Time-invariant Model Parameters Research Articles

Grey-box modeling for thermal dynamics of buildings under the presence of unmeasured internal heat gains

An accurate grey-box building thermal model is an essential component for prediction-based control of split air conditioners. As the thermal performance of building envelope improves, the internal heat gains play an increasingly noteworthy influence on the building’s thermal dynamics. However, the internal heat gains are usually not measured, which makes the conventional data-dependent identification methods of building thermal models fail. To improve the accuracy of building thermal models under unmeasured internal heat gains, a two-step parameter identification framework for resistance–capacitance (RC) models is proposed in this paper. First, the time-invariant building model parameters are estimated by designing a novel optimization objective function. Next, the time-varying internal heat gains are identified based on the mismatch in predictions of the estimated building model from the first step and the measured temperature. The effectiveness of the method is evaluated using data from a simulation case and an experiment case. The results show that the proposed method outperforms the conventional identification method as well as two other identification methods that handle the unmeasured internal heat gains. Besides, the internal heat gains estimated by the proposed method can capture the trend of the actual internal loads well.

A time-varying state-space model for real-time temperature predictions in rack-based cooling data centers

Fast-growing data centers (DCs) require efficient cooling systems (such as rack-based cooling architectures) and control strategies to reduce operating costs and guarantee desired indoor conditions. Thus, this study proposed a novel real-time temperature prediction model for rack-based cooling DCs, in order to facilitate advanced control regarding cooling management and workload assignment. Specifically, a data-driven technology was introduced to estimate time-invariant model parameters, in order to avoid the time-consuming physics-based parameters extracting process. The mass conservation relationships were employed to update time-varying flow parameters in real-time to capture the nonlinear behaviors in DCs. Moreover, the proposed control-oriented thermal modeling method can model hot air recirculation and cold air bypass occurring simultaneously for the first time. The performance of the developed time-varying state-space model was validated by CFD simulation data. Additionally, the timeliness of modeling and temperature prediction was also investigated. The results show that the developed model achieves sufficient accuracy with a mean absolute error (MAE) equal to 0.28 °C, even for long prediction horizons and dynamic IT workloads. Also, the developed model has outstanding timeliness for advanced control techniques, in terms of less than 30 min for parameter identification and less than 10 s for temperature prediction.

A Big Data-Driven Intelligent Knowledge Discovery Method for Epidemic Spreading Paths

The prevention and control of communicable diseases such as COVID-19 has been a worldwide problem, especially in terms of mining towards latent spreading paths. Although some communication models have been proposed from the perspective of spreading mechanism, it remains hard to describe spreading mechanism anytime. Because real-world communication scenarios of disease spreading are always dynamic, which cannot be described by time-invariant model parameters, to remedy such gap, this paper explores the utilization of big data analysis into this area, so as to replace mechanism-driven methods with big data-driven methods. In modern society with high digital level, the increasingly growing amount of data in various fields also provide much convenience for this purpose. Therefore, this paper proposes an intelligent knowledge discovery method for critical spreading paths based on epidemic big data. For the major roadmap, a directional acyclic graph of epidemic spread was constructed with each province and city in mainland China as nodes, all features of the same node are dimension-reduced, and a composite score is evaluated for each city per day by processing the features after principal component analysis. Then, the typical machine learning model named XGBoost carries out processing of feature importance ranking to discriminate latent candidate spreading paths. Finally, the shortest path algorithm is used as the basis to find the critical path of epidemic spreading between two nodes. Besides, some simulative experiments are implemented with use of realistic social network data.

On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration

Abstract Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on model parameters. In this context, on-line (recursive) Bayesian filtering algorithms typically fail to properly quantify the full posterior uncertainty of time-invariant model parameters. Off-line (batch) algorithms are—in principle—better suited for the uncertainty quantification task, yet they are computationally prohibitive in sequential settings. In this work, we adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov Chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model approximates the posterior distribution within the resampling process in all three filters. Two numerical examples provide the basis for a comparative assessment. The first example considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential monitoring measurements. The second high-dimensional, linear, Gaussian example employs a random field to model corrosion deterioration across a beam, which is updated with sequential sensor measurements. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.

