Problem Of Parameter Calibration Research Articles

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we parameterize the dynamical system state path using a linear basis. Then, we construct a physics-informed prior probability measure for the coefficients of the linear basis such that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Performance-Driven Safe Bayesian Optimization for Intelligent Tuning of High-Order Cascade Systems

Automatic parameter tuning of high-order cascade controllers suffers from sampling inefficiency and strong couplings. This work presents a performance-driven, systematic, and safe intelligent parameter-tuning framework for high-order cascade systems. To achieve data-efficient and noise-robust hyper-parameter calibration, an intelligent tuning framework based on Bayesian optimization is proposed to calibrate the control parameters from the buffer of performance-metric measurements. Furthermore, we improve the Bayesian-optimization-based framework in three aspects, involving effectiveness, security, and sampling efficiency. Firstly, a comprehensive control performance assessment combining the error-integral and statistical performance criteria is designed to evaluate the cost of a sampling point in terms of final precision, response rapidity, and vibration. Meanwhile, the security of sampling exploration is heightened by imposing composite hard parametric and soft performance-metric (maximum input, overshoot, etc.) constraints on the acquisition points. Additionally, a hierarchical optimization strategy is proposed to further boost sampling exploitation by alternatively tuning the control parameters of subsystems and refining the constraint on the sampling space. The proposed framework is applied to automatic parameter tuning of high-order dynamic-surface-based backstepping control combined with anti-disturbance rejection control. The comparative simulation results demonstrate that the proposed intelligent tuning possesses superiorities in sampling efficiency and security for parameter calibration problems.

State of health estimation for lithium-ion batteries based on current interrupt method and genetic algorithm optimized back propagation neural network

Accurate state-of-health (SOH) estimation is an essential prerequisite for a battery management system (BMS) to improve battery utilization efficiency. The impedance information can be utilized to reflect the SOH. However, the traditional electrochemical impedance spectroscopy (EIS) method suffers from time-consuming measurements and specialized equipment. This study aims to establish a connection between EIS and the current interrupt method, which reduces the difficulty of obtaining impedance information through its utilization. This method can be applied in real time during charging, enabling it to be incorporated into a BMS. A genetic algorithm optimized back propagation neural network (GA-BPNN) is developed to estimate the SOH based on the impedance information obtained in the current interrupt method as inputs. The genetic algorithm improves the weights and thresholds of the neural network, which solves the parameter calibration problem. In this study, besides utilizing measurement data from different aging conditions as training set data, hybrid tests comparable to the actual usage environment are employed as validation set data. The experimental results show that a combination of the proposed current interrupt method and GA-BPNN can estimate SOH accurately with the root mean square error (RMSE) as low as 0.77 % in a complex hybrid test environment.

Comparison of Parallel Genetic Algorithm and Particle Swarm Optimization for Parameter Calibration in Hydrological Simulation

ABSTRACT Parameter calibration is an important part of hydrological simulation and affects the final simulation results. In this paper, we introduce heuristic optimization algorithms, genetic algorithm (GA) to cope with the complexity of the parameter calibration problem, and use particle swarm optimization algorithm (PSO) as a comparison. For large-scale hydrological simulations, we use a multilevel parallel parameter calibration framework to make full use of processor resources, and accelerate the process of solving high-dimensional parameter calibration. Further, we test and apply the experiments on domestic supercomputers. The results of parameter calibration with GA and PSO can basically reach the ideal value of 0.65 and above, with PSO achieving a speedup of 58.52 on TianHe-2 supercomputer. The experimental results indicate that using a parallel implementation on multicore CPUs makes high-dimensional parameter calibration in large-scale hydrological simulation possible. Moreover, our comparison of the two algorithms shows that the GA obtains better calibration results, and the PSO has a more pronounced acceleration effect.

Bayesian-based calibration for water quality model parameters.

To improve the efficiency and accuracy of water quality model parameter calibration and avoid local optima and the phenomenon in which different parameters have the same effect, this paper proposed a novel Bayesian-based water quality model parameter calibration method. Using Bayesian inference, the parameter calibration problem was converted into a posterior probability function sampling problem, which was sampled using the Markov Chain Monte Carlo algorithm. The convergence speed of the calibration was further improved by setting the optimized initial sampling value. The influences of the initial sampling value, Markov chain length, and proposal distribution form on the calibration effect were evaluated using four specific cases. The results indicate that (1) the mean relative error (MRE) of the parameter calibration results of this method is less than 10%, with the calibration MRE of Dx and Dy being 5.3% and 8.3%, respectively; (2) when the parameter sensitivity is low, the calibration effect of this method is relatively poor, with a calibration MRE of 46% for k; (3) the parameter calibration can be completed more efficiently by setting an optimized initial value for the MCMC, choosing a reasonable Markov chain length and a suitable proposal distribution form. PRACTITIONER POINTS: Bayesian-based water quality model parameter calibration method is proposed and posterior probability distribution was sampled using the MCMC algorithm. Parameter calibration can be completed more efficiently by setting an optimized initial value for the MCMC. As a result, efficient and accurate parameter calibration of water quality models was achieved. This method is widely applicable to various models, and the calibration speed depends on the calculation speed of the model.

