Simultaneous Estimator Research Articles

Co-Estimating State of Charge and Capacity of Automotive Lithium-Ion Batteries Under Deep Degradation Using Multiple Estimators

Since battery systems typically account for over 40% of the cost of an electric vehicle, their mid-life replacements are exceptional. Therefore, the battery’s lifespan must exceed that of the vehicle. To ensure long-term and safe use, accurate state-of-charge (SOC) estimation must be maintained throughout the battery’s lifespan. This requires appropriate updates to parameters, such as capacity, in the battery model. In this context, dual extended Kalman filters, which simultaneously estimate both states and parameters, have gained interest. While existing reports on simultaneous estimators seemed promising, our study found that they performed well under low levels of battery aging but encountered issues at higher levels. Accurately reflecting the actual physicochemical changes of the parameters in aging cells is challenging for two reasons: the limited number of measurements of terminal voltage available for numerous parameters, and the weak observability of the capacity. Therefore, we combined the simultaneous estimator with a capacity estimator operated separately during charging and a sequential estimator specialized for an enhanced self-correcting model, achieving SOC accuracy within 5% even when the SOH decreased by 30%. However, there is still much work to be carried out to implement sequential estimators in battery management systems operating in real time with limited computational resources.

Price Prediction of Staples with Simultaneous Fourier Series Estimator as a Contribution to Solve the National Food Problem

This study provides an overview related to the prediction of prices for staples that are widely consumed by the Indonesian people and often experience price fluctuations at certain times, namely cooking oil, chili, and chicken eggs. Based on the Market Monitoring System and Staples of the Ministry of Trade, the national average price of cooking oil as of January 3, 2022, reached USD 1.17per liter. The average price of chicken eggs reached USD 1,98 per kilogram, an increase of 20.16% at the same time. In addition, based on the National Strategic Food Price Information Center, the average price of chili in traditional markets throughout the province rose by USD 0.19 or about 3.16% and reached USD 6.29 per kilogram. The prediction of staple food prices in this study was formed using a nonparametric regression model of the Fourier series estimator. This regression model has high flexibility in forming the model and estimating the fluctuation data pattern, which is not known in the form of time-series data. The data in this study is sourced from the National Strategic Food Price Information Center website with the response variables used being the daily prices of cooking oil, chicken eggs, and chili from September 1, 2021, to December 31, 2021, as training data. In addition, the same commodity data from January 1, 2022, to January 10, 2022, is used as testing data. The best model from the estimation results with the Fourier series is a model with an oscillation parameter of 25 which contains a sine cosine basis with a coefficient of determination of 83.05%and an MSE value of 1.628. The selected model also has a very good performance predicting the prices of the three staples with a MAPE value of 1.082%.

The effect of public funding and government effectiveness on CO2 emissions in developing countries: Evidence from panel quantile analysis

AbstractEnvironmental concerns emphasize the need for sustainable finance now more than ever. The study aims to provide a comprehensive analysis of whether public funding for renewable energy impacts environmental degradation in developing countries over time. It emphasizes the relationship between green finance, renewable energy adoption, and government effectiveness in driving sustainable development. This study examines the relationship between CO2 emissions, gross domestic product, renewable energy consumption, investments in renewable and government effectiveness. The study sample includes 34 developing countries for the period between 2000 and 2020. The analysis specifically employs public flows as a measure to gauge a country's commitment to green finance. It also employs a simultaneous panel quantile regression estimator. The results reveal a cointegrating relationship among variables, with notable findings: GDP increase correlates with CO2 emissions rise, while higher renewable energy consumption correlates with CO2 emissions decrease. Interestingly, increased public funding correlates with reduced CO2 emissions for the upper quantile. Furthermore, the analysis uncovers that government policies have yet to fully align with the sustainable development goals. These findings hold critical implications for informed policymaking. Developing countries should opt for sustainable financing and create a favorable environment for investment. Moreover, funders should ensure equitable distribution of public flows within developing countries and fund less mature technologies.

