Unscented Transformation Research Articles

Estimation of optical model parameters and their correlation matrix using Unscented Transform Kalman Filter technique

In the present study, we have optimized the optical model parameters and also calculated their correlation matrix using the Unscented Transform Kalman Filter technique for the first time. We have used n+56Fe, n+45Sc and n+59Co reactions for this study in order to verify the application of this method. We have used the experimental differential cross section data for the elastically scattered neutrons from the EXFOR data library and DWBA calculations to determine the parameters. In this study we have assumed that the optical model provides correct results and the uncertainties come from the variation of fitting parameters only. We have used the TALYS nuclear reaction code for the DWBA calculations. The optical model parameters determined through this study, reproduce the calculations which are consistent with the experimental trends for the elastically scattered neutrons and total reaction cross sections. Also the correlations calculated in this work are consistent with the earlier study of n+56Fe reaction.

Efficient and robust state estimation: Application to a copolymerization process

AbstractPolymerization processes are highly non‐linear systems that require strict control of their dynamic operation to be competitive. The unscented Kalman filter is a filtering strategy that has shown a rewarding performance for non‐linear state estimation. Besides, filters based on robust statistics have been proposed to deal with the presence of outliers. However, reported robust filters have employed only the Huber M‐estimator as the loss function of the estimation problem. This work presents a new state‐estimation procedure based on the unscented transformation and robust statistics concepts. When outliers are present, estimates are more accurate than when using the conventional filter. In contrast to previous research, our methodology is also efficient when there are no outliers. The performances of different loss functions for solving the estimation problem are presented. The results show that redescending M‐estimators outperform the Huber function. The behaviour of the technique is analyzed for a copolymerization process.

A general model-based filter initialization approach for linear and nonlinear dynamic systems

Tracking performance significantly relies on the quality of filter initialization, including accuracy and consistency, especially in a nonlinear filtering system. Most existing methods are built on assumptions that the target position varies linearly with time or the dynamic model is linear. In practical applications where the assumptions are violated, these methods may suffer from performance degradation or cannot be applied. To address this limitation, a general model-based initialization method for both linear and nonlinear dynamic systems is proposed. According to the dynamic model, the relationships between the first several measurements and the state to be initialized are analyzed and several equations are constructed to solve the initial state estimate. When transcendental equations are involved, numeric root-finding methods are employed to find numeric solutions. In cases with linear analytic solutions, the initial state covariance can be derived explicitly. In other cases, the unscented transformation is employed to calculate the initial covariance. Two commonly used linear dynamic models and three representative nonlinear dynamic models are used as examples to illustrate the procedure of the proposed algorithm. Monte Carlo simulation results demonstrate the effectiveness of the proposed filter initialization algorithm.

PremiUm-CNN: Propagating Uncertainty Towards Robust Convolutional Neural Networks

Deep neural networks (DNNs) have surpassed human-level accuracy in various learning tasks. However, unlike humans who have a natural cognitive intuition for probabilities, DNNs cannot express their uncertainty in the output decisions. This limits the deployment of DNNs in mission-critical domains, such as warfighter decision-making or medical diagnosis. Bayesian inference provides a principled approach to reason about model's uncertainty by estimating the posterior distribution of the unknown parameters. The challenge in DNNs remains the multi-layer stages of non-linearities, which make the propagation of high-dimensional distributions mathematically intractable. This paper establishes the theoretical and algorithmic foundations of uncertainty or belief propagation by developing new deep learning models named PremiUm-CNNs (Propagating Uncertainty in Convolutional Neural Networks). We introduce a tensor normal distribution as a prior over convolutional kernels and estimate the variational posterior by maximizing the evidence lower bound (ELBO). We start by deriving the first-order mean-covariance propagation framework. Later, we develop a framework based on the unscented transformation (correct at least up to the second-order) that propagates sigma points of the variational distribution through layers of a CNN. The propagated covariance of the predictive distribution captures uncertainty in the output decision. Comprehensive experiments conducted on diverse benchmark datasets demonstrate: 1) superior robustness against noise and adversarial attacks, 2) self-assessment through predictive uncertainty that increases quickly with increasing levels of noise or attacks, and 3) an ability to detect a targeted attack from ambient noise.

