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In this paper we have considered the chirp like model which has been recently introduced, and it has a very close resemblance with a chirp model. We consider the weighted least squares estimators of the parameters of a chirp like model in presence of an additive stationary error, and study their properties. It is observed that although the least squares method seems to be a natural choice to estimate the unknown parameters of a chirp like model, the least squares estimators are very sensitive to the outliers. It is observed that the weighted least squares estimators are quite robust in this respect. The weighted least squares estimators are consistent and they have the same rate of convergence as the least squares estimators. We have further extended the results in case of multicomponent chirp like model. Some simulations have been performed to show the effectiveness of the proposed method. In simulation studies, weighted least squares estimators have been compared with the least absolute deviation estimators which, in general, are known to work well in presence of outliers. One EEG data set has been analyzed and the results are quite satisfactory. [ABSTRACT FROM AUTHOR]

Wanting to minimize a non-linear least squares function penalized with an L p -norm, with p ∈ (1 , 2) , stemming from a 4DVar formulation of a data assimilation problem, we propose a modification of the non-linear conjugate gradient by making the iterations and the step search in the topological dual space of L p . We prove the convergence of this new algorithm and look at its performance on a data assimilation setup based on the shallow-water equations where the use of such an L p -norm regularization is justified. [ABSTRACT FROM AUTHOR]

Lumpy skin disease (LSD) is an economically significant viral disease of cattle caused by the lumpy disease virus (LSDV) which is primarily spread mechanically by blood feeding vectors such as particular species in flies, mosquitoes and ticks. Despite efforts to control its spread, LSD has been expanding geographically, posing challenges for effective control measures. This study develops a Susceptible–Exposed–Infectious–Recovered–Susceptible (SEIRS) model that incorporates cattle and vector populations to investigate LSD transmission dynamics. The model considers the waning rate of natural active immunity in recovered cattle, disease-induced mortality, and the biting rate. Using a standard dynamical system approach, we conducted a qualitative analysis of the model, defining the invariant region, establishing conditions for solution positivity, computing the basic reproduction number, and examining the stability of disease-free and endemic equilibria. We employ a non-linear least squares method for model calibration, fitting it to a synthetic dataset. We subsequently test it with actual infectious cases data. Results from the calibration and testing phases demonstrate the model’s validity and reliability for diverse settings. Local and global sensitivity analyses were conducted to determine the model’s robustness to parameter values. The biting rate emerged as the most significant parameter, followed by the probabilities of infection from either population and the recovery rate. Additionally, the waning rate of LSD infection-induced immunity gained positive significance in LSD prevalence from the beginning of the infectious period onward. Simulation results suggest reducing the biting rate as the most effective LSD control measure, which can be achieved by applying vector repellents in cattle farms/herds, thereby mitigating the disease’s prevalence in both cattle and vector populations and reducing the chances of infection from either population. Furthermore, measures aiming to boost LSD infection-induced immunity upon recovery are recommended to preserve the immune systems of the cattle population.

This research article develops two adaptive, efficient, structured non-linear least-squares algorithms, NLS. The approach taken to formulate these algorithms is motivated by the classical Barzilai and Borwein (BB) (IMA J Numer Anal 8(1):141–148, 1988) parameters. The structured vector approximation, which is an action of a vector on a matrix, is derived from higher order Taylor series approximations of the Hessian of the objective function, such that a quasi-Newton condition is satisfied. This structured approximation is incorporated into the BB parameters' weighted adaptive combination. We show that the algorithm is globally convergent under some standard assumptions. Moreover, the algorithms' robustness and effectiveness were tested numerically by solving some benchmark test problems. Finally, we apply one of the algorithms to solve a robotic motion control model with three degrees of freedom, 3DOF. [ABSTRACT FROM AUTHOR]

