Noise Uncertainty Research Articles

An Approach to Quantifying the Distribution of Resonance and Cancellation Train Speeds of Railway Bridges with Random Uncertainties

An Approach to Quantifying the Distribution of Resonance and Cancellation Train Speeds of Railway Bridges with Random Uncertainties

Prescribed performance dynamic surface control based on dual extended state observer for 2-dof hydraulic cutting arm

In tunnel section forming operations, the boom-type roadheader tracking target trajectory with high precision is greatly significant in avoiding over and under excavation and improving excavation efficiency. However, there exist complex cutting loads, measurement noise, and model uncertainties, seriously degrading the tracking performance of traditional nominal model-based controllers. Hence, this study first fully analyzes the kinematics of all members of the cutting mechanism and establishes its complete multi-body dynamic model using the Lagrange method. Furthermore, a dual extended state observer is designed to estimate the mechanical system’s angular velocity and unmodeled disturbances and actuators’ uncertain nonlinearities. In particular, introducing a nonlinear filter replaces the traditional first-order filter in dynamic surface technology, overcoming the “explosion of complexity” while attenuating the conservatism of gains tuning. Then, a dual extended state observer-based prescribed performance dynamic surface controller is developed for roadheaders for the first time. Simultaneously, integrating an improved error transformation function into controller design effectively avoids the online computational burden caused by traditional logarithmic operations. Utilizing Lyapunov theory, the cutting system’s prescribed transient response and steady-state performance are guaranteed. Finally, the proposed controller’s effectiveness is verified by comparative experiments on the roadheader.

Enhanced operational modal analysis and change point detection for vibration-based structural health monitoring of bridges

One of the most promising uses of vibration-based structural health monitoring (VBSHM) in bridge damage detection is the tracking of modes through long-term repeated or continuous operational modal analysis (OMA). Any shifts in modal parameters over time can signal structural damage. However, in real-world applications, noise and environmental uncertainties introduce variability in the data, potentially obscuring damage-related changes. To address this, it is essential to establish and understand the temporal trends and behavior of the estimated modal parameters, enabling accurate interpretation of the engineering data. This paper presents a detailed study focusing on data-driven techniques to improve the OMA results by determining the causes of modal variability and establishing modal models to filter out these known causes of variability. It explores the use of data continuously collected over a period of one month in November 2017 on the Confederation Bridge in eastern Canada. Operational modal analysis is conducted to extract modal frequencies and mode shapes, revealing correlations with environmental and operational factors such as wind, temperature and vehicular traffic. A novel approach using the residuals from regression modal models for damage detection is proposed, utilizing a change point detection algorithm. Results indicate the potential to detect shifts in modal frequencies corresponding to damage scenarios, at lower levels than was previously possible, highlighting the feasibility of using enhanced modal features for sensitive damage identification. Overall, the paper contributes to advancing the understanding of variability in vibration-based structural health monitoring and presents a promising practical technique for improving damage detection results using enhanced operational modal estimates in realistic field applications of a real-world structure.

The importance of adding unbiased Argo observations to the ocean carbon observing system

The current coverage of direct, high-quality ship-based observations of surface ocean pCO2 includes large gaps in time and space, and has been declining since 2017. These ocean observations provide the basis for the data products that reconstruct surface ocean pCO2 and estimate ocean carbon uptake. Improved data coverage is needed to advance our understanding of the ocean carbon sink and air–sea CO2 exchange. Targeted sampling from autonomous platforms, such as biogeochemical floats, combined with traditional shipboard measurements represents a promising path forward to improve surface ocean pCO2 reconstructions. However, floats provide indirect pCO2 estimates derived from pH, and thus have higher uncertainty and are biased compared to direct shipboard measurements. Here, we use a Large Ensemble Testbed (LET) of Earth System Models and the pCO2-Residual method to reconstruct surface ocean pCO2 globally to test the impact of additional float observations, both with and without measurement uncertainties. Through comparison to the ‘model truth’, the LET allows for robust evaluation of the reconstructions. With only shipboard sampling, surface ocean pCO2 is overestimated, and the 2000–2016 global ocean carbon sink is underestimated by 0.1 Pg C year−1. Additional float observations significantly reduce this underestimation, and deviate from the ‘model truth’ by as little as 0.01 Pg C year−1, even when floats have random uncertainties of ± 11 μatm. However, systematic bias in the float observations significantly degrades the accuracy of pCO2 reconstructions, leading to an even stronger underestimation of the global ocean carbon sink of up to 0.32 Pg C year−1. We conclude that adding float-based observations to the global observing system can significantly improve reconstructions of global surface ocean pCO2, but only if these data are unbiased.