Intelligent state estimation for fault tolerant integrated frequent RTO and adaptive nonlinear MPC

Combinations of real-time optimization (RTO) and model predictive control (MPC) have been widely employed in the process industry for tracking the economic optimum in the face of drifting disturbances and parameters. Online update of model parameters is a critical step in the implementation of RTO. In this work, an intelligent state and parameter estimation approach is developed by combining a fault diagnosis approach with a simultaneous state and parameter estimator. Since faults are more likely to develop as slow drifts, a nonlinear generalized likelihood ratio (GLR) approach available in the literature is modified by considering ramp models for the progression of faults with time. When a fault is isolated by the fault diagnosis and identification (FDI) component, the magnitude of the isolated fault is refined using a moving window state and parameter estimator until the fault magnitude continues to change. The estimation of fault magnitudes is carried out only when required and triggered by the fault identification scheme. Thus, the subset of parameters/faults that are being estimated online can change with time. The intelligent state and parameter estimator is further combined with an online optimizing control scheme consisting of integrated frequent RTO and adaptive MPC. The integrated optimizing control scheme has embedded intelligence to auto-correct models used for estimation, control, and optimization and decide whether the detected changes require the invocation of RTO. The proposed approach employs a single model to carry out four different tasks: process monitoring, state and parameter estimation, nonlinear predictive control, and real-time optimization. This eliminates difficulties that can arise due to model mismatch between different components of the online optimizing control scheme. The efficacy of the proposed scheme is investigated using the benchmark Williams Otto reactor and a continuously operated fermenter. The economic optimum operating point of these systems is sensitive to mean shifts in unmeasured disturbances or system parameters. The proposed ramp model based approach successfully isolates the parameter/ unmeasured disturbance/ sensor bias/ actuator bias that has undergone slow drift and tracks the shifting economic optimum without significant delays. Thus, the proposed integrated approach has the ability to handle normal and abnormal operating envelopes of the system.

Stochastic Approximation for Multi-period Simulation Optimization with Streaming Input Data

We consider a continuous-valued simulation optimization (SO) problem, where a simulator is built to optimize an expected performance measure of a real-world system while parameters of the simulator are estimated from streaming data collected periodically from the system. At each period, a new batch of data is combined with the cumulative data and the parameters are re-estimated with higher precision. The system requires the decision variable to be selected in all periods. Therefore, it is sensible for the decision-maker to update the decision variable at each period by solving a more precise SO problem with the updated parameter estimate to reduce the performance loss with respect to the target system. We define this decision-making process as the multi-period SO problem and introduce a multi-period stochastic approximation (SA) framework that generates a sequence of solutions. Two algorithms are proposed: Re-start SA ( ReSA ) reinitializes the stepsize sequence in each period, whereas Warm-start SA ( WaSA ) carefully tunes the stepsizes, taking both fewer and shorter gradient-descent steps in later periods as parameter estimates become increasingly more precise. We show that under suitable strong convexity and regularity conditions, ReSA and WaSA achieve the best possible convergence rate in expected sub-optimality either when an unbiased or a simultaneous perturbation gradient estimator is employed, while WaSA accrues significantly lower computational cost as the number of periods increases. In addition, we present the regularized ReSA which obviates the need to know the strong convexity constant and achieves the same convergence rate at the expense of additional computation.

Distributed Fault-Tolerant Bipartite Output Synchronization of Discrete-Time Linear Multiagent Systems.

