Joint State-parameter Estimation Research Articles

Data assimilation for online model calibration in discrete event simulation

The increasing availability of real-time data collected from dynamic systems brings opportunities for simulation models to be calibrated online for improving the accuracy of simulation-based studies. Systematical methods are needed for assimilating real-time measurement data into simulation models. This paper presents a particle filter-based data assimilation method to support online model calibration in discrete event simulation. A joint state-parameter estimation problem is defined, and a particle filter-based data assimilation algorithm is presented. The developed method is applied to a discrete event simulation of a one-way traffic control system. Experiments results demonstrate the effectiveness of the developed method for calibrating simulation models’ parameters in real time and for improving data assimilation results.

Population-based estimation for PDE system – Applications in electroporation of tumor spheroids

The estimation of partial differential systems (PDE) – in particular, the identification of their parameters – is fundamental in many applications to combine modeling and available measurements. However, it is well known that parameter prior values must be chosen appropriately to balance our distrust of measurements, especially when data are sparse or corrupted by noise. A classic strategy to compensate for this weakness is to use repeated measurements collected in configurations with common priors, such as multiple subjects in a clinical trial. In the mixed-effects approach, all subjects are pooled and a global distribution of model parameters in the population is estimated. However, due to the high computational cost, this strategy is often not applicable in practice for PDE. In this paper, we propose an estimation strategy to overcome this challenge. This sophisticated method is based on two important existing methodological strategies: (1) a population-based Kalman filter and, (2) a joint state-parameter estimation. More precisely, the errors coming from the initial conditions are controlled by a Luenberger observer and the parameters are estimated using a population-based reduced-order Kalman filter restricted to the parameter space. The performance of the algorithm is evaluated using synthetic and real data for tumor spheroid electroporation.

Quantitative Fault Diagnostics of Hydraulic Cylinder Using Particle Filter

Condition-based hydraulic cylinder maintenance necessitates quantitative fault diagnostics. However, existing methods are characterized by either qualitative or limited quantitative capabilities. In this paper, a quantitative fault diagnostic method using a particle filter for hydraulic cylinders is proposed. The problem of quantitative fault diagnostics is formally formulated in a stochastic framework to assess the health/fault state, and an architecture based on joint state-parameter estimation is proposed. Through the establishment and analysis of a nonlinear dynamic model of the hydraulic cylinder, the impact of time-varying parameters on the state variables is revealed. Three fault modes of the cylinder, including friction, internal leakage, and external leakage, are theoretically identified. The proposed method allows for a simultaneous quantitative diagnosis of these three fault modes. The performance of the proposed method is evaluated using meticulously designed experiments. The results demonstrate that the mean absolute percentage errors in the parameter estimations are below 9% (accuracy exceeding 91%), thus validating its feasibility and effectiveness.

Joint state–parameter estimation for structures with seismic isolation and damping systems: Theoretical observability and experimental verification

The objective of this study is to examine the feasibility of estimating the parameters of various devices in seismic control systems and evaluating the maximum responses of the quantities of interest. The observability condition was applied to determine the sensor layout and modeling assumptions of the structure for the joint estimation problem and to eliminate unsuitable layouts. To estimate the parameters of multiple members at the isolation layer, including laminated rubber bearings, oil dampers, and elastic sliding bearings, and to evaluate the maximum response, an adaptive unscented Kalman filter was utilized. Moreover, the study investigated the influence of partially unmeasured inputs on the observability of the established system through a case study involving the base layer of the building model colliding with the retaining walls. Experimental data from a full-scale shaking table test on a seismic isolation building was used as an example for validation purposes. The results demonstrated that even under varying initial estimates, varying sensor layouts, and the occurrence of unmeasured impact forces, the parameters and maximum responses of interest can be estimated with acceptable accuracy when the observability condition is met.

