Unscented Transformation Research Articles

Implementation and testing of unscented transformation and low rank approximation to enhance SCALE code uncertainty calculations

Recently, the SCALE6.2 code has implemented the Sampler module for randomly sampling important reactor physics inputs from their parental distributions. The Sampler module uses a stochastic sampling technique based on multivariate (MV) sampling which assumes that the input cross-sections are correlated according to a predefined covariance matrix. Although the methodology used in the Sampler module is relatively straightforward and robust, it can be computationally expensive for applications where a large number of Monte Carlo samples are required. In this paper, the SCALE6.2 capabilities are enhanced by implementing the Unscented Transformation (UT) and Low Rank Approximation (LRA) to decrease computational time. The uncertainties are calculated for k-inf due to perturbations in the multi-group cross-sections for a standard PWR fuel pin but the methodology can be applied to any output parameter of interest (such as few group cross sections). First, the UT is applied to generate a set of sigma points which represent the behavior of the system over the entire space. However, since the input model dimensionality is very high, due to the number of isotopes, reactions, and energy-groups, the generation of the sigma sample points may be computationally burdensome. Therefore, the LRA is applied to reduce the order of sampling space which can significantly reduce the computational cost; this model is called the Truncated Unscented Transformation (TUT). The results show that the input-dimension can be reduced from 896 to 112-subspace and the uncertainties in k-inf calculated by TUT sampling with 225 samples are about 5.62×10-1 which agrees well with the full MV sampling with N = 1000 runs and results from TSUNAMI. The results also indicate that the uncertainties calculated by the TUT methodology are not sensitive to the scaling parameter λ assumed in the LRA as long as the appropriate weights are applied.

A blockchain‐enabled secured fault allocation in smart grids based on μ PMUs and UT

Improvements in the high accuracy of micro-phasor measurement unit (μPMU) and synchrophasor unit provide the distribution network a special perspective to access full observability in the presence of renewable distribution generations (DGs). In this regard, modelling the uncertainty effects for accurate fault detection in smart grids has become a novel turning point. This research work attempts to develop a novel stochastic architecture based on unscented transform (UT), which requires a very few number of μPMUs, to communicate in a secured blockchain-enabled structure to allocate and detect the smart grid irregularities and faults. Such a blockchain-based technique can be beneficial for encrypting the data transmitted among the μPMUs in the smart grid consisting of a variety of distributed energy sources (DERs) and high impedance fault events, while incorporating the uncertainties associated with the load and individual installation sensors. The proposed stochastic structure benefits from voltage measurement and uses its angle in event placement that performs more efficiently than the conventional sensors based on high-voltage and current metering. The simulation results show the great precision and effectiveness of the proposed model during various fault scenarios in smart grid.

Improved Harris hawks optimization algorithm based on random unscented sigma point mutation strategy

The Harris hawks optimization algorithm (HHO) is a new swarm intelligence algorithm for simulating the capture and attack of the hawks which has good global exploration and local exploitation capabilities. In order to further improve the optimization performance of the algorithm, quasi-opposite learning and quasi-reflection learning strategies performed according to probability are involved in the attack phase to enhance the diversity of the population and accelerate the convergence rate of HHO while a logarithmic nonlinear convergence factor is designed to balance the ability of global search and local optimization of the algorithm. Furthermore, in order to avoid the algorithm falling into a local optimum, using the characteristics of the unscented transform (UT) to estimate the mean and variance of a random variable function can achieve second-order accuracy, a new strategy for generating random symmetric sigma points is designed to mutate the current best individual in the visible range, at last, an improved Harris hawk algorithm (IHHO) based on random unscented sigma point mutation is proposed. The new stochastic UT ensures the random exploitation of the algorithm and has a certain theoretical support, which overcomes the theoretical deficiency of the stochastic optimization algorithm to some extent. The numerical optimization ability of IHHO is verified by CEC2017 benchmark functions, CEC2020 benchmark function and fifteen standard test functions. Finally, the practicality and effectiveness of the IHHO algorithm are verified by three engineering constraint optimization and the discounted {0-1} knapsack problem.

