Random Temperature Field Research Articles

Self-organized structures induced by external white noise and nanosized levels of their formation in the non-crystalline As-S(Se) semiconductor systems

Discussed in this paper are the singularity and self-organizing effect of instability and randomness under the influence of external white noise on formation of non-crystalline materials. The random nature of the receiving medium together with the disorganizing effect was found to be capable to initiate formation of qualitatively new self-organized structures in non-crystalline solids. Also analyzed in the paper is the effect of a random temperature field applied to the melt during the cooling process in non-crystalline As-S(Se) semiconductor systems. The conditions for a non-crystalline system in a fluctuating external environment to adjust its properties to the average properties of the environment and to correspond to the deterministic case were identified. Furthermore, the conditions for non-additive reaction of the system to a random environment and formation of a new mode of energy conversion in the self-organized structure at the nanoscale level are determined. The spectrum of the structures created in this way is more diverse as compared to the spectrum corresponding to respective deterministic conditions.

Experimental study on random temperature field of ultra-high performance concrete filled steel tube columns under elevated temperature

Due to the change of microstructure and increased heterogeneity of ultra-high-performance concrete (UHPC) in comparison with normal concrete, the thermal properties of UHPC are much less uniform within the material. Consequently, the fire performance of UHPC filled steel tubes (UHPCFST) columns are affected by the random distribution of temperature within the concrete. In order to study the distribution of the random temperature field within UFPCFST columns under elevated temperature, high temperature tests on 16 circular UHPCFST columns subjected to the ISO-834 standard fire and a linear heating mode are carried out. The average temperature, temperature difference, temperature probability density distribution and the temporal and spatial correlation of the random temperature field are investigated. It is found that the columns with more steel fiber and coarse aggregate contents have higher temperature, small temperature gradient and higher temperature difference. It is also found that the correlation of the zero-centered temperature in the circumferential direction between different time is strong when the temperature continues to rise or fall. The aims of this paper is to provide the reference for the analysis of temperature field of UHPCFST considering the heterogeneity of UHPC core.

Numerical Investigation of Thermal Stability of Catalyst Granules with Internal Heat Generation in a Random Temperature Field

Method for numerical simulation of temperature of granules with internal heat release in a medium with random temperature fluctuations it is proposed. The method utilized solution of a system of ordinary stochastic differential equations describing temperature fluctuations of surrounding and granules. Autocorrelation function of temperature fluctuations has a finite decay time. The suggested method is verified by the comparison with exact analytical results. Random temperature behavior of a granule with internal heat release qualitatively differs from the results obtained in the deterministic approach. Mean first passage time of granules temperature intersects critical temperature is estimated at different regime parameters.

Cauchy problem of non-homogenous stochastic heat equation and application to inverse random source problem

In this paper, a Cauchy problem of non-homogenous stochastic heat equation is considered together with its inverse source problem, where the source term is assumed to be driven by an additive white noise. The Cauchy problem (direct problem) is to determine the displacement of random temperature field, while the considered inverse problem is to reconstruct the statistical properties of the random source, i.e. the mean and variance of the random source. It is proved constructively that the Cauchy problem has a unique mild solution, which is expressed an integral form. Then the inverse random source problem is formulated into two Fredholm integral equations of the first kind, which are typically ill-posed. To obtain stable inverse solutions, the regularized block Kaczmarz method is introduced to solve the two Fredholm integral equations. Finally, numerical experiments are given to show that the proposed method is efficient and robust for reconstructing the statistical properties of the random source.

Model order reduction assisted by deep neural networks (ROM-net)

In this paper, we propose a general framework for projection-based model order reduction assisted by deep neural networks. The proposed methodology, called ROM-net, consists in using deep learning techniques to adapt the reduced-order model to a stochastic input tensor whose nonparametrized variabilities strongly influence the quantities of interest for a given physics problem. In particular, we introduce the concept of dictionary-based ROM-nets, where deep neural networks recommend a suitable local reduced-order model from a dictionary. The dictionary of local reduced-order models is constructed from a clustering of simplified simulations enabling the identification of the subspaces in which the solutions evolve for different input tensors. The training examples are represented by points on a Grassmann manifold, on which distances are computed for clustering. This methodology is applied to an anisothermal elastoplastic problem in structural mechanics, where the damage field depends on a random temperature field. When using deep neural networks, the selection of the best reduced-order model for a given thermal loading is 60 times faster than when following the clustering procedure used in the training phase.

