Parameter Estimation Research Articles

Integrated Hybrid Modelling and Surrogate Model-Based Operation Optimization of Fluid Catalytic Cracking Process

Fluid Catalytic Cracking (FCC) is one of the most important conversion processes in oil refineries, widely used to convert high-boiling, high-molecular-weight hydrocarbon components from crude oil into more valuable products like gasoline and diesel. Advanced simulation and optimization technologies are critical for improving the operational efficiency and economic performance of the FCC process. First-principles-based simulators rely on parameter estimation and are computationally intensive, making them unsuitable for online optimization. In recent years, with the development of deep learning, data-driven models have made significant progress in FCC modeling. However, due to their black-box nature and difficulty with extrapolation, they are rarely used for optimization. To bridge this gap, we propose an integrated framework that combines hybrid modeling and surrogate model-based optimization. This approach combines plant and simulation data to train a multi-task learning prediction model, which then serves as a surrogate for operational optimization. Validated on a large-scale FCC unit in southern China, the model predicts product yields with an error margin of under 4.84% for all products. Following optimization, yields of LNG, gasoline, and diesel rose by an average of 0.10 wt%, 1.58 wt%, and 1.05 wt%, respectively, resulting in a 3.67% increase in product revenues. This highlights the substantial potential of this framework for industrial applications.

Optimal Estimation of Reliability Parameters for Modified Frechet-Exponential Distribution Using Progressive Type-II Censored Samples with Mechanical and Medical Data

The aim of this research is to estimate the parameters of the modified Frechet-exponential (MFE) distribution using different methods when applied to progressive type-II censored samples. These methods include using the maximum likelihood technique and the Bayesian approach, which were used to determine the values of parameters in addition to calculating the reliability and failure functions at time t. The approximate confidence intervals (ACIs) and credible intervals (CRIs) are derived for these parameters. Two bootstrap techniques of parametric type are provided to compute the bootstrap confidence intervals. Both symmetric loss functions such as the squared error loss (SEL) and asymmetric loss functions such as the linear-exponential (LINEX) loss are used in the Bayesian method to obtain the estimates. The Markov Chain Monte Carlo (MCMC) technique is utilized in the Metropolis–Hasting sampler approach to obtain the unknown parameters using the Bayes approach. Two actual datasets are utilized to examine the various progressive schemes and different estimation methods considered in this paper. Additionally, a simulation study is performed to compare the schemes and estimation techniques.

Enhancing Efficiency: Halton Draws in the Generalized True Random Effects Model

This paper measures the impact of the number of Halton draws in excess of ⌈n⌉ on technical efficiency in the generalized true random effects (four-component) stochastic frontier model estimated by simulated maximum likelihood. A substantial set of Monte Carlo simulations demonstrates that increasing the number of Halton draws to ⌈n3/4⌉ (⌈n2/3⌉) decreases the mean squared error of the total technical efficiency estimates by 6.1 (4.9) percent. Furthermore, increasing the number of Halton draws either improves or has no detrimental impact on correlation, mean squared error, relative bias, and upward bias for persistent, transient, and total technical efficiency. An energy sector application is included, to demonstrate how these issues can arise in practice, and how increasing Halton draws can improve parameter and efficiency estimates in empirical work.

Validating a Calibrated Model of a Groundwater Pump-And-Treat System Using Robust Multiple Regression

Validation of groundwater models is relatively challenging due to the need to reserve scarce water level data for calibration targets. In addition, traditional statistical validation metrics are unintuitive for non-technical audiences and do not directly identify model behaviors that require further refinement. We developed a novel model validation method that analyzes rate change events at pump-and-treat wells and statistically compares the water level responses at nearby monitoring wells between the data and model. The method takes advantage of events that occur alongside ambient pumping, unlike parameter estimation techniques that require independent drawdown or recovery events. The ability of the model to match well connections that are evident (or not evident) in the observations is characterized statistically, leading to four decision scenarios: model matches the observed connection (1) or lack thereof (2), model exhibits a connection that is not observed (3), or model over- or understates the observed connection (4). The method is applied to an FEHM-based groundwater flow and transport model that is shown to match 84.5% of the well connections analyzed. The method provides novel perspectives on the influence of calibration targets on the flow field and suggests that although the overall effect of drawdown targets was to improve the model, the choice of target well pairs creates flow pathways that may be inconsequential during normal operational conditions. The model adequately matches the flow over short spatial scales (<800 m) and over-represents the flow over greater distances (300–1200 m), suggesting the need for “null” drawdown targets in subsequent rounds of calibration.