Effective Energy Management via False Data Detection Scheme for the Interconnected Smart Energy Hub–Microgrid System under Stochastic Framework

During the last few years, attention has overwhelmingly focused on the integrated management of urban services and the demand of customers for locally-based supply. The rapid growth in developing smart measuring devices has made the underlying systems more observable and controllable. This exclusive feature has led the system designers to pursue the implementation of complex protocols to provide faster services based on data exchanges. On the other hand, the demands of consumers for locally-based supply could cause a disjunction and islanding behavior that demands to be dealt with by precise action. At first, keeping a centralization scheme was the main priority. However, the advent of distributed systems opened up new solutions. The operation of distributed systems requires the implementation of strong communication links to boost the existing infrastructure via smart control and supervision, which requires a foundation and effective investigations. Hence, necessary actions need to be taken to frustrate any disruptive penetrations into the system while simultaneously benefiting from the advantages of the proposed smart platform. This research addresses the detection of false data injection attacks (FDIA) in energy hub systems. Initially, a multi-hub system both in the presence of a microgrid (the interconnected smart energy hub-based microgrid system) and without it has been modeled for energy management in a way that allows them to cooperate toward providing energy with each other. Afterward, an FDIA is separately exerted to all three parts of the energy carrier including the thermal, water, and electric systems. In the absence of FDIA detection, the impact of FDIA is thoroughly illustrated on energy management, which considerably contributes to non-optimal operation. In the same vein, the intelligent priority selection based reinforcement learning (IPS-RL) method is proposed for FDIA detection. In order to model the uncertainty effects, the unscented transformation (UT) is applied in a stochastic framework. The results on the IEEE standard test system validate the system’s performance.

An Experimental Multi-Target Tracking of AM Radio-Based Passive Bistatic Radar System via Multi-Static Doppler Shifts.

This paper presents a description of recent research and the multi-target tracking in experimental passive bistatic radar (PBR) system taking advantage of numerous non-cooperative AM radio signals via multi-static doppler shifts. However, it raises challenges for use by multiple spatially distributed AM radio illuminators for multi-target tracking in PBR system due to complex data association hypotheses and no directly used tracking algorithm in the practical scenario. To solve these problems, after a series of key array signal processing techniques in the self-developed system, by constructing a nonlinear measurement model, the novel method is proposed to accommodate nonlinear model by using the unscented transformation (UT) in Gaussian mixture (GM) implementation of iterated-corrector cardinality-balanced multi-target multi-Bernoulli (CBMeMBer). Simulation and experimental results analysis verify the feasibility of this approach used in a practical PBR system for moving multi-target tracking.

AN UNCERTAINTY PROPAGATION ANALYSIS METHOD FOR STOCHASTIC SYSTEM BASED ON EXTENDED CONJUGATE UNSCENTED TRANSFORM

The statistical moments of response are one of the main ways to describe the response of a random structural system. Compared with the probability density function (PDF) of the response, the statistical moments of the structural response can be easily obtained, and therefore it is quite concerned by researchers. Among them, the efficient calculation method for statistical moments of structural response has always been a hot research topic. The conjugate unscented transformation method (CUT), which keeps the tradeoff of accuracy and efficiency, is used as the basis in this paper. By introducing the normal-nonnormal transformation (NNT), the first type of extended conjugate unscented transformation method (ECUTI) is proposed, which is appropriate for the statistical moment estimation of random systems involving arbitrary random variables. Secondly, based on the high dimensional reduction model (HDRM) and the ECUTI, the second type of extended conjugate unscented transform method (ECUTⅡ) which is suitable for the statistical moment estimation of random system of arbitrary dimensions is proposed. The proposed methods are verified through three numerical examples. The results of examples show that: The two types of proposed methods can satisfy the accuracy and efficiency on the basis of expanding the scope of application of the CUT; The ECUTI and the ECUTⅡ are recommended for statistical moment estimation of the response for low-dimensional and high-dimensional problems, respectively.