A Secured Advanced Management Architecture in Peer-to-Peer Energy Trading for Multi-Microgrid in the Stochastic Environment

Careful consideration of grid developments illustrates the fundamental changes in its structure which its developments have taken place gradually for a long time. One of the most important developments is the expansion of the communication infrastructure that brings many advantages in the cyber layer of the system. The actual execution of the peer-to-peer (P2P) energy trading is one core advantage which also may lead to the systematic risks such as cyber-attacks. Consequently, it is necessary to form a useful way to cover such challenges. This paper focuses on the online detection of false data injection attack (FDIA), which tries to disrupt the trend of optimal peer-to-peer energy trading in the stochastic condition. Moreover, this article proposes an effective modified Intelligent Priority Selection based Reinforcement Learning (IPS-RL) method to detect and stop the malicious attacks in the shortest time for effective energy trading based on the peer to peer structure. The presented method is compared with other methods such as support vector machine (SVM), reinforcement learning (RL), particle swarm optimization (PSO)-RL, and genetic algorithm (GA)-RL to validate the functionality of the method. The proposed method is implemented and examined on three interconnected microgrids in the form of peer-to-peer structure wherein each microgrid has various agents such as photovoltaic (PV), wind turbine, fuel cell, tidal system, storage unit, etc. Eventually, the unscented transformation (UT) is applied for uncertainty analysis and making the near-reality simulations.

An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering

An unscented transformation approach to stochastic analysis of measurement uncertainty in magnet resonance imaging with applications in engineering

A Higher Order Unscented Transform

We develop a new approach for estimating the expected values of nonlinear functions applied to multivariate random variables with arbitrary distributions. Rather than assuming a particular distribu...

Short-Term Scheduling of a Renewable-Based Microgrid: Stochastic/Economic Battery Modeling

This paper endeavors a probabilistic framework to ascertain optimal operation of a microgrid with a special focus on challenges that storage systems bring about. The objective function optimizes the operation of renewable energy resources and startup/shutdown costs of nonrenewable energy resources along with the main grid and storage units' costs as a mixed-integer nonlinear programming (MINLP) problem. The optimization problem is solved based on a modified bird mating optimization (MBMO) algorithm and a novel cumulative mutation process. In order to capture the high uncertainties associated with the market price, Photovoltaic, Wind Turbine output powers, and load demands, a reduced unscented transformation (RUT) method has been exploited. The RUT method can effectively model the correlation of variables using (m+2) sampling points. The framework presented in this paper has considered five case studies with multiple seasonal and property features. Implementing the proposed framework on a typical test microgrid and a real large-scale microgrid proves its effectiveness and accuracy through various operational conditions, changing the storage units' structure and characteristics, RESs' correlation modeling, and avoiding convergence to local minimums by adopting a newly mutated population. This extensive analysis provides options for MG operation by studying compound cases and providing solutions for every scenario. Promising results regarding the execution time, cost function and its SD values as well as head-to-head points for battery investment costs have been found.

Orbit insertion error analysis for a space-based gravitational wave observatory

Constellation is required to be highly stable over several years for a space-based gravitational wave observatory. However, the stability of the constellation can be affected by orbit insertion errors. The effects of orbit insertion errors on the constellation are mainly studied in this paper. Firstly, Monte-Carlo, Unscented Transformation Covariance Analysis Method (UTCAM) and Spherical Simplex Unscented Transformation Covariance Analysis Method (SSUTCAM) are used for simulation. The results indicate that UTCAM and SSUTCAM are highly efficient in calculating, with a relative error of less than 6%. Therefore, it is concluded that because of their accuracy and high efficiency, UTCAM and SSUTCAM can be adequately used in orbit insertion error analysis for a space-based gravitational wave observatory. Secondly, SSUTCAM is used to study the effects of position and velocity errors on the constellation. For the case in this paper, when the position error does not exceed 300 km, and the velocity error does not exceed 4 cm/s, the constellation remains stable.