Forests are traditionally characterized by stand-level descriptors, such as basal area, mean diameter, and stem density. In recent years, there has been a growing interest in enhancing the resolution of forest inventory to examine the spatial structure and patterns of trees across landscapes. The spatial arrangement of individual trees is closely linked to various non-monetary forest aspects, including water quality, wildlife habitat, and aesthetics. Additionally, associating individual tree positions with dendrometric variables like diameter, taper, and species can provide data for highly optimized, site-specific silvicultural prescriptions designed to achieve diverse management objectives. Aerial photogrammetry has proven effective for mapping individual trees; however, its utility is limited due to the inability to directly estimate many dendrometric variables. In contrast, terrestrial mapping methods can directly observe essential individual tree characteristics, such as diameter, but their mapping accuracy is governed by the accuracy of the global satellite navigation system (GNSS) receiver and the density of the canopy obstructions between the receiver and the satellite constellation. In this paper, we introduce an integrated approach that combines a camera-based motion and tree detection system with GNSS positioning, yielding a stem map with twice the accuracy of using a consumer-grade GNSS receiver alone. We demonstrate that large-scale stem maps can be generated in real time, achieving a root mean squared position error of 2.16 m. We offer an in-depth explanation of a visual egomotion estimation algorithm designed to enhance the local consistency of GNSS-based positioning. Additionally, we present a least squares minimization technique for concurrently optimizing the pose track and the positions of individual tree stem[s]. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids are commonly used in a wide range of industries; one example are in biogas power plants. Proper measurements and modeling of such fluids can be crucial from the design and operations point of view. Results presented in this study covered seven samples from three plants (a sewage sludge treatment plant, utilization biogas station and a biogas plant in a sugar factory), including mechanically thickened excessive activated sludge (MTEAS), sugar beet pulp (SBP), liquid fruit and vegetable waste (FVW), beet roots (BR) and corn waste (CW); their mixtures were prepared as in a real plant. The total solid content remained below 6.8% for all samples. The apparent viscosity (15 RPM) did not exceed 10 Pas in any sample. A correlation analysis for solvent type influence on the viscosity was carried out. The obtained results were analyzed, and the Herschel–Bulkley rheological model was selected for the fluid description. Then, the Moullinex method was applied to determine the H–B model parameters. The obtained results may contribute to the proper design and operation of various biogas power plants, in which viscosity seems to be one of the crucial flow parameters that influences the device types used, as well as energy consumption. [ABSTRACT FROM AUTHOR]

The least squares method seems to be a natural choice in estimating the parameters of a chirp model. But the least squares estimators are very sensitive to the outliers. Even in presence of very few outliers, the performance of the least squares estimators becomes quite unsatisfactory. Due to this reason, the least absolute deviation method has been proposed in the literature. But implementing the least absolute deviation method is quite challenging particularly for the multicomponent chirp model. In this paper, we propose to use the weighted least squares estimators, which seem to be more robust in presence of a few outliers. First, we consider the weighted least squares estimators of the unknown parameters of a single component chirp signal model. It is assumed that the weight function is a finite degree polynomial and the errors are independent and identically distributed random variables with mean zero and finite variance. It is observed that the weighted least squares estimators are strongly consistent and they have the same convergence rate as the least squares estimators. The weighted least squares estimators can be obtained by solving a two dimensional optimization problem. In case of the multicomponent chirp signal, we provide a sequential weighted least squares estimators and provide the consistency and asymptotic normality properties of these sequential weighted least squares estimators. To compute the sequential weighted least squares estimators one needs to solve only one two dimensional optimization problem at each stage. Extensive simulations have been performed to see the performances of the proposed estimators. Two data sets have been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Forests are traditionally characterized by stand-level descriptors, such as basal area, mean diameter, and stem density. In recent years, there has been a growing interest in enhancing the resolution of forest inventory to examine the spatial structure and patterns of trees across landscapes. The spatial arrangement of individual trees is closely linked to various non-monetary forest aspects, including water quality, wildlife habitat, and aesthetics. Additionally, associating individual tree positions with dendrometric variables like diameter, taper, and species can provide data for highly optimized, site-specific silvicultural prescriptions designed to achieve diverse management objectives. Aerial photogrammetry has proven effective for mapping individual trees; however, its utility is limited due to the inability to directly estimate many dendrometric variables. In contrast, terrestrial mapping methods can directly observe essential individual tree characteristics, such as diameter, but their mapping accuracy is governed by the accuracy of the global satellite navigation system (GNSS) receiver and the density of the canopy obstructions between the receiver and the satellite constellation. In this paper, we introduce an integrated approach that combines a camera-based motion and tree detection system with GNSS positioning, yielding a stem map with twice the accuracy of using a consumer-grade GNSS receiver alone. We demonstrate that large-scale stem maps can be generated in real time, achieving a root mean squared position error of 2.16 m. We offer an in-depth explanation of a visual egomotion estimation algorithm designed to enhance the local consistency of GNSS-based positioning. Additionally, we present a least squares minimization technique for concurrently optimizing the pose track and the positions of individual tree stem[s].