Uncertainty quantification for natural frequency and mode of variable angle tow composite plates with random and interval uncertainties

Variable angle tow (VAT) composite laminated structures are produced by automated tow-placement technology which can take advantage of the designability of composites to meet the aerospace industry’s need for dynamic properties. Complex production techniques inevitably lead to uncertainties in material properties due to manufacturing defects. The aim of this work is to present an efficient computational method for estimating the dynamical properties of VAT composite laminated plates due to multiscale hybrid uncertainties. This method consists of perturbation stochastic finite element method and particle swarm optimization combined with Mori-Tanaka homogenization. The degree of influence of the multiscale parameters on the dynamic properties of VAT composites with different structural forms has been obtained by sensitivity analyses of the frequency and mode. The method is applied to investigate variations in natural frequency and mode of a variety of VAT composite laminated plates with different fiber tow paths, layers, and boundary conditions. The results indicate that variations in natural frequencies and mode shapes are strongly linked to fiber tow paths and boundary conditions. The frequency and modes of the VAT show a nonlinear variation with angle. This method can quickly obtain the probability distribution intervals of the frequency, which is of great significance for assessing the reliability of VAT composites laminated plates dynamic designs.

Coordinated energy storage and network expansion planning considering the trustworthiness of demand-side response

The enhancement of economic sustainability and the reduction of greenhouse gas (GHG) emissions are becoming more relevant in power system planning. Thus, renewable energy sources (RESs) have been widely used as clean energy for their lower generation costs and environmentally friendly characteristics. However, the strong random uncertainties from both the demand and generation sides make planning an economic, reliable, and ecological power system more complicated. Thus, this paper considers a variety of resources and technologies and presents a coordinated planning model including energy storage systems (ESSs) and grid network expansion, considering the trustworthiness of demand-side response (DR). First, the size of a single ESS was considered as its size has a close effect on maintenance costs and ultimately affects the total operating cost of the system. Second, it evaluates the influence of the trustworthiness of DR. Third, multiple resources and technologies were included in this high-penetration renewable energy integrated power system, such as ESSs, networks, DR technology, and GHG reduction technology. Finally, this model optimizes the decision variables such as the single size and location of ESSs and the operation parameters such as thermal generation costs, loss load costs, renewable energy curtailment costs, and GHG emission costs. Since the problem scale is very large not only due to the presence of various devices but also both binary and continuous variables considered simultaneously, we reformulate this model by decomposition. Then, we transform it into a master problem (MP) and a dual sub-problem (SP). Finally, the proposed method is applied to a modified IEEE 24-bus test system. The results show computational effectiveness and provide a helpful method in planning low-carbon electricity power systems.

Physics-informed neural network estimation of material properties in soft tissue nonlinear biomechanical models

AbstractThe development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach, which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties and secondary variables such as stresses and strains. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method with respect to noise and model uncertainty and its great potential to enable the effective identification of patient-specific, heterogeneous physical properties, e.g. tissue stiffness properties. In particular, we demonstrate the capability of PINNs to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

Stochastic Model Predictive Control Based on Polynomial Chaos Expansion With Application to Wind Energy Conversion Systems

The wind energy conversion system (WECS) has a complex structure, and its state space model is highly nonlinear. Due to the random uncertainty of wind speed, it poses a huge challenge to achieve optimal control tasks and ensure the safe and stable operation of the system. Therefore, this article proposes a stochastic model predictive control strategy based on Polynomial Chaotic Expansion (PCE), which achieves the control tasks of MPPT and constant power regions in wind energy conversion systems. Firstly, a simple algorithm is proposed to obtain a set of basis functions that are suitable for the stochastic variable wind speed. Then, the obtained basis functions are used to propagate the uncertainty of the original uncertain differential equation of the wind energy conversion system through polynomial chaotic expansion. Combining the operating region and constraint conditions of the wind energy conversion system, the original stochastic uncertainty problem is transformed into a deterministic convex optimization problem. Using NREL 5MW wind turbine as the research object for simulation, the task of capturing maximum wind energy in MPPT area and tracking rated power points in constant power area was achieved. The experimental results show that the proposed control method can effectively improve the wind energy capture capability and achieve accurate tracking of output power to rated power.