A day-ahead economic scheduling of microgrids equipped with plug-in hybrid electric vehicles using modified shuffled frog leaping algorithm

With the ever-increasing energy demand for energy all across the world and also, the increasing concern on environmental issues due to using fossil fuels mostly in power systems, some appropriate alternatives should be used to solve the issue. In this respect, renewable energy sources (RESs) with almost zero pollution have been turned into the first choice for supplying the required energy. In this study, to achieve the minimum total cost of the grid, a novel problem formulation is proposed to reduce the reliability costs. Simultaneously, the transportation sector has been replacing the current conventional fossil-fuel vehicles with electrified ones, where plug-in electric vehicles (PEVs) as well as plug-in hybrid electric vehicles (PHEV) have captured the attention and there is an increasing rate in using electric vehicles (EVs). These vehicles are capable of connecting to the electrical grid to absorb/deliver energy from/to the grid through the grid-to-vehicle (G2V) and vehicle-to-grid (V2G) technologies. On the other hand, a new concept in power systems, namely microgrid (MG) has been introduced to facilitate the integration of RESs and make the most of EVs’ capabilities using the smart infrastructure. In fact, the vehicle to grid (V2G) capability is used to decrease the operating cost to achieve a proper opportunity to accommodate PEVs in the network. The output power produced by RESs is volatile, which is more obvious in wind energy and solar power. Thus, the resource management issue of MGs would be of very high significance. In this regard, this paper proposes an efficient optimization framework for the optimal day-ahead energy management of MGs, including PEVs and RESs, utilizing an effective stochastic programming method, i.e. unscented transformation (UT). It is significant to note that the problem has tackled as a single-objective stochastic optimization problem, while the objective has been defined as minimizing the total cost of operation, The presented stochastic optimization problem is then solved by employing a nature-inspired efficient method, named “modified shuffled frog leaping algorithm (MSFLA)” and the obtained results are compared to those reported by other methods to verify its performance.

Research on Estimation Method of Fuel Cell Health State Based on Lumped Parameter Model

The increasingly serious environmental pollution and the shortage of social energy have promoted the rapid development of fuel cell vehicles. The major factor which limits the commercialization of fuel cell vehicles is durability. Accurately estimating the state and parameters of a fuel cell is critical to extending the life of the fuel cell. To address this challenge, we extended a proton exchange membrane fuel cell (PEMFC) lumped parameter model and incorporated new algorithms that are essential to estimate the health of the fuel cell in a range-extended fuel cell car. The unscented Kalman filter (UKF) algorithm has been used to estimate the ohmic internal resistance of the fuel cell in real time. By using the unscented transformation (UT) method, the linearization of the nonlinear state equation is avoided, and the filtering accuracy is improved without increasing the complexity of the system. By comparing simulation and experimental results, the feasibility and accuracy of the algorithm in this paper are further verified. This method has high estimation accuracy and is suitable for an embedded system. The research of this method is an important basis for improving the control strategy of fuel cell vehicles. Reasonable use of fuel cells can extend battery life, and this method is of great significance to the commercialization of fuel cell vehicles.

Vehicle-trailer lateral velocity estimation using constrained unscented transformation

Using a 3-degree-of-freedom lateral dynamic vehicle-trailer system model with the LuGre tyre model, this paper proposes a constrained unscented transformation based scheme for estimating the lateral velocity of a vehicle trailer. It is shown that the proposed lateral velocity estimation scheme is robust to the road condition. An affine quadratic stability approach is used to analyze the stability of the proposed estimation scheme. Simulations studies in CarSim/Simulink along with experimental tests are used to validate the proposed scheme. The test results confirm the accuracy of the developed estimation scheme and convergence of the vehicle-trailer lateral velocity estimate to the actual value.

