Multiple Unknown Parameters Research Articles

A Bayesian learning and pricing model with multiple unknown demand parameters

A Bayesian learning and pricing model with multiple unknown demand parameters

Elucidation of DPP-4 involvement in systemic distribution and renal reabsorption of linagliptin by PBPK modeling with a cluster Gauss-Newton method.

The dipeptidyl peptidase-4 (DPP-4) inhibitor linagliptin (LNG) exhibits target-mediated drug disposition (TMDD) in clinical settings, characterized by saturable binding to plasma soluble DPP-4 (sDPP-4) and tissue transmembrane DPP-4 (tDPP-4). Previous studies have indicated that saturable renal reabsorption of LNG contributes to its nonlinear urinary excretion observed in humans and wild-type mice, but not in Dpp-4 knockout mice. To elucidate the mechanisms underlying these complex phenomena, including DPP-4-related renal reabsorption of LNG, we employed physiologically-based pharmacokinetic (PBPK) modeling combined with a cluster Gauss-Newton method (CGNM). The CGNM facilitated the exploration of parameters in rat and human PBPK models for LNG and the determination of parameter identifiability. Through PBPK-CGNM analysis using reported autoradiography data ([14C]-LNG) in wild-type and Dpp-4-deficient rats, DPP-4-specific distributions of LNG in various tissues were clearly differentiated from nonspecific parts. By fitting to human plasma concentrations and urinary and fecal excretions of LNG after intravenous and oral administrations, multiple unknown PBPK parameters were simultaneously estimated by the CGNM. Notably, the amount of tDPP-4 and the reabsorption clearance for LNG-DPP-4 complexes were identifiable, indicating their critical role in explaining the complex nonlinear pharmacokinetics of LNG. Compared with previous PBPK analyses, the CGNM allowed us to incorporate greater model complexity (e.g., consideration of tDPP-4 expressions and invitro binding kinetics), ultimately resulting in a more accurate reproduction of LNG's TMDD. In conclusion, by considering LNG as a high-affinity probe for DPP-4, comprehensive PBPK-CGNM analyses suggested a dynamic whole-body distribution of DPP-4, including its involvement in the renal reabsorption of LNG.

Impact of Composition Ratio on the Expansion Behavior of Polyurethane Grout.

Different formulations of foaming polyurethane grout offer controlled expansion rates. This is crucial for precision in filling voids without exerting excessive pressure on surrounding structures, which could potentially cause damage. This study focuses on the impact of composition on the expansion performance of tailor-made polyurethane grouting materials. Initially, multiple unknown chemical reaction kinetic parameters were identified by combining free expansion tests, which involved measuring density and temperature changes, with the particle swarm optimization algorithm. A numerical simulation, integrating chemical kinetic models and fluid flow equations, was established to replicate the free expansion process of polyurethane grout in a cup, aligning with our experimental results. Subsequently, we analyzed the polymerization process of polyurethane grout with varying compositions to determine the effect of composition ratios on grout expansion. Our findings reveal that the expansion ratio of foaming polyurethane is predominantly influenced by the concentrations of physical and chemical foaming agents, followed by isocyanate concentration. Polyol, in contrast, exerts a relatively minor influence. Furthermore, the solubility of the physical foaming agent in the grout determines both its maximum allowable concentration and its maximum contribution to volume increase. This study provides valuable insights for the design and selection of polyurethane grout components tailored to diverse applications.

HomPINNs: Homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions

Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we propose homotopy physics-informed neural networks (HomPINNs), a novel framework that leverages homotopy continuation and neural networks (NNs) to solve inverse problems. The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Through homotopy continuation, the proposed method solves the inverse problem by tracing the observations and identifying multiple solutions. The experiments involve testing the performance of the proposed method on one-dimensional DEs and applying it to solve a two-dimensional Gray-Scott simulation. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters. Moreover, it has significant potential for various applications in scientific computing, such as modeling complex systems and solving inverse problems in physics, chemistry, biology, etc.