The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling

Random dynamic analysis of the thin-walled structure subjected to coupling loads from three fields is addressed in the frame of the finite element method. Based on the proposed dynamic finite element equation of the deterministic structure under thermal–structural–acoustic coupling, when the randomness of structural physical parameters, temperature load and fatigue test data is fully considered, the dynamic responses of random structure subjected to coupling loads from three fields are dealt with by random factor method. The numerical characteristic values of the random temperature field and that of random dynamic responses are then derived through the moment method of random variables. Subsequently, the dynamic reliability of the stochastic structure under three-field coupling is evaluated using residual strength model, dynamic stress-intensity interference theory and the cumulative damage equal principle. Finally, the results from the methodology proposed are compared with that from Monte-carlo method for a case of numerical example, along with an inspection of the impacts of random variables on dynamic analysis results.

The analyses of dynamic response and reliability for failure-dependent stochastic micro-resonator with thermoelastic coupling effects

A crucial measure for the design of high-performance micro-resonators is to consider the randomness of structural parameters when analyzing the structural system reliability. In this work, the stochastic dynamic response analysis and subsequently, a dynamic reliability assessment of the random micro-resonators are originally presented, where the thermoelastic coupling effects are freshly incorporated in the models proposed. The dynamic characteristics equation of the deterministic micro-resonator is firstly established based on the finite element method. The random dynamic characteristics of the resonator are then solved by implementing the left and right eigenvectors and the block Lanczos algorithm, and the random temperature field and structural random dynamic stress are also tackled. Afterwards, the overall structural reliability is investigated with a comprehensive consideration of the strength failure and frequency resonance failure, in which the Copula function is used for describing the dynamic correlation between two failure modes. Finally, the feasibility and rationality of the method put forward are demonstrated via a practically motivated example.

Technique developments and performance analysis of chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering combustion thermometry.

This work characterizes the state of the art in the analysis of high-repetition-rate, ultrafast combustion thermometry using chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs-CARS). Several key aspects of the CARS spectroscopy system are described, including: (1)the ultrafast laser source, (2)use of the frequency-doubled idler versus signal from the optical parametric amplifier, (3)the geometry constraints for phase matching, and (4)spectral fitting for single-shot temperature measurements. A frequency-dependent instrument response function (IRF) for the detection system was modeled as a variable-width Gaussian and implemented through a frequency convolution of synthetic spectra. Proper accounting of the IRF increased spectral fitting performance in the high-frequency region where signal oscillations are weaker and narrower. Aggregated data from 25 system performance assessments taken over four months yielded accuracy and precision of 2.7% and ±3.5% for flame temperatures, and 9.9% and ±6.1% at room temperature, using the commonly reported method. A new processing technique, based on the statistical method of maximum likelihood, was implemented for turbulent flames where strong fluctuations in expected temperatures necessitate use of multiple temperature calibrations. Results from multiple sets of laser parameters are combined to generate an error-weighted temperature from the top-performing calibrations. A testing procedure was designed to characterize system performance when the range of expected temperatures is unknown, simulating the random temperature field of a highly turbulent flame. Accuracy error of the CPP fs-CARS system increased in this more-stressing test at all temperatures, but precision was significantly affected only at room temperature. System stability is characterized, and the contribution from shot-to-shot laser fluctuations on measurement precision is quantified. Finally, the near-adiabatic and steady assumptions for the Hencken burner calibration flame are examined in an axial scan; significant deviations from ideal behavior were observed only at heights of more than four diameters above the burner surface.

Estimation on the influence of uncertain parameters on stochastic thermal regime of embankment in permafrost regions

For embankments in permafrost regions, the soil properties and the upper boundary conditions are stochastic because of complex geological processes and changeable atmospheric environment. These stochastic parameters lead to the fact that conventional deterministic temperature field of embankment become stochastic. In order to estimate the influence of stochastic parameters on random temperature field for embankment in permafrost regions, a series of simulated tests are conducted in this study. We consider the soil properties as random fields and the upper boundary conditions as stochastic processes. Taking the variability of each stochastic parameter into account individually or concurrently, the corresponding random temperature fields are investigated by Neumann stochastic finite element method. The results show that both of the standard deviation under the embankment and the boundary increase with time when considering the stochastic effect of soil properties and boundary conditions. Stochastic boundary conditions and soil properties play a different role in random temperature field of embankment at different times. Each stochastic parameter has a different effect on random temperature field. These results can improve our understanding of the influence of stochastic parameters on random temperature field for embankment in permafrost regions.

