Unknown Model Parameters Research Articles

Bayesian finite element model inversion of offshore wind turbine structures for joint parameter-load estimation

Operating in harsh and unsteady marine environment, offshore wind turbine (OWT) structures are exposed to unpredictable wind and wave loads. Identifying the structural loads and their effects on the OWTs allow for predicting the remaining fatigue life of these structures and improving the structural design procedure. In this paper, a finite element (FE) model inversion method is presented to estimate the unknown loads and model parameters of OWTs using sparse measurement data. A realistic FE model of an OWT structure with jacket substructure is created in the open-source simulation platform, OpenSees. A Bayesian inference framework is presented to integrate the measured data with the FE model to estimate unknown wind loads and mass of rotor-nacelle assembly. To evaluate the performance of this data assimilation framework, the effect of sensor type, number of sensors, and modeling errors on the estimation accuracy of wind loads and model parameters are investigated through different case studies where synthetic data are used as measurements. The results of this study are important to guide instrumentation of new OWT structures, and to understand the potential limitations and sources of error in the real-world application of this data assimilation framework for joint model parameter and input load estimation.

Parametric identification of coefficients for a model of fatigue stiffness degradation of a composite material

The problem of finding the fatigue characteristics of a composite material based on test results is considered. The results of endurance tests of unidirectional polymer composite materials with different initial stiffness, breaking stress and working cycle stress were used as the initial data. As a mathematical model of stiffness degradation, a nonlinear ordinary differential equation with five unknown parameters is used, reflecting characteristic changes in the properties of the material. It is required to find such parameter values that the solution of the differential equation should describe the available test results with sufficient accuracy. The solution procedure is reduced to the problem of optimizing the objective function, the value of which characterizes the achieved accuracy. As optimization methods, a method simulating the behavior of a flock of moths and a method of sequential reduction of the search set were used. A step-by-step algorithm for finding unknown model parameters is proposed, and numerical results of processing input data containing information on changing the elasticity modulus of the composite material in the course of applying load cycles are presented.

Q‐Learning Based Adaptive Kalman Filtering With Adaptive Window Length

ABSTRACTIn this article, we propose an adaptive Kalman filtering with adaptive window length based on Q‐learning for dynamic systems with unknown model information. The iteration step length of the Q‐function is quantitatively adjusted through the influence function. The adaptive Kalman filtering algorithm is used to set an appropriate weight matrix for the Q‐function to estimate unknown model parameters. One numerical example and a practice‐oriented case are given to illustrate the effectiveness of the proposed method. It is shown that this filtering can provide state estimates of best accuracy among all the compared methods when the model mismatch and noise statistical characteristics change.

Adaptive control of magnetic levitation system based on fuzzy inversion

A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

Bayesian Ensemble Kalman Filter for Gaussian Mixture Models

AbstractInverse theory and data assimilation methods are commonly used in earth and environmental science studies to predict unknown variables, such as the physical properties of underground rocks, from a set of measured geophysical data, like geophysical seismic or electromagnetic data. A new Bayesian approach based on the ensemble Kalman filter using Gaussian mixture models is presented to overcome the assumption of Gaussian distribution of the unknown variables commonly used in the data assimilation literature and to generalize the algorithm to inverse problems with multimodal probability distributions. In applications of subsurface characterization, the multimodality of the unknown variables is generally due to the presence of different rock types, also known as geological facies. In the proposed method, the weights of the Gaussian mixture model represent the facies proportions, and they follow a Markov chain model. The proposed Bayesian model generates the unknown model parameters conditioned on measured data using a Markov chain Monte Carlo sampler. The validity of the method is demonstrated on a data assimilation problem where the goal is to estimate the posterior distribution of the unknown rock density from a set of repeated measurements of acoustic wave velocity measured at different times. The proposed method provides accurate estimates with efficient computational times.