Optimal swimming locomotion of snake-like robot in viscous fluids

Snake-like robots have several joints that enable them to swim in various types of viscous fluids such as water, mud, and clay by varying the undulation. Because the optimal swimming motion is assumed to be different in fluids with different viscosities, we constructed an equation of motion for a snake-like robot swimming in viscous fluids and attempted to find the optimal swimming motion via numerical analysis. We constructed a snake-like robot comprising eight links in this study that could swim in four fluids with different kinematic viscosities, and measured their joint positions and relative angles during swimming. Accordingly, we proposed a method for identifying multiple unknown parameters of fluid forces acting on a body using the unscented Kalman filter, which could determine the unknown added mass and drag coefficient. Subsequently, we clarified that the inertial drag model is effective in water (small viscosity, μ∼1mPas), while the friction drag model is effective in oil (large viscosity, μ>100mPas). By considering the increase in frictional drag due to boundary layer thinning in the proposed model, we identified the constant drag coefficient regardless of the swimming frequency. Next, we employed the constructed numerical model to explore the trade-off relationship between consumed power and velocity during swimming using exhaustive search. Consequently, we confirmed that the swimming frequency decreased as the fluid viscosity increased under the same swimming power consumption. Moreover, the wavelength of undulation was confirmed to be between half and one wavelength, regardless of the viscosity.

Global Stabilizability Theorems on Discrete-Time Nonlinear Uncertain Systems

This paper focuses on the a basic class of discrete-time nonlinear systems with multiple unknown parameters. We claim that such a system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. This rule cannot be relaxed in general since it becomes a necessary and sufficient condition when the system has a polynomial form [10]. We further prove that the concerned stabilizable system is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed herein.

Data‐driven control for networked systems with multiple packet dropouts

AbstractThis paper investigates data‐driven control for a class of networked control systems with multiple packet dropouts and unknown system parameters. Here, multiple packet dropouts occur randomly in the controller‐to‐actuator (C/A) and sensor‐to‐controller (S/C) channels, where successive packet dropouts are limited by known upper bounds. By introducing the summation inequality, a model‐based mean‐square asymptotic stability condition is established for the closed‐loop networked control system with the potential to migrate to a data‐driven solution. Then, the data‐driven mean‐square asymptotic stability condition for the closed‐loop system is presented by merging the model‐based stability condition with noisy data‐parameterized representations. On this basis, the data‐driven controller gain design approaches for combining unknown and known input gain matrices are presented in turn. Finally, two simulation examples are provided to show the applicability of the developed approaches.

ИСПОЛЬЗОВАНИЕ МОДЕЛИ МНОЖЕСТВЕННОЙ ЛИНЕЙНОЙ РЕГРЕССИИ ДЛЯ КРАТКОСРОЧНОГО ПРОГНОЗИРОВАНИЯ ЦЕН НА КАЛИЙНУЮ ПРОДУКЦИЮ

The modern economy instability due to global and regional conflicts and contradictions leads to significant fluctuations in commodity markets. The demand and prices unpredictability leads to the raw materials in-dustries risks increase and limits their successful functioning and development. The purpose of the study. In this paper, we made an attempt of a multiple linear regression model application to obtain a forecast price of potash products acceptable quality. Despite the wide application and simplicity of construction and interpretation, the forecasting properties of such models are usually unsatisfactory. Nevertheless, an adequate selection of factors and the sample size used to estimate unknown parameters of the model, al-lows to achieve an acceptable forecasting quality. Materials and methods. In the issue the evaluation of the multiple linear regression model unknown parameters is performed on the basis of United States of America Geological Survey data. The sample contains information about the American potash market in the period from 1900 to 2020. The quality of forecasting is tested using the post-forecast method for years 2019 and 2020. The model built using the entire dataset gives an unsatisfactory relative prediction error. To reduce its value, a search of the sample volumes of data used for model parameters estimation was per-formed, and the one with the minimal forecast error was selected as optimal. The calculations were per-formed using MS Excel and Jupyter Notebook 6.1.4 environment for Python 3.8.5. Results. The conducted research allowed us to determine that in order to minimize the US domestic market potash products price relative error, it is necessary to use from 9 to 13 years time intervals for modeling. By doing that it is possi-ble to improve the 118-year time interval forecast for 2019 year by 23.9%, and a similar forecast for 2020 by 83.70%. Conclusion. Based on the results of the work done, it can be stated that the multiple linear re-gression model can be successfully used for short-term forecasting of the potash products price, and by an adequate modeling interval length choice it is possible to achieve acceptable forecasting quality.