Non-Newtonian fluids are commonly used in a wide range of industries; one example are in biogas power plants. Proper measurements and modeling of such fluids can be crucial from the design and operations point of view. Results presented in this study covered seven samples from three plants (a sewage sludge treatment plant, utilization biogas station and a biogas plant in a sugar factory), including mechanically thickened excessive activated sludge (MTEAS), sugar beet pulp (SBP), liquid fruit and vegetable waste (FVW), beet roots (BR) and corn waste (CW); their mixtures were prepared as in a real plant. The total solid content remained below 6.8% for all samples. The apparent viscosity (15 RPM) did not exceed 10 Pas in any sample. A correlation analysis for solvent type influence on the viscosity was carried out. The obtained results were analyzed, and the Herschel–Bulkley rheological model was selected for the fluid description. Then, the Moullinex method was applied to determine the H–B model parameters. The obtained results may contribute to the proper design and operation of various biogas power plants, in which viscosity seems to be one of the crucial flow parameters that influences the device types used, as well as energy consumption.

We shed light on computational challenges when fitting the Nelson-Siegel, Bliss and Svensson parsimonious yield curve models to observed US Treasury securities with maturities up to 30 years. As model parameters have a specific financial meaning, the stability of their estimated values over time becomes relevant when their dynamic behavior is interpreted in risk-return models. Our study is the first in the literature that compares the stability of estimated model parameters among different parsimonious models and for different approaches for predefining initial parameter values. We find that the Nelson-Siegel parameter estimates are more stable and conserve their intrinsic economical interpretation. Results reveal in addition the patterns of confounding effects in the Svensson model. To obtain the most stable and intuitive parameter estimates over time, we recommend the use of the Nelson-Siegel model by taking initial parameter values derived from the observed yields. The implications of excluding Treasury bills, constraining parameters and reducing clusters across time to maturity are also investigated. [ABSTRACT FROM AUTHOR]

The networked thermopile array in row-column fashion suffered from the crosstalk caused by parasitic parallel paths. To measure accurate two-dimensional thermal information, it is of great importance to eliminate the crosstalk. In this work, based on the response voltage non-linearity of thermopile pixels as well as the response voltage non-uniformity of array, a projection transformation method that suits for small-scale networked thermopile arrays is proposed. It transforms the crosstalk elimination problem into an overdetermined non-linear least squares problem, and is solved by the Newton-Raphson iterative algorithm. Its reconstruction error is analyzed carefully by Monte Carlo simulation, and its ability to implement non-uniformity and defective pixel correction is also discussed. Its validity is verified experimentally using a $3 \times 3$ networked thermopile array. The experimental result shows that the original IR image can be reconstructed from measured IR images by this method, and the reconstruction error is significantly decreased from 17.03% to 2.10%. [ABSTRACT FROM AUTHOR]