An improved limited memory-Sage Husa-cubature Kalman filtering algorithm for the state of charge and state of energy co-estimation of lithium-ion batteries based on hysteresis effect-dual polarization model

The accurate estimation of battery state of charge (SOC) and state of energy (SOE) are the key technologies in researching battery management systems. Due to the uncertainty of prior noise in practical engineering, traditional cubature Kalman filters (CKF) have lower filtering accuracy. This paper proposes an improved limited memory-Sage Husa-cubature Kalman (LM–SH–CKF) algorithm to estimate the SOC and SOE of lithium-ion batteries. During the filtering process, the Sage-Husa estimator is introduced to estimate the noise, correcting the statistical characteristics of the noise in real-time, thereby improving the estimation accuracy. Meanwhile, establish a filtering divergence criterion to determine whether the filtering is abnormal and ensure the real-time performance of the algorithm. To improve the accuracy of parameter identification, the Hysteresis Effect-Dual Polarization (HE-DP) model is established and the limited memory recursive least square (LMRLS) algorithm is proposed. The results show that the LM–SH–CKF has the smallest mean absolute error (MAE) and root mean square error (RMSE). Under the dynamic stress test (DST) at 15 °C, the estimated MAE and RMSE of SOC and SOE are both less than 1 %. The LM–SH–CKF has high accuracy and robustness, and short calculation time, providing a reference for battery status monitoring.

Guided-wave Dynamic Probability Model-based Crack Quantification Method for Metal Structures

In the process of applying guided-wave-based aircraft online structural health monitoring, the characteristics of guided wave signals used to represent structural status exhibit random uncertainty due to the interference of loads on guided wave propagation. The trend of signal feature changes caused by damage is often obscured, making the quantification of cracks under loads one of the challenges in online structural health monitoring for aircraft. To address this challenge, this paper proposes a crack quantification method using an adaptive Gaussian mixture model (GMM) and optimized probability migration distance measurement. This method effectively mitigates the uncertainty caused by loads by constructing an adaptive Gaussian mixture model to track the probability distribution changes of guided wave signal features under different structural health conditions. Subsequently, an optimized probability migration distance measurement method is employed to characterize the structural state, further enhancing the correlation between features and the extent of structural damage. Finally, an optimized probability migration distance relationship with crack length is established to estimate the crack length of new structural specimens. The effectiveness of this method is validated using load-induced crack propagation experiments on metal structures.

Prediction of Operational Noise Uncertainty in Automotive Micro-Motors Based on Multi-Branch Channel–Spatial Adaptive Weighting Strategy

The acoustic performance of automotive micro-motors directly impacts the comfort and driving experience of both drivers and passengers. However, various motor production and testing uncertainties can lead to noise fluctuations during operation. Thus, predicting the operational noise range of motors on the production line in advance becomes crucial for timely adjustments to production parameters and process optimization. This paper introduces a prediction model based on a Multi-Branch Channel–Spatial Adaptive Weighting Strategy (MCSAWS). The model includes a multi-branch feature extraction (MFE) network and a channel–spatial attention module (CSAM). It uses the vibration and noise data from micro-motors’ idle operations on the production line as input to efficiently predict the operational noise uncertainty interval of automotive micro-motors. The model employs the VAE-GAN approach for data augmentation (DA) and uses Gammatone filters to emphasize the noise at the commutation frequency of the motor. The model was compared with Convolutional Neural Networks (CNNs) and Multilayer Perceptrons (MLPs). Experimental results demonstrate that the MCSAWS method is superior to conventional methods in prediction accuracy and reliability, confirming the feasibility of the proposed approach. This research can help control noise uncertainty in micro-motors’ production and manufacturing processes in advance.

Uncertainty estimates in the NISAR high-resolution soil moisture retrievals from multi-scale algorithm