A novel performance prediction method for harmonic reducers based on the trend-enhanced Fisher’s discriminant ratio-Wiener process

Abstract Harmonic reducers, as core components of industrial robots, play a critical role in maintaining robot health. Performance degradation assessment (PDA) and remaining useful life (RUL) prediction are essential for ensuring the operational reliability of such robots. To address the multistage characteristics and stochastic uncertainties in the performance degradation of harmonic reducers, a performance prediction method based on Fisher’s discriminant ratio and Wiener process is proposed. Firstly, the health indicator (HI) construction is defined as an optimization problem based on Fisher’s discriminant ratio and trend monotonicity constraints. By leveraging the sum of the multiplication of frequency amplitudes and optimized weights, precise segmentation of the multistage degradation process over the entire lifecycle is achieved. Notably, the optimized weights can automatically identify the resonance frequency bands caused by damage. Subsequently, a nonlinear Wiener process model with a drift coefficient in the form of a power function is established. The probability density function (PDF) expression for RUL is derived based on the concept of first hit time (FHT). Additionally, a logarithmic likelihood function (Log-LF) for the unknown parameters in the degradation model is constructed. The experimental results indicate that the proposed method surpasses the other two Wiener process models in terms of root mean square error (RMSE), mean absolute percentage error (MAPE), and cumulative relative accuracy (CRA). This provides robust support for preventive maintenance decision-making for harmonic reducers.

Adaptive impedance control method for manipulator based on radial basis function

Purpose In view of the unknown environmental parameters and uncertain interference during gripping by the manipulator, it is difficult to obtain an effective gripping force with the traditional impedance control method. To avoid this dilemma, the purpose of this study is to propose an adaptive control strategy based on an adaptive neural network and a PID search optimization algorithm for unknown environments. Design/methodology/approach The method is based on a variable impedance model, and a new impedance model is established using a radial basis function (RBF) neural network to estimate unknown parameters of the impedance model. The approximation errors of the adaptive neural network and the uncertain disturbance are effectively suppressed by designing the adaptive rate. In the meantime, auxiliary variables are constructed for Lyapunov stability analysis and adaptive controller design, and PSA is used to ensure the stability of the adaptive impedance control system. Based on the Lyapunov stability criterion, the adaptive im-pedance control system is proved to have progressive tracking convergence property. Findings Through comparative simulations and experiments, the superiority of the proposed adaptive control strategy in position and force tracking has been verified. For objects with low flexibility and light-weight (such as a coke, a banana and a nectarine), this control method demonstrates errors of less than 10%. Originality/value This paper uses RBF neural networks to estimate unknown parameters of the impedance model in real-time, enhancing system adaptability. Neural network weights are updated online to suppress errors and disturbances. Auxiliary variables are designed for Lyapunov stability analysis. The PSA algorithm is used to adjust controller parameters in real-time. Additionally, comparative simulations and experi-ments are designed to analyze and validate the performance of controller.

Motion State Estimation of Preceding Vehicles With Packet Loss and Unknown Model Parameters

Motion State Estimation of Preceding Vehicles With Packet Loss and Unknown Model Parameters

Reliability estimation and statistical inference under joint progressively Type-II right-censored sampling for certain lifetime distributions

In this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request.

A multi-step mathematical model-based predictive strategy for software release timing during testing stage

Mathematically precise modeling is important to be established to accurately examine the quantitative relationship between software testing and software reliability. Software testing process is complex since it is concerned with various factors such as test case execution, defect debugging, tester expertise, test case selection, and so forth. For this reason, it is required to be meticulous in formulating the software testing process in a manner which is mathematically concise. The software release life cycle or sequential release timeline, referring to the process related to the development, testing and distribution of a software product comprises several critical stages, and the length of this particular life cycle reveals variations depending on different factors like the type of product, the intended use of it, industry security, general standards and compliance. One consideration software engineers have is related to the release date of the software so that future commitments about the software’s release time can be formulated beforehand. In view of these aspects, a multi-step strategy for predicting software release dates is proposed in the current study along with the following stages: firstly, the proposed technique selects the utmost reliability growth model that very well fits the observed test data halfway through the testing period, and then employs it to forecast the probable date of release. This technique entails approximating the unknown parameters of suitable Software Reliability Growth Models (SRGMs). Finally, the chosen SRGM is used to forecast the release date of the software under test by fitting it to available fault data. The proposed method is straightforward and applied to test on a total of ten actual datasets collected from the literature. The results of the proposed technique reveal that in the majority of the situations, nearly exact approximation of date of release can be made halfway through the testing period. Moreover, the proposed method’s performance is also compared to that of a number of previous strategies present in the literature. The outcomes obtained by our study demonstrate that the proposed strategy may be used to forecast the release date of software in practical situations.