Groundwater Responses to Earth Tides: Evaluation of Analytical Solutions Using Numerical Simulation

AbstractHarmonic Earth tide components in well water levels have been used to estimate hydraulic and geomechanical subsurface properties. However, the robustness of various methods based on analytical solutions has not been established. First, we review the theory and examine the latest analytical solution used to relate well water levels to Earth tides. Second, we develop and verify a novel numerical model coupling hydraulics and geomechanics to Earth tide strains. Third, we assess subsurface conditions over depth for a range of realistic properties. Fourth, we simulate the well water level response to Earth tide strains within a 2D poroelastic layered aquifer system confined by a 100 m thick aquitard. We find that the non‐linear inversion of analytical solutions to match two observations (amplitudes and phases) to multiple unknown parameters is sensible to the initial guess. We reveal that undrained, confined conditions are necessary for the analytical solution to be valid. This occurs for the dominant M2 frequency at depths >50 m and requires specific storage at constant strain of Sϵ ≥ 10−6 m−1, hydraulic conductivity of the aquitard of kl ≤ 5 ⋅ 10−5 ms−1 and aquifer of ka ≥ 10−4 ms−1. We further illustrate that the analytical solution is valid in unconsolidated systems, whereas consolidated systems require additional consideration of the Biot modulus. Overall, a priori knowledge of the subsurface system supports interpretation of the groundwater response. Our results improve understanding of the effect of Earth tides on groundwater systems and its interpretation for subsurface properties.

A Novel Grating Coupling Coefficient Extraction Method for DFB Laser Diodes Based on Side Mode Spacing

A novel method to extract the grating coupling coefficient of distributed feedback (DFB) lasers by comparing the theoretical and experimental values of the side mode spacing is demonstrated. Compared with the traditional method, the proposed method in this paper transforms the solution process of the lasing model with multiple unknown parameters into that with only the side mode spacing and coupling coefficient, which significantly reduces the computational workload. Furthermore, the bias current of the measured spectrum can be much higher than the threshold current, which makes the method less affected by noise. This paper theoretically analyzes the changing relationship between multiple parameters by calculating the lasing mode distribution, and the results show that the side mode spacing is only sensitive to the coupling coefficient. In addition, the grating coupling coefficients (57–61 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> ) of the fabricated DFB laser diodes are experimentally extracted at 40-80 mA currents. The variation of the coupling coefficient with current is less than 2‰/mA, and the method exhibits pretty good stability. Meanwhile, the grating coupling coefficient extraction method for the complex grating types is also considered in this paper.

Tuning of Elasticsearch Configuration: Parameter Optimization Through Simultaneous Perturbation Stochastic Approximation.

Elasticsearch is currently the most popular search engine for full-text database management systems. By default, its configuration does not change while it receives data. However, when Elasticsearch stores a large amount of data over time, the default configuration becomes an obstacle to improving performance. In addition, the servers that host Elasticsearch may have limited resources, such as internal memory and CPU. A general solution to these problems is to dynamically tune the configuration parameters of Elasticsearch in order to improve its performance. The sheer number of parameters involved in this configuration makes it a complex task. In this work, we apply the Simultaneous Perturbation Stochastic Approximation method for optimizing Elasticsearch with multiple unknown parameters. Using this algorithm, our implementation optimizes the Elasticsearch configuration parameters by observing the performance and automatically changing the configuration to improve performance. The proposed solution makes it possible to change the configuration parameters of Elasticsearch automatically without having to restart the currently running instance of Elasticsearch. The results show a higher than 40% improvement in the combined data insertion capacity and the system's response time.

Salp Swarm Optimization Algorithm for Estimating the Parameters of Photovoltaic Panels Based on the Three-Diode Model

Due to the the lack of information about parameters in the datasheets of photovoltaic (PV) panels, it is difficult to study their modeling because PV behavior is based on voltage–current (V-I) data, which present a highly nonlinear relationship. To solve this difficulty, this study presents a mathematical three-diode model of a PV panel that includes multiple unknown parameters: photoinduced current, saturation currents of the three diodes, three ideality factors, serial resistance, and parallel resistance. These parameters should be estimated in the three-diode model of a PV panel to obtain the actual values that represent the voltage–current profile or the voltage–power profile (because of its visual simplicity) of the PV panel under analysis. In order to solve this problem, this paper proposes a new application of the salp swarm algorithm (SSA) to estimate the parameters of a three-diode model of a PV panel. Two test scenarios were implemented with two different PV panels, i.e., Kyocera KC200GT and Solarex MSX60, which generate different power levels and are widely used for commercial purposes. The results of the simulations were obtained using different irradiance levels. The proposed PV model was evaluated based on the experimental results of the PV modules analyzed in this paper. The efficiency of the optimization technique proposed here, i.e., SSA, was measured by a fair comparison between its numerical results and those of other optimization techniques tuned to obtain the best response in terms of the objective function.

