Two-step Estimation Method Research Articles

Remaining Useful Life Prediction of Lithium-ion Batteries Based on Wiener Process Under Time-Varying Temperature Condition

Time-varying temperature condition has a significant impact on discharge capacity and aging law of lithium-ion battery. Consequently, a novel remaining useful life (RUL) prediction method for lithium-ion battery under time-varying temperature condition is developed in this paper. Firstly, a stochastic degradation rate model based on Arrhenius temperature model is proposed, and an interesting battery capacity conversion path from random temperature condition to reference temperature condition is established. Secondly, the aging model of lithium-ion battery under time-varying temperature condition is developed based on Wiener process, and a two-step unbiased estimation method based on maximum likelihood estimation (MLE) combined with genetic algorithm (GA) is proposed. Next, the random parameter is online updated under Bayesian framework. Then the probability density function (PDF) of the RUL for lithium-ion battery under time-varying temperature condition is derived. Finally, a case study is implemented to verify the effectiveness, and the results show that the proposed prediction method has higher accuracy and smaller uncertainty.

Economic policy uncertainty and stock liquidity: the role of board networks in an emerging market

PurposeThe purpose of this study is to examine the role of board networks in promoting stock liquidity when there is high economic policy uncertainty using a sample of Brazilian firms from 2002 to 2015.Design/methodology/approachThe study employs the ordinary least squares estimation method with standard errors clustered at the firm level for preliminary analysis, besides the study employs the two-step GMM dynamic estimation method to deal with potential endogeneity issues.FindingsFirst, the findings show that economic policy uncertainty disproportionately contributes to stock illiquidity and the impact is mainly prominent for high risky companies, small firms and firms in competitive industries. Second, the author provides evidence that board networks promote stock liquidity more via the information channel when economic policy uncertainty is very high.Practical implicationsGiven the adverse effects of economic policy uncertainty on stock liquidity, governments need to swiftly communicate and implement policies that affect the capital market to avoid the drying up of liquidity, which is exacerbated by communication or implementation lags. Also, there is a need for the regulators to continuously encourage the inclusion of independent directors in boards, which helps to increase board monitoring capacity and the firms' ability to respond to changes in the external environment.Originality/valueUnlike other studies that focus on the adverse effects of economic policy uncertainty on firm outcomes, the novel contribution is that the author uncovers the role of board networks in mitigating the negative effects of economic policy uncertainty on stock liquidity.

A Structural Model of a Multitasking Salesforce: Multidimensional Incentives and Plan Design

The paper broadens the focus of empirical research on salesforce management to include multitasking settings with multidimensional incentives, where salespeople have private information about customers. This allows us to ask novel substantive questions around multidimensional incentive design and job design while managing the costs and benefits of private information. To this end, the paper introduces the first structural model of a multitasking salesforce in response to multidimensional incentives. The model also accommodates (i) dynamic intertemporal tradeoffs in effort choice across the tasks and (ii) salespersoni?½s private information about customers. We apply our model in a rich empirical setting in microfinance and illustrate how to address various identification and estimation challenges. We extend two-step estimation methods used for unidimensional compensation plans by embedding a flexible machine learning (random forest) model in the first-stage multitasking policy function estimation within an iterative procedure that accounts for salesperson heterogeneity and private information. Estimates reveal two latent segments of salespeople- a i?½hunteri?½ segment that is more efficient in loan acquisition and a i?½farmeri?½ segment that is more efficient in loan collection. Counterfactuals reveal heterogeneous effects: huntersi?½ private information hurts the firm as they engage in adverse selection; farmersi?½ private information helps the firm as they use it to better collect loans. The payoff complementarity induced by multiplicative incentive aggregation softens adverse specialization by hunters relative to additive aggregation, but hurts performance among farmers. Overall, task specialization in job design for hunters (acquisition) and farmers (collection) hurts the firm as adverse selection harm overwhelms efficiency gain.

Two-stage physics-based Wiener process models for online RUL prediction in field vibration data

Due to most failure mechanisms, such as fatigue crack growth and fatigue spall, the degradation process of rotating machinery commonly exhibits two-stage features in engineering practice. Other minor factors are also the key issues affecting the health evolution process, including the component structure, assembly accuracy, and working environment. Ignoring such a mechanism may lead to imprecise in degradation modeling, life prognostic, and ultimately lead to safety risk. Besides, achieving high accuracy of prognostic emphasizes the influence of random effect in the degradation process. The contribution of this study lies in addressing this issue by proposing two-stage physics-based Wiener process models integrating: (a) fatigue crack mechanism and crack growth law, and (b) other minor factors. A general prognostic framework is formulated by jointly employing the online change point detection, parameter estimation, and remaining useful life (RUL) prediction, which has good statistic inference and applicability in two general nonlinear systems, i.e., power-law and exponential-law. A joint implement of offline two-step parameter estimation method and the online Bayesian update method is executed, making full advantage of historical and in-service data, based on which the RUL prediction transcends into an imperative PHM module. A practical case study on the vibration dataset of wheel treads demonstrates the practically implement ability of the proposed method in achieving high accuracy of RUL prediction.