This article studies the distributed fault-tolerant bipartite output synchronization problem of discrete-time linear multiagent systems (MASs) with process faults under a general directed signed graph. The reference signal is generated by an autonomous exosystem, which can also be seen as a leader. All followers are divided into two subgroups with antagonistic interactions, and the followers in each subgroup are cooperative. We aim to solve the bipartite fault-tolerant control (FTC) problem via the output regulation theory such that bipartite output synchronization can be achieved in the presence of process faults, that is, the outputs of followers with different subgroups can approach the output of exosystem with the same magnitude and the opposite sign regardless of process faults. To estimate the states and the faults of each follower, a simultaneous state and fault estimator based on the neighboring signed output estimation error and the standard discrete-time algebraic Riccati equation (ARE) is designed. Besides, a new exosystem observer with two classes of convergence conditions relying on the respective solutions of standard and modified AREs is provided. All eigenvalues of the exosystem matrix can lie completely outside the unit circle. Based on these estimations, we present a distributed fault-tolerant output feedback controller, which can overcome the no-loops constraint. Finally, simulation results are given to demonstrate the analytic results.

Mapping conduits in two-dimensional heterogeneous karst aquifers using hydraulic tomography

Hydraulic tomography (HT) is a well-established approach to yield the spatial distribution of hydraulic conductivity of an aquifer. This work explores the potential of HT for the characterization of the distribution and connectivity of conduits in a two-dimensional sandbox and its corresponding synthetic aquifer. Two inversion techniques were implemented and compared: the geostatistics-based inversion which uses the simultaneous successive linear estimator (SimSLE) algorithm to conduct stochastic inversions on the transient hydraulic heads, and the travel time-based inversion which employs the simultaneous iterative reconstruction technique (SIRT) algorithm on the hydraulic travel times for tomography reconstructions. Four artificial karst conduits of different geometries were placed in an aquifer of layer with different hydraulic conductivities. We conducted 6 pumping tests at 6 different locations, and the resultant pressure responses were recorded at 42 observation points in both the sandbox and the corresponding synthetic aquifer. The measured data were then used for the inversion of hydraulic diffusivity using the SimSLE and SIRT algorithms. Our results show that both algorithms were able to approximately identify the embedded karst conduits and yield similar hydraulic diffusivity distribution. Statistically, the travel time-based inversion re-constructed high-contrast diffusivities which clearly differentiate the karst structures from the surrounding matrix. The geostatistics-based SimSLE algorithm yields a better agreement on the positions and the shapes of the embedded karst structures, compared to those obtained by the travel time-based SIRT algorithm. Uncertainties and limitations of our results are also discussed in this work, followed by recommendations on hydraulic tests in karst aquifers.

Simultaneous state and parameter estimation method for a conventional ozonation system

This article presents a simultaneous state (via a nonlinear form of Luenberger observer) and parameter (using a proportional–integral least mean square form) estimator design method for a conventional ozonation system. The suggested state observer assumes that the only available output signal is the concentration of the ozone gas at the output of the reactor. The estimation of the reaction rate constants of ozonation in the presence of contaminants uses the suggested proportional–integral estimation method. The convergence proof of the developed state-parameter identification method was confirmed using a Lyapunov based stability analysis. This analysis characterizes the quality of estimation considering the presence of modeled uncertainties and external perturbations. The implementation of the super-twisting algorithm as a robust and exact differentiator allowed to perform the estimation of the reaction rate constants of the ozonation, the temporal evolution of the dissolved ozone and the evolution of contaminants concentrations. The simultaneous state and parameter estimator design method was implemented in real-time using phenol as a model contaminant. The numerically simulated and real-time implementations showed that the method provides accurate estimates of the contaminant concentration and the reaction rate coefficient in all the evaluated cases.

Exploration of Ordovician limestone aquifer heterogeneity with tomographic water releasing tests

Water inrush is a typical geological disaster in the process of underground mining. It is crucial to depict potential water inrush areas for mining safety. In this study, mining activity in Dongtan coal mine is under the water inrush threat from deep Ordovician limestone confined aquifers. Tomographic water releasing tests and simultaneous successive linear estimator (SimSLE) were conducted to characterize aquifer heterogeneity by stimulating hundreds of square kilometers. An artificial injection well was firstly introduced to alleviate the influence from identified recharge channels. The estimated parameter distributions indicated that the study area was divided into two separately hydrogeological compartments. Transmissivity (T) and storativity (S) in the north were relatively higher due to water-conducting structures, and more attention should be paid to this region which may develop into water inrush incidents. The southern area is occupied with lower T and S, which indicated relatively worse flow conditions. Auxiliary drawdown recovery data, borehole chemistry variations, drilling fluid losses, and existing geological features further confirmed the estimated parameter distributions. In the end, we concluded that Hydraulic Tomography technique (HT) could obtain aquifer parameter information in large scales and provide supports to formulate reasonably effective water prevention and control schemes before mining deep coal seams.