A Novel Spotted Hyena Optimizer for the Estimation of Equivalent Circuit Model Parameters in Li-Ion Batteries

Li-ion batteries possess significant advantages like large energy density, fast recharge, and high reliability; hence, they are widely adopted in electric vehicles, portable electronics, and military and aerospace applications. Albeit having their merits, accurate battery modeling is subjected to problems like prior information on internal chemical reactions, complexity in problem formulation, a large number of unknown parameters, and the need for extensive experimentation. Hence, this article presents a reliable Spotted Hyena Optimizer (SHO) to determine the equivalent circuit parameters of lithium-ion (Li-ion) batteries. The methodology of the SHO is derived from the living and hunting tactics of spotted hyenas, and it is efficiently applied to solve the battery parameter estimation problem. Nine unknown battery model parameters of a Samsung INR 18650-25R are determined using this method. The model parameters estimated are endorsed for five different datasets with various discharge current values. Further, the effect of parameter range and its selection is also emphasized. Secondly, for validation, various performance metrics such as Integral Squared Error, mean best, mean worst, and Standard Deviation are evaluated to authenticate the superiority of the proposed parameter extraction. From the computed results, the SHO algorithm is able to explore the search area up to 89% in the case of larger search ranges. The chosen model and range of the SHO precisely predict the behavior of the proposed Li-ion battery, and the results are in accordance with the catalog data.

Coagulo-Net: Enhancing the mathematical modeling of blood coagulation using physics-informed neural networks

Blood coagulation, which involves a group of complex biochemical reactions, is a crucial step in hemostasis to stop bleeding at the injury site of a blood vessel. Coagulation abnormalities, such as hypercoagulation and hypocoagulation, could either cause thrombosis or hemorrhage, resulting in severe clinical consequences. Mathematical models of blood coagulation have been widely used to improve the understanding of the pathophysiology of coagulation disorders, guide the design and testing of new anticoagulants or other therapeutic agents, and promote precision medicine. However, estimating the parameters in these coagulation models has been challenging as not all reaction rate constants and new parameters derived from model assumptions are measurable. Although various conventional methods have been employed for parameter estimation for coagulation models, the existing approaches have several shortcomings. Inspired by the physics-informed neural networks, we propose Coagulo-Net, which synergizes the strengths of deep neural networks with the mechanistic understanding of the blood coagulation processes to enhance the mathematical models of the blood coagulation cascade. We assess the performance of the Coagulo-Net using two existing coagulation models with different extents of complexity. Our simulation results illustrate that Coagulo-Net can efficiently infer the unknown model parameters and dynamics of species based on sparse measurement data and data contaminated with noise. In addition, we show that Coagulo-Net can process a mixture of synthetic and experimental data and refine the predictions of existing mathematical models of coagulation. These results demonstrate the promise of Coagulo-Net in enhancing current coagulation models and aiding the creation of novel models for physiological and pathological research. These results showcase the potential of Coagulo-Net to advance computational modeling in the study of blood coagulation, improving both research methodologies and the development of new therapies for treating patients with coagulation disorders.

Fractional calculus integration for improved ECG modeling: A McSharry model expansion

This study introduces a new method for modeling electrocardiogram (ECG)11- CR: Compression Ratio; FDE: Fractional Differential Equation; GA: Genetic Algorithm; IDE: Integer Differential Equation; MAE: Mean Absolute Error; MSE: Mean Square Error; NRMSE: Normalized Root Mean Square Error; PC: Predictor Corrector; PRD: Percentage Root Mean Square Difference; QS: Quality Score; RMSE: Root Mean Square Error waveforms using Fractional Differential Equations (FDEs). By incorporating fractional calculus into the well-established McSharry model, the proposed approach achieves improved representation and high precision for a wide range of ECG waveforms. The research focuses on the impact of integrating fractional derivatives into Integer Differential Equation (IDE) models, enhancing the fidelity of ECG signal modeling.To optimize the model's unknown parameters, a combination of the Predictor-Corrector method for solving FDEs and genetic algorithms for optimization is utilized. The effectiveness of the fractional-order model is assessed through distortion metrics, providing a comprehensive evaluation of the modeling quality.Comparisons show that the fractional-order model outperforms the traditional McSharry IDE model in modeling quality and compression efficiency. It improves modeling quality by 48.40 % in MSE and compression efficiency by 23.18 % when applied on five beat types of MIT/BIH arrhythmia database. The fractional-order model demonstrates enhanced flexibility while preserving essential McSharry model characteristics, with fractional orders (α) ranging from 0.96 to 0.99 across five beat types.