Back-and-forth nudging for the quasi-geostrophic ocean dynamics with altimetry: Theoretical convergence study and numerical experiments with the future SWOT observations

<p style='text-indent:20px;'>In data assimilation for geophysical problems, the increasing amount of satellite data to analyze makes it more and more challenging to guarantee near real time forecasting. Thus, low time and memory consuming data assimilation methods become very attractive. The back-and-forth nudging (BFN) method is a non-classical data assimilation method that can be seen as a deterministic and smoothing version of the Kalman filter. From a practical point of view, the BFN method is very valuable for its simplicity of implementation (no optimization, no differentiation, ...) and its rapidity of convergence. Under observability conditions, we prove the mathematical convergence of BFN at deep layers for a multi-layer quasi-geostrophic (MQG) ocean circulation model using an infinite dimensional variant of LaSalle's invariance principle. We also extend the BFN to the problem of joint state-parameter identification. The numerical experiments, performed on 120km large swath sea surface height (SSH) simulated data of the Surface Water Ocean Topography (SWOT) satellite, show the high robustness of the algorithm to uncertainties and the few iterations needed to reach convergence, whereas some problems remain due to non-reversibility properties in time. We also give a strategy to improve geophysical model accuracy, considering the large number of uncertain parameters inherent to models and their impacts on state estimation performance. We propose here a joint state-parameter estimation, tested on the baroclinic wavenumber as an unobserved parameter.</p>

Switching Kalman filter for damage estimation in the presence of sensor faults

Bayesian filtering based approaches for diagnosis of structural damage have been widely employed in structural health monitoring (SHM) research. The approach however may lead to an inaccurate alarm/decision due to the presence of faulty sensor/s. Nevertheless, sensor faults are inevitable during real field SHM in which sensor may malfunction or get detached from the structural surface, registering completely irrelevant information as measurement. Eventually, such erroneous information induce error in the estimation which leads to an inaccurate, sometimes divergent and impractical solution. The current study deals with Bayesian filtering based structural damage detection in the presence of one or multiple (consecutive) sensor faults. The damage detection is addressed with joint state-parameter estimation approach while a switching filtering strategy is employed for sensor fault detection. Switching approach employs multiple possible sensor fault models which are subsequently integrated to the measurement model of the joint estimation approach. The selection of the competent model (/switching between model ensembles) is undertaken recursively based on their likelihood against measured response. The proposed approach is tested on a numerical lumped mass model of a shear frame building, followed by a laboratory experiment on a cantilever beam. It has been perceived that estimation of health for structures measured with faulty sensors can actually lead to a false (positive and negative) alarm which can, however, be avoided by the employment of the proposed approach. The performance of the proposed approach is further established for healthy and damaged system with pre-existing and sudden sensor faults.

Regularized adaptive Kalman filter for non-persistently excited systems

Most available methods for joint state-parameter estimation in discrete-time stochastic time-varying systems suffer from severe performance degradation if the system is not persistently excited. We revisit and extend a recently proposed adaptive Kalman filter in order to enhance its robustness against periods of poor excitation. A Levenberg–Marquardt-like regularization algorithm is integrated in the filter to preclude the estimator from becoming unreliable due to wind-up effects. It is proven that, under uniform complete observability–controllability conditions and a persistent excitation condition, the expectations of the state and parameter estimation errors tend to zero exponentially fast. Furthermore, their stability (in the sense of Lyapunov) is guaranteed even if the persistent excitation condition is not satisfied. The effectiveness of the algorithm is demonstrated using real sensor data from a vehicle motion estimation application. Unlike the original algorithm, the proposed regularized adaptive Kalman filter provides accurate and reliable estimates of the states and parameters despite periods of poor excitation.

Stochastic filter-based fatigue crack growth prediction for pipelines considering unknown model parameters and measurement uncertainty

In this study a methodology is developed and implemented in Python for fatigue crack growth prediction in pipelines, by leveraging measurement data and fatigue growth model predictions. Specifically, Particle Filter (PF) algorithm, Paris law, and the stress intensity factor (SIF) model in API 579 are integrated into a tool to use noisy crack size measurements for estimating the current crack size and fatigue model parameters, also known as joint state-parameter estimation. For illustration purpose, pseudo-data set for crack size measurements is generated considering additive Gaussian white noise of two different noise levels, aiming to mimic crack size data obtained from In-line Inspection (ILI) tools. It is found that the crack state can be reliably estimated compared to noisy measurements and initial model predictions, and the true model parameters can be updated with good accuracy. As such, the current crack size estimated and model parameters updated can be used in the fatigue growth model (i.e., Paris law) to predict the future trajectory of the fatigue crack growth. As more measurement data becomes available, the developed tool more reliably estimates the future crack growth trajectory.