Sterling interpolation method for precision estimation of total least squares

The randomness of the biases of parameter estimates, residuals and some variables is seldom considered for calculating covariance matrix of parameter estimates in total least squares (TLS) iterative algorithm. There are few studies on the precision estimation with the approximate probability distribution method of function in the TLS. In order to get more reasonable precision information for the TLS adjustment, the derivative-free Sterling interpolation method is introduced and implemented. The errors-in-variables (EIV) model and its TLS algorithm are introduced. The TLS iterative algorithm is combined with the Sterling interpolation, and two kinds of schemes for calculating biases of the TLS parameter estimates and approximate mean squared error matrix are designed. The method is used to four examples: line fitting model, coordinate transformation model, auto-regression model and variation function model. Comparing the results with the scaled unscented transformation (SUT) method, the feasibility and effectiveness of the Sterling interpolation method in the TLS precision estimation are verified. The Sterling interpolation method has fewer parameters than the SUT method, and it is simpler to implement. And the scheme two in this paper can be applied to the case where some matrix elements are nonlinear functions of the observation. The application of the precision estimation is expanded by this method, and the theory for precision estimation of TLS is further improved.

Robust Interacting Multiple Model Unscented Particle Filter for Navigation

In order to solve the problems of particle degradation and difficulty in selecting importance density function in particle filter algorithm, a robust interacting multiple model unscented particle filter algorithm is presented, which is based on the advantages of interacting multiple model and particle filter algorithms. This algorithm can use the unscented transformation to get the particles that contain the latest measurement information of each model and calculate the robust equivalent weight function. This robust factor is designed to adjust the estimation and variance, and the important distribution function adaptively obtained is closer to the true distribution. Then, the particles weights can be flexibly adjusted in real time by using Euclidean distance to improve the computational efficiency during the resampling process. In addition, this filter process can comprehensively describe the uncertainty of the statistics characteristic of observation noise between different models. The diversity of available particles is increased, and the filter precision is improved. The proposed algorithm is applied to the SINS/GPS integrated navigation system, and the simulation analysis results demonstrate that the algorithm can effectively improve the filter performance and the calculation precision in positioning of integrated navigation system; thus, it provides a new method for nonlinear model filter.

Techno-economic assessment of combined power to hydrogen technology and hydrogen storage in optimal bidding strategy of high renewable units-penetrated microgrids

The decision-making process for the optimal bidding strategy of microgrids (MGs), which suffer from the surplus power due to the high penetration of the intermittent resources, is not without challenge. To deal with this problem, this paper proposes a new approach for determining the optimal bidding strategies for the MG modified by the renewable resources in the day-ahead energy and spinning reserve markets using the capacities of the power to hydrogen (P2H) and hydrogen storage (HS) technologies. To fulfill this aim, the unscented transformation has been used to model the uncertainties related to renewable resources, load consumption and electricity price in the entity in an efficient way. The findings reveal that the cost of operating the system without energy storage is 779$ while by using an energy storage system (ESS) it is reduced to 741$ which shows a 4% reduction in the costs. Also, by using ESS as both energy and reserve suppliers, the cost of operating becomes 640$ indicating an 18% reduction. However, using HS system reduces the operational cost as much as 26% and 40% for energy supplier and both energy and reserve suppliers, leading to 577$ and 487$, respectively.

Considering forecasting errors in flexibility‐oriented distribution network expansion planning using the spherical simplex unscented transformation

The rapid rise in the grid integration of low-carbon technologies, e.g. renewable energy sources (RESs) and plug-in electric vehicles (PEVs), has led to several challenges in distribution networks (DNs). This is due to the intermittent generation of RESs and uncertain loads of PEVs, both of which necessitate enhancing the flexibility requirements at the distribution level so as to accommodate the high penetration of these clean technologies in the future. To address such issues, this study proposes a mixed-integer linear programming-based expansion planning model for DNs considering the impact of high RES and PEV penetration, the associated uncertainties, and providing flexibility requirements at the distribution level. In this respect, the spherical simplex unscented transformation, an analytical uncertainty modelling method, is implemented in the planning model to take into account the forecasting errors of the uncertain green technologies. Also, in order to estimate the electric vehicle parking lot demand at each load node of the network, a new approach for PEV-charging model is suggested. To investigate the effectiveness and efficiency of the proposed probabilistic planning model, it is implemented on two test DNs, and the obtained results are thoroughly discussed.