Estimation of solid-state sintering and material parameters using phase-field modeling and ensemble four-dimensional variational method

Sintering is a fundamental technology for powder metallurgy, the ceramics industry, and additive manufacturing processes such as three-dimensional printing. Improvement of the properties of sintered materials requires prediction of their microstructure using numerical simulations. However, the physical values and material parameters used for such predictions are generally unknown. Data assimilation (DA) enables the estimation of unobserved states and unknown material parameters by integrating simulation results and observational data. In this paper, we develop a new model that couples an ensemble-based four-dimensional variational (En4DVar) DA with a phase-field model of solid-state sintering (En4DVar-PF model) to estimate the state of the sintered material and multiple unknown material parameters. The developed En4DVar-PF model is validated by numerical experiments called twin experiments, in which a priori assumed-true initial state and multiple material parameters are estimated. The results of the twin experiments demonstrate that, using only three-dimensional morphological data of the sintered microstructure, our developed En4DVar-PF model can simultaneously and accurately estimate the particle shape, distribution of grain boundaries, and material parameters, including diffusion coefficients and mobilities related to grain boundary migration. Furthermore, our work identifies criteria for determining appropriate DA conditions such as the observational time interval required to accurately estimate the material parameters using our developed model. The developed En4DVar-PF model provides a promising framework to obtain unobservable states and difficult-to-measure material parameters in sintering, which is crucial for the accurate prediction of sintering processes and for the development of superior materials.

Potential for New Constraints on Tropical Cyclone Surface-Exchange Coefficients through Simultaneous Ensemble-Based State and Parameter Estimation

AbstractThe tropical cyclone (TC) surface-exchange coefficients of enthalpy (Ck) and momentum (Cd) at high wind speeds have been notoriously challenging to estimate. This difficulty arises from many factors, including the difficulties in collecting observations within the turbulent TC boundary layer, and the complex coupled physical interactions between the TC boundary layer and ocean surface, which are challenging to accurately model. Motivated by recent studies highlighting the limited practical predictability of TC intensity as a result of uncertainty in the physical representation of the air–sea fluxes of momentum and enthalpy at high wind speeds, we investigate the potential to estimate the surface enthalpy and momentum exchange coefficients through ensemble data assimilation. Significant ensemble correlations between tangential wind, radial wind, and simulated infrared brightness temperatures with parameters controlling the enthalpy and momentum exchange coefficients suggest potential to use all-sky satellite and/or airborne radial velocity observations to estimate these unknown parameters. Using a series of observing system simulation experiments (OSSEs), simulated infrared brightness temperature observations, and a known truth, we demonstrate some potential for simultaneous state and parameter estimation with an ensemble-based data assimilation system to converge toward the correct known parameter values. In all OSSEs with either one or multiple unknown parameters, the initial parameter errors are reduced through simultaneous model state and parameter estimation. However, challenges still exist in converging to the precise true parameter values, as state errors during rapid intensification can project onto the parameter estimates.

Sequential Learning of Cryptocurrency Volatility Dynamics: Evidence Based on a Stochastic Volatility Model with Jumps in Returns and Volatility

This paper studies the dynamics of cryptocurrency volatility using a stochastic volatility model with simultaneous and correlated jumps in returns and volatility. We estimate the model using an efficient sequential learning algorithm that allows for learning about multiple unknown model parameters simultaneously, with daily data on four popular cryptocurrencies. We find that these cryptocurrencies have quite different volatility dynamics. In particular, they exhibit different return-volatility relationships: While Ethereum and Litecoin show a negative relationship, Chainlink displays a positive one and interestingly, Bitcoin’s one changes from negative to positive in June 2016. We also provide evidence that the sequential learning algorithm helps better detect large jumps in the cryptocurrency market in real time. Overall, incorporating volatility jumps helps better capture the dynamic behavior of highly volatile cryptocurrencies.