Population-based cross-sectional survey of cervical cancer screening prevalence and socio-demographic correlates in Bangladeshi women.

Cervical cancer, albeit preventable, is the second-most deadly gynecological cancer in developing nations. Little is known about cervical cancer among Bangladeshi women. This study aims to estimate the prevalence of cervical cancer screening and demographic correlates to identify potential variabilities in screening rates among different demographic groups and regions. This study used secondary data from the WHO STEPS 2018 Survey. We used Bayesian regression to perform the bivariate analyses between the outcome and each explanatory factor, as it generates more acceptable results and improves parameter estimates. The top-ranked socio-demographic factors were identified using a two-step cluster analysis. This method determines the relevance of predictor variables and automatically establishes the number of clusters. The prevalence of Bangladeshi women who had ever been screened for cervical cancer was 6.2%. In the adjusted model, women with the following socio-demographic factors had a higher likelihood of developing cervical cancer: being 18-29 years old (AOR = 3.3, 95% CI: 0.24, 15.27) or 45-59 years old (AOR = 2.8, 95% CI: 1.22, 6.0), currently married (AOR = 2.3, 95% CI: 1.36, 3.70), and employed (AOR = 2.4, 95% CI: 1.40, 4.06). Women in the Barisal division were found to have higher odds of being screened for cervical cancer (AOR = 21, 95% CI: 0.66, 121.97). Cluster analysis found residence status predisposes women to cervical cancer screening. There is a significant potential for substantial reductions in the burden of cervical cancer in Bangladesh by strengthening the application of cervical cancer screening. Future studies should examine how socioeconomic status, culture, and healthcare access affect cervical cancer screening trends for different divisions in Bangladesh. An independent national cancer registry is urgently needed to evaluate screening trends and outcomes.

A note on potential gains in precision of radiation risk estimates from joint analysis.

In estimating radiation-related risk of cancer and other diseases based on the RERF Life Span Study (LSS), joint analyses can be performed where multiple health outcome endpoints are combined in the same model, allowing some parameters to be estimated in common among all endpoints with possible increase in precision of radiation risk and other model parameter estimates. Using as a basis excess relative risk (ERR) and excess absolute risk (EAR) models of the type commonly used in analysis of LSS data at RERF, we use maximum likelihood theory to compute the asymptotic relative standard error of endpoint-specific radiation effect and other parameter estimates using joint analyses as compared to traditional independent analysis. We show that some gains in precision of endpoint-specific radiation risk parameter estimates can be achieved by sharing effect modifier and other model parameters, but only small or negligible gains in precision are achieved for endpoint-specific background modifying or effect modifying parameters when other model parameters are shared. The magnitude of the precision gain for radiation risk estimates depends on the number of endpoints, the baseline incidence rate of the endpoint, and the type of model being used.

A rapid multi-modal parameter estimation technique for LISA

Abstract The Laser Interferometer Space Antenna (LISA) will observe gravitational-wave signals from a wide range of sources, including massive black hole binaries. Although numerous techniques have been developed to perform Bayesian inference for LISA, they are often computationally expensive; analyses often take at least $\sim 1$ month on a single CPU, even when using accelerated techniques. Not only does this make it difficult to concurrently analyse more than one gravitational-wave signal, it also makes it challenging to rapidly produce parameter estimates for possible electromagnetic follow-up campaigns. simple-pe was recently developed to produce rapid parameter estimates for gravitational-wave signals observed with ground-based gravitational-wave detectors. In this work, we extend simple-pe to produce rapid parameter estimates for LISA sources, including the effects of higher order multipole moments. We show that simple-pe infers the source properties of massive black hole binaries in zero-noise at least $\sim 100\times$ faster than existing techniques; $\sim 12$ hours on a single CPU. We further demonstrate that simple-pe can be applied before existing Bayesian techniques to mitigate biases in multi-modal parameter estimation analyses of MBHBs.