Improving multi-decadal coastal shoreline change predictions by including model parameter non-stationarity

Our ability to predict sandy shoreline evolution resulting from future changes in regional wave climates is critical for the sustainable management of coastlines worldwide. To this end, the present generation of simple and efficient semi-empirical shoreline change models have shown good skill at predicting shoreline changes from seasons up to several years at a number of diverse sites around the world. However, a key limitation of these existing approaches is that they rely on time-invariant model parameters, and assume that beaches will evolve within constrained envelopes of variability based on past observations. This raises an interesting challenge because the expected future variability in key meteocean and hydrodynamic drivers of shoreline change are likely to violate this ‘stationary’ approach to longer-term shoreline change prediction. Using a newly available, multi-decadal (28-year) dataset of satellite-derived shorelines at the Gold Coast, Australia, this contribution presents the first attempt to improve multi-decadal shoreline change predictions by allowing the magnitude of the shoreline model parameters to vary in time. A data assimilation technique (Ensemble Kalman Filter, EnKF) embedded within the well-established ShoreFor shoreline change model is first applied to a 14-year training period of approximately fortnightly shoreline observations, to explore temporal variability in model parameters. Then, the magnitudes of these observed non-stationary parameters are modelled as a function of selected wave climate covariates, representing the underlying seasonal to interannual variability in wave forcing. These modelled time-varying parameters are then incorporated into the shoreline change model and tested over the complete 28-year dataset. This new inclusion of non-stationary model parameters that are directly modelled as a function of the underlying wave forcing and corresponding time scales of beach response, is shown to outperform the multi-decadal predictions obtained by applying the conventional stationary approach (RMSEnon-stationary = 11.1 m; RMSEstationary = 254.3 m). Based on these results, it is proposed that a non-stationary approach to shoreline change modelling can reduce the uncertainty associated with the misspecification of physical processes driving shoreline change and should be considered for future shoreline change predictions.

A method for capacity estimation of lithium-ion batteries based on adaptive time-shifting broad learning system

Accurate capacity estimation of lithium-ion batteries can improve the safety and reliability of equipment. Deep learning provides a new approach for capacity estimation. However, it is still difficult to adapt to the changes in different stages of capacity degradation due to many and complex parameters in deep structure network and the time-invariant model parameters. Considering that Broad Learning System is a neural network independent of deep structure, which has a simple single hidden layer structure and fewer parameters, this paper proposes an Adaptive Time-shifting Broad Learning System (ATBLS) capacity estimation model. For input layer, the input data of each time step is combined with the output of previous time step to get a new input, so as to provide local information to hidden unit of the network and provide guidance for local parameters. For hidden layer, the hidden unit of each time step is weighted-fused with the hidden unit of previous time step to update the parameters, so as to reflect the long-term dynamics of sequence. The experiment are conducted on three different data sets. And the effectiveness of ATBLS is verified by comparing with other methods.

Sampling methods for solving Bayesian model updating problems: A tutorial

This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the context of Bayesian model updating for engineering applications. Markov Chain Monte Carlo, Transitional Markov Chain Monte Carlo, and Sequential Monte Carlo methods are introduced, applied to different case studies and finally their performance is compared. For each of these methods, numerical implementations and their settings are provided.Three case studies with increased complexity and challenges are presented showing the advantages and limitations of each of the sampling techniques under review. The first case study presents the parameter identification for a spring-mass system under a static load. The second case study presents a 2-dimensional bi-modal posterior distribution and the aim is to observe the performance of each of these sampling techniques in sampling from such distribution. Finally, the last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data.The case studies presented in this paper consider the recorded data set as a single piece of information which is used to make inferences and estimations on time-invariant model parameters.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Robust identification of discrete-time linear systems with unknown time-varying disturbance

In this paper, one robust identification method is proposed for the discrete-time linear systems with unknown time-varying disturbance. The disturbance is considered as a time-varying parameter for tracking estimation. A robust recursive least squares method is proposed using a forgetting factor. Moreover a new forgetting scheme to update the covariance matrix is developed to improve the stable convergence property of the time-invariant model parameters and the tracking performance of time-varying disturbance. The convergence performance of parameter estimation is analyzed with a proof. Two examples with different types of time-varying disturbance are shown to illustrate the effectiveness and advantage of the proposed method.

Optimality and identification of dynamic models in systems biology: an inverse optimal control framework.

Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies. The code used to obtain the results reported here is available at https://zenodo.org/record/1009541. Supplementary data are available at Bioinformatics online.

