Initial Guess Of Parameters Research Articles

LECalib: Line-based event camera calibration

Camera calibration is an essential prerequisite for event-based vision applications. Current event camera calibration methods typically involve using flashing patterns, reconstructing intensity images, and utilizing the features extracted from events. Existing methods are generally time-consuming and require manually placed calibration objects, which cannot meet the needs of rapidly changing scenarios. In this paper, we propose a line-based event camera calibration framework exploiting the geometric lines of commonly-encountered objects in man-made environments, e.g., doors, windows, boxes, etc. Different from previous methods, our method detects lines directly from event streams and leverages an event-line calibration model to generate the initial guess of camera parameters, which is suitable for both planar and non-planar lines. Then, a non-linear optimization is adopted to refine camera parameters. Both simulation and real-world experiments have demonstrated the feasibility and accuracy of our method, with validation performed on monocular and stereo event cameras. The source code is released at https://github.com/Zibin6/line_based_event_camera_calib.

Physics-guided generative adversarial network for probabilistic structural system identification

Structural system identification (ID) is an important tool for many structural and infrastructure applications, such as structural health monitoring and structural model updating. A novel physics-guided generative adversarial network (PG-GAN) is proposed in this study for probabilistic structural parameter ID. The PG-GAN leverages the powerful distribution learning ability of GANs while also enabling physical awareness by incorporating additional generators for physical parameters and developing a physics-based loss function that links the data generator with the parameter generators through existing physics knowledge to guide the training of generative models. Two experiments are performed to validate the effectiveness of the PG-GAN for structural parameter ID and demonstrate its application in structural damage detection. The PG-GAN is shown to successfully capture the uncertainty inherent in structural parameter estimation and accurately locate and quantify structural damages in terms of probabilistic distributions of the damage extent. The main contributions of this study are threefold: (1) compared with traditional methods for structural parameter ID, the proposed PG-GAN provides an intelligent framework for probabilistic identification of structural parameters without the need for any assumption on the data distribution and does not require an initial guess of parameters; (2) unlike traditional data-driven GANs, the proposed PG-GAN provides a linkage between GAN and physics knowledge to enables physical awareness in generative model training; and (3) the proposed PG-GAN can serve as an intelligent diagnostic system to better inform the decision-making on structural health management as it can quantify the uncertainty in the structural damage extent.

Identifying Parameters of Reactor Operation Digital Twin by Using Swarm and Evolutionary Algorithms

Digital twin (DT) technology is currently gaining popularity in a variety of industrial applications. Recently, the China Institute of Nuclear Power proposed a data driven by nuclear reactor digital twin. The digital twin solves the forward problem for physical field simulation and the inverse problem for parameter identification. The inverse problem can be viewed as a black-box optimization problem where the input parameters are identified by the Latin hypercube sampling (LHS) method based on a given partial observation. While LHS is relatively naive, in this paper, we proposed to apply swarm and evolutionary algorithms to solve the inverse problem. Specifically, we present an experimental comparative study for LHS and four popular SEAs, Particle Swarm Optimizer (PSO), Differential Evolution (DE), Evolutionary Strategy (ES), and evolution strategy with covariance matrix adaptation (CMA-ES). The results show that, for this inverse problem, SEAs are more accurate and efficient than LHS. We also investigate the comparative optimization algorithm’s searching capability under the conditions of noisy observations and no initial input parameter guesses. The experimental results show that DE and CMA-ES have strong robustness and high searching ability.

An inverse analysis method for determining tensile softening relationship of concrete considering local response

This study presents an inverse analysis algorithm for deriving the softening relationship of concrete. The algorithm can not only reproduce the influence of local response on the σ-w curve by introducing additional load criteria but also reduce the dependence of optimization results on the initial guesses by combining global best-fitting with the automatic parameter updating technique, improving the prediction accuracy and lowing the possibility of obtaining pseudo-solutions. Then, the fracture tests were carried out on the wedge splitting specimens. The validity and versatility of the algorithm were verified using experimental data. The findings show that the simulation responses agree well with the test ones in all regions of the load-CMOD curve, and the values of fracture energy determined by the load-CMOD and σ-w curves are consistent. The derived σ-w curve is independent of the initial guesses of parameters. The widely used bi-linear σ-w curve tends to overestimate the load in the post-peak of load-CMOD, and the tri-linear model is recommended after considering the accuracy, computation time, and convergence. The tensile strength evaluated by the inverse analysis method is 75% of the splitting tension test and 91% of the fracture theory method. Further, the proposed algorithm exhibits outstanding versatility, applying to various concrete materials and specimen configurations.