It is important to know the amount of systematic and random uncertainties in any state variable to improve its geophysical application potential. The expected high-resolution (200 [m]) soil moisture product from the NASA-ISRO Synthetic Aperture Radar (NISAR) mission is no exception. Thus, knowing the quality of the soil moisture retrievals through the estimation of various error sources is imperative. The estimation error sources in soil moisture retrievals can be obtained by various methods. In situ measurements provide a reliable estimate of the uncertainty of soil moisture retrievals. However, in situ measurements are available only for limited locations, as they are typically very tedious and expensive to obtain. Thus, an analytical approach has been developed to obtain an estimate of the uncertainty in the soil moisture retrievals that vary in space and time across grid-cells. This uncertainty estimation is specifically developed for the multi-scale algorithm of the upcoming NISAR mission, which will provide soil moisture retrievals at 200 [m] resolution. The multi-scale algorithm for the NISAR mission disaggregates the coarser resolution soil moisture (∼9 [km]) to high-resolution (∼200 [m]) using NISAR L-band SAR measurements. However, uncertainty in high-resolution soil moisture retrievals might be introduced due to errors in input datasets (e.g., coarse resolution soil moisture, instrument error of SAR, etc.) and multi-scale algorithm parameters. Therefore, this study carried out a detailed sensitivity analysis of input datasets and algorithm parameters using the proposed approach. The sensitivity analysis shows that error in the input coarse resolution soil moisture is one of the primary drivers of uncertainty in the high-resolution soil moisture retrievals. The other portion of the uncertainty comes from errors in the algorithm parameters, and noise in SAR co-pol and cross-pol backscatter observations. Furthermore, the approach was tested on the UAVSAR L-band data time-series that had been simulated to closely match the expected characteristics of NISAR (e.g., spatial resolution and noise). The uncertainty estimates in UAVSAR-based high-resolution retrievals were compared with the SMAPVEX-12 in situ measurements. The uncertainties estimated for different crops were found to be close to the ubRMSE metric, which is also lower than the NISAR mission accuracy goal (0.06 [m3/m3]).

Intuitionistic Connection Cloud Model Based on Rough Set for Evaluation of the Shrinkage–Swelling of Untreated and Lime-Treated Expansive Clays

The evaluation of the shrinkage–swelling characteristic of expansive clay is of great significance, but it is a complex problem since the evaluation process involves numerous uncertain factors, such as randomness, non-subordination, and hesitation uncertainties. Here, an intuitionistic connection cloud model has been proposed to address this issue. First, an evaluation index system is established. According to the reliability of interval-valued evaluation indexes, the corresponding cloud numerical characteristic parameters are specified based on the membership interval generated by the intuitionistic fuzzy principle. Moreover, the improved conditional information entropy based on rough set theory is utilized to assign the index weight. Subsequently, combined with the weight, the intuitionistic connection degree of the sample to the classification standard is determined to identify the shrinkage–swelling grade. Finally, a case study on the shrinkage–swelling grade of untreated and lime-treated expansive clays in Hefei Xinqiao International Airport was performed to illustrate the validity and reliability of the model. The results show that the proposed model is reasonable and feasible for the evaluation of the shrinkage–swelling grade of untreated and lime-treated expansive clays.

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.

Adaptive Load Frequency Control in Microgrids Considering PV Sources and EVs Impacts: Applications of Hybrid Sine Cosine Optimizer and Balloon Effect Identifier Algorithms

The negative impacts of microgrids (µGs) on the load frequency highlight the importance of implementing a robust, efficient, and adaptable controller to ensure stability. This work introduces an adaptive load frequency control (LFC) for an isolated µG that includes a PV system and electric vehicles (EVs), which have a significant impact on frequency. This control utilizes a combination of sine cosine optimization (SCO) and balloon effect identifier (BEI) algorithms. The controller presented in this work transforms the LFC process into an optimization problem that is highly compatible with various random situations encountered in the control process. The suggested control method is a novel approach by utilizing SCO+BEI for adaptive LFC application, resulting in a highly efficient response. The effectiveness of the proposed adaptive controller is assessed under the conditions of 17 MW variable load, system parameters uncertainties, and installed PV systems of 6 MW. MATLAB / Simulink package is rummage-sale as a digital test environment. According to simulation results, the proposed adaptive controller succeeds in regulating the frequency and power of an islanded µG. To measure the efficiency of the proposed control scheme, a comparison between other control techniques (such as adaptive controller using Jaya+BEI and classical integral controller) is done. The findings of the studied scenarios assured that the not compulsory control method using (SCO+BEI) has an obvious superiority over other control methods in terms of frequency solidity in case of random load instabilities and parameter uncertainties. Finally, it can be said that the proposed controller can better ensure the safe operation of the µGs.

Modeling correlated uncertainties in stochastic compartmental models

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein–Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles–Infected–Susceptibles (SIS) model and a Susceptibles–Exposed–Infected–Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model’s asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Integration of High-Rate GNSS and Strong Motion Record Based on Sage–Husa Kalman Filter with Adaptive Estimation of Strong Motion Acceleration Noise Uncertainty