Positioning Parameter Determination Based on Statistical Regression Applied to Autonomous Underwater Vehicle

The underwater environment is complex and changeable, and it is hard but irreplaceable to research the time-varying noises that have a significant influence on navigation information determination with higher accuracy. To solve the problems of the inaccurate noise information, this paper proposes a novel statistical regression adaptive Kalman filtering (SRAKF) algorithm that makes better use of the merits of the expectation maximization and unscented transformation. The SRAKF is verified from theoretical perspectives, and meanwhile, the stability and accuracy of the algorithm are evaluated by real lake trials. Relying on the properties of the statistical linear regression and the positioning parameter estimation of latent variables, higher precise positioning parameters can be acquired by the SRAKF, even for the measurement noise values with great variation. Hence, the performance of SRAKF is more useful in underwater positioning applications than other traditional algorithms due to its stronger robustness and higher accuracy.

Optimal operation and management of multi‐microgrids using blockchain technology

This paper tries to address the optimal operation of networked microgrid from the reliability perspective in a correlated atmosphere for the wind generators. The suggested approach performs based on unscented transformation in the form of a nonlinear projection and the heuristic method as the optimizer. The proposed structure is arranged as a complex constraint optimization problem with several targets seeing the varied objectives such as energy not supplied, system interruption frequency, system interruption duration and energy losses. Owing to the interrelated natural surroundings of multi-microgrids, it is a necessity for the microgrids to let the each other access the operation info and with the central unit. In this situation, it is quite wise to provide a secured construction made of the blockchain for the assurance of the reliability and adequate security of data sharing in the microgrids. With the aim of validation of the proposed model, an IEEE standard system is considered and divided into four interrelated microgrids with one side connection to the main grid. The simulation results show the high capability of the proposed framework for enhancing the operation and reliability indices. Moreover, it is seen that almost 0.6% and 0.77% additional cost is imposed to the system in the deterministic framework in the first and second scenarios, respectively.

Risk-based functional black-box optimization: Contribution to the NASA Langley UQ challenge on optimization under uncertainty

This paper presents an approach to solve the 2019/2020 NASA Langley UQ challenge problem on optimization under uncertainty. We define an uncertainty model (UM) as a pair fa|e,E, where fa|e is a probability density over a for each e∈E, and proceed to infer fa|e in a Bayesian fashion. Special attention is given to dimensionality reduction of the functional (time-series) data, to obtain a finite dimensional representation suitable for robust Bayesian inversion. Reliability analysis is performed using fa|e, whereas for design optimization we approximate fa|e using truncated Gaussians and a Gaussian copula. We apply an unscented transform (UT) in the standard normal space to estimate moments of the limit state, which is numerically very efficient. Design optimization is performed with this procedure to obtain negligible failure probability in g1 and g3 and acceptable failure probability and severity in g2.

Multi-objective dynamic generation and transmission expansion planning considering capacitor bank allocation and demand response program constrained to flexible-securable clean energy

This paper presents the dynamic generation and transmission expansion planning considering switched capacitor bank allocation and demand response program. This scheme is in the form of four-objective optimization to supply flexible-securable and highly reliable energy. The scheme minimizes the planning costs, expected pollution, expected energy not-supplied, and voltage security index in separate objective functions. It is constrained to network AC power flow equations, operation, reliability, flexibility, network voltage security constraints, capacitor planning model, and demand response operating formulation. Then, the ε constraint-based Pareto optimization technique obtains a single-objective model for the proposed scheme. The unscented transformation method models the uncertainties of load, renewable power, and network equipment availability. To achieve an optimal solution including a low standard deviation in the final response, a hybrid meta-heuristic algorithm is used. This solver is based on merging the firefly algorithm and harmonic search algorithm. Eventually, the scheme is applied to IEEE 6-bus and 118-bus transmission networks. Then, the numerical results confirm the capability of the proposed strategy in improving the operation, reliability, security, and flexibility of the network, as well as enhancing the economic and environmental status.