Calculating the ground-state energy of benzene under spatial deformations with noisy quantum computing

In this paper we calculate the ground-state energy of benzene under spatial deformations by using the variational quantum eigensolver. The primary goal of the study is to estimate the feasibility of using quantum computing Ans\"atze on near-term devices to solve problems with a large number of orbitals in regions where classical methods are known to fail. Furthermore, by combining our advanced simulation platform with real quantum computers, we provide an analysis of how the noise, inherent to quantum computers, affects the results. At the center of our study are the hardware efficient and quantum unitary coupled-cluster (QUCC) Ans\"atze. First, we find that the hardware efficient Ansatz has the potential to outperform mean-field methods for extreme deformations of benzene. However, key problems remain at equilibrium, preventing real chemical application. Moreover, the hardware efficient Ansatz yields results that strongly depend on the initial guess of parameters (in both noisy and noiseless cases) and optimization issues have a higher impact on their convergence than noise. This is confirmed by comparison with real quantum computing demonstrations. On the other hand, the QUCC Ansatz alternative exhibits deeper circuits. Therefore, noise effects increase and are so extreme that the method never outperform mean-field theories. Our dual simulator, (8--16)-qubit QPU computations of QUCC Ansatz appears to be much more sensitive to hardware noise than shot noise, which further indicates where the noise-reduction efforts should be directed. Finally, the study shows that the QUCC method better captures the physics of the system as the QUCC method can be utilized together with the H\"uckel approximation. We discussed how going beyond this approximation sharply increases the optimization complexity of such a difficult problem.

Setting Free Fault Location for Three-Terminal Hybrid Transmission Lines Connected With Conventional and Renewable Resources

Three-terminal hybrid transmission lines (TTHTLs) are attractive from both environmental and commercial view. Hybrid transmission lines are growing due to urbanization, connecting an industrial load and renewable integration. A TTHTL comprises sections of both overhead lines and underground/subsea cables or overhead lines with different X/R ratios. Faulted section identification (FSI) is key for defining the adaptive/selective auto-reclosing scheme and estimation of the fault location for TTHTLs. In this paper, FSI and fault location algorithms are proposed without using the parameters of any line section. Novelty of the methodology lies in a two-stage approach to the problem. In the first stage, series impedance parameters of all the sections are calculated using closed loop formulae. These parameters are then utilized in identifying the faulted section. In the second stage, the above calculated line section parameters and faulted section are used to estimate complete line parameters including shunt capacitance and subsequently the fault location. The advantage of the proposed method is that it does not require an initial guess of the line section parameters, is non-iterative in the first stage, and provides correct fault section identification for TTHTLs. These features make it suitable for designing the selective auto-reclosing protection scheme for the TTHTLs within traditional protection relaying hardware. More importantly, the series impedance parameters calculated in the first stage constitute good initialization values for the non-linear problem of estimating the complete line parameters. This results in better convergence of the algorithm and accurate parameter estimation. The developed solution is verified using the PSCAD/EMTDC simulations for TTHTLs connected with conventional and different inverter-based renewable resources. The performance of the proposed solution is compared with commercially available solutions, and it is found to be accurate. This solution is amenable for implementation in line differential protection relays without additional infrastructural changes.

Design of a differential power oscillator for 433 MHz WPT using e-GaN HEMTs

This paper presents a new differential power oscillator design based on a differential class-E power amplifier. The designs use high power enhancement-GaN HEMT (e-GaN) for its fast switching time, low ON resistance and wide energy band gap properties. The target application is far field wireless power transfer for wireless charging applications. The initial guess for design parameters follows the well known Sokal approach then LTSpice simulator is used to finalize the design. The simulated output power of the power oscillator is 60 W at the 433 MHz ISM band with high DC-to-RF conversion efficiency. Effect of process and design parameter variability is considered to assess the design sensitivity to manufacturing tolerances in both active and passive components.