Reliability analysis of face stability for tunnel excavation in a dependent system

From a practical perspective, it is necessary to consider multivariate failure mechanisms in reliability analysis. The multivariate in a system may be dependent on each other, which should be considered in reliability analysis. To investigate the reliability of a structural system, this study develops a copula-based approach to construct dependence structures of different failure mechanisms. Herein, a novel two-step parameter estimation method based on a hybrid-evolution Markov chain Monte Carlo (MCMC) algorithm has been developed to estimate copula parameters with high accuracy and less bias. To verify the validity and robustness of proposed method, the face stability issue in shield tunneling has been used as an illustrative example. Results indicate that: (1) the novel two-step parameter estimation method yields reasonable parameter values; (2) the calculated values based on copula model are more accurate than Nataf model in practical engineering; (3) the failure probability pf calculated by copula model is obviously different (almost over 50% in both examples) from Independent scenario. The proposed reliability analysis using the copula model provides guidelines for face stability control under uncertainty and randomness, which can reduce the failure probability ahead of time and mitigate risk magnitudes to some degree after failure occurrence.

A Two-Step Parameter Optimization Method for Low-Order Model-Based State-of-Charge Estimation

The state-of-charge (SOC) estimation is an enabling technique for the efficient management and control of lithium-ion batteries (LIBs). This article proposes a novel method for online SOC estimation, which manifests itself with both high accuracy and low complexity. Particularly, the particle swarm optimization (PSO) algorithm is exploited to optimize the model parameters to ensure high modeling accuracy. Following this endeavor, the PSO algorithm is used to tune the error covariances of extended Kalman filter (EKF) leveraging the early stage segmental data of LIB utilization. Within this PSO-based tuning framework, the searching boundary is derived by scrutinizing the error transition property of the system. Experiments are performed to validate the proposed two-step PSO-optimized SOC estimation method. Results show that even by using a simple first-order model, the proposed method can give rise to a high SOC accuracy, which is comparative to those using complex high-order models. The proposed method is validated to excavate fully the potential of model-based estimators so that the computationally expensive model upgrade can be avoided.

Improvement of the distribution network state estimation with increase of accurate information and using a two-step method

Distribution networks (DNs) are gradually changing and this makes their control and utilization complicated. State estimation (SE) plays a significant role in active distribution networks. The performance of the energy management center in modern distribution networks is highly dependent on the results obtained from the SE. In the present study, considering the shortage of measurements in the DN, a two-step state estimation method with a new network reduction process (NRP) is proposed. In the proposed method, a new NRP is used in a two-step state estimation method to improve the performance of SE in a DN. Obtaining accurate initial information on the network condition improves the performance of SE. The initial SE is performed using a new NRP process to obtain accurate initial data. This information is used as the measurement to improve the performance of secondary SE. This method resolves the shortage of accurate measurements and redundancy measurements, and it improves network SE accuracy without adding any real-time measurement. Moreover, the proposed method is economically affordable. Simulations are performed on the 18-bus UK radial feeder and the IEEE 69-bus distribution network in MATLAB software to guarantee valid operation of the proposed style.

Multi-objective optimization design of accelerated degradation test based on Wiener process

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test.

Interval Estimation for Discrete-Time Switched Linear Systems Based on L∞ Observer and Ellipsoid Analysis

This letter proposes a two-step interval estimation method for discrete-time switched linear systems with unknown but bounded uncertainties. Based on the ellipsoidal analysis, the proposed estimator provides upper and lower bounds of the system state with high computational analysis. The size of the obtained ellipsoids is minimized using the trace criterion. The idea of introducing an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is also employed in order to improve the estimation accuracy. Its design conditions are given in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example emphasizes the effectiveness of the contribution.