Event-Triggered Forecasting-Aided State Estimation for Active Distribution System With Distributed Generations

In this study, the forecasting-aided state estimation (FASE) problem for the active distribution system (ADS) with distributed generations (DGs) is investigated, considering the constraint of data transmission. First of all, the system model of the ADS with DGs is established, which expands the scope of the ADS state estimation from the power network to the DGs. Moreover, in order to improve the efficiency of data transmission under the limited communication bandwidth, a component-based event-triggered mechanism is employed to schedule the data transmission from the measurement terminals to the estimator. It can efficiently reduce the amount of data transmission while guaranteeing the performance of system state estimation. Second, an event-triggered unscented Kalman filter (ET-UKF) algorithm is proposed to conduct the state estimation of the ADS with mixed measurements. To this end, the unscented transform (UT) technique is employed to approximate the probability distribution of the state variable after nonlinear transformation, which can reach more than second order, and then, an upper bound of the filtering error covariance is derived and subsequently minimized at each iteration. The gain of the desired filter is obtained recursively by following a certain set of recursions. Finally, the effectiveness of the proposed method is demonstrated by using the IEEE-34 distribution test system.

Hybrid stochastic/robust flexible and reliable scheduling of secure networked microgrids with electric springs and electric vehicles

Electric spring (ES) as a novel concept in power electronics has been developed for the purpose of dealing with demand-side management. In this paper, to conquer the challenges imposed by intermittent nature of renewable energy sources (RESs) and other uncertainties for constructing a secure modern microgrid (MG), the hybrid distributed operation of ESs and electric vehicles (EVs) parking lot is suggested. The proposed approach is implemented in the context of a hybrid stochastic/robust optimization (HSRO) problem, where the stochastic programming based on unscented transformation (UT) method models the uncertainties associated with load, energy price, RESs, and availability of MG equipment. Also, the bounded uncertainty-based robust optimization (BURO) is employed to model the uncertain parameters of EVs parking lot to achieve the robust potentials of EVs in improving MG indices. In the subsequent stage, the proposed non-linear problem model is converted to linear approximated counterpart to obtain an optimal solution with low calculation time and error. Finally, the proposed power management strategy is analyzed on 32-bus test MG to investigate the hybrid cooperation of ESs and EVs parking lot capabilities in different cases. The numerical results corroborate the efficiency and feasibility of the proposed solution in modifying MG indices.

A novel streamlined particle‐unscented Kalman filtering method for the available energy prediction of lithium‐ion batteries considering the time‐varying temperature‐current influence

Effective energy prediction is of great importance for the operational status monitoring of high-power lithium-ion battery packs. It should be embedded in the battery system performance evaluation, energy management, and safety protection. A new Streamlined Particle-Unscented Kalman Filtering method is proposed to predict the available energy of lithium-ion batteries, in which an Adaptive-Dual Unscented Transform treatment is conducted to realize the precise mathematical expression of its working conditions. For the accurate mathematical description purpose, an improved Synthetic-Electrical Equivalent Circuit modeling method is introduced into the internal effect equivalent process considering the influence of time-varying temperature and current conditions. As can be known from the experimental results, the proposed prediction method has a maximum estimation error of 2.27% and an average error of 0.80%, for the complex varying-current Beijing Bus Dynamic Stress Test. Under the Urban Dynamometer Driving Schedule working conditions, the available energy prediction has high accuracy with a maximum error of 1.83% and a voltage traction error of 3.28%. It provides vehicle-mounted available energy prediction schemes for effective management and safety protection of high-power lithium-ion batteries. Highlights A new Streamlined Particle-Unscented Kalman Filtering method is proposed to predict the available energy of lithium-ion batteries. Improved Synthetic-Electrical Equivalent Circuit modeling strategies are established to describe the nonlinear battery characteristics. Adopted predictive correction is investigated by considering the time-varying temperature and current influence. For effective convergence, an adaptive windowing function factor is introduced into the correction process with a maximum estimation error of 2.27% and an average error of 0.80% for the complex varying-current Beijing Bus Dynamic Stress Test working conditions. The vehicle battery available energy prediction is realized with a maximum error of 1.83% and a maximum voltage traction error of 3.28% for the Urban Dynamometer Driving Schedule working conditions.