Effects of oblateness of the primaries on natural periodic orbit-attitude behaviour of satellites in three body problem

• Equations of Motion for the Perturbed Circular Restricted Three Body Problem (P-CR3BP) with considering A 2 - A 6 primaries oblate coefficients have derived for the first time. • It was shown that considering primaries zonal harmonic coefficients j 2 - j 6 has a significant effect on satellite orbit-attitude behavior. It is observed that considering A 2 - A 6 primaries oblate coefficients amplify the effect of oblate perturbations and the zonal harmonic coefficients after j 6 have negligible effect. • Proper initial guess of periodic solution of perturbed model identified by Poincaré maps. • As an innovation, finding the appropriate value of inertia ratio K to find periodic response of orbit-attitude was performed using Poincaré mapping for the first time. • It was shown for the first time, by more accurately simulating the study environment by considering oblate perturbations, the density of points on the islands created on Poincaré map appeared to increase, and in fact, it became easier to identify the initial guess of attitude states. • Increasing the inertia ratio and increasing the orbital period reduces the chances of finding periodic responses. This study was done to investigate the effect of perturbations of both oblate massive primaries on the periodic orbit-attitude behavior of satellites at the three-body problem. Governing equations of the perturbed coupled orbit-attitude were derived using principles of the Lagrangian mechanics. As initial conditions of the coupled model play a key role in finding periodic responses of both orbit and attitude, so the perturbed circular restricted three-body problem (P-CR3BP) coupled orbit-attitude correction algorithm was proposed to correct the initial guess of the coupled model. The correction algorithm requires an appropriate initial guess vector as the number of periodic solutions is limited. This initial guess vector consists of two parts: orbital and attitude dynamic state parameters. A suitable initial guess was suggested for orbital parameters considering a small error at the initial conditions of the unperturbed periodic orbits. These initial conditions were extracted by another orbital correction algorithm to correct orbital states of periodic orbits in the unperturbed circular restricted three-body problem (U-CR3BP). Furthermore, the initial guess of attitude dynamic parameters was identified by the Poincaré mapping method. Considering oblate perturbations would change the initial conditions of periodic orbits at P-CR3BP relative to U-CR3BP. Also, because the proposed model of the coupled orbit-attitude governing equations is such that only orbital state parameters influence attitude dynamic parameters, so the behavior of attitude dynamics will also change by altering orbital motion. Comparison of patterns in Poincaré maps, satellites angular velocity, and initial conditions of periodic coupled orbit-attitude response in U-CR3BP and P-CR3BP indicated the effect of both oblate primaries perturbations. Consideration of these perturbations resulted in a more accurate simulation of the study environment that helps to understand the natural motion of the satellite.

A semi-quantum approach for modelling the accelerated test data

The traditional models for the analysis of the accelerated test data cannot physically explains how the environment affects lifetime and its uncertainty. To solve this problem, this paper utilizes the theory of open quantum system, the theory about random behaviour of microparticles under the external environment, to describe the effects of stresses on lifetime uncertainty. The interaction between the system and environments motivates us to describe the accelerated test data from a quantum perspective. A quantum master equation is used as the reliability dynamics, which can be separated into a conservation term and a decay term. Then, the acceleration model is further incorporated into the decay term of the dynamic and forms a semi-quantum model. A practical procedure is proposed to obtain the initial guesses of parameters and do a graphic check on the assumption. Applications on two sets of real accelerated life test data show the proposed model outperforms the existing ones and hence verify its validity. This paper makes the first attempt to quantify the uncertainty under different environments from a quantum perspective and shows that it is feasible to utilize quantum theory to make a further exploration.

A Low-Complexity Method for Parameter Estimation of the Simplified Randles Circuit With Experimental Verification

In this paper we present a processing-efficient method for parameter estimation of a Randles circuit. As our approach is not iterative, it does not require for an initial guess of model parameters to be provided. The low-complexity of the provided set of closed-form expressions enables the implementation on microcontroller-based platforms. The presented approach is verified with simulations (using both noiseless data and data with noise) and with experimentally obtained data (Randles circuit made from discrete components; impedance of microfluidic platform for isomalt detection; impedance of Panasonic 18650PF Li-ion Battery). Additionally, it was implemented on a microcontroller board based on ATmega2560 microcontroller with available 256 kB of flash memory, 8 kB of SRAM and clock speed of 16 MHz. Reliable and accurate estimations of such implementations confirmed the suitability of this work for low-cost embedded hardware.