Parameter extraction of proton exchange membrane fuel cell based on artificial rabbits’ optimization algorithm and conducting laboratory tests

Proton exchange membrane fuel cell (PEMFC) parameter extraction is an important issue in modeling and control of renewable energies. The PEMFC problem’s main objective is to estimate the optimal value of unknown parameters of the electrochemical model. The main objective function of the optimization problem is the sum of the square errors between the measured voltages and output voltages of the proposed electrochemical optimized model at various loading conditions. Natural rabbit survival strategies such as detour foraging and random hiding are influenced by Artificial rabbit optimization (ARO). Meanwhile, rabbit energy shrink is mimicked to control the smooth switching from detour foraging to random hiding. In this work, the ARO algorithm is proposed to find the parameters of PEMFC. The ARO performance is verified using experimental results obtained from conducting laboratory tests on the fuel cell test system (SCRIBNER 850e, LLC). The simulation results are assessed with four competitive algorithms: Grey Wolf Optimization Algorithm, Particle Swarm Optimizer, Salp Swarm Algorithm, and Sine Cosine Algorithm. The comparison aims to prove the superior performance of the proposed ARO compared with the other well-known competitive algorithms.

Supercritical fluid extraction of coumarins and flavonoids from citrus peel

The production manufacture of juices generates a large amount of waste consisting mainly of fruit peels. The peels are source of molecules such as coumarins and flavonoids. In this study, the peels of Citrus limonia, Citrus deliciosa, Citrus latifolia and Citrus sinensis were the raw material for supercritical fluid extraction. The Box-Behnken design was used to optimize the global yield in function of process variables. The chemical analysis of the extract was carried out by LC-MS and GC-MS. CFD was applied to the mass and momentum conservation equations in the study of supercritical extraction using citrus peels, which allowed the determination of unknown parameters of the bidimensional mathematical model. The flavonoids, nobiletin, sinensetin and tangeretin, as well as the coumarin, citropten, were identified in all species investigated. The maximum global yield obtained were 3.93 % for Citrus limonia, 4.18 % for Citrus deliciosa, 3.48 % for Citrus latifolia and 5.32 % for Citrus sinensis.

BO4IO: A Bayesian optimization approach to inverse optimization with uncertainty quantification

Data-driven inverse optimization (IO) aims to estimate unknown parameters in an optimization model from observed decisions. The IO problem is commonly formulated as a large-scale bilevel program that is notoriously difficult to solve. We propose a derivative-free optimization approach based on Bayesian optimization, BO4IO, to solve general IO problems. The main advantages of BO4IO are two-fold: (i) it circumvents the need of complex reformulations or specialized algorithms and can hence enable computational tractability even when the underlying optimization problem is nonconvex or involves discrete variables, and (ii) it allows approximations of the profile likelihood, which provide uncertainty quantification on the IO parameter estimates. Our extensive computational results demonstrate the efficacy and robustness of BO4IO to estimate unknown parameters from small and noisy datasets. In addition, the proposed profile likelihood analysis effectively provides good approximations of the confidence intervals on the parameter estimates and assesses the identifiability of the unknown parameters.

A Linear Regression Approach for Best Scanline Determination in the Object to Image Space Transformation Using Pushbroom Images.

The use of linear array pushbroom images presents a new challenge in photogrammetric applications when it comes to transforming object coordinates to image coordinates. To address this issue, the Best Scanline Search/Determination (BSS/BSD) field focuses on obtaining the Exterior Orientation Parameters (EOPs) of each individual scanline. Current solutions are often impractical for real-time tasks due to their high time requirements and complexities. This is because they are based on the Collinearity Equation (CE) in an iterative procedure for each ground point. This study aims to develop a novel BSD framework that does not need repetitive usage of the CE with a lower computational complexity. The Linear Regression Model (LRM) forms the basis of the proposed BSD approach and uses Simulated Control Points (SCOPs) and Simulated Check Points (SCPs). The proposed method is comprised of two main steps: the training phase and the test phase. The SCOPs are used to calculate the unknown parameters of the LR model during the training phase. Then, the SCPs are used to evaluate the accuracy and execution time of the method through the test phase. The evaluation of the proposed method was conducted using ten various pushbroom images, 5 million SCPs, and a limited number of SCOPs. The Root Mean Square Error (RMSE) was found to be in the order of ten to the power of negative nine (pixel), indicating very high accuracy. Furthermore, the proposed approach is more robust than the previous well-known BSS/BSD methods when handling various pushbroom images, making it suitable for practical and real-time applications due to its high speed, which only requires 2-3 s of time.