Objective: As the coronavirus disease 2019 (COVID-19) pandemic continues to proliferate globally, this paper shares the findings of modelling the outbreak in China at both provincial and national levels. This paper examines the applicability of the logistic growth model, with implications for the study of the COVID-19 pandemic and other infectious diseases. Methods: An NLS (Non-Linear Least Squares) method was employed to estimate the parameters of a differentiated logistic growth function using new daily COVID-19 cases in multiple regions in China and in other selected countries. The estimation was based upon training data from January 20, 2020 to March 13, 2020. A restriction test was subsequently implemented to examine whether a designated parameter was identical among regions or countries, and the diagnosis of residuals was also conducted. The model's goodness of fit was checked using testing data from March 14, 2020 to April 18, 2020. Results: The model presented in this paper fitted time-series data exceedingly well for the whole of China, its eleven selected provinces and municipalities, and two other countries - South Korea and Iran - and provided estimates of key parameters. This study rejected the null hypothesis that the growth rates of outbreaks were the same among ten selected non-Hubei provinces in China, as well as between South Korea and Iran. The study found that the model did not provide reliable estimates for countries that were in the early stages of outbreaks. Furthermore, this study concured that the R2 values might vary and mislead when compared between different portions of the same non-linear curve. In addition, the study identified the existence of heteroskedasticity and positive serial correlation within residuals in some provinces and countries. Conclusions: The findings suggest that there is potential for this model to contribute to better public health policy in combatting COVID-19. The model does so by providing a simple logistic framework for retrospectively analyzing outbreaks in regions that have already experienced a maximal proliferation in cases. Based upon statistical findings, this study also outlines certain challenges in modelling and their implications for the results.

Background:: Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth. Methods:: We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were put in place during the first wave of the pandemic. A non-linear least-squares minimization algorithm is used to map the parameter space and make optimal predictions. Results:: Unlike other logistic growth models, our presented model is shown to consistently make accurate predictions of peak heights, peak locations and cumulative saturation values for incomplete epidemic growth curves. We further show that the power-law growth model also works reasonably well when containment and lock down strategies are not as stringent as they were during the first wave of infections in 2020. On the basis of this agreement, the model was used to forecast COVID-19 fatalities for the third wave in South Africa, which was in progress during the time of this work. Conclusion:: We anticipate that our presented model will be useful for a similar forecasting of COVID-19 induced infections/deaths in other regions as well as other cases of infectious disease outbreaks, particularly when power-law scaling is observed.

The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for several solutions with different degrees of smoothness of the distribution contour, are considered. Methods for evaluating the stability of both the whole distribution contour and its individual parts are discussed. The work of the program is illustrated by examples of the analysis of polydisperse spherical particles in silicasol solutions.

Abstract The paper addresses design and analysis of communication-efficient distributed algorithms for solving weighted non-linear least squares problems in multi-agent networks. Communication efficiency is highly relevant in modern applications like cyber-physical systems and the Internet of things, where a significant portion of the involved devices have energy constraints in terms of limited battery power. Furthermore, non-linear models arise frequently in such systems, e.g., with power grid state estimation. In this paper, we develop and analyze a non-linear communication-efficient distributed algorithm dubbed CREDO−Nℒ $\mathcal {CREDO-NL}$ (non-linear CREDO $\mathcal {CREDO}$). CREDO−Nℒ $\mathcal {CREDO-NL}$ generalizes the recently proposed linear method CREDO $\mathcal {CREDO}$ (Communication efficient REcursive Distributed estimatOr) to non-linear models. We establish for a broad class of non-linear least squares problems and generic underlying multi-agent network topologies CREDO−Nℒ $\mathcal {CREDO-NL}$’s strong consistency. Furthermore, we demonstrate communication efficiency of the method, both theoretically and by simulation examples. For the former, we rigorously prove that CREDO−Nℒ $\mathcal {CREDO-NL}$ achieves significantly faster mean squared error rates in terms of the elapsed communication cost over existing alternatives. For the latter, the considered simulation experiments show communication savings by at least an order of magnitude.