Assimilation of Cosmogenic Neutron Counts for Improved Soil Moisture Prediction in a Distributed Land Surface Model

Cosmic-Ray Neutron Sensing (CRNS) offers a non-invasive method for estimating soil moisture at the field scale, in our case a few tens of hectares. The current study uses the Ensemble Adjustment Kalman Filter (EAKF) to assimilate neutron counts observed at four locations within a 655 km2 pre-alpine river catchment into the Noah-MP land surface model (LSM) to improve soil moisture simulations and to optimize model parameters. The model runs with 100 m spatial resolution and uses the EU-SoilHydroGrids soil map along with the Mualem–van Genuchten soil water retention functions. Using the state estimation (ST) and joint state–parameter estimation (STP) technique, soil moisture states and model parameters controlling infiltration and evaporation rates were optimized, respectively. The added value of assimilation was evaluated for local and regional impacts using independent root zone soil moisture observations. The results show that during the assimilation period both ST and STP significantly improved the simulated soil moisture around the neutron sensors locations with improvements of the root mean square errors between 60 and 62% for ST and 55–66% for STP. STP could further enhance the model performance for the validation period at assimilation locations, mainly by reducing the Bias. Nevertheless, due to a lack of convergence of calculated parameters and a shorter evaluation period, performance during the validation phase degraded at a site further away from the assimilation locations. The comparison of modeled soil moisture with field-scale spatial patterns of a dense network of CRNS observations showed that STP helped to improve the average wetness conditions (reduction of spatial Bias from –0.038 cm3 cm−3 to –0.012 cm3 cm−3) for the validation period. However, the assimilation of neutron counts from only four stations showed limited success in enhancing the field-scale soil moisture patterns.

Inverse modeling and joint state-parameter estimation with a noise mapping meta-model.

This study aims to produce dynamic noise maps based on a noise model and acoustic measurements. To do so, inverse modeling and joint state-parameter methods are proposed. These methods estimate the input parameters that optimize a given cost function calculated with the resulting noise map and the noise observations. The accuracy of these two methods is compared with a noise map generated with a meta-model and with a classical data assimilation method called best linear unbiased estimator. The accuracy of the data assimilation processes is evaluated using a "leave-one-out" cross-validation method. The most accurate noise map is generated computing a joint state-parameter estimation algorithm without a priori knowledge about traffic and weather and shows a reduction of approximately 26% in the root mean square error from 3.5 to 2.6 dB compared to the reference meta-model noise map with 16 microphones over an area of 3 km2.

Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.

Modified Ensemble Kalman filter for reservoir parameter and state estimation in the presence of model uncertainty

Ensemble Kalman filter (EnKF) is widely used in reservoir modelling for on-line history matching. Typically, it is assumed that structurally the model is an accurate representation of the reservoir and uncertainty exists only in the parameters. This paper focuses on estimating reservoir static parameters (i.e., porosity and permeability) and dynamic states using EnKF in the presence of mismatch between the reservoir and the model. An in depth investigation of the application challenges of EnKF is reported. Two modifications are introduced for joint state-parameter estimation: i) addition of error to the model to represent the mismatch between the predictive model and real system, and ii) introduction of a tuning parameter called ‘forcing data’ to the perturbation variable for dealing with a noisy system. A benchmark problem defined as ‘tank series model’ has been designed for the verification of the EnKF algorithm. Using the simplified model mathematical formulation of state estimation combined with parameter calibration is presented systematically. Later similar approach is applied to a nonlinear two-dimensional reservoir under water flooding operation. To assess the performance in history matching, a sensitivity analysis is conducted. It was observed that due to forcing data perturbation, about 13.6% and 9% improvement is possible in history matching of the tank and reservoir cases respectively when model mismatch and uncertainty in measurement is high.

