentration, purely based on the cell voltage data requiring neither diffusivity nor concentration measurement. Notably, it can accurately predict non-monotonic, many-to-one relations such as “w” shape functions. Moreover, this method is immune to measurement noise and capable of simultaneously estimating multiple parameters. In experiments, our method demonstrates more robust diffusivity estimation than a pure physics-based parameter fitting method and a widely used experimental technique. Our results suggest that the approach enables identifying physical parameters and their interdependence without direct measurements of those parameters.

Study on dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials based on DMA

Abstract Nonwater reacted polyurethane grouting materials are new materials developed to make up for the shortcomings of water-reactive materials in emergency rescue. However, its viscoelastic properties and constitutive model under dynamic loads have not been systematically studied. Based on dynamic thermal mechanical analysis (DMA), the dynamic viscoelastic indexes such as storage modulus, loss modulus, and loss factor of nonwater reacted polymer grouting material were obtained, and the frequency spectrum of polymer with different densities were analyzed. In addition, comparing and analyzing the classical viscoelastic constitutive models such as Maxewell model, Kelvin model, and Fractional model, the fourth-order generalized Maxwell model (GMM) was selected to construct the viscoelastic constitutive model of polyurethane grounding materials. Then, the parameters of the viscoelastic constitutive model of polyurethane grounding materials were obtained by using multi-objective shared parameter fitting method, and dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials was established. Furthermore, the viscoelastic constitutive model with different densities was verified by the DMA test. The results show that the dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials in the article can accurately and efficiently describe the dynamic viscoelastic properties of polyurethane grounding materials, which lays a foundation for the dynamic response analysis of polymer structures.

Temperature measurement with photodiodes: Application to laser diode temperature monitoring

The temperature feedback of solid state laser diodes and various photovoltaic devices is critical for stable and reliable usage. We demonstrate that with a simple and passive electrical measurement process and optical calibration method the temperature of a photodiode can be determined, while keeping its original purpose. We present the idea with simulation and experiments, and provide an illumination-based parameter fitting method. The presented use case is a 5.6 mm IR laser diode. We used its monitor photodiode to track the temperature inside the package with significantly better temporal resolution than the off-the-shelf external heat sink sensor provides. We reached a time resolution in the range of milliseconds and achieved precision of ±10 mK with ±3 K absolute, uncalibrated precision. The technique is not restricted to laser diodes, it is applicable to photovoltaic cells, photodiode arrays, organic diodes as well. The stability of atoms when they are released from confinement is studied. We consider H atom inside a spherical hard wall potential. The ionization probability is calculated for different initial confined states and radii. In the figure the probability density function for the ionization energy when the electron is ejected from the N shell confined to 6 au. The minima are close to zero the maximum is at the energy of the confined orbital. • A TO can packaged laser diode temperature is measured by its monitoring photodiode. • Time resolution in the range of milliseconds and precision of ±10 mK with ±3 K absolute temperature achieved. • No complex instrumentation is needed, changing external illumination is used only for photodiode parameter identification. • Existing setups can be extended to monitor temperature with no additional sensors. • Other photosensitive devices can be monitored, such as photovoltaic cells, organic diodes, photo diode arrays.

In-flight polarization angle calibration for LiteBIRD: blind challenge and cosmological implications

We present a demonstration of the in-flight polarization angle calibration for the JAXA/ISAS second strategic large class mission, LiteBIRD, and estimate its impact on the measurement of the tensor-to-scalar ratio parameter, r, using simulated data.We generate a set of simulated sky maps with CMB and polarized foreground emission, and inject instrumental noise and polarization angle offsets to the 22 (partially overlapping) LiteBIRD frequency channels. Our in-flight angle calibration relies on nulling the EB cross correlation of the polarized signal in each channel. This calibration step has been carried out by two independent groups with a blind analysis, allowing an accuracy of the order of a few arc-minutes to be reached on the estimate of the angle offsets. Both the corrected and uncorrected multi-frequency maps are propagated through the foreground cleaning step, with the goal of computing clean CMB maps. We employ two component separation algorithms, the Bayesian-Separation of Components and Residuals Estimate Tool (B-SeCRET), and the Needlet Internal Linear Combination (NILC). We find that the recovered CMB maps obtained with algorithms that do not make any assumptions about the foreground properties, such as NILC, are only mildly affected by the angle miscalibration. However, polarization angle offsets strongly bias results obtained with the parametric fitting method. Once the miscalibration angles are corrected by EB nulling prior to the component separation, both component separation algorithms result in an unbiased estimation of the r parameter. While this work is motivated by the conceptual design study for LiteBIRD, its framework can be broadly applied to any CMB polarization experiment. In particular, the combination of simulation plus blind analysis provides a robust forecast by taking into account not only detector sensitivity but also systematic effects.

Relative Pose Determination of Uncooperative Spacecraft Based on Circle Feature

This paper investigates the problem of spacecraft relative navigation with respect to an unknown target during the close-proximity operations in the on-orbit service system. The serving spacecraft is equipped with a Time-of-Flight (ToF) camera for object recognition and feature detection. A fast and robust relative navigation strategy for acquisition is presented without any extra information about the target by using the natural circle features. The architecture of the proposed relative navigation strategy consists of three ingredients. First, a point cloud segmentation method based on the auxiliary gray image is developed for fast extraction of the circle feature point cloud of the target. Secondly, a new parameter fitting method of circle features is proposed including circle feature calculation by two different geometric models and results’ fusion. Finally, a specific definition of the coordinate frame system is introduced to solve the relative pose with respect to the uncooperative target. In order to validate the efficiency of the segmentation, an experimental test is conducted based on real-time image data acquired by the ToF camera. The total time consumption is saved by 94%. In addition, numerical simulations are carried out to evaluate the proposed navigation algorithm. It shows good robustness under the different levels of noises.

Improvements in Sub-Catchment Fractional Snowpack and Snowmelt Parameterizations and Hydrologic Modeling for Climate Change Assessments in the Western Himalayas

The present work proposes to improve estimates of snowpack and snowmelt and their assessment in the steep Himalayan ranges at the sub-catchment scale. Temporal variability of streamflow and the associated distribution of accumulated snow in catchments with glacier presence in the Himalayas illustrates how changes in snowpack and snowmelt can affect the water supply for local water management. The primary objective of this study is to assess the role of elevation, temperature lapse rate (TLR), and precipitation lapse rate (PLR) in the computation of snowpack (or snowfall) and snowmelt in sub-catchments of the Satluj River basin. Modeling of snowpack and snowmelt was constructed using the Soil Water Assessment Tool (SWAT) in both historical (1991–2008) and near-time scenarios (2011–2030) by implementing real-time hydrometeorological, snow-hydrological parameters, and Global Circulation Model (GCM) datasets. The modeled snowmelt-induced streamflow showed a good agreement with the observed streamflow (~60%), calibrated and validated at three gauges. A Sequential Uncertainty Parameter Fitting (SUFI2) method (SUFI2) resulted that the curve number (CN2) was found to be significantly sensitive during calibration. The snowmelt hydrological parameters such as snowmelt factor maximum (SMFMX) and snow coverage (SNO50COV) significantly affected objective functions, such as R2 and NSE, during the model optimization. For the validation of snowpack and snowmelt, the results have been contrasted with previous studies and found comparable. The computed snowpack and snowmelt were found highly variable over the Himalayan sub-catchments, as also reported by previous researchers. The magnitude of snowpack change consistently decreases across all the sub-catchments of the Satluj river catchment (varying between 4% and 42%). The highest percentage of changes in the snowpack was observed over high-elevation sub-catchments.

OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany.

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.