A strong motion seismometer is a kind of inertial sensor, and it can record middle- to high-frequency ground accelerations. The double-integration from acceleration to displacement amplifies errors caused by tilt, rotation, hysteresis, non-linear instrument response, and noise. This leads to long-period, non-physical baseline drifts in the integrated displacements. GNSS enables the direct observation of the ground displacements, with an accuracy of several millimeters to centimeters and a sample rate of 1 Hz to 50 Hz. Combining GNSS and a strong motion seismometer, one can obtain an accurate displacement series. Typically, a Kalman filter is adopted to integrate GNSS displacements and strong motion accelerations, using the empirical values of noise uncertainty. Considering that there are significantly different errors introduced by the above-mentioned tilt, rotation, hysteresis, and non-linear instrument response at different stations or at different times at the same station, it is inappropriate to employ a fixed noise uncertainty for strong motion accelerations. In this paper, we present a Sage–Husa Kalman filter, where the noise uncertainty of strong motion acceleration is adaptively estimated, to integrate GNSS and strong motion acceleration for obtaining the displacement series. The performance of the proposed method was validated by a shake table simulation experiment and the GNSS/strong motion co-located stations collected during the 2023 Mw 7.8 and Mw 7.6 earthquake doublet in southeast Turkey. The experimental results show that the proposed method enhances the adaptability to the variation of strong motion accelerometer noise level and improves the precision of integrated displacement series. The displacement derived from the proposed method was up to 28% more accurate than those from the Kalman filter in the shake table test, and the correlation coefficient with respect to the references arrived at 0.99. The application to the earthquake event shows that the proposed method can capture seismic waveforms at a promotion of 46% and 23% in the horizontal and vertical directions, respectively, compared with the results of the Kalman filter.

Performance enhancement of PPP/SINS tightly coupled navigation based on improved robust maximum correntropy kalman filtering

Extended kalman filter (EKF) is widely used to integrated navigation system of global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS). However, non-Gaussian noise and the uncertainty of measurement noise can seriously reduce the performance of EKF, so it is difficult to obtain an optimal GNSS/INS integration solution. At present, non-Gaussian noise processing is still a difficult issue in filter research. In this paper, an adaptive and robust maximum correntropy extended kalman filter (MCEKF) method based on Cauchy kernel function is proposed to solve the above problem. Thanks to the excellent properties of Cauchy kernel function, the proposed method can effectively avoid filter faults and has better stability. However, the performance of MCEKF depends on the select of kernel bandwidth parameter, which is a difficult problem in the engineering application of MCEKF. In this paper, the switching kernel bandwidth algorithm is employed to adaptively estimate the kernel bandwidth parameter to solve the tradeoff between convergence rate and steady-state misalignment in the MCEKF algorithm under constant kernel bandwidth. Finally, the performance of the proposed algorithm is verified by two sets of vehicle-mounted precise point positioning (PPP) and SINS tightly coupled integration experiments in urban environment. The results show that compared with EKF, the proposed method can significantly improve the positioning accuracy, that is, the PPP/SINS positioning accuracy based on GE, GR and GRE system is improved by 25.1 %, 2.5 % and 17.0 % in D196 experiment, and 23.5 %, 16.5 % and 31.8 % in D107 experiment, respectively. The velocity and attitude accuracy of the two methods are similar. The velocity errors of all schemes can reach cm/s level. The roll, pitch and heading errors of navigation-grade inertial sensor are all less than 0.12 degree. The roll and pitch errors of MEMS are less than 1.0 degree, the heading error of the G, GE, GR, and GRE systems are 1.719, 1.464, 1.676, and 1.475 degree, respectively.

Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model

Context. Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines. Aims. We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them. Methods. We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cramér-Rao lower bound. Results. Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO (1 – 0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases. Conclusions. Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.

An online battery–state of charge estimation method using the varying forgetting factor recursive least square - unscented Kalman filter algorithm on electric vehicles

Accurate and fast estimation of the state of charge is important for the battery management system of electric vehicles. This paper proposes a method to estimate the state of charge of Lithium-ion batteries by the <span lang="EN-US">variable</span> forgetting factor recursive least square (VFFRLS) – unscented Kalman filter (UKF) algorithm in real-time without the off-line battery testing data. Since the state observation requires an accurate model, an equivalent circuit model was constructed. Then, the VFFRLS algorithm is used to identify online the battery model parameters based on voltage and current measurements. An advantage of this algorithm is that it requires less initial information and shorter identification time than offline parameter identification. After the model parameters are well identified, the unscented Kalman filter estimates the state of charge and minimizes noise characteristics and uncertainty in the parameter identification process. The VFFRLS algorithm applied in this paper has shown a good result with the model output error of less than 1%, and the identification achieves real-time response. The state of charge obtained by the UKF algorithm has shown satisfactory estimation results with fast convergence speed and small errors. The UKF filter provides the results with a 1.5% error from the reference and converges after 10 cycles.