Stochastic Analysis Method Research Articles

Investigations on the influence of prestressed concrete creep on train-track-bridge system

In response to long-term operation of prestressed concrete railway bridges, the girder body will arch because of creep, which may influence the running stability of high-speed trains. Usually, the deformation of the rail-bridge system under the creep effect is calculated by a finite element model with the rail geometry deformation input as additional irregularity. The original irregularity is superimposed to the coupled system of the train and bridge to calculate the dynamic response of the system. However, such a strategy is time-consuming and cannot accurately integrate the uncertainty of the original rail irregularity. This paper presents an analytical formula for predicting the rail deformation caused by concrete creep. The rail deformation caused by the bridge upper arch can be quickly predicted by the creep amplitude of the bridge. The creep deformation of the rail is applied as an irregularity excitation to the train-track-bridge coupled system (TTBCS). In addition to creep irregularities, original random irregularities also exist on the track. The Karhunen-Loéve expansion method is adopted to represent the random track irregularity that considers creep deformation. The results achieve good agreement with the initial samples. Subsequently, the TTBCS model is established to analyze the dynamic responses of different train speeds and different bridge creep deformations using a stochastic dynamic analysis method. This method achieves very high agreement with the Monte Carlo method, and the error rate of the mean bridge displacement calculated by both methods under the same working conditions was only 0.0351%. Finally, the upper probability limit value of the creep of the bridge is put forward: at a speed of a high-speed train of 350 km/h, the creep upper arch limit is only 7 mm. These probability limits at different train speeds have guiding significance for the design, maintenance, and repair of the actual medium–high-speed railway concrete supported beam bridge.

Performance evaluation of wind power industry chain based on three-stage DEA

With the development of the economy and society, the problems of resources and the environment are becoming more and more prominent. As an environmentally friendly and clean energy, wind energy is developing rapidly with the support of relevant policies and technologies. At the same time, the development of the wind power industry is also faced with some problems, as the “abandoning wind” phenomenon of wind farms is still relatively common; the continuous decline of wind turbine prices and the sharp rise in operation and maintenance costs have further reduced the profit space of wind power manufacturers. The fundamental reason for the series of difficulties in the development of the wind power industry is the imbalance between the various links in the wind power industry chain. There is an urgent need to evaluate the performance of the wind power industry chain to improve the weak links. In this paper, by using the three-stage data envelopment analysis (DEA) model, the input-oriented BCC model is used in the first stage, and the stochastic Frontier analysis method is used to analyze the input relaxation variables in the second stage to eliminate two exogenous factors. In the third stage, the adjusted input variables are recalculated in the first stage, and the chain performance value of the wind power industry excluding environmental factors and random errors is obtained in the performance evaluation. This paper takes China's wind power industry as an example and makes an overall analysis of the upstream, middle, and downstream of the wind power industry chain from three aspects: technology performance, scale performance, and pure technology performance. The results show that under the support of policy and economy, the technical performance of the upper and lower reaches of China's wind power industry chain is higher, while the performance of the wind power industry chain is underestimated by environmental factors. The three-stage DEA model can eliminate the influence of environmental and random errors, which makes the evaluation of the wind power industry chain more objective. In addition, according to the evaluation results, the optimization direction of each structure of the industrial chain is put forward.

Formula omitted] estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays

This article is devoted to the