• This study applied a logistic growth model with parameters estimated by a non-linear least squares (NLS) method to daily new COVID-19 cases. • The model fitted time-series data exceedingly well for the whole of China, eleven selected Chinese provinces and municipalities, South Korea and Iran. • This study provided key estimates and a 95% confidence interval for parameters K , r, and P 0. • This study found that the growth rates of outbreaks differed between provinces in China and between South Korea and Iran. • As of March 13, 2020, this study's model suggested that countries such as the U.S.A., France, Italy, and Spain were still in the early stages of outbreaks. As the coronavirus disease 2019 (COVID-19) pandemic continues to proliferate globally, this paper shares the findings of modelling the outbreak in China at both provincial and national levels. This paper examines the applicability of the logistic growth model, with implications for the study of the COVID-19 pandemic and other infectious diseases. An NLS (Non-Linear Least Squares) method was employed to estimate the parameters of a differentiated logistic growth function using new daily COVID-19 cases in multiple regions in China and in other selected countries. The estimation was based upon training data from January 20, 2020 to March 13, 2020. A restriction test was subsequently implemented to examine whether a designated parameter was identical among regions or countries, and the diagnosis of residuals was also conducted. The model's goodness of fit was checked using testing data from March 14, 2020 to April 18, 2020. The model presented in this paper fitted time-series data exceedingly well for the whole of China, its eleven selected provinces and municipalities, and two other countries - South Korea and Iran - and provided estimates of key parameters. This study rejected the null hypothesis that the growth rates of outbreaks were the same among ten selected non-Hubei provinces in China, as well as between South Korea and Iran. The study found that the model did not provide reliable estimates for countries that were in the early stages of outbreaks. Furthermore, this study concured that the R 2 values might vary and mislead when compared between different portions of the same non-linear curve. In addition, the study identified the existence of heteroskedasticity and positive serial correlation within residuals in some provinces and countries. The findings suggest that there is potential for this model to contribute to better public health policy in combatting COVID-19. The model does so by providing a simple logistic framework for retrospectively analyzing outbreaks in regions that have already experienced a maximal proliferation in cases. Based upon statistical findings, this study also outlines certain challenges in modelling and their implications for the results. [ABSTRACT FROM AUTHOR]

We demonstrate that unit errors of measurement will lead to significant biases in estimating the constant elasticity of substitution (CES) function. Monte-Carlo simulations show that estimation results tend to reach Cobb–Douglas (CD) functions or extreme values if units of input variables are incorrectly used. To avoid this problem, we suggest adding an overall efficiency parameter and a unit correction parameter which is similar to biased technological change parameter when estimating CES functions. Any unit error of measurement can be captured by these two parameters while allowing researchers to get unbiased estimation results of other parameters. [ABSTRACT FROM AUTHOR]

This paper proposes a panel data based stochastic frontier model which accommodates time-invariant unobserved heterogeneity along with efficiency effects. The efficiency effects are specified by a standard normal cumulative distribution function of exogenous variables which ensures the efficiency scores to lie in a unit interval. The model is within-transformed and then estimated with non-linear least squares. The finite sample properties of the proposed estimator are investigated through a set of Monte Carlo experiments. The experiments suggest that our estimation procedure generally performs well also in small samples. Finally, an empirical illustration based on widely used panel data on Indian farmers reveals the simplicity and easy applicability of the model. [ABSTRACT FROM AUTHOR]

We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain predicted option prices. Firstly we ensure that the prediction from stage one is positive by using log-linear regression. Secondly, we correct the bias that results from the transformation applied to the fitted values (i.e., the Black-Scholes formula) being a highly non-linear function of implied volatility. We apply the smearing technique in order to correct this bias. An alternative means of implementing the PBS approach is to use the market option price as the dependent variable and estimate the parameters of the IV equation by the method of non-linear least squares (NLLS). A problem we identify with this method is one of model incoherency: the IV equation that is estimated does not correspond to the set of option prices used to estimate it. We use the Monte Carlo method to verify that (1) standard PBS gives biased option values, both in-sample and out-of-sample; (2) using standard (log-linear) PBS with smearing almost completely eliminates the bias; (3) NLLS gives biased option values, but the bias is less severe than with standard PBS.We are led to conclude that, of the range of possible approaches to implementing PBS, log-linear PBS with smearing is preferred on the basis that it is the only approach that results in valuations with negligible bias. [ABSTRACT FROM AUTHOR]