Modeling and Simulation of Thermal Effects on Electrical Behavior in Lithium-Ion Cells

Thermal effects exert a crucial influence on the electrical behavior of lithium-ion batteries, significantly impacting key parameters such as the open circuit voltage curve, internal impedance, and cell degradation rate. Furthermore, these effects may give rise to electrolyte loss, resulting in a reduction in capacity. The cycling of batteries inherently generates internal heat, establishing a direct relationship between cell temperature and power demand. This article aims to provide a methodology to model electrothermal relations and temperature influence on electrical behavior in lithium-ion cells, as well as a simulation of extended cell operation under arbitrary power loads, presenting a novel approach not previously explored. It does this by considering three models: the Bernardi model for heat generation within the cell, a thermal lumped model for the cell’s temperature, and the Vogel-Fulcher-Tammann model for the capacity change as a function of temperature. These models are then connected to a state-of-the-art open circuit voltage model of a cell, providing a connection from the thermal world back into the electrical world. Experiments with different power demands occur on the simulation, including estimation of thermal parameters with relative errors under 1%, visualizing the effects of the integrated models and potential for real-cell applications.

Water quality estimates using machine learning techniques in an experimental watershed

ABSTRACT Estimation of the water quality parameters is important to enhance time and cost-effectiveness to that of the conventional approach. This study is aimed to identify the best machine learning (ML) approach to predict concentrations of biochemical oxygen demand (BOD), nitrate, and phosphate. Four ML techniques including decision tree, random forest, gradient boosting, and XGBoost were compared to estimate the water quality parameters based on biophysical (i.e., population, basin area, river slope, water level, and stream flow) and physicochemical properties (i.e., conductivity, turbidity, pH, temperature, and dissolved oxygen) as input parameters. The data were split into training and test sets, and the model performances were evaluated using coefficient of determination (R2), Nash–Sutcliffe efficiency coefficient (NSE), and root mean squared error (RMSE). The mean squared error (MSE) was used as the optimization target. The robust fivefold cross-validation, along with hyperparameter tuning, achieved R2 values of 0.76, 0.67, and 0.71 for phosphate, nitrate, and BOD, and NSE values of 0.73, 0.67, and 0.66, respectively. XGBoost yielded the lowest RMSE across all parameters, showcasing superior performance when considering all metrics performed. In conclusion, ML techniques, particularly with a robust cross-validation technique and hyperparameter optimization, showed good results in water quality parameter prediction.

Full-field Modal Analysis of a Tensegrity Column Using a Three-dimensional Scanning Laser Doppler Vibrometer with a Mirror

Abstract Tensegrity structures become important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on their dynamic analyses mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study proposes a non-contact approach for experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer is used with a mirror for extending its field of view to measure full-field vibration of a novel three-strut metal tensegrity column with free boundaries. Tensions and axial stiffnesses of its cable members are determined using natural frequencies of their transverse and longitudinal modes, respectively, to build its theoretical model for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and theoretical mode shapes are used to identify their paired modes. Modal parameters of the first 15 elastic modes of the tensegrity column identified from the experiment, including those of the overall structure and its cable members, can be classified into five mode groups depending on their types. Modes paired between experimental and theoretical results have MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The proposed non-contact 3D vibration measurement approach allows accurate estimation of 3D full-field modal parameters of the tensegrity column.

How the window of visibility varies around polar angle.

Contrast sensitivity, the amount of contrast required to discriminate an object, depends on spatial frequency (SF). The contrast sensitivity function (CSF) peaks at intermediate SFs and drops at other SFs. The CSF varies from foveal to peripheral vision, but only a couple of studies have assessed how the CSF changes with polar angle of the visual field. For many visual dimensions, sensitivity is better along the horizontal than the vertical meridian and at the lower than the upper vertical meridian, yielding polar angle asymmetries. Here, for the first time, to our knowledge, we investigate CSF attributes around polar angle at both group and individual levels and examine the relations in CSFs across locations and individual observers. To do so, we used hierarchical Bayesian modeling, which enables precise estimation of CSF parameters. At the group level, maximum contrast sensitivity and the SF at which the sensitivity peaks are higher at the horizontal than vertical meridian and at the lower than the upper vertical meridian. By analyzing the covariance across observers (n = 28), we found that, at the individual level, CSF attributes (e.g., maximum sensitivity) across locations are highly correlated. This correlation indicates that, although the CSFs differ across locations, the CSF at one location is predictive of that at another location. Within each location, the CSF attributes covary, indicating that CSFs across individuals vary in a consistent manner (e.g., as maximum sensitivity increases, so does the corresponding SF), but more so at the horizontal than the vertical meridian locations. These results show similarities and uncover some critical polar angle differences across locations and individuals, suggesting that the CSF should not be generalized across isoeccentric locations around the visual field.