JOINT ESTIMATION OF STATES AND PARAMETERS OF LINEAR SYSTEMS WITH PARAMETER FAULTS UNDER NON-GAUSSIAN NOISES

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameter-dependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

Hierarchical parameter and state estimation for bilinear systems

ABSTRACTThe identification of state-space models of bilinear systems is studied in this paper. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem more difficult than that of the linear state-space model. For the coupled variables, this paper introduces the interaction estimation theory to study an on-line algorithm for joint state-parameter estimation. To be more specific, a state observer in the bilinear form is established by minimising the state estimation error covariance matrix in the same way of a Kalman filter on the condition that the parameters are known. Then, a bilinear state observer based recursive least squares algorithm is developed using the least squares method. Moreover, for the purpose of improving the computational efficiency, a bilinear state observer based two-stage recursive least squares algorithm and a bilinear state observer based multi-stage recursive least squares algorithm are proposed by decomposing the system into several subsystems based on the hierarchical identification. Finally, a numerical simulation is employed to show the specific performance of the proposed approaches.

Enhanced flood forecasting through ensemble data assimilation and joint state-parameter estimation

Accurate water level forecasts during flood events are crucial to mitigate the loss of human lives and economic damages. However, the accuracy of flood models can be affected by various factors, including the complexity of the terrain geometry and bathymetry, imperfect physics as well as uncertainties in the inflows and parameters. This paper describes a practical implementation of an ensemble Kalman filter (EnKF) based data assimilation system that is aimed towards enhancing the forecasting skill of flood models. The system was implemented and tested with a real world dam break flood, based on the experimentally scaled Toce River valley flood that occurred on July 8th, 1996. Water depth data are available for assimilation from a network of 21 sensors distributed across the domain. Our results demonstrate that assimilating data into the flood model significantly improves the model prediction by up to 90% after assimilation and 60% during forecasting. Assimilating the data more frequently significantly enhances the system performances. Estimating the two-dimensional Manning coefficient together with the model’s dynamical variables (water depth and velocities) further improves the model prediction skill. Overall, our results suggest that assimilating data into the flood model, while jointly inferring the state and (poorly known) parameters, using an EnKF may provide an efficient framework for developing an operational flood forecasting system.

An EM-based multipath interference mitigation in GNSS receivers

In multipath (MP) environments, the received signals depend on several factors related to the global navigation satellite systems (GNSS) receiver environment and motion. Thus it is difficult to use a specific propagation model to accurately capture the dynamics of the MP signal when the GNSS receiver is moving in urban canyons. This paper formulates the problem of MP interference mitigation in the GNSS receiver as a joint state (containing the direct signal parameters) and time-varying model parameter (containing the MP signal parameters) estimation. Accordingly, we propose to exploit the EM algorithm for achieving the joint state and time-varying parameter estimation in the context of MP interference mitigation in GNSS receivers. More precisely, the proposed EM-based MP mitigation approach is decomposed into two iterative steps: (a) the posterior pdf of the direct signal parameters and the expected log-likelihood function necessary in the expectation step of the EM algorithm are approximated by using an appropriate particle filter; (b) the maximum likelihood solution for MP signal parameters is then obtained using Newton’s method in the maximization step. The convergence of the proposed approach is analyzed based on the existing convergence theorem associated with the EM algorithm. Finally, a comprehensive simulation study is conducted to compare the performance of the proposed EM-based MP mitigation approach with other state-of-the-art MP mitigation approaches in static and realistic scenarios.

Bayesian seismic strong-motion response and damage estimation with application to a full-scale seven story shear wall structure