An optimal Bayesian strategy for comparing Wiener–Hunt deconvolution models in the absence of ground truth

Abstract This paper considers the quantitative comparison of several alternative models to perform deconvolution in situations where there is no ground truth data available. With applications to very large data sets in mind, we focus on linear deconvolution models based on a Wiener filter. Although comparatively simple, such models are widely prevalent in large scale setting such as high-resolution image restoration because they provide an excellent trade-off between accuracy and computational effort. However, in order to deliver accurate solutions, the models need to be properly calibrated in order to capture the covariance structure of the unknown quantity of interest and of the measurement error. This calibration often requires onerous controlled experiments and extensive expert supervision, as well as regular recalibration procedures. This paper adopts an unsupervised Bayesian statistical approach to model assessment that allows comparing alternative models by using only the observed data, without the need for ground truth data or controlled experiments. Accordingly, the models are quantitatively compared based on their posterior probabilities given the data, which are derived from the marginal likelihoods or evidences of the models. The computation of these evidences is highly non-trivial and this paper consider three different strategies to address this difficulty—a Chib approach, Laplace approximations, and a truncated harmonic expectation—all of which efficiently implemented by using a Gibbs sampling algorithm specialised for this class of models. In addition to enabling unsupervised model selection, the output of the Gibbs sampler can also be used to automatically estimate unknown model parameters such as the variance of the measurement error and the power of the unknown quantity of interest. The proposed strategies are demonstrated on a range of image deconvolution problems, where they are used to compare different modelling choices for the instrument’s point spread function and covariance matrices for the unknown image and for the measurement error.

Approximate Bayesian Computation for structural identification of ancient tie-rods using noisy modal data

Masonry arches and vaults are common historic structural elements that frequently experience asymmetric loading due to seismic action or abutment settlements. Over the past few decades, numerous studies have sought to enhance our understanding of the structural behavior of these elements for the purpose of preventive conservation. The assessment of the structural performance of existing constructions typically relies on effective numerical models guided by a set of unknown input parameters, including geometry, mechanical characteristics, physical properties, and boundary conditions. These parameters can be estimated through deterministic optimization functions aimed at minimizing the discrepancy between the output of a numerical model and the measured dynamic and/or static structural response. However, deterministic approaches overlook uncertainties associated with both input parameters and measurements. In this context, the Bayesian approach proves valuable for estimating unknown numerical model parameters and their associated uncertainties (posterior distributions). This involves updating prior knowledge of model parameters (prior distributions) based on current measurements and explicitly considering all sources of uncertainties affecting observed quantities through likelihood functions. However, two significant challenges arise: the likelihood function may be unknown or too complex to evaluate, and the computational costs for approximating the posterior distribution can be prohibitive. This study addresses these challenges by employing Approximate Bayesian Computation (ABC) to handle the intractable likelihood function. Additionally, the computational burden is mitigated through the use of accurate surrogate models such as Polynomial Chaos Expansions (PCE) and Artificial Neural Networks (ANN). The research focuses on setting up numerical models for simple structural systems (tie-rods) and inferring unknown input parameters, such as mechanical properties and boundary conditions, through Bayesian updating based on observed structural responses (modal data, strains, displacements). The main novelties of this research regard, on the one hand, the proposal of a methodology for obtaining a reliable estimate of the axial force in ancient tie-rods accounting for different sources of uncertainty and, on the other hand, the application of ABC to obtain the structural identification inverse problem solution.

Optimizing the secondary drying phase of a continuous Spin-Freeze Drying process: A semi-mechanistic modelling approach

Over the past decade, continuous spin freeze-drying technology has emerged as a promising alternative to conventional batch freeze-drying, effectively addressing many of the latter’s inherent disadvantages. Much of the focus during this period has been on controlling and optimizing the primary drying phase of this process. However, optimizing the secondary drying step is equally critical for the overall efficiency of the process. The primary aim of this study was to develop a comprehensive semi-mechanistic model for the secondary drying phase in continuous spin freeze-drying, accounting for the effects of process settings such as freezing rate and product temperature on desorption kinetics. Additionally, the study aimed to address discrepancies between conventional desorption models, typically applied in batch freeze-drying, and the observed data in this research. To achieve this, a residual moisture-dependent activation energy was introduced to improve the accuracy of the desorption model. Using NIR spectroscopy and IR-thermography, unknown model parameters could reliably be estimated using a simple and fast procedure. The calibrated model successfully predicted the final moisture content with an accuracy within 0.11% of the measured value under previously untested process conditions. Ultimately, the proposed semi-mechanistic model demonstrated its reliability in predicting the impact of new process conditions on both product temperature and residual moisture over time, enabling the development of a practical design space.