Estimating uncertainties and parameters for fundamental models used in online monitoring and control

AbstractMany model‐based online process monitoring and control applications rely on state estimation techniques that use noisy process data to update states, thereby ensuring that imperfect model predictions are consistent with process behaviour. Techniques for tuning state estimators are reviewed, and their effectiveness and limitations are summarized in this article. A new simultaneous parameter and estimator tuning (SPET) methodology is proposed, one in which parameter estimation techniques for stochastic differential equations (SDEs) are used to simultaneously estimate measurement‐error covariances and model‐error covariances along with the model parameters. The resulting information is then used to compute state‐estimator tuning information. This study shows how SPET can be used, along with old dynamic process data, to obtain reliable tuning information. The proposed methodology is tested using a nonlinear two‐state continuous stirred‐tank reactor (CSTR) model with simulated data. Comparisons are made with a more‐conventional approach that uses WLS to estimate fixed model parameters and autocovariance least squares (ALS) to estimate extended Kalman filter (EKF) tuning factors. The main benefit of the proposed approach is that fixed model parameters and tuning factors for the EKF are estimated simultaneously, resulting in significant improvements to state estimates and online model predictions.

Numerical investigation of hydraulic tomography for mapping karst conduits and its connectivity

Hydraulic tomography (HT) is a well-established approach to successfully describe subsurface hydraulic heterogeneity. This work explored the potential of HT and the simultaneous successive linear estimator algorithm to map the distribution and connectivity of karst conduits and their hydraulic parameters at the engineering scale. Three generalized synthetic karst conduit models, auxiliary conduit, cave and waterfall, were established. A series of pumping tests were conducted at different locations as forward simulations to collect hydraulic head responses. These responses were then used for the HT inversion analysis to estimate hydraulic parameter fields of karst aquifers under steady-state and transient conditions. Our results show that high-density observation wells substantially assist with interpreting the reliable spatial distribution of hydraulic parameters. With the increase in the number of pumping wells in the HT inversion, the estimates of hydraulic conductivity and specific storage became more accurate for the auxiliary conduit model, but for the cave and waterfall models, there was no significant improvement. The hydraulic conductivity (K) tomograms from transient hydraulic tomography (THT) better indicated the heterogeneity of the three karst models than those from steady-state hydraulic tomography (SSHT) because a large number of hydraulic head records were introduced into the THT inversion process. Moreover, when reliable geological data are available, the accuracy of the estimated hydraulic parameter maps can be greatly improved even if only infrequent hydraulic head measurements can be obtained, implying that a priori geological information may be extremely valuable in mapping karst conduit heterogeneity. Finally, the robustness of HT in mapping karst conduits is verified through the simulation of independent cross-hole pumping tests. This study proved that hydraulic tomography utilizing groundwater responses from a series of cross-hole pumping tests is an efficient and cost-effective way and provided a feasible method for accurate identification of hydraulic heterogeneity of karst aquifers.

Financial depth and electricity consumption in Africa: Does education matter?