A novel two step method to extract the parameters of the single diode model of Photovoltaic module using experimental Power–Voltage data

Accurate modeling of the Photovoltaic (PV) module is required to find the location of the fault in the PV array. It also helps in designing a precise MPPT algorithm and avoiding uncertainties in the Micro-grids. This paper uses a Two-Step Linear Least Square Error (LLSE) method to extract the parameters of the PV module. The proposed method utilizes the experimental data of the Power–Voltage (P–V) curve to estimate the PV module parameters. The proposed method does not require any datasheet information and avoids initial guesses of parameters. To validate the proposed method, three different PV modules, Mono-crystalline STM6-40/36, Poly-crystalline SMP6-120/36, PWP-201, and one Real-Time Clock France solar cell have been considered. The performance of the proposed method was studied using the Root Mean Square Error, Mean Absolute Error (MAE), Normalized Root Mean Square Error (NRMSE), and Normalized Mean Absolute Error (NMAE). The proposed LLSE method exhibited the low Root-Mean-Square-Error (RMSE) for all three PV modules and the R.T.C France solar cell.

A numerical scheme based on the collocation and optimization methods for accurate solution of sensitive boundary value problems

Despite the significant advances in the numerical solution of nonlinear boundary value problems, most of the existing methods still encounter with a high sensitivity to the initial guess. The aim of this paper is to propose a less sensitive robust numerical scheme for accurate solution of sensitive boundary value problems. For this purpose, an orthogonal collocation approach for discretization of the problem is utilized. Thereby, the problem is converted to the solution of nonlinear algebraic equations. However, due to the difficulties of solving the obtained system of nonlinear equations, particularly in providing the proper initial guess, the obtained system of equations is transferred to an optimization problem in which the values of the solution at collocation points are considered as decision parameters. The method finds good results even using not good initial guess for decision parameters and even using a small number of discretization points. Numerical results of five benchmark examples are presented and the efficiency of the method is reported.

Identification of constitutive parameters for thin-walled aluminium tubes using a hybrid strategy

The paper presents a hybrid strategy to determine constitutive parameters for thin-walled tubes based on experimental responses from hydraulic bulge tests. This developed procedure integrates the analytical model, finite element analysis and gradient-based optimization algorithm, where initial guesses of material parameters are generated quickly by a theoretical method, then they are input to an inverse framework integrating Gauss-Newton algorithm and finite element method. The solving for this inverse problem leads to a more accurate identification of material parameters by reducing the discrepancies between simulated results and experimental data. To evaluate its feasibility and performance, hydraulic bulge tests with different end-conditions for annealed 6060 and 5049 aluminium tubes are carried out. The strength coefficient and hardening exponent are determined using the hybrid strategy based on the collected measurements in the experiment. These material parameters are used to compare with those obtained by a single analytical model and inverse model. The comparison validates that the proposed hybrid strategy is not sensitive to starting points and can improve the calculation efficiency and determine more accurate constitutive parameters.

Diffuse optical tomography by simulated annealing via a spin Hamiltonian.

Diffuse optical tomography (DOT) is an imaging modality that uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT, which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA), which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis-Hastings algorithm is used. By numerical experiments, it is shown that an initial random spin configuration is brought to a converged configuration by SA, and targets in the medium are reconstructed. The proposed numerical method solves the inverse problem for DOT by finding the ground state of a spin Hamiltonian with SA.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the “identifiability” or “uniqueness” of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

Two-stage surrogate model-assisted Bayesian framework for groundwater contaminant source identification

