A two-dimensional inverse heat conduction problem in estimating the fluid temperature in a pipeline

An inverse heat conduction problem (IHCP) was investigated in the two-dimensional section of a pipe elbow with thermal stratification to estimate the unknown transient fluid temperatures near the inner wall of the pipeline. An inverse algorithm based on the conjugate gradient method (CGM) was proposed to solve the IHCP using temperature measurements on the outer wall. In order to examine the accuracy of estimations, some comparisons have been made in this case. The temperatures obtained from the solution of the direct heat conduction problem (DHCP) using the finite element method (FEM) were pseudo-experimental input data on the outer wall for the IHCP. Comparisons of the estimated fluid temperatures with experimental fluid temperatures near the inner wall showed that the IHCP could accurately capture the actual temperature in form of the frequency of the temperature fluctuations. The analysis also showed that the IHCP needed at least 13 measurement points for the average absolute error to be dramatically reduced for the present IHCP with 37 nodes on each half of the pipe wall.     

基于幂律过程的风力机故障建模方法研究

针对传统风力机故障建模方法存在的适用条件不符、误差较大等问题,提出一种基于幂律过程的风力机故障建模方法.首先对风力机故障数据进行趋势检验,结合故障数据的非齐次泊松特点,建立基于幂律过程的风力机故障模型;然后分别利用最小二乘法、极大似然估计法及列文伯格-马夸尔特算法求解模型参数,并比较不同参数估计方法的优越性;最后通过求...     

The Estimation of Fluid Temperatures Through an Inverse Heat Conduction Technique

Transient, internal temperatures within an instrumented probe are considered as part of an inverse heat conduction problem (IHCP) to compute the temperature of the surrounding fluid. A linear scheme is used where the exchange coefficients are treated as known parameters.Input data to the IHCP have been generated numerically. When these are uncorrupted, the inverse algorithm works well without stabilization. However, in practice the algorithm must be stabilized, as it is shown that noise is amplified substantially. It becomes necessary both to parameterize spatial variations in the fluid temperature and to utilize a functional specification method to address the noncausal solution.     

Transient heat flux function estimation utilizing the variable metric method

A new method is presented to solve inverse heat conduction problems (IHCP's). The method belongs to the whole domain type of IHCP and utilizes the variable metric method (VMM) instead of the conjugate gradient method (CGM) in order to minimize the function of sum of square errors. Appropriate formulations for sensitivity coefficients, objective function and its gradient are set up in a manner suitable for computer programming of VMM. Numerically simulated data are utilized to assess the effectiveness of the method in comparison with the conjugate gradient method in estimation of space and time varying heat flux. Results indicate that the presented method is quite faster and more accurate than the conjugate gradient method in estimation of unknowns in the whole domain inverse problems.     

A SERIAL SOLUTION FOR THE 2-D INVERSE HEAT CONDUCTION PROBLEM FOR ESTIMATING MULTIPLE HEAT FLUX COMPONENTS

A serial algorithm for the inverse heat conduction problem (IHCP) has been developed to estimate the individual flux components, one by one, at the unknown boundary, based on the function specification method. The sensitivity coefficient defined in this algorithm brings out the influence of the heat flux components independent of each other. The objective function minimizes the difference in the measured temperature and the contribution of the individual flux component to the thermal field at the sensor location. The serial algorithm developed here could be used with data from both overspecified and underspecified sensors with respect to the number of flux components. The method was tested for delineating independent heat fluxes at the boundary of a two-dimensional solid for both space- and time-varying heat fluxes. Simulated thermal histories obtained from direct solution were used as inputs for the inverse problem for characterizing the new algorithm.

Three types of analyses were done on the results of the IHCP, focused on (1) the convergence of error in estimated temperatures at the different sensor locations, (2) overall error in estimated temperatures for the whole domain, and (3) the total heat energy transferred across the boundary. It is shown that the optimum configuration of independent unknown fluxes is given by the one with minimum energy estimates across the boundary, for both cases.     

A robust and fast algorithm for three-dimensional transient inverse heat conduction problems

Despite numerous studies of inverse heat conduction problems (IHCP) over the last several decades, their solutions still suffer from the mathematical difficulties and the bottleneck of currently available numerical methods for large-scale problems. In this paper, we present a robust and efficient algorithm for the solution of a specific type of three-dimensional (3D) IHCP commonly involved in various engineering applications. The solution method incorporates the Tikhonov regularization for tackling the severe ill-posedness and the conjugate gradient (CG) method for solving the resulting minimization problems. A model function approach is used to significantly reduce the effort needed to find the optimal Tikhonov regularization parameter. The proposed solution method requires no a priori knowledge of the measurement noise and is much more computationally efficient than the traditional Tikhonov regularization-based inversion approaches. Thus, it can be used for the efficient solution of large-scale practical problems. Two simulation case studies of practical significance are presented to validate and assess the performance of the proposed method. Finally, the solution method is successfully applied to the reconstruction of instantaneous heat fluxes from experimentally measured temperature data.     