Gradient-based parameter calibration of an anisotropic interaction model for pedestrian dynamics

AbstractWe propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces (Totzeck (2020) Kinet. Relat. Models13(6), 1219–1242.) by including the agents’ body size. The influence of the body size on the self-organisation of the agents in channel and crossing scenarios as well as the fundamental diagram is studied. Since the model is stated as a coupled system of ordinary differential equations, we are able to give a rigorous well-posedness analysis. Then we state a parameter calibration problem that involves data from real experiments. We prove the existence of a minimiser and derive the corresponding first-order optimality conditions. With the help of these conditions, we propose a gradient descent algorithm based on mini-batches of the data set. We employ the proposed algorithm to fit the parameter of the collision avoidance and the strength parameters of the interaction forces to given real data from experiments. The results underpin the feasibility of the method.

Model Calibration for a Hydraulic Network Using Genetic Algorithms

This paper addresses the problem of parameter calibration in pipelines based on a Genetic Algorithm (GA). The parameters under consideration are the pipe roughness and the minor loss coefficient caused by fittings like valves, elbows, and couplings. These parameters cannot be directly measured, and their accuracy plays an essential role in successfully implementing leak diagnosis algorithms. The proposed GA generates calibrated values for both pipe roughness and minor loss coefficient by minimizing the root mean squared error (RMSE) in predicting pressures. The method was implemented in MATLAB and the calibration was validated in an experimental network by comparing the pressure heads measured at the nodes of the network and those from the calibrated model simulated with EPANET.

Design and implementation of the movement gauge for rail clearance based on combination measurement method

PurposeAs the infrastructure of the railway, the rail could sink or deform to different degrees due to the impact of train operation or the geological changing force for years, which will lead to the possibility that the facilities on both sides of the rail invade the rail clearance and bring hidden dangers to the safe operation of the train. The purpose of this paper is to design the gauge to measure the clearance parameters of rail.Design/methodology/approachAiming at the problem, the gauge for clearance measurement was designed based on a combination measurement method in this paper. It consists of the measurement box and the rail measurement vehicle, which integrates a laser displacement sensor, inclination sensor, gauge sensor and mileage sensor. The measurement box was placed outside the rail vehicle. Through the design of a hardware circuit and software system, the movement measurement of the clearance parameters was realized.FindingsIn this paper, the measurement equations of horizontal distance and vertical height were established, the optimal solutions of the structural parameters in the equations were obtained by Levenberg–Marquardt method, then the parameter calibration problem was also solved.Originality/valueThe gauge has high precision; its measurement uncertainty reaches 1.27 mm. The gauge has manual and automatic working modes, which are convenient to operate and have practical popularization value.

Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks

We propose a neural network approach to model general interaction dynamics and an adjoint-based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first-order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach, we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill–Whitham–Richards model for traffic and the social force model for crowd motion.

A Gaussian Process Emulator Based Approach for Bayesian Calibration of a Functional Input

Bayesian calibration of a functional input/parameter to a time-consuming simulator based on a Gaussian process (GP) emulator involves two challenges that distinguish it from other parameter calibration problems. First, one needs to specify a flexible stochastic process prior for the input, and reduce it to a tractable number of random variables. Second, a sequential experiment design criterion that decreases the effect of emulator prediction uncertainty on calibration results is needed and the criterion should be scalable for high-dimensional input and output. In this article, we address these two issues. For the first issue, we employ a GP with a prior density for its correlation parameter as prior for the functional input, and the Karhunen-Loève (KL) expansion of this non-Gaussian stochastic process to reduce its dimension. We show that this prior gives far more robust inference results than a GP with a fixed correlation parameter. For the second issue, we propose the weighted prediction variance (WPV) criterion (with posterior density of the calibration parameter as weight) and prove the consistency of the sequence of emulator-based likelihoods given by the criterion. The proposed method is illustrated with examples on hydraulic transmissivity estimation for groundwater models.

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

Research on tomographic image reconstruction algorithms based on fixed-point rotation X-CT system

Aiming at the problem of parameter calibration and image reconstruction of typical two-dimensional CT system, this paper uses back projection, iradon function, Fourier transform, Lambert law, visualization and other methods to establish projection centroid model, convolution back projection model, TV constrained iterative filtering back projection model, and uses MATLAB, Solidworks, Lingo and other software to visualize data types, so as to achieve better results. Better to find X-CT system tomography reconstruction methods.