This article estimates the effect of financial development on electricity consumption for economies with above and below mean human capital index in 45 African countries. The study applied the simultaneous system GMM estimator (adjusted for cross-sectional dependence) and the Aiken and West slope difference test. We performed further robustness checks, such as sample sensitivity analysis to address potential outlier problem. The result showed that the total effect of financial development on electricity consumption is negative, but the direct and indirect effects are different. While, directly, financial development increases electricity consumption, indirectly (via education), it reduces electricity consumption. The Aiken and West slope difference test revealed that the reduction in electricity consumption is twice bigger (in standard deviation terms) in economies with an above mean human capital than in economies with a below mean human capital. In maximum and minimum value terms, it is about seven times bigger for economies with maximum human capital than those with minimum human capital are. The computed country-specific conditional mean marginal effect estimates of financial development revealed significant heterogeneities between economies with well-developed and less-developed human capital. These results suggest that the level of education drives the technical effects associated with financial development, which leads to a reduction in electricity consumption. By implication, advancing the SDG4 goal in Africa is critical to achieving the SDG7 goal.

Multiscale change point detection for dependent data

AbstractIn this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise‐constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference‐type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical‐dependent error processes and illustrate the finite sample performance by means of a simulation study.

Identification of groundwater basin shape and boundary using hydraulic tomography

Shapes and boundary types of a groundwater basin play essential roles in the analysis of groundwater management and contaminant migration. Hydraulic tomography (HT), a recently developed new approach for high-resolution characterization of aquifers, is not only an inverse method but a logical strategy for collecting non-redundant hydraulic information. In this study, HT was applied to synthetic 2-D aquifers to investigate its feasibility to map the irregular shapes and types of the aquifer boundaries. We first used the forward model of VSAFT2 to simulate hydraulic responses due to HT surveys in the aquifer with irregular geometry and predetermined constant head conditions at some boundaries, and no-flow conditions at others. The SimSLE (Simultaneous Successive Linear Estimator) inverse model in VSAFT2 was then used to interpret the simulated HT data to estimate the spatial distribution of hydraulic properties of the aquifer using a domain with a wrong geometry surrounded by boundaries of a constant head condition. The inverse modeling experiment used steady-state and transient-states data from the HT forward simulations, and it used the same monitoring network as in the aquifer with irregular geometry to assess the ability of HT for detecting types and shapes of the boundary as well as heterogeneity in the aquifer. Results of the experiment show that no-flow boundaries, which were incorrectly treated as constant head boundaries in inverse models, were portrayed as low permeable zones of the aquifer near the boundaries. Overall, the results show that HT could delineate not only the irregular shape of the aquifer in general but also heterogeneity in the aquifer. Improvements of the estimation with prior information of transmissivity and storage coefficient was also investigated. The study shows that using homogeneous initial guess parameters resulted in a slightly better estimate than others. Moreover, this study employs Monte Carlo simulations to ensure statistically meaningful conclusions.

Efficient Operation of Continuous Reactor Systems using Economic Nonlinear MPC Formulations

A combination of real-time steady-state optimization (RTO) and model predictive control (MPC) used in the process industry for maximizing economic performance can result in sub-optimal operation due to the model mismatch between the RTO and MPC components and delays involved in carrying out RTO step. These problems are alleviated by recently proposed economic nonlinear MPC (ENMPC) that merges the optimization and control layers. For an e¤ective implementation of ENMPC, it is essential that accurate information of states and parameters is available at every sampling instant. The ENMPC schemes proposed in the literature either assume that the model parameters are not time-varying or are measurable/known quantities when they change with time. In practice, variations in these model parameters are seldom measurable online. In this work, two novel ENMPC formulations are proposed to address this problem: (i) Output Feedback ENMPC integrated with state estimator that employs innovation feedback for correcting model predictions and (ii) Adaptive ENMPC integrated with simultaneous state and parameter estimator, in which parameters are estimated simultaneously with the states and are updated in the model used by ENMPC. The efficacies of the proposed approaches are demonstrated by simulating two benchmark reactor control problems. Analysis of the simulation results reveals that the proposed Adaptive ENMPC is able to achieve performance comparable to the ideal case where all states and parameter variations are perfectly known. Also, Adaptive ENMPC as well as Output Feedback ENMPC formulations result in significantly better control when compared with the conventional ENMPC formulation.