Groundwater contaminant source identification is normally a prerequisite for contaminant remediation. This study proposes a new two-stage surrogate-assisted Markov chain Monte Carlo (MCMC)-based Bayesian framework to identify contaminant source parameters for groundwater polluted by dense nonaqueous phase liquid. In the framework, an adaptive update feedback process is proposed to construct a locally accurate surrogate model over posterior distributions to replace the time-consuming multiphase flow model. To increase the efficiency of the MCMC simulation, a multiobjective feasibility-enhanced particle swarm optimization algorithm (MOFEPSO) is adopted to generate the initial guess of the contamination source parameters. The accuracy and efficiency of the proposed framework are confirmed via a synthetic study. The contaminant source parameters generated by the proposed approach are compared with those computed by the one-stage surrogate-assisted MCMC-based Bayesian approach. The results demonstrate that the root mean squared error (RMSE) between true value of parameters and maximum a-posteriori density values (MAP) obtained by the proposed method decreased by 71.3% compared with those obtained by one-stage surrogate-based framework. To further assess the efficiency of MOFEPSO, the same inversion problem is solved with random values as the initial guesses of the unknown parameters during MCMC simulation; the other conditions are the same as the proposed framework. The results indicate that adopting MOFEPSO improves the efficiency of MCMC simulation. Therefore, the proposed approach can accurately and effectively identify the contaminant source parameters with achieving about 148 times of speed-up compared to the simulation-based MCMC simulation.

A pre-processing method for digital image correlation on rotating structures

Inter-frame structural motions are required to be small for classic Digital Image Correlation (DIC) algorithms, which severely limits the application of the technique in large rotation cases. To solve the problem, multiple methods to obtain initial guesses of deformation parameters have been introduced over recent years. However, the success rate is still limited by rotation angles and the efficiency is low due to extra calculations with these methods. To further develop the application of DIC in large rotation cases, Phase Mapping Method (PMM) is introduced in this paper. The principle of the proposed method is to rearrange the obtained images to be sorted by the structural rotating phases, which are previously mapped into the range of 0 to 2π. As a result, for an image set of n frames, the average inter-frame rotating angle is reduced to 2πn-1, and the original image set is transferred into an equivalent semi-static one by PMM. Additionally, a fast phase-detection approach is introduced to automate PMM in cases that the structural rotating speeds are unknown. By performing multiple tests, it is proved that PMM, as a pre-processing method, can significantly improve the success rate and the efficiency of DIC, whether used alone or concurrently with other algorithms. The first natural frequencies and mode shapes of a rotating beam under different rotating speeds are extracted through vibration test, from which the hardening effect is observed.

General fractional models for linear viscoelastic characterization of asphalt cements

Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra.

On Nonlinear Regression for Trends in Split-Belt Treadmill Training.

Single and double exponential models fitted to step length symmetry series are used to evaluate the timecourse of adaptation and de-adaptation in instrumented split-belt treadmill tasks. Whilst the nonlinear regression literature has developed substantially over time, the split-belt treadmill training literature has not been fully utilising the fruits of these developments. In this research area, the current methods of model fitting and evaluation have three significant limitations: (i) optimisation algorithms that are used for model fitting require a good initial guess for regression parameters; (ii) the coefficient of determination () is used for comparing and evaluating models, yet it is considered to be an inadequate measure of fit for nonlinear regression; and, (iii) inference is based on comparison of the confidence intervals for the regression parameters that are obtained under the untested assumption that the nonlinear model has a good linear approximation. In this research, we propose a transformed set of parameters with a common language interpretation that is relevant to split-belt treadmill training for both the single and double exponential models. We propose parameter bounds for the exponential models which allow the use of particle swarm optimisation for model fitting without an initial guess for the regression parameters. For model evaluation and comparison, we propose the use of residual plots and Akaike’s information criterion (AIC). A method for obtaining confidence intervals that does not require the assumption of a good linear approximation is also suggested. A set of MATLAB (MathWorks, Inc., Natick, MA, USA) functions developed in order to apply these methods are also presented. Single and double exponential models are fitted to both the group-averaged and participant step length symmetry series in an experimental dataset generating new insights into split-belt treadmill training. The proposed methods may be useful for research involving analysis of gait symmetry with instrumented split-belt treadmills. Moreover, the demonstration of the suggested statistical methods on an experimental dataset may help the uptake of these methods by a wider community of researchers that are interested in timecourse of motor training.

Identifying a stochastic clock network with light entrainment for single cells of Neurosporacrassa

Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurosporacrassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit {x}^{2} was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting {x}^{2} per data point was only {chi }^{2}/n = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for “cell size”. The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 107 cells.