On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds

We develop tight bounds and a fast parallel algorithm to compute the Markov renewal kernel. Knowledge of the kernel allows us to solve Markov renewal equations numerically to study non-steady state behavior in a finite state Markov renewal process. Computational error and numerical stability for computing the bounds in parallel are discussed using well-known results from numerical analysis. We use our algorithm and computed bounds to study the expected number of departures as a function of time for a two node overflow queueing network.     

深度卷积网络的多品种多厂商药品近红外光谱分类

近红外光谱（NIR）分析具有分析高效、样品无损、环境无污染以及可现场检测等优点,特别适合药品的快速建模分析。但NIR存在吸收强度弱以及谱带重叠等缺点,需要建立稳健可靠的化学计量学模型对其进行分析。深度卷积神经网络是深度学习方法中一个重要分支,它通过逐层抽取数据特征并进行组合、转换,形成更高层的语义特征,具有极强的建模能力,广泛应用于计算机视觉、语音识别等领域,而在药品NIR分析方面尚未见报道。基于深度卷积网络模型,对药品NIR多分类建模进行研究。针对药品NIR数据的特点,设计若干个面向多品种、多厂商药品NIR分类的一维深度卷积网络模型。模型中卷积层和池化层交叠排列用于逐层抽取NIR数据特征,输出层连接softmax分类器,对药品NIR数据进行分类概率预测。在输出层之前采用全局最大池化层,将特征图进行整体池化,形成一个特征点,用于解决全连接层存在的限制输入维度大小,参数过多的问题。同时,在网络模型中引入批处理操作和dropout机制,以防止梯度消失和减小网络过拟合的风险。在网络模型的设计过程中,通过设计不同的卷积网络层数以及不同的卷积核尺寸大小,分析其对建模效果的影响,同时分析五种经典数据预处理方法对NIR分析的影响。以我国7个厂商生产的头孢克肟片和11个厂商生产的苯妥英钠片样本NIR为实验对象, 建立药品的多品种、多厂商分类模型,该模型在二分类、多分类实验中取得了良好的分类效果。在十八分类实验中,当训练集与测试集比例为7∶3时,分类准确率为99.37±0.45,比SVM, BP, AE和ELM算法取得更优的分类性能。同时,深度卷积神经网络模型推理速度较快,优于SVM和ELM算法,但训练速度慢于二者。大量实验结果表明,深度卷积神经网络可对多品种、多厂商药品NIR数据准确、可靠地判别分类,且模型具有良好的鲁棒性和可扩展性。该方法也可推广到烟草、石化等其他领域的NIR数据分类应用中。     

Calculation of the reactor neutron time of flight spectrum by convolution technique

It is a very complex and time-consuming process to simulate the nuclear reactor neutron spectrum from the reactor core to the export channel by applying a Monte Carlo program. This paper presents a new method to calculate the neutron spectrum by using the convolution technique which considers the channel transportation as a linear system and the transportation scattering as the response function. It also applies Monte Carlo Neutron and Photon Transport Code （MCNP） to simulate the response function numerically. With the application of convolution technique to calculate the spectrum distribution from the core to the channel, the process is then much more convenient only with the simple numerical integral numeration. This saves computer time and reduces some trouble in re-writing of the MCNP program.     

卷积型加权残值法求解薄壳的动力学问题

板壳等弹性体,受到动荷载作用时,其动力分析问题是比较重要且难于解决的．利用卷积型加权残值法,推导出Gurtin变分原理,并应用卷积型加权残值法计算了薄壳的动力学问题,为计算薄壳的结构动力学问题提供了一种有效的方法．     

An Improved Temporal Fusion Transformers Model for Predicting Supply Air Temperature in High-Speed Railway Carriages

A key element for reducing energy consumption and improving thermal comfort on high-speed rail is controlling air-conditioning temperature. Accurate prediction of air supply temperature is aimed at improving control effects. Existing studies of supply air temperature prediction models are interdisciplinary, involving heat transfer science and computer science, where the problem is defined as time-series prediction. However, the model is widely accepted as a complex model that is nonlinear and dynamic. That makes it difficult for existing statistical and deep learning methods, e.g., autoregressive integrated moving average model (ARIMA), convolutional neural network (CNN), and long short-term memory network (LSTM), to fully capture the interaction between these variables and provide accurate prediction results. Recent studies have shown the potential of the Transformer to increase the prediction capacity. This paper offers an improved temporal fusion transformers (TFT) prediction model for supply air temperature in high-speed train carriages to tackle these challenges, with two improvements: (i) Double-convolutional residual encoder structure based on dilated causal convolution; (ii) Spatio-temporal double-gated structure based on Gated Linear Units. Moreover, this study designs a loss function suitable for general long sequence time-series forecast tasks for temperature forecasting. Empirical simulations using a high-speed rail air-conditioning operation dataset at a specific location in China show that the temperature prediction of the two units using the improved TFT model improves the MAPE by 21.70% and 11.73%, respectively the original model. Furthermore, experiments demonstrate that the model effectively outperforms seven popular methods on time series computing tasks, and the attention of the prediction problem in the time dimension is analyzed.     

加权Herz型Hardy空间上的强奇异积分算子

本文证明了当α＝ｎ１－１ｑ时，强奇异积分算子是从齐次加权Ｈｅｒｚ型Ｈａｒｄｙ空间ＨＫα，ｐｑ（ｗ１；ｗ２）到齐次加权Ｈｅｒｚ空间Ｋα，ｐｑ（ｗ１；ｗ２）上的有界算子．而且，该算子在非齐次加权Ｈｅｒｚ型Ｈａｒｄｙ空间ＨＫα，ｐｑ（ｗ１；ｗ２）上的有界性也被考查．     

Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods

This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.     

球面卷积算子的饱和阶

本文给出了确定球面卷积算子饱和阶的一般方法并举例说明了它的应用．