Calibration of linear contact stiffnesses in discrete element models using a hybrid analytical-computational framework

Efficient selections of particle-scale contact parameters in discrete element modelling remain an open question. The aim of this study is to provide a hybrid calibration framework to estimate linear contact stiffnesses (normal and tangential) for both two-dimensional and three-dimensional simulations. Analytical formulas linking macroscopic parameters (Young's modulus, Poisson's ratio) to mesoscopic particle parameters for granular systems are derived based on statistically isotropic packings under small-strain isotropic stress conditions. By taking the derived analytical solutions as initial approximations, the gradient descent algorithm automatically obtains a reliable numerical estimation. The proposed framework is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. The results show that this hybrid method practically reduces the time for artificial trials and errors to obtain reasonable stiffness parameters. The proposed framework can also be extended to other parameter calibration problems in DEM.

Generalized parameter estimation and calibration for biokinetic models using correlation and single variable optimisations: Application to sulfate reduction modelling in anaerobic digestion

In this work, a generalized method for the estimation of biokinetic parameters in anaerobic digestion (AD) models is proposed. The method consists of a correlation-based approach to estimate specific groups of parameters mechanistically, followed by a sensitivity-based hierarchical and sequential single parameter optimisation (SHSSPO) calibration method for the remaining groups of parameters. The method was evaluated to estimate and calibrate the parameter values for sulfate reduction processes when included into the IWA Anaerobic Digestion Model No. 1 (ADM1) and simulations were compared with experimental data from literature. Under the proposed method, a large number of biokinetic parameters, namely biomass yields, maximum specific uptake rates, and half saturation constants, can first be estimated using mechanistic correlations. This achieves a significant reduction in the number of parameters to be fitted to data. For the remaining parameters, a method is proposed based on the overall sensitivity and degree of ubiquity of each parameter to establish a hierarchy in a sequential single parameter optimisation against the experimental data. This approach aims at eliminating the uncertainty on optimality (and therefore parameter identification) associated to multivariable parameter calibration problems. The method was applied to the sulfate reduction related parameters and led to the hydrogen sulfide inhibition parameters as the only ones requiring optimisation against experimental data. Comparison of the proposed SHSSPO performance with that of multi-dimensional parameter optimisation methods shows a superior performance in terms of overall error and computation times. Also, final simulation results led to model predictions of similar, if not better, quality than those achieved by multivariable parameter optimisation methods. The experimental variables optimized for included liquid effluent concentrations of sulfur species and volatile fatty acids as well as effluent methane gas flow. Overall, the proposed parameter estimation and calibration method provides a deterministic step-by-step approach to parameter estimation that decreases identifiability uncertainty at a very low computational effort. The results obtained suggest that the method could be generically applied with similar success to other biokinetic models frequently used in wastewater treatment.

Modelling the effect of land use change on hydrological model parameters via linearized calibration method in the upstream of Huaihe River Basin, China

Conceptual rainfall–runoff models have become a basic tool for evaluating effects of land use/cover changes on the hydrologic processes in small-scale as well as large watersheds. The runoff-producing mechanism is influenced by land use/cover changes. In this study, we analysed the effect of land use change on hydrological model parameters by calibrating the model parameters of different time periods with different land use via a linearized calibration method. The parameter calibration of a conceptual model usually involves the construction of objective function and optimization methods for good performance of observed data. However, the objective function of the minimum-sum-squared error will introduce an unrelated optimum solution for the parameter calibration problem of a conceptual model, which belongs to a highly complex nonlinear system. Thus, a linearized parameter calibration method, which searches for the optimal value on a parameter surface, is presented, based on the analysis of the problems of the objective function of the minimum-sum-squared error. Firstly, an ideal model is shown that illustrates the efficiency and applicability of this method. Secondly, the novel method is demonstrated for solving the Xinanjiang daily model parameter calibration. Finally, 50 years of data are divided into 4 different periods for parameter comparison, through which the effects of land use/cover changes on runoff in Dapoling watershed are evaluated. The results show that the linearized parameter calibration method is convergent, reasonable and effective. For example, the model parameter of evapotranspiration coefficient KC varied considerably, from 0.658 to 0.922, in response to land use/cover change within the watershed. Keywords: land use/cover change; parameter calibration; linearized; upper Huaihe River Basin

A projection pursuit dynamic cluster model based on a memetic algorithm

A Projection Pursuit Dynamic Cluster (PPDC) model optimized by Memetic Algorithm (MA) was proposed to solve the practical problems of nonlinearity and high dimensions of sample data, which appear in the context of evaluation or prediction in complex systems. Projection pursuit theory was used to determine the optimal projection direction; then dynamic clusters and minimal total distance within clusters (min TDc) were used to build a PPDC model. 17 agronomic traits of 19 tomato varieties were evaluated by a PPDC model. The projection direction was optimized by Simulated Annealing (SA) algorithm, Particle Swarm Optimization (PSO), and MA. A PPDC model, based on an MA, avoids the problem of parameter calibration in Projection Pursuit Cluster (PPC) models. Its final results can be output directly, making the cluster results objective and definite. The calculation results show that a PPDC model based on an MA can solve the practical difficulties of nonlinearity and high dimensionality of sample data.