Heteroscedastic Change Point Analysis and Application to Footprint Data

Analysis of footprint data is important in the tire industry. Estimation procedures for multiple change points and unknown parameters in a segmented regression model with unknown heteroscedastic variances are developed for analyzing such data. Our approaches include both likelihood and Bayesian, with and without continuity constraints at the change points. A model selection procedure is also proposed to choose among competing models for fitting a middle segment of the data between change points. We study the performance of the two approaches and apply them to actual tire data examples. Our Maximization－Maximization－Posterior (MMP) algorithm and the likelihood－based estimation are found to be complimentary to each other.

Adaptive Torsional Vibration Control of the Nonlinear Rolling Mill Main Drive System with Performance Constraints and Sensor Errors

This paper studies the torsional vibration suppression control problem for the nonlinear rolling mill main drive system with performance constraint requirements and unknown measurement sensitivities. Firstly, considering the nonlinear friction between the roll gaps, a torsional vibration model of the main drive system of rolling mill is established. Then, with the asymmetric performance constraints transformation, the motor torque control law is proposed based on backstepping algorithm. By introducing an adaptive bound estimation approach, the multiple unknown parameters caused by the sensor sensitivities can be approximated with very few adaptive laws. The dynamic surface technology is introduced to simplified the control design procedure and solve the computational explosion problem. It is strictly proved that the resulting closed-loop system is stable in the sense of uniformly ultimately boundedness and both transient and steady-state performances of the load speed are preserved. Finally, the simulation is provided to show the validity and the advantages of the proposed techniques.

Near Real-Time Freeway Accident Detection

In this paper, the problem of detecting accidents using speed sensors distributed spatially on a freeway is considered. Due to the significant impact of road accidents on health and development, early and accurate detection of accidents is crucial. To address this issue, a novel Bayesian quickest change detection formulation is introduced, which considers both average detection delay and false alarm rate. The optimum strategy is derived via dynamic programming and shown to compare a recursively computed statistic with a function of false alarm to identify accidents as they happen. Considering that post-accident conditions are typically not known, two methods are proposed that recursively estimate multiple unknown parameters during the accident detection process. Further, four aggregation methods are proposed to improve performance exploiting spatial correlations between sensors. Extensive evaluation results demonstrate improvement up to 65.2% and 87.2% in average detection delay and false alarm rate, respectively, against prior work.

Determining Attributes of Finite Fracture Networks in Low-Permeability Carbonate Reservoirs

SummaryCarbonate reservoirs usually consist of multiple units each with different degrees of layer-bound fracture density, height, length, and angular scatter. Some units may have finite fracture networks (FFNs), and some others may contain only isolated fractures. FFNs are islands of interconnected fractures within a sea of isolated fractures. The fracture volume can be estimated from the initial surge in production if a wellbore intersects only a single FFN. Combining with fracture density and aperture measurements from borehole images, FFN volume, drainage area, and other relevant attributes can be calculated. If, however, a slanted well intersects an unknown number of FFNs each in a different unit, it is not possible to estimate each FFN fracture volume from initial fracture production. Because the connectivity threshold for initiation of FFNs is not known or cannot be calculated, it is not possible to determine how many FFNs the borehole intersects. One way is to set an arbitrary threshold of fracture connectivity, λc.Based on this initial value, a fracture-flow model can be generated and adjusted until the inferred rate time and cumulative time curves converge to observed values. The adjustment is accomplished by changing the number of FFNs using different connectivity threshold λc and estimating their size by modifying unknown or uncertain parameters such as fracture aperture. The final model yields the mostly likely number and size of all FFNs and provides an approximate forecast for future production performance.The ability to match production performance without taking pressure into consideration shows that rate decrease in fractured reservoirs with FFNs is not only related to pressure drawdown but also, perhaps more importantly, to depletion of FFNs starting from the smallest size or the one with highest drainage efficiency.One drawback of the method is that different numbers of FFNs may have similar inferred production performance and cumulative production. This is an inevitable drawback inherent in most models that must rely on multiple uncertain or unknown parameters. The only way to decrease the range of possible solutions is to decrease the uncertainties in the underlying input parameters. In any case, alternative results may be presented as a range of possible solutions.

Multiparameter squeezing for optimal quantum enhancements in sensor networks

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.