Indoor Positioning Algorithm Based on Maximum Correntropy Unscented Information Filter

In view of the fact that indoor positioning systems are usually affected by non-Gaussian noise in complex indoor environments, this paper tests the data in the actual scene and analyzes the distribution characteristics of noise, and proposes a new indoor positioning algorithm based on maximum correntropy unscented information filter (MCUIF). The proposed indoor positioning algorithm includes three steps: First, the estimation of the state matrix and the corresponding covariance matrix are predicted through the unscented transformation (UT). Second, the observed information is reconstructed by using a nonlinear regression method on the basis of the maximum correntropy criterion (MCC). Third, the contribution of information vector is gained by non-Gaussian measurement and the predicted information vector is corrected by the contribution of information vector. Finally, the gain of information filtering is got by the information entropy state matrix and the information entropy measurement matrix to calculate the position coordinates of the unknown nodes. This algorithm enhances the robustness of the MCUIF to non-Gaussian noise in complex indoor environments. The results from the indoor positioning experiments show that MCUIF is better than the traditional methods in state estimation and position location of the unknown nodes.

An effective secured peer-to-peer energy market based on blockchain architecture for the interconnected microgrid and smart grid

One of the most significant current topics in the energy market is the decentralized operation of the power system wherein the entire discipline is constructed based on the consensus concept. In such a framework, an agreement among all effective participants in the market should be brought without the presence of an independent arbitrator. This paper proposes a secured energy market architecture based on peer-to-peer (P2P) idea to provide an appropriate platform based on the decentralized network and key aspects of energy market, including network architecture, interface communication, and network security. It is apparent that communication interfaces connecting the market participants is a fundamental property for achieving this purpose and that must be secured against the malicious attacks. In this regard, reaching the secured consensus is guaranteed by providing a new blockchain platform coincided by P2P energy market. The energy market is conducted by an effective Relaxed Consensus-Innovation (RCI) based algorithm with the aim of bringing the power/price exchanged among connecting participants in the form of P2P structure. In the proposed model, a microgrid and a smart grid are considered as the market participants, who tend to negotiate with each other in a way that follow their own benefits in the secured environment. The microgrid includes the wind turbine (WT), photovoltaic (PV), tidal turbine and storage unit to satisfy its demand and the smart grid is composed of distributed generations (DGs) and lines in the form of the IEEE 24-bus test system. In order to handle the uncertainty effects in the problem, a stochastic framework based on unscented transform (UT) is proposed in the P2P energy market. In order to assess and verify the fault-tolerant system ability against the cyber-attack, the fault data injection attack (FDIA) is modeled and applied to the P2P energy market in a blockchain platform. The simulation results approve the appropriate performance and applicable nature of the proposed concepts in this paper.

A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters

For engineering products with uncertain input variables and distribution parameters, a sampling-based sensitivity analysis methodology was investigated to efficiently determine the influences of these uncertainties. In the calculation of the sensitivity indices, the nonlinear degrees of the performance function in the subintervals were greatly reduced by using the integral whole domain segmentation method, while the mean and variance of the performance function were calculated using the unscented transformation method. Compared with the traditional Monte Carlo simulation method, the loop number and sampling number in every loop were decreased by using the multiplication approximation and Gaussian integration methods. The proposed algorithm also reduced the calculation complexity by reusing the sample points in the calculation of two sensitivity indices to measure the influence of input variables and their distribution parameters. The accuracy and efficiency of the proposed algorithm were verified with three numerical examples and one engineering example.

Nonlinear State Estimation With Multisensor Stochastic Scheduling

In this article, the problem of a nonlinear system states estimation with multisensor stochastic scheduling is investigated. In order to solve the non-Gaussian property induced by the nonlinear transformation, the unscented transformation (UT) technique is applied. Since the sensor networks channel is limited, the stochastic event-triggered mechanisms (SETMs) are proposed to reduce the network transmission burden. Under the SETMs, the modified unscented Kalman filter is proposed. Additionally, the sufficient conditions are given to guarantee the stabilities of the error covariance and the estimation error. Finally, extensive examples are carried out. Performances evaluation and comparison with existing methods are given to demonstrate the superiority of the proposed methods.