In this paper a Bayesian framework is employed to estimate the seismic strong-motion response and the state of structural integrity of a full-scale structure. The approach is applied in the context of a full-scale section of a seven-story shear wall building designed for southern California and tested at the George E. Brown Jr. Network for Earthquake Engineering Simulation shake table site at the University of California San Diego. The test structure was subjected to earthquake records of increasing amplitude until severe damage was observed, and the dynamic response was measured during the experimental program using an array of sensors. The proposed approach provides an estimate of the nonlinear dynamic response at unmeasured degrees of freedom by combining a potentially inaccurate structural model with sparse acceleration measurements using an unscented Kalman filter. Although the method also provides an optimal estimate of the parameters that define the mathematical models, joint state-parameter estimation is not the main purpose of this study. To assess the modeling robustness of the approach two model classes are considered: a linear time-varying cantilever beam model that accounts only for flexural deformations, and a coupled nonlinear chain-cantilever model that accounts for both flexural and shear deformations. It is shown that the approach has the capability to accurately estimate the time-history response and engineering demands of interest, such as floor displacements and accelerations, inter-story drifts, base shear, and overturning moment induced by strong base excitations where the structure experienced considerable nonlinear excursions. The estimated demands are subsequently used to compute damage measures to perform a quantitative assessment of the state of structural integrity.

Online model calibration for a simplified LES model in pursuit of real-time closed-loop wind farm control

Abstract. Wind farm control often relies on computationally inexpensive surrogate models to predict the dynamics inside a farm. However, the reliability of these models over the spectrum of wind farm operation remains questionable due to the many uncertainties in the atmospheric conditions and tough-to-model dynamics at a range of spatial and temporal scales relevant for control. A closed-loop control framework is proposed in which a simplified model is calibrated and used for optimization in real time. This paper presents a joint state-parameter estimation solution with an ensemble Kalman filter at its core, which calibrates the surrogate model to the actual atmospheric conditions. The estimator is tested in high-fidelity simulations of a nine-turbine wind farm. Exclusively using measurements of each turbine's generated power, the adaptability to modeling errors and mismatches in atmospheric conditions is shown. Convergence is reached within 400 s of operation, after which the estimation error in flow fields is negligible. At a low computational cost of 1.2 s on an 8-core CPU, this algorithm shows comparable accuracy to the state of the art from the literature while being approximately 2 orders of magnitude faster.

Sequential data assimilation for 1D self-exciting processes with application to urban crime data

A number of models – such as the Hawkes process and log Gaussian Cox process – have been used to understand how crime rates evolve in time and/or space. Within the context of these models and actual crime data, parameters are often estimated using maximum likelihood estimation (MLE) on batch data, but this approach has several limitations such as limited tracking in real-time and uncertainty quantification. For practical purposes, it would be desirable to move beyond batch data estimation to sequential data assimilation. A novel and general Bayesian sequential data assimilation algorithm is developed for joint state-parameter estimation for an inhomogeneous Poisson process by deriving an approximating Poisson-Gamma ‘Kalman’ filter that allows for uncertainty quantification. The ensemble-based implementation of the filter is developed in a similar approach to the ensemble Kalman filter, making the filter applicable to large-scale real world applications unlike nonlinear filters such as the particle filter. The filter has the advantage that it is independent of the underlying model for the process intensity, and can therefore be used for many different crime models, as well as other application domains. The performance of the filter is demonstrated on synthetic data and real Los Angeles gang crime data and compared against a very large sample-size particle filter, showing its effectiveness in practice. In addition the forecast skill of the Hawkes model is investigated for a forecast system using the Receiver Operating Characteristic (ROC) to provide a useful indicator for when predictive policing software for a crime type is likely to be useful. The ROC and Brier scores are used to compare and analyze the forecast skill of sequential data assimilation and MLE. It is found that sequential data assimilation produces improved probabilistic forecasts over the MLE.

Joint state-parameter estimation for a control-oriented LES wind farm model

Wind farm control research typically relies on computationally inexpensive, surrogate models for real-time optimization. However, due to the large time delays involved, changing atmospheric conditions and tough-to-model flow and turbine dynamics, these surrogate models need constant calibration. In this paper, a novel real-time (joint state-parameter) estimation solution for a medium-fidelity dynamical wind farm model is presented. In this work, we demonstrate the estimation of the freestream wind speed, local turbulence, and local wind field in a two-turbine wind farm using exclusively turbine power measurements. The estimator employs an Ensemble Kalman filter with a low computational cost of approximately 1.0 s per timestep on a dual-core notebook CPU. This work presents an essential building block for real-time wind farm control using computationally efficient dynamical wind farm models.