Household expenditure patterns in Kuwait

Household expenditure is the second prominent component of GDP for Kuwait, consisting of 43% GDP, and it has been moderately growing for the past decade. It is essential to understand the nature of household expenditure, a fundamental macroeconomic driver with immense significance for policymaking. This paper utilises the latest Kuwait Household Expenditure Survey data to study household expenditure patterns in Kuwait. It examines and compares the variation of household expenditure patterns for nationals (Kuwaitis) and expatriate households over nine different major commodity groups. The paper investigates the patterns of household expenditure and the response of their characteristics on the level of expenditure by employing Heckman two-step estimation method. The results suggest that different factors affect the probability of consuming a commodity and the level of expenditure between the two household groups. Kuwaiti’s expenditure is more responsive to food, housing, communication and recreation commodities and less responsive to clothing, health, transportation and restaurants than expatriates. In general, there is a significant variation of expenditure patterns across all commodities between the two household groups.

Interval Estimation for Uncertain Systems via Polynomial Chaos Expansions

This article investigates interval estimation for linear systems with time-invariant probabilistic uncertainty. A two-step interval estimation method, which consists of nominal observer design and estimation error bound analysis, is proposed based on polynomial chaos expansion (PCE) and zonotopic technique. To deal with time-invariant probabilistic uncertainty, the error dynamics is approximated via PCE, which leads to an expanded deterministic linear system. Then intervals of the expanded system and error system are analyzed by zonotopic technique. The interval estimation is achieved by combining nominal observer state and estimated error interval. In a case study, an experimental example and a simulation example show the effectiveness of the proposed method.

Reliability assessment for products with two performance characteristics based on marginal stochastic processes and copulas

Many highly reliable products (systems) usually have multiple dependent degradation processes because of their complex structure. Therefore, it is important to investigate the multivariate degradation models along with the reliability assessment in the stochastic modeling. This article proposes a framework for bivariate degradation modeling based on hybrid stochastic processes for products with two performance characteristics (PCs), the dependence of which is captured by copula functions. Considering heterogeneities among product units, different random effects are introduced in marginal stochastic processes. Then two classes of reliability functions based on joint posterior distributions are derived. In addition, a simulation study indicates that the holistic Bayesian parameter estimation method is better than the two-step Bayesian parameter estimation method. Finally, this article concludes with a case application to demonstrate the effectiveness of the proposed model.

The dynamics and volatility of prices in multiple markets: a quantile approach

This paper presents an econometric investigation of price dynamics and volatility in multiple markets. The econometric approach relies on a quantile autoregressive (QAR) model and a copula to provide a flexible representation of price dynamics and volatility in related markets. The analysis allows for an arbitrary distribution of prices across markets, nonlinear dynamics and the presence of price cycles. We propose a two-step estimation method to support a consistent estimation of the multivariate price distribution and its evolution over time. The analysis is illustrated in an econometric application to price dynamics in the US pork vertical sector. The application provides new and useful information on the nature of the pork cycle, the linkages between farm price and retail price and the evolving price volatility in this market.

A two-step approach to interval estimation for continuous-time switched linear systems

Abstract This paper proposes a two-step interval estimation method for continuous-time switched linear systems subject to unknown but bounded disturbance and measurement noise. We first use an L∞ norm-based approach to attenuate the effect of uncertainties in observer design. Then, based on the obtained observer, interval estimation can be achieved via analyzing the bounds of estimation error. The proposed method is intuitive and independent of cooperativity constraint, which is main restriction of interval observer theory. The performance of the proposed method is demonstrated through a numerical simulation.

Positioning in a Multipath Channel Using OFDM Signals With Carrier Phase Tracking

In developing a high accuracy terrestrial radio navigation system, as a complement to a global navigation satellite system (GNSS), it is recognized that the performance of time delay estimation is proportional to, and thereby limited by, the signal bandwidth. Given a possibly narrow signal bandwidth, the central carrier phase can, alternatively, provide a better distance accuracy, though the central carrier phase cycle ambiguity should be resolved. In practice, the carrier phase may be perturbed by multipath. In this paper, considering an orthogonal frequency division multiplexing (OFDM) signal, we propose a two-step carrier phase estimation method to reduce the error introduced by multipath. First, the propagation delay of the LoS path is coarsely determined, then the carrier phase is estimated using the earlier determined coarse time delays. Furthermore, a positioning model only based on carrier phase estimates is presented in this paper. The proposed technique is evaluated by statistical analyses and a simulated OFDM-based terrestrial positioning system in different roadway multipath environments. The results show that the impact of multipath on carrier phase estimation can be largely mitigated, so that the carrier phase can be used for precise positioning. In addition, fixing the integer carrier phase cycle ambiguities can significantly reduce the time for the position solution to converge to high precision.