Stochastic synergies of urban transportation system and smart grid in smart cities considering V2G and V2S concepts

Serious challenges such as rapid growth in population, environmental pollution, and possibility of energy shortage have motivated researchers for designing optimal energy operation strategies through the concept of smart city. Buildings and electric transport systems, especially subway systems and Plug in Electric Vehicles (PEVs), are among the major energy consumption systems in a smart city. In this paper, a linear model is proposed for the co-optimization planning and operation of distributed energy resources and transportation systems in an interconnected system that analyzes the interactions of such an interconnected system. The idea of Regenerative Breaking Energy (RBE) is deployed to improve the operation of the subway system through the interconnected subway system in the smart city. For the optimal operation of the smart city, an optimization formulation is devised to minimize the total cost of the city in the presence of subway RBE. In this paper, the traffic and length of the routes are modeled considering Vehicle to Grid (V2G) and Vehicle to Subway (V2S) located in the parking lots. Furthermore, the degradation model is developed to increase the PEVs’ battery life. An unscented transformation (UT) approach is utilized to construct a stochastic framework based on the uncertainty method, to handle the uncertain behaviors of PEVs and distributed energy resource and loads in the smart city. Finally, the proposed model is implemented and its performance is analyzed in both the stochastic and deterministic frameworks.

A modified unscented transformation method for uncertainty propagation in neutron induced cross section measurement

This paper investigates the application of the modified unscented transformation (MUT) method for uncertainty propagation in neutron induced cross section measurement in Nuclear Science. The method is the improvement on unscented transformation (UT) technique by incorporating more parameters (not random) to increase the number of sigma points.We examined the application of MUT method for covariance analysis of cross section measurement in comparison to the first order sensitivity analysis method and Monte Carlo methods. The MUT method is simple to use and easier to implement in comparison to the sandwich formula. The Monte Carlo simulations had been carried out to illustrate the good performance of the MUT method in covariance analysis in neutron activation cross section measurement.

Improving S-MSCKF With Variational Bayesian Adaptive Nonlinear Filter

In recent years, multi-sensor fusion has been paid a great attention and is widely applied to simultaneous localization and mapping (SLAM), e.g. Visual-Inertial Odometry (VIO). However, in the most of previous works the observation noise of sensor is assumed to be Gaussian with invariant constant mean and covariance, which is not the case actually. In this paper, a variational Bayesian adaptive algorithm is proposed to improve the performance of visual-inertial odometry, where covariance of observation noise is modeled as inverse-Wishart distribution with harmonic mean so that observation noise is non-Gaussian. Besides, unscented transformation is utilized to handle the nonlinear system problem. The proposed algorithm is applied to the framework of stereo multi-state constraint Kalman filter system (S-MSCKF), which is a state-of-the-art VIO system with low computational cost and good robustness. Extensive experiments are performed on simulation data and open source datasets. The results demonstrate that our proposed algorithm is more robust and accurate compared with S-MSCKF.

Model‐data fusion for seismic performance evaluation of an instrumented highway bridge

SummaryThe paper presents a computationally efficient algorithm to integrate a probabilistic, non‐Gaussian parameter estimation approach for nonlinear finite element models with the performance‐based earthquake engineering (PBEE) framework for accurate performance evaluations of instrumented civil infrastructures. The algorithm first utilizes a minimum variance framework to fuse predictions from a numerical model of a civil infrastructure with its measured behavior during a past earthquake to update the parameters of the numerical model that is, then, used for performance prediction of the civil infrastructure during future earthquakes. A nonproduct quadrature rule, based on the conjugate unscented transformation, forms an enabling tool to drive the computationally efficient model prediction, model‐data fusion, and performance evaluation. The algorithm is illustrated and validated on Meloland Road overpass, a heavily instrumented highway bridge in El Centro, CA, which experienced three moderate earthquake events in the past. The benefits of integrating measurement data into the PBEE framework are highlighted by comparing damage fragilities of and annual probabilities of damages to the bridge estimated using the presented algorithm with that estimated using the conventional PBEE approach.