Multi-innovation based Identification of Output Error Model with Time Delay under Load Disturbance

In this paper, a robust output error model identification method is proposed for industrial processes with time delay subject to load disturbance. By viewing the load disturbance response as a time-variant parameter to be estimated, an extended recursive least-squares (RLS) identification method is established to simultaneously estimate the model parameters and the disturbance response, based on a multi-innovation fitting strategy. The integer type time delay parameter is determined by using a one-dimensional searching approach. An auxiliary model is used to estimate the noise-free output against stochastic noise. Besides, two adaptive forgetting factors are introduced to improve the convergence rates of estimating the time-invariant model parameters and the time-variant disturbance response, respectively. The effectiveness and merit of the proposed method is demonstrated by an illustrative example.

A Data-Driven Hybrid ARX and Markov Chain Modeling Approach to Process Identification With Time-Varying Time Delays

In this paper, we consider an important practical industrial process identification problem where the time delay can change at every sampling instant. We model the time-varying discrete time-delay mechanism by a Markov chain model and estimate the Markov chain parameters along with the time-delay sequence simultaneously. Besides time-varying delay, processes with both time-invariant and time-variant model parameters are also considered. The former is solved by an expectation-maximization (EM) algorithm, while the latter is solved by a recursive version of the EM algorithm. The advantages of the proposed identification methods are demonstrated by numerical simulation examples and an evaluation on pilot-scale experiments.

Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures

A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer–Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

Efficient Characterization of Uncertain Model Parameters with a Reduced-Order Ensemble Kalman Filter

Spatially variable model parameters are often highly uncertain and difficult to observe. This has prompted the widespread use of Bayesian characterization methods that can infer parameter values from measurements of related variables, while explicitly accounting for uncertainty. Ensemble versions of Bayesian characterization are particularly convenient when uncertain variables have complex spatial structures that do not conform to Gaussian descriptions. However, ensemble methods can be time consuming for high-dimensional problems. This paper describes a reduced-order approach to ensemble characterization that is particularly well suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform to reduce the dimensionality of spatially variable time-invariant model parameters and a nonlinear extension of principle orthogonal decomposition to reduce the dimensionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step of ...

Creating Dynamic Images of Short-lived Dopamine Fluctuations with lp-ntPET: Dopamine Movies of Cigarette Smoking

We describe experimental and statistical steps for creating dopamine movies of the brain from dynamic PET data. The movies represent minute-to-minute fluctuations of dopamine induced by smoking a cigarette. The smoker is imaged during a natural smoking experience while other possible confounding effects (such as head motion, expectation, novelty, or aversion to smoking repeatedly) are minimized. We present the details of our unique analysis. Conventional methods for PET analysis estimate time-invariant kinetic model parameters which cannot capture short-term fluctuations in neurotransmitter release. Our analysis - yielding a dopamine movie - is based on our work with kinetic models and other decomposition techniques that allow for time-varying parameters 1-7. This aspect of the analysis - temporal-variation - is key to our work. Because our model is also linear in parameters, it is practical, computationally, to apply at the voxel level. The analysis technique is comprised of five main steps: pre-processing, modeling, statistical comparison, masking and visualization. Preprocessing is applied to the PET data with a unique 'HYPR' spatial filter 8 that reduces spatial noise but preserves critical temporal information. Modeling identifies the time-varying function that best describes the dopamine effect on 11C-raclopride uptake. The statistical step compares the fit of our (lp-ntPET) model 7 to a conventional model 9. Masking restricts treatment to those voxels best described by the new model. Visualization maps the dopamine function at each voxel to a color scale and produces a dopamine movie. Interim results and sample dopamine movies of cigarette smoking are presented.

Creating Dynamic Images of Short-lived Dopamine Fluctuations with lp-ntPET: Dopamine Movies of Cigarette Smoking

We describe experimental and statistical steps for creating dopamine movies of the brain from dynamic PET data. The movies represent minute-to-minute fluctuations of dopamine induced by smoking a cigarette. The smoker is imaged during a natural smoking experience while other possible confounding effects (such as head motion, expectation, novelty, or aversion to smoking repeatedly) are minimized.We present the details of our unique analysis. Conventional methods for PET analysis estimate time-invariant kinetic model parameters which cannot capture short-term fluctuations in neurotransmitter release. Our analysis - yielding a dopamine movie - is based on our work with kinetic models and other decomposition techniques that allow for time-varying parameters 1-7. This aspect of the analysis - temporal-variation - is key to our work. Because our model is also linear in parameters, it is practical, computationally, to apply at the voxel level. The analysis technique is comprised of five main steps: pre-processing, modeling, statistical comparison, masking and visualization. Preprocessing is applied to the PET data with a unique 'HYPR' spatial filter 8 that reduces spatial noise but preserves critical temporal information. Modeling identifies the time-varying function that best describes the dopamine effect on 11C-raclopride uptake. The statistical step compares the fit of our (lp-ntPET) model 7 to a conventional model 9. Masking restricts treatment to those voxels best described by the new model. Visualization maps the dopamine function at each voxel to a color scale and produces a dopamine movie. Interim results and sample dopamine movies of cigarette smoking are presented.