Stochastic analysis for the uncertain temperature field of tunnel in cold regions

In cold regions, the temperature is important to determine the stability of tunnel construction. However, the conventional finite element methods for stability analysis are always deterministic, rather than taking stochastic parameters and conditions into account. In this paper, the boundary conditions are considered as stochastic processes and the rock properties are considered as random fields. A stochastic analysis for the uncertain temperature characteristics of tunnel is presented. The stochastic finite element formulae are obtained by Neumann stochastic finite element method (NSFEM), and the stochastic finite element program is compiled by Matrix Laboratory (MATLAB) software. Using our program, the random temperature fields of a tunnel in a cold region are obtained and analyzed. The results show that the temperature of a large quantity of frozen surrounding rock is stochastic, and it is bad for the thermal stability of actual tunnel engineering in cold regions. The distributions of mean temperature are the same and the distributions of standard deviation are similar for the two cases in this paper. The average standard deviation increases with time, which implies that the results of conventional deterministic analysis may be far from the true value. These results can improve our understanding of the random temperature field of tunnel and provide a theoretical basis for actual engineering design in cold regions.

Uncertainty propagation of heat conduction problem with multiple random inputs

Uncertainty propagation analysis in engineering systems constitutes a significant challenge. To effectively solve the uncertain heat conduction problem with multiple random inputs, a random collocation method (RCM) and a modified random collocation method (MRCM) are established based on the spectral analysis theory. In both methods, the truncated high-order polynomial series is adopted to approximate the temperature responses with respect to random parameters, and the eventual probabilistic moments are derived by using the orthogonal relationship of polynomial bases. In the pivotal process of calculating the expansion coefficients, RCM evaluates the deterministic solutions directly on full tensor product grids, whereas the Smolyak sparse grids are reconstructed in MRCM to avoid the huge computational cost caused by high dimensions. Comparing the results with traditional Monte Carlo simulation, two numerical examples verify the remarkable accuracy and effectiveness of the proposed methods for random temperature field prediction in engineering.

Stochastic analysis of uncertain thermal characteristic of foundation soils surrounding the crude oil pipeline in permafrost regions

For foundation soils surrounding the crude oil pipeline in permafrost regions, the soil properties and the upper boundary conditions are stochastic because of complex geological processes and changeable atmospheric environment. The conventional finite element analysis of thermal characteristics for crude oil pipeline is always deterministic, rather than taking stochastic parameters and conditions into account. This study investigated the stochastic influence of an underground crude oil pipeline on the thermal stability of the permafrost foundation on the basis of a stochastic analysis model and the stochastic finite element method. A stochastic finite element program is compiled by Matrix Laboratory (MATLAB) software, and the random temperature fields of foundation soils surrounding a crude oil pipeline in a permafrost region are obtained and analyzed by Neumann stochastic finite element method (NSFEM). The results provide a new way to predict the thermal effects of the crude oil pipeline in permafrost regions, and it shows that the standard deviations in temperature increase with time when considering the stochastic effect of soil properties and boundary conditions, which imply that the results of conventional deterministic analysis may be far from the true value, even if in different seasons. It can improve our understanding of the random temperature field of foundation soils surrounding the crude oil pipeline and provide a theoretical basis for actual engineering design in permafrost regions.

Stochastic analysis of uncertain temperature characteristics for expressway with wide subgrade in cold regions

In cold regions, it is more difficult to ensure the stability of wide embankment than ordinary embankment because of a larger heat absorption area. Also, the soil properties and the upper boundary conditions are stochastic because of complex geological processes and changeable atmospheric environment. However, the conventional finite element analysis of temperature characteristics for embankment is always deterministic, rather than taking stochastic parameters and conditions into account. In this paper, the upper boundary conditions are considered as stochastic processes and the soil properties are considered as random fields. A stochastic analysis model for the uncertain temperature characteristics of expressway embankment is presented. The stochastic finite element program is compiled by Matrix Laboratory (MATLAB) software, and the random temperature fields of an expressway embankment in a cold region are investigated by Neumann stochastic finite element method (NSFEM). The results show that the randomness of soil properties and boundary conditions play a different role at different times. NSFEM can solve the random temperature field for expressway embankment when the perturbations of random variables are more than 20%. It can improve our understanding of the random temperature field of expressway embankment and provide a theoretical basis for actual engineering design in cold regions.