Inverse design of thermal systems with spectrally dependent emissivities

This work extends the inverse design methodology to systems in which the emissivities of the surfaces are dependent on the wavelength. The objective is to find the powers of the heaters to achieve uniform temperature and heat flux on the design surface. The mathematical formulation is described by an ill-conditioned system of non-linear equations, which is regularized by the TSVD method. The solution involves an iterative approach in which the radiation distribution in the spectrum bands is repeatedly guessed and corrected as the estimation of the heaters temperatures evolves. The example cases demonstrate the effectiveness of the proposed methodology.     

Accurate estimation of cost function parameters for thermal power plants using a novel optimization approach

Accurate parameter estimation of the input-output characteristics in thermal power plants is an important issue in power system because these characteristics directly affect the economic dispatch calculations. Parameter estimation is an optimization problem in which the optimal values of the unknown parameters should be estimated by an optimization technique. By considering the valve-point effect, the parameter estimation will be more difficult since the fitness function of this optimization problem turns into a non-smooth and non-convex function in which finding the global optimal is a challenging task. In this paper, a recently proposed metaheuristic approach, crow search algorithm (CSA), is proposed for accurate estimation of the input-output characteristics of thermal power plants with and without valve-point effect. Simulation results show that CSA finds more promising results than least squares method (LSM), particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC).     

Identification of boundary heat fluxes in a falling film experiment using high resolution temperature measurements

In this paper, we consider a three-dimensional inverse heat conduction problem (IHCP) in a falling film experiment. The wavy film is heated electrically by a thin constantan foil and the temperature on the back side of this foil is measured by high resolution infrared (IR) thermography. The transient heat flux at the inaccessible film side of the foil is determined from the IR data and the electrical heating power. The IHCP is formulated as a mathematical optimization problem, which is solved with the conjugate gradient method. In each step of the iterative process two direct transient heat conduction problems must be solved. We apply a one step θ-method and piecewise linear finite elements on a tetrahedral grid for the time and space discretization, respectively. The resulting large sparse system of equations is solved with a preconditioned Krylov subspace method. We give results of simulated experiments, which illustrate the performance and tuning of the solution method, and finally present the estimation results from temperature measurements obtained during falling film experiments.     

An online state of health estimation method based on battery management system monitoring data

A state of health (SOH) estimation method that can be achieved online and only requires battery management system (BMS) detection data is proposed in this article. In the State of Health mathematical model proposed in this article, the using time of power battery is treated as an independent variable and SOH is treated as a hidden variable. And the mathematical model just used online process data from BMS. So it would make the SOH estimation method more suitable for actual engineering. Then, the article proposes an interleaved time model parameter update framework to reduce the computational complexity of the algorithm in a single sampling period. In this framework, we propose a fast model parameter identification algorithm that uses nonlinear least squares to initialize a genetic algorithm searched range. Finally, the whole method is verified by using the NASA database. The results prove that the proposed online SOH estimation method has higher SOH estimation accuracy and is more suitable for engineering applications in the field of electric vehicles than the existing SOH estimation methods.     

Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object

In many dynamic heat transfer situations, the temperature at the heated boundary is not directly measurable and can be obtained by solving an inverse heat conduction problem (IHCP) based on measured temperature or/and heat flux at the accessible boundary. In this study, IHCP in a two-dimensional rectangular object is solved by using the conjugate gradient method (CGM) with temperature and heat flux measured at the boundary opposite to the heated boundary. The inverse problem is formulated in such a way that the heat flux at heated boundary is chosen as the unknown function to be recovered, and the temperature at the heated boundary is computed as a byproduct of the IHCP solution. The measurement data, i.e., the temperature and heat flux at the opposite boundary, are obtained by numerically solving a direct problem where the heated boundary of the object is subjected to spatially and temporally varying heat flux. The robustness of the formulated IHCP algorithm is tested for different profiles of heat fluxes along with different random errors of the measured heat flux at the opposite boundary. The effects of the uncertainties of the thermophysical properties and back-surface temperature measurement on inverse solutions are also examined.     