Stochastic multi-carrier energy management in the smart islands using reinforcement learning and unscented transform

This article investigates the optimal management of multi-carrier water and energy system(MCWES) considering the high penetration of renewable energy sources as non-dispatchable units and the seawater desalinization mechanism for serving water demand in the target area. The proposed model encompasses several demand layers including power energy, natural gas and water layer which supplies the electricity, thermal and drinkable water demands in the smart island. In order to capture the uncertainty effects in the technical decisions of optimal scheduling, a stochastic approach based on unscented transform (UT) is developed to handle the forecast error in the electrical and thermal energy demands, market energy prices related to the different energy layers and the output power forecast error in the renewable energy sources. Solving the proposed coordinated scheduling problem in an hourly timescale requires heavy calculations that make it impractical. Therefore, a novel reinforcement learning (RL) based approach is devised for finding a near optimal solution and facilitates the searching process with a trivial computational burden. The simulation results indicate that the proposed cooperation approach minimizes both the operation and investment costs substantially with an efficient computational burden based on the advanced features coming out of the proposed RL approach. Last but not least, the simulation results on a practical smart island advocate the effectiveness and high efficacy of the proposed model. Also it was seen that the RL approach could properly solve the optimization model and the selection of the sizes of the components was highly linked to the hourly values of demands and prices of the energy.

ILRS Reference Point Determination Using Close Range Photogrammetry

A global geodetic reference system (GGRS) is realized by physical points on the Earth’s surface and is referred to as a global geodetic reference frame (GGRF). The GGRF is derived by combining several space geodetic techniques, and the reference points of these techniques are the physical points of such a realization. Due to the weak physical connection between the space geodetic techniques, so-called local ties are introduced to the combination procedure. A local tie is the spatial vector defined between the reference points of two space geodetic techniques. It is derivable by local measurements at multitechnique stations, which operate more than one space geodetic technique. Local ties are a crucial component within the intertechnique combination; therefore, erroneous or outdated vectors affect the global results. In order to reach the ambitious accuracy goal of 1 mm for a global position, the global geodetic observing system (GGOS) aims for strategies to improve local ties, and, thus, the reference point determination procedures. In this contribution, close range photogrammetry is applied for the first time to determine the reference point of a laser telescope used for satellite laser ranging (SLR) at Geodetic Observatory Wettzell (GOW). A measurement campaign using various configurations was performed at the Satellite Observing System Wettzell (SOS-W) to evaluate the achievable accuracy and the measurement effort. The bias of the estimates were studied using an unscented transformation. Biases occur if nonlinear functions are replaced and are solved by linear substitute problems. Moreover, the influence of the chosen stochastic model onto the estimates is studied by means of various dispersion matrices of the observations. It is shown that the resulting standard deviations are two to three times overestimated if stochastic dependencies are neglected.

Onboard tuning of vessel seakeeping model parameters and sea state characteristics

It is essential for a safe and cost-efficient marine operation to improve the knowledge about the real-time onboard vessel conditions. This paper proposes a novel algorithm for simultaneous tuning of important vessel seakeeping model parameters and sea state characteristics based on onboard vessel motion measurements and available wave data. The proposed algorithm is fundamentally based on the unscented transformation and inspired by the scaled unscented Kalman filter, which is very computationally efficient for large dimensional and nonlinear problems. The algorithm is demonstrated by case studies based on numerical simulations, considering realistic sensor noises and wave data uncertainties. Both long-crested and short-crested wave conditions are considered in the case studies. The system state of the proposed tuning framework consists of a vessel state vector and a sea state vector. The tuning results reasonably approach the true values of the considered uncertain vessel parameters and sea state characteristics, with reduced uncertainties. The quantification of the system state uncertainties helps to close a critical gap towards achieving reliability-based marine operations.