Improved adaptive robust control of direct-drive pump-valve cooperative brake-by-wire unit with disturbance compensation

Abstract Aiming at the needs of high-level autonomous driving, a direct-drive pump-valve coordinated brake-by-wire unit was designed. To improve the response speed, control accuracy, and robustness of the brake-by-wire unit, an improved adaptive integral robust control method (AIRC-AD) based on a novel adaptive law and disturbance compensation was proposed. By integrating pressure tracking error information and overall parameter estimation error information, a novel parameter adaptive law with fast convergence speed was designed. A finite-time disturbance observer was designed to observe the overall system disturbance, improving the system’s anti-disturbance performance. Finally, the stability of the control method was proven using the Lyapunov stability proof method. The results show that under step target signals, sinusoidal target signals and triangular wave target signals, AIRC-AD has better response speed and control accuracy. In conditions such as increased permanent magnet temperature, increased coil resistance, or reduced flow area due to hydraulic pipeline blockage, AIRC-AD has better adaptability. The unit and the method can meet the demand for precise braking force control in high-level autonomous driving.

Real-time correction of gain nonlinearity in electrostatic actuation for whole-angle micro-shell resonator gyroscope

MEMS gyroscopes are well known for their outstanding advantages in Cost Size Weight and Power (CSWaP), which have inspired great research attention in recent years. A higher signal-to-noise ratio (SNR) for MEMS gyroscopes operating at larger vibrating amplitudes provides improved measuring resolution and ARW performance. However, the increment of amplitude causes strong nonlinear effects of MEMS gyroscopes due to their micron size, which has negative influences on the performance. This paper carries out detailed research on a general nonlinear mechanism on the sensors using parallel-plate capacitive transducers, which is called the gain nonlinearity in electrostatic actuation. The theoretical model established in this paper demonstrates the actuation gain nonlinearity causes the control-force coupling and brings extra angle-dependent bias with the 4th component for the whole-angle gyroscopes, which are verified by the experiments carried out on a micro-shell resonator gyroscope (MSRG). Furthermore, a real-time correction method is proposed to restore a linear response of the electrostatic actuation, which is realized by the gain modification with an online parameter estimation based on the harmonic-component relationship of capacitive detection. This real-time correction method could reduce the 4th component of the angle-dependent bias by over 95% from 0.003°/s to less than 0.0001°/s even under different temperatures. After the correction of actuation gain nonlinearity, the bias instability (BI) of whole-angle MSRG is improved by about 3.5 times from 0.101°/h to 0.029°/h and the scale factor nonlinearity (SFN) is reduced by almost one order of magnitude from 2.02 ppm to 0.21 ppm.

Quantum correlations and parameter estimation for two superconducting qubits interacting with a quantized field

In the present manuscript, we introduce a quantum system of two superconducting qubits (S–Qs) interacting with a quantized field under the influence of the Kerr nonlinear medium and Ising interaction. We formulate the Hamiltonian of the quantum model and determine the density operator of whole quantum system as well as quantum subsystems. We examine the dynamics of the quantumness measures for subsequent times including the S–Qs entanglement, S–Qs-field entanglement and quantum Fisher information in relation to the system parameters. Finally, we display the connection among the measures of quantumness during the time evolution.

Jupyter Notebooks for Parameter Estimation, Uncertainty Analysis, and Optimization with PEST+.

Jupyter Notebooks for Parameter Estimation, Uncertainty Analysis, and Optimization with PEST+.