Intelligent fuzzy weighted input estimation method applied to inverse heat conduction problems

The innovative intelligent fuzzy weighted input estimation method which efficiently and robustly estimates the unknown time-varying heat flux in real-time is presented in this paper. The algorithm includes the Kalman Filter (KF) and the recursive least square estimator (RLSE), which is weighted by the fuzzy weighting factor proposed based on the fuzzy logic inference system. To directly synthesize the Kalman filter with the estimator, this work presents an efficient robust forgetting zone, which is capable of providing a reasonable compromise between the tracking capability and the flexibility against noises. The capability of this inverse method are demonstrated in one- and two-dimensional time-varying estimation cases and the proposed algorithm is compared by alternating between the constant and adaptive weighting factors. The results show that this method has the properties of faster convergence in the initial response, better target tracking capability and more effective noise reduction.     

Simple method for monitoring transient thermal stresses in pipelines

This paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler components.     

改进的WLS-TF动态同步相角和频率估计算法

为提高电力系统相角和频率的测量精度,基于加权最小二乘泰勒展开傅里叶算法(WLS-TF),将带通信号模型扩展到考虑二阶谐波的更一般的信号模型,提出一种利用二阶多项式插值函数进行频率估计的新方法。仿真结果表明,在信号模型中考虑不同稳态和动态条件下,所提算法可显著提高相角和频率的估计精度。     

Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

In this paper an efficient sequential method is developed in order to estimate the unknown boundary condition on the surface of a body from transient temperature measurements inside the solid. This numerical approach for solving an inverse heat conduction problem (IHCP) takes into account two-dimensional problems, planar or axisymmetric cylindrical, composite materials with irregular boundaries and temperature-dependent thermal properties. The unknown surface condition is assumed to have abrupt changes at unknown times. The regularization procedure used for the solution of the IHCP is based on the singular value decomposition technique. An overall estimate of error is defined in order to find the optimal estimation in the 2D IHCP (linear and non-linear). The stability and accuracy of the scheme presented is evaluated by comparison with the Function Specification Method. This comparative study has been carried out using numerically simulated data, and the parameters considered include shape of input, noise level of measurement, size of time step and temperature-dependent thermal properties. A good agreement was found between both methods. Beside this, the slight differences on estimations and number of future temperatures are discussed in this paper.     

Practical application of inverse heat conduction for wall condition estimation on a rotating cylinder

The solution of the linear, inverse, transient heat conduction problem (IHCP) in a cylindrical geometry is analysed. The rotating cylinder under investigation is experiencing boiling convection induced by the impingement of a water jet. The initial temperature is known, additional temperature measurements in time are taken with sensors positioned at a constant radius within the solid material, and the estimation of the wall heat flux at the external radius is sought. First, simulated temperature measurements inside the cylinder are processed in order to be used to estimate the wall heat flux. When noise is present in the data, some of the simulated results obtained using the least squares method exhibit oscillatory behavior, but these large oscillations are substantially reduced by the implementation of a regularization technique. Real experimental data are also used for the wall condition estimation and for the subsequent building of local boiling curves are plotted and discussed. The question of the possible effect of a temperature dependent conductivity on the reconstructed wall condition is also considered.     

CHARACTERIZATION OF SPACE DEPENDENT THERMAL CONDUCTIVITY WITH A BEM-BASED GENETIC ALGORITHM

An inverse boundary element method is developed to characterize the spatially dependent conductivity k(x) of heterogeneous materials. Surface measurements at exposed boundaries serve as additional input to a genetic algorithm (GA) minimizing a regularized functional measuring the difference between observed and boundary element method (BEM)-predicted surface temperatures under current conductivity estimates. Analytical integration for a given estimate of k(x) provides explicit evaluation of influence coefficients, and series expansions are used to approximate integrands in expressions for these coefficients. Numerical integration is performed just once, a significant speedup in updates of the functional in evolution of the GA.     

含DG随机出力的配电网多目标无功优化

针对分布式电源(DG)出力具有间歇性和不确定性的问题,建立了基于两点估计法(2PEM)含DG随机出力的配电网概率潮流计算模型,并将基于Pareto最优前沿解集的多目标进化算法(MOEA)与两点估计概率计算模型相结合,建立了以网损、节点电压偏移量及优化成本为目标函数的多目标无功优化模型。将该优化模型应用于IEEE33标准节点测试系统中的仿真结果表明,该方法具有较好的适应性,能为决策者提供多样性选择,增加了决策的灵活性。     

Two-Dimensional Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux

Two-dimensional transient inverse heat conduction problem (IHCP) of functionally graded materials (FGMs) is studied herein. A combination of the finite element (FE) and differential quadrature (DQ) methods as a simple, accurate, and efficient numerical method for FGMs transient heat transfer analysis is employed for solving the direct problem. In order to estimate the unknown boundary heat flux in solving the inverse problem, conjugate gradient method (CGM) in conjunction with adjoint problem is used. The results obtained show good accuracy for the estimation of boundary heat fluxes. The effects of measurement errors on the inverse solutions are also discussed.