Modern techniques for the map analysis allow for the creation of full or partial geometric reconstruction of its content. The projection is described by the set of estimated constant values: transformed pole position, standard parallel latitude, longitude of the central meridian, and a constant parameter. Analogously the analyzed map is represented by its constant values: auxiliary sphere radius, origin shifts, and angle of rotation. Several new methods denoted as M6-M9 for the estimation of an unknown map projection and its parameters differing in the number of determined parameters, reliability, robustness, and convergence have been developed. However, their computational demands are similar. Instead of directly measuring the dissimilarity of two projections, the analyzed map in an unknown projection and the image of the sphere in the well-known (i.e., analyzed) projection are compared. Several distance functions for the similarity measurements based on the location as well as shape similarity approaches are proposed. An unconstrained global optimization problem poorly scaled, with large residuals, for the vector of unknown parameters is solved by the hybrid BFGS method. To avoid a slower convergence rate for small residual problems, it has the ability to switch between first- and second-order methods. Such an analysis is beneficial and interesting for historic, old, or current maps without information about the projection. Its importance is primarily referred to refinement of spatial georeference for the medium- and small-scale maps, analysis of the knowledge about the former world, analysis of the incorrectly/inaccurately drawn regions, and appropriate cataloging of maps. The proposed algorithms have been implemented in the new version of the detectproj software.

• Geometric constraints are precisely preserved during real-time editing of man-made mesh models. • Shape parameters are introduced to explicitly and concisely represent the geometry/relationship constraints. • A proper subspace of the constrained deformation is explored by analyzing an auxiliary function. Editing man-made mesh models under multiple geometric constraints is a crucial need for product design to facilitate design exploration and iterative optimization. However, the presence of multiple geometric constraints (e.g. the radius of a cylindrical shape, distance from a point to a plane) as well as the high dimensionality of the discrete mesh representation of man-made models make it difficult to solve this constraint system in real-time. In this paper, we propose an approach based on subspace decomposition to achieve this goal. When a set of variables are edited by the user, the proposed method minimizes the residual of the constraint system in a least square sense to derive a new shape. The resulting shape shall comply with the assigned (extrinsic) constraints while maintaining the original (intrinsic) constraints analyzed from the given mesh model. In particular, we extract a meaningful subspace of the entire solution space based on the user's edits to reduce the order of the problem, and solve the constraint system globally in real-time. Finally, we project the approximate solution back to the original solution space to obtain the editing result. [ABSTRACT FROM AUTHOR]

The space resection of single image can be described as a problem of non-linear least squares, and the non-derivative, ill-conditioned coefficient matrix of normal equation and local extremum are main reasons for non-convergence in its numerical procedure. The spatial distribution of control points in different regions is not similar. If we put down the multiple images and have known their exterior orientation ele⁃ ments regarding the same control points under the same region, as a sample set, the overall descent direc⁃ tion can be obtained by supervised learning under the circumstance that every initial values of exterior orien⁃ tation elements have been given. What’s more, in the case of non-convergence in original space resection of single image because of the reasons mentioned before, it can be approximately solved by using the over⁃ all descent direction. From this angle, a supervised learning method for solving space resection of single im ⁃ age is proposed. The process mainly includes: ①Training stage, in which supervised learning process is uti⁃ lized and the descend direction set of exterior orientation elements is obtained by solving the overall exterior orientation elements of images set with different attitude in the same survey area. ②Testing stage, in which for any image in study area, the exterior orientation elements can be calculated iteratively if the initial value and the descend direction set were given from the process of supervised training. Experimental results show that the method in this paper is more efficient in numerical procedure convergence and dependence of the ini⁃ tial value than the current there realized. Besides, it can overcome the non-convergence of Euler angles caused by the ill-conditioned coefficient matrix of normal equation, which is essentially the gradient matrix. [ABSTRACT FROM AUTHOR]

Highlights • A physics-based approach to lithium-ion battery prognostics is proposed. • It considers degradation mechanisms in remaining useful life (RUL) prediction. • A non-linear least squares method with dynamic bounds is employed in the approach. • The proposed approach predicts RULs more accurately than a capacity-based approach. Abstract Real-time health diagnostics/prognostics and predictive maintenance/control of lithium-ion (Li-ion) batteries are essential to reliable and safe battery operation. This paper presents a physics-based (or mechanistic) approach to Li-ion battery prognostics, which enables online prediction of remaining useful life (RUL) with consideration of multiple concurrent degradation mechanisms. In the proposed approach, robust online prediction of RUL is achieved by employing a non-linear least squares method with dynamic bounds that traces the evolution of individual degradation parameters. The novelty of this approach lies in its ability to incorporate mechanistic degradation analysis results into RUL predictions using nonlinear models. Results from a simulation study with eight Li-ion battery cells demonstrate that the mechanistic prognostics approach produces more accurate RUL predictions than a traditional capacity-based prognostics approach in 78 of the 80 cases considered (97.5% of the time). Additionally, it is shown that the use of dynamic bounds ensures a low level of uncertainty in the prediction throughout the entire life of a cell. [ABSTRACT FROM AUTHOR]