Panel Data Quantile Regression for Treatment Effect Models

In this study, we develop a novel estimation method for quantile treatment effects (QTE) under rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and proposes a parametric estimation based on the minimum distance method. However, when the dimensionality of the covariates is large, the minimum distance estimation using this process is computationally demanding. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance methods. We then show the uniform asymptotic properties of our estimator and the validity of the nonparametric bootstrap. The Monte Carlo studies indicate that our estimator performs well in finite samples. Finally, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and TV watching on child cognitive development.

Oracally efficient estimation and testing for an ARCH model with trend

This article investigates an ARCH model with trend and proposes a two-step estimation method and develops an ARCH effect test. The trend is estimated by the linear B-spline method, and then the least squares estimation (LSE) and a Lagrange multiplier (LM) test based on the residuals are presented. Under mild conditions, it is shown that the proposed LSE and the test statistic enjoy the oracle properties; namely, they perform as well as if the true trend function were known and then removed to obtain the ARCH errors. Simulation studies assess the finite-sample performance of the LSE and the test statistic. An empirical example on the US gross private saving series is analyzed to illustrate the usefulness of our procedure.

Micrometer Accuracy Phase Modulated Radar for Distance Measurement and Monitoring

An enhanced accuracy random binary phase modulated radar is proposed. It can be used in high accuracy monitoring in manufacturing. Compared with the traditional high accuracy radar using frequency modulated continuous wave (FMCW), the proposed radar system can be used in a multi-user scenario without occupying more bandwidth. A two-step distance estimation method is introduced to estimate the distance. First, the distance estimation accuracy is narrowed down to a half carrier wavelength by analyzing the envelope of the phase modulated signal. Then the carrier phase information increases the distance accuracy to several micrometers. An equalization method is introduced to solve the I/Q imbalance problem. The proposed radar system is demonstrated at a carrier frequency of 80 GHz with a bandwidth of 2 GHz. The measured distance error was within ±7 $\mu $ m. In addition, a high measurement repetition rate of 500 kHz was reached which is suitable for real-time monitoring in automatic manufacturing.

A Structural Model of a Multitasking Salesforce: Job Task Allocation and Incentive Plan Design

The paper broadens the focus of empirical research on salesforce management to include multitasking settings with multidimensional incentives, where salespeople have private information about customers. This allows us to ask novel substantive questions around multidimensional incentive design and job design while managing the costs and benefits of private information. To this end, the paper introduces the first structural model of a multitasking salesforce in response to multidimensional incentives. The model also accommodates (i) dynamic intertemporal tradeoffs in effort choice across the tasks and (ii) salesperson’s private information about customers. We apply our model in a rich empirical setting in microfinance and illustrate how to address various identification and estimation challenges. We extend two-step estimation methods used for unidimensional compensation plans by embedding a flexible machine learning (random forest) model in the first-stage multitasking policy function estimation within an iterative procedure that accounts for salesperson heterogeneity and private information. Estimates reveal two latent segments of salespeople- a “hunter” segment that is more efficient in loan acquisition and a “farmer” segment that is more efficient in loan collection. Counterfactuals reveal heterogeneous effects: hunters’ private information hurts the firm as they engage in adverse selection; farmers’ private information helps the firm as they use it to better collect loans. The payoff complementarity induced by multiplicative incentive aggregation softens adverse specialization by hunters relative to additive aggregation, but hurts performance among farmers. Overall, task specialization in job design for hunters (acquisition) and farmers (collection) hurts the firm as adverse selection harm overwhelms efficiency gain.

Fatigue crack growth assessment method subject to model uncertainty

Fatigue crack growth (FCG) is an important degradation process of many critical mechanical equipment. Probabilistic FCG models are often used to account for the variability among FCG process conditions. In the well-known model of Yang and Manning, a deterministic FCG model is randomized by multiplying the crack growth rate with a random multiplier assumed to obey a lognormal distribution and unknown parameters are jointly estimated through Maximum likelihood estimation. By so doing, the modeling error due to inappropriate choice of the deterministic FCG model and that due to unsuitable assignment of the probability distribution of the random multiplier cannot be distinguished. Besides, the model uncertainty of the random multiplier is not explicitly considered. In this paper, a two-step least-square estimation method is proposed, which estimates the unknown parameters in the deterministic FCG model at first, and generates a sample set for the estimation of the random multiplier considering model uncertainty by way of Bayesian model selection. In Bayesian model selection, three types of Bayes factor are considered to select the appropriate candidate model and a simulation experiment is carried out to guide their selection. The effectiveness and feasibility of the proposed method are illustrated through two case studies using the real FCG datasets.