Stochastic analysis model of uncertain temperature characteristics for embankment in warm permafrost regions

For embankments in cold regions, the soil properties and the upper boundary conditions are stochastic because of complex geological processes and changeable atmospheric environment. In this study, we model the soil properties as random fields and the upper boundary conditions as stochastic processes. A triangular local average (TLA) method is used to discretize the two-dimensional (2D) random fields. The random temperature fields of an embankment in a cold region are investigated by Neumann stochastic finite element method (NSFEM), and the computational formulas of mean and standard deviation are developed. In the calculation flow chart, a stochastic finite element (FE) program has been compiled by Matrix Laboratory (MATLAB) software. The results show that TLA method perfectly matches with triangular FE method. The randomness of soil properties and boundary conditions lead to the randomness of temperature. The results will improve our understanding of the random temperature field of embankments in cold regions. The proposed method can be used to solve other uncertain thermodynamic problems.

Analysis of random temperature field for freeway with wide subgrade in cold regions

In cold regions, the freeway with wide pavement has larger heat absorption area than the normal, resulting in more difficulties to ensure the stability of embankment. However, the conventional finite element methods for stability analysis are always deterministic, rather than taking random parameters and conditions into account. In this paper, using stochastic finite element methods, the parameters of boundary conditions are considered as random variables, and the random temperature fields for wide-subgrade freeway are obtained and analyzed. The results show that heat accumulation effect is obvious in the central section of subgrade and that the closer it is to the upper boundary of the roadbed, the greater the temperature variance is. Besides, both effects increase with time.

Solidification dynamics under random external-temperature fluctuations

The nonlinear dynamic mechanisms of solid-phase formation with a phase transition region are studied under periodic and random fluctuations of the cooling-boundary temperature. It is theoretically shown that a mushy zone can form even at close liquid and cooling-boundary temperatures due to random temperature field fluctuations. The growth of a solid phase with the mushy zone is investigated as a function of the autocovariance characteristics of random noises.

Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory (MATLAB) software, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by comparing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatially random fields.

Probabilistic models for reactive behaviour in heterogeneous condensed phase media

This work presents statistically-based models to describe reactive behaviour in heterogeneous energetic materials. Mesoscale effects are incorporated in continuum-level reactive flow descriptions using probability density functions (pdfs) that are associated with thermodynamic and mechanical states. A generalised approach is presented that includes multimaterial behaviour by treating the volume fraction as a random kinematic variable. Model simplifications are then sought to reduce the complexity of the description without compromising the statistical approach. Reactive behaviour is first considered for non-deformable media having a random temperature field as an initial state. A pdf transport relationship is derived and an approximate moment approach is incorporated in finite element analysis to model an example application whereby a heated fragment impacts a reactive heterogeneous material which leads to a delayed cook-off event. Modelling is then extended to include deformation effects associated with shock loading of a heterogeneous medium whereby random variables of strain, strain-rate and temperature are considered. A demonstrative mesoscale simulation of a non-ideal explosive is discussed that illustrates the joint statistical nature of the strain and temperature fields during shock loading to motivate the probabilistic approach. This modelling is derived in a Lagrangian framework that can be incorporated in continuum-level shock physics analysis. Future work will consider particle-based methods for a numerical implementation of this modelling approach.

Random Heat Temperature Field Model Analysis on Buried Pipe of Ground Source Heat Pump

The random properties on buried pipe of ground-source heat pump (GSHP) is analyzed, the equation of Kelvin one-dimensional line source of heat transfer model is discussed. The model randomness is analyzed also, and the GSHP buried pipe to random excess temperature field, space-time statistics and the correlation of features are studied. The engineering example shows that heat transfer in buried pipe has relationship with the distance from the pipe center and run time of the system, and also the heat transfer between buried pipes can not be ignored. The method in this paper has great significance for improving the reliability design theory and reducing the construction cost of GSHP buried pipe in this paper.

One‐dimensional disordered magnetic Ising systems: A new approach

AbstractWe reconsider the problem of a one‐dimensional Ising model with an arbitrary nearest‐neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest‐neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of δ‐function potentials.