From finance to ITS: traffic data fusion based on Markowitz' portfolio theory

SummaryTraffic data fusion has much to do with combining available or considered data sources in the best possible way. In this, it is very similar to optimizing a portfolio of financial assets in regard of return and risk. This article draws the analogy between these two mostly different scientific worlds, i.e. finance and engineering. Similarities and differences in context of weighted‐mean data fusion based on numerical traffic flow measurements such as travel times or speeds are discussed. This, in particular, includes guessing the potential benefit of negative weights. Optimal weights are derived following a strict mathematical theory based on assumptions (parameters) about systematic bias and correlations of the considered data sources. Moreover, a specific way of reducing the systematic bias of the fusion results is proposed and compared to common methods. The whole approach is demonstrated based on position data from two independent vehicle fleets in Athens, Greece. In this context, the problem of parameter calibration is solved by applying an advanced tool for such floating car data systems, called “self‐evaluation”. The experiments show that the proposed methods reliably reduce the systematic bias and variance of the fusion results with regard to the original data as well as in comparison to the naïve fusion approach that uses equal weights for all data sources. Copyright © 2015 John Wiley & Sons, Ltd.

Overview of nonlinear programming methods suitable for calibration of traffic flow models

The calibration of a macroscopic traffic flow model aims at enabling the model to reproduce, as accurately as possible, the real traffic conditions on a motorway network. Essentially, this procedure targets the best value for the parameter vector of the model and this can be achieved using appropriate optimization algorithms. The parameter calibration problem is formulated as a nonlinear, non-convex, least-squares optimization problem, which is known to attain multiple local minima; for this reason gradient-based solution algorithms are not considered to be an option. The methodologies that are more appropriate for application to this problem are mainly some meta-heuristic algorithms which use direct search approaches that allow them to avoid bad local minima. This paper presents an overview of the most suitable nonlinear programming methods for the calibration procedure of macroscopic traffic flow models. Furthermore, an application example, where two well-known macroscopic traffic flow models are evaluated through the calibration procedure, is presented.

Two-stage based ensemble optimization framework for large-scale global optimization

Large-scale global optimization (LSGO) is a very important and challenging task in optimization domain, which is embedded in many scientific and engineering applications. In order to strengthen both effectiveness and efficiency of LSGO algorithm, this paper designs a two-stage based ensemble optimization evolutionary algorithm (EOEA) framework, which serially implements two sub-optimizers. These two sub-optimizers mainly focus on exploration and exploitation separately. The EOEA framework can be easily generated, flexibly altered and modified, according to different implementation conditions. In order to analyze the effects of EOEA’s components, we compare its performance on diverse kinds of problems with its two sub-optimizers and three variants. To show its superiorities over the previous LSGO algorithms, we compare its performance with six classical LSGO algorithms on the LSGO test functions of IEEE Congress of Evolutionary Computation (CEC 2008). The performance of EOEA is further evaluated by experimental comparison with four state-of-the-art LSGO algorithms on the test functions of CEC 2010 LSGO competition. To benchmark the practical applicability of EOEA, we adopt EOEA to the parameter calibration problem of water pipeline system. Based on the experimental results on diverse scales of systems, EOEA performs steadily and robustly.

Projection Pursuit Dynamic Cluster Model and its Application to Water Resources Carrying Capacity Evaluation

The research shows that projection pursuit cluster (PPC) model is able to form a suitable index for overcom-ing the difficulties in comprehensive evaluation, which can be used to analyze complex multivariate prob-lems. The PPC model is widely used in multifactor cluster and evaluation analysis, but there are a few prob-lems needed to be solved in practice, such as cutoff radius parameter calibration. In this study, a new model-projection pursuit dynamic cluster (PPDC) model-based on projection pursuit principle is developed and used in water resources carrying capacity evaluation in China for the first time. In the PPDC model, there are two improvements compared with the PPC model, 1) a new projection index is constructed based on dynamic cluster principle, which avoids the problem of parameter calibration in the PPC model success-fully; 2) the cluster results can be outputted directly according to the PPDC model, but the cluster results can be got based on the scatter points of projected characteristic values or the re-analysis for projected character-istic values in the PPC model. The results show that the PPDC model is a very effective and powerful tool in multifactor data exploratory analysis. It is a new method for water resources carrying capacity evaluation. The PPDC model and its application to water resources carrying capacity evaluation are introduced in detail in this paper.