Testing Linear and Nonlinear Hypotheses in a Cox Proportional Hazards Model with Errors in Covariates

We investigate linear and nonlinear hypotheses testing in a Cox proportional hazards model for right-censored survival data when the covariates are subject to measurement errors. In Kukush and Chernova (2018) [Theor. Probability and Math. Statist. 96, 101–110], a consistent simultaneous estimator is introduced for the baseline hazard rate and the vector of regression parameters. Therein the baseline hazard rate belongs to an unbounded set of nonnegative Lipschitz functions, with fixed constant, and the vector of regression parameters belongs to a compact parameter set. Based on the estimator, we develop two procedures to test nonlinear and linear hypotheses about the vector of regression parameters: Wald-type and score-type tests. The latter is based on an unbiased estimating equation. The consistency of the tests is shown.

A simultaneous perturbation weak derivative estimator for stochastic neural networks

In this paper we study gradient estimation for a network of nonlinear stochastic units known as the Little model. Many machine learning systems can be described as networks of homogeneous units, and the Little model is of a particularly general form, which includes as special cases several popular machine learning architectures. However, since a closed form solution for the stationary distribution is not known, gradient methods which work for similar models such as the Boltzmann machine or sigmoid belief network cannot be used. To address this we introduce a method to calculate derivatives for this system based on measure-valued differentiation and simultaneous perturbation. This extends previous works in which gradient estimation algorithm’s were presented for networks with restrictive features like symmetry or acyclic connectivity.

Robust state and fault estimation for non‐linear stochastic systems with unknown disturbances: a multi‐step delayed solution

A study on the simultaneous state and fault estimation for non-linear discrete-time stochastic systems subjected to unknown disturbances is presented. The augmented system approach, system reformation using the state-dependent coefficient (SDC) factorisation, and unknown input filtering method are integrated to simultaneously estimate the state of the system and actuator and/or sensor faults. To achieve this aim, the non-linear system with faults and unknown disturbances is first transformed into an equivalent augmented system by using delayed measurements and the SDC factorisation. Next, within the SDC factorised linear-like augmented system and inspired by the robust two-stage Kalman filter, a novel multi-step estimator named as the robust simultaneous state and fault estimator is proposed to yield a robust state and fault estimation with a multi-step delay. Moreover, a novel real-time state estimator is designed based on the proposed hybrid fault reconstruction model in order to address the inherent time-delay problem. A comparison of the performance of the proposed filters with those of existing methods from the literature is demonstrated using a non-linear two-link manipulator system with friction forces acting simultaneously at each joint.

Simultaneous Estimation of Hidden State and Unknown Input Using Expectation Maximization Algorithm

An expectation maximization (EM) algorithm-based simultaneous state and input estimator for nonlinear systems is developed. This study uses a Bayesian solution to estimate the states and unknown inputs simultaneously. It was assumed that a joint distribution between states and inputs exists. The joint distribution was estimated sequentially using an EM algorithm. The EM algorithm has two steps: expectation step (E-step) and maximization step (M-step). In the E-step, a particle filter was used to estimate the conditional probability of states. The conditional distribution of the measurements conditioned on the estimated states was maximized with respect to inputs in the M-step, and inputs were estimated. These two steps were performed alternatively until both states and inputs converge to steady values. The effectiveness of the proposed method was demonstrated using simulation and experimental case studies.

Consistent estimation in Cox proportional hazards model with measurement errors and unbounded parameter set

Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic properties of simultaneous estimator $\lambda_n(\cdot)$, $\beta_n$ were studied for baseline hazard rate $\lambda(\cdot)$ and regression parameter $\beta$, at that the parameter set $\Theta=\Theta_{\lambda}\times \Theta_{\beta}$ was assumed bounded. In the present paper, the set $\Theta_{\lambda}$ is unbounded from above and not separated away from $0$. We construct the estimator in two steps: first we derive a strongly consistent estimator and then modify it to provide its asymptotic normality.