This paper presents a novel non-linear least squares enhanced proper orthogonal decomposition (POD)-based 4DVar algorithm (referred as NLS-4DVar) for the non-linear ensemble-based 4DVar. In the algorithm, the Gauss–Newton iterative method is employed to handle the non-quadratic non-linearity of the 4DVar cost function while the overall structure of the algorithm still resembles the original POD-4DVar algorithm. It is proved that the original POD-4DVar algorithm is a special case of the proposed NLS-4DVar algorithm under the assumption of the linear relationship between the model perturbations (MPs) and the simulated observation perturbations (OPs). Under the assumption it is also shown that the solution of POD-4DVar algorithm coincides with the solution of the proposed NLS-4DVar algorithm. On the contrary, if the linear relationship assumption is dropped, the solution of the POD-4DVar algorithm is only the first iteration of the proposed NLS-4DVar algorithm. As a result, our analysis provides an explanation for the degraded and inaccurate performance of the POD-4DVar algorithm when the underlying forecast model or (and) the observation operator is strongly non-linear. The potential merits and advantages of the proposed NLS-4DVar are demonstrated by a group of Observing System Simulation Experiments with Advanced Research WRF (ARW) using accumulated rainfall-observations.

Summary: Many industrial and engineering applications are built on the basis of differential equations. In some cases, parameters of these equations are not known and are estimated from measurements leading to an inverse problem. Unlike many other papers, we suggest to construct new designs in the adaptive fashion ‘on the go’ using the A‐optimality criterion. This approach is demonstrated on determination of optimal locations of measurements and temperature sensors in several engineering applications: (1) determination of the optimal location to measure the height of a hanging wire in order to estimate the sagging parameter with minimum variance (toy example), (2) adaptive determination of optimal locations of temperature sensors in a one‐dimensional inverse heat transfer problem and (3) adaptive design in the framework of a one‐dimensional diffusion problem when the solution is found numerically using the finite difference approach. In all these problems, statistical criteria for parameter identification and optimal design of experiments are applied. Statistical simulations confirm that estimates derived from the adaptive optimal design converge to the true parameter values with minimum sum of variances when the number of measurements increases. We deliberately chose technically uncomplicated industrial problems to transparently introduce principal ideas of statistical adaptive design. [ABSTRACT FROM AUTHOR]

In this paper, we study application of Le Cam's one‐step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one‐step method starts from a preliminary n‐consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n→∞) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one‐step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary n‐consistent estimator that we use depends on non‐parametric smoothing, and we provide a data‐driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one‐step method for practical use is pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of parameter identification for models defined by dynamical systems with structured uncertainty. This type of problem often occurs in science and engineering and we show how parameter estimation can be improved by taking advantage of the specific structure of the model form. We distinguish between model identification and model calibration and discuss approaches to deal with model discrepancy when the systems are described by classes of parameterized models where the uncertainties have a specified structure. The results are applicable to problems where, in the process of modelling a complex system, one ignores ‘small’ parameters to obtain simplified models and when infinite-dimensional systems are approximated to obtain finite-dimensional models. We show for these common sources of model discrepancies, hierarchical modelling can be employed to aid in the development of prior knowledge about the model form caused by uncertain or ignored parameters. We focus on a special class of inverse problems arising from model calibration and parameter estimation and illustrate how one can use information about the structure of the dynamical system to help deal with model discrepancy. Examples from the life sciences and engineering design are given to illustrate the ideas. [ABSTRACT FROM PUBLISHER]