Including slot harmonics to mechanical model of two-pole induction machine with a force actuator

A simple mechanical model is identified for a two-pole induction machine that has a four-pole extra winding as a force actuator. The actuator can be used to suppress rotor vibrations. Forces affecting the rotor of the induction machine are separated into actuator force, purely mechanical force due to mass unbalance, and force caused by unbalanced magnetic pull from higher harmonics and unipolar flux. The force due to higher harmonics is embedded to the mechanical model. Parameters of the modified mechanical model are identified from measurements and the modifications are shown to be necessary. The force produced by the actuator is calculated using the mechanical model, direct flux measurements, and voltage and current of the force actuator. All three methods are shown to give matching results proving that the mechanical model can be used in vibration control. The test machine is shown to have time periodic behavior and discrete Fourier analysis is used to obtain time-invariant model parameters.

A simulation model of glucose regulation in the critically ill

Focused research is underway to improve the delivery of tight glycaemic control at the intensive care unit. A major component is the development of safe, efficacious and effective insulin titration algorithms, which are normally evaluated in time-consuming resource-demanding clinical studies. Simulation studies with virtual critically ill patients can substantially accelerate the development process. For this purpose, we created a model of glucoregulation in the critically ill. The model includes five submodels: a submodel of endogenous insulin secretion, a submodel of insulin kinetics, a submodel of enteral glucose absorption, a submodel of insulin action and a submodel of glucose kinetics. Model parameters are estimated utilizing prior knowledge and data collected routinely at the intensive care unit to represent the high intersubject and temporal variation in insulin needs in the critically ill. Bayesian estimation combined with the regularization method is used to estimate (i) time-invariant model parameters and (ii) a time-varying parameter, the basal insulin concentration, which represents the temporal variation in insulin sensitivity. We propose a validation process to validate virtual patients developed for the purpose of testing glucose controllers. The parameter estimation and the validation are exemplified using data collected in six critically ill patients treated at a medical intensive care unit. In conclusion, a novel glucoregulatory model has been developed to create a virtual population of critically ill facilitating in silico testing of glucose controllers at the intensive care unit.

Causes of interannual variability in ecosystem–atmosphere CO 2 exchange in a northern Wisconsin forest using a Bayesian model calibration

Variability in fluxes of CO 2 observed at the WLEF tall tower in northern Wisconsin was analyzed for the years 1997–2004. During this time, the WLEF region was a source of CO 2 to the atmosphere averaging 120 g C m −2 year −1, with a range of interannual variability of 140 g C m −2 year −1. Random uncertainty in annual sums of net ecosystem exchange (NEE) due to turbulent variability and gap-filling was estimated to be 15–20 g C m −2 year −1. Although magnitudes of NEE sums were affected systematically by the choice of friction velocity ( u*) threshold, this choice had little effect on interannual variability of annual sums. The WLEF region was, on average, a source of carbon from 1997 to 2004 regardless of the u* threshold applied. Interannually, daytime NEE sums varied more than nighttime NEE sums, and spring and summer NEE sums varied more than autumn and winter NEE sums. Interannual variations in seasonal sums of daytime, nighttime and total NEE were often strongly correlated with changes in soil moisture and soil temperature. Standard nonlinear gap-filling regression models of respiration and gross ecosystem productivity were extended to incorporate the effects of soil moisture and phenology and combined into a single model of NEE. The Markov Chain Monte Carlo (MCMC) data assimilation technique was performed using observed WLEF NEE to derive full probability density functions (PDFs) of time-invariant model parameters. Prior values had little effect on posterior parameter PDFs, but significant differences in parameter PDFs occurred depending on whether daytime NEE, nighttime NEE, or total NEE data were used. This simple model was moderately successful in producing statistically significant correlations with interannual variations in annual and growing season NEE sums, but was generally unsuccessful in spring and autumn. In all cases, the model underestimated the degree of variability in NEE sums.