Extending a Level Three Order Polynomial Probability Model

Inverse and power extensions were derived for a three order polynomial probability distribution and studied in this paper as post-development. The two extensions serve to make up for the limitations of their baseline model. Some relevant properties—shape of the PDF, moments, survival function, hazard function, quantile function, stress-strength reliability, order statistics and parameter estimations—were studied. The hazard shapes of the distributions were found to be inverted bathtub for the former and three different shapes namely: increasing function, decreasing function and bathtub, for the latter. This implies that the distributions can altogether model many varieties of datasets emanating from different life phenomena. This statement “if S(∞)=0, then H(∞)=∞” was examined and was discovered to apply for exponential distribution but not any of the extended distributions, and the baseline distribution too. Finally, the extensions showed to be competent over both the baseline distribution and their respective counterpart distributions, with respect to the datasets used. For the latter, the superiority was accountably hinged on the extra parameters, since the dataset has an outlier.

Evaluation of spatial models in the estimation of genetic parameters for incidence of frosty pod rot and production in Theobroma cacao full-sib family trials

Evaluation of spatial models in the estimation of genetic parameters for incidence of frosty pod rot and production in Theobroma cacao full-sib family trials

Variational inference for acceleration of SN Ia photometric distance estimation with BayeSN

Abstract Type Ia supernovae (SNe Ia) are standarizable candles whose observed light curves can be used to infer their distances, which can in turn be used in cosmological analyses. As the quantity of observed SNe Ia grows with current and upcoming surveys, increasingly scalable analyses are necessary to take full advantage of these new datasets for precise estimation of cosmological parameters. Bayesian inference methods enable fitting SN Ia light curves with robust uncertainty quantification, but traditional posterior sampling using Markov Chain Monte Carlo (MCMC) is computationally expensive. We present an implementation of variational inference (VI) to accelerate the fitting of SN Ia light curves using the BayeSN hierarchical Bayesian model for time-varying SN Ia spectral energy distributions (SEDs). We demonstrate and evaluate its performance on both simulated light curves and data from the Foundation Supernova Survey with two different forms of surrogate posterior – a multivariate normal and a custom multivariate zero-lower-truncated normal distribution – and compare them with the Laplace Approximation and full MCMC analysis. To validate of our variational approximation, we calculate the pareto-smoothed importance sampling (PSIS) diagnostic, and perform variational simulation-based calibration (VSBC). The VI approximation achieves similar results to MCMC but with an order-of-magnitude speedup for the inference of the photometric distance moduli. Overall, we show that VI is a promising method for scalable parameter inference that enables analysis of larger datasets for precision cosmology.

Two New Families of Local Asymptotically Minimax Lower Bounds in Parameter Estimation

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate and the true underlying parameter value (i.e., the estimation error), whereas the second is more specifically oriented to the moments of the estimation error. The proposed bounds are relatively easy to calculate numerically (in the sense that their optimization is over relatively few auxiliary parameters), yet they turn out to be tighter (sometimes significantly so) than previously reported bounds that are associated with similar calculation efforts, across many application examples. In addition to their relative simplicity, they also have the following advantages: (i) Essentially no regularity conditions are required regarding the parametric family of distributions. (ii) The bounds are local (in a sense to be specified). (iii) The bounds provide the correct order of decay as functions of the number of observations, at least in all the examples examined. (iv) At least the first family of bounds extends straightforwardly to vector parameters.

Novel family of probability generating distributions: Properties and data analysis

Abstract Current probability distributions often fall short when modeling lifespan data with non-monotonic hazard rate shapes, highlighting a gap in probability theory. To address this issue, this study introduces the novel family of probability-generating distributions (NP-G) as a solution to capture complex data patterns better. This research aims to develop and validate the NP-G distributions, which include a two-parameter continuous model based on the Weibull distribution. The study extensively explores the mathematical properties of the NP-G distributions, including series expansions of probability density functions, and evaluates various probabilistic measures such as moments, stress strength, mean deviations, entropy measures, and order statistics. Using the maximum likelihood method for parameter estimation and conducting a numerical simulation analysis, the study assesses the performance of the proposed extended exponentiated Weibull model. The findings demonstrate that this new model offers superior fit and accuracy compared to existing distributions when applied to two referenced datasets. This advancement is significant as it provides a more effective tool for analyzing lifespan data with non-monotonic hazard rates, enhancing both theoretical understanding and practical applications in fields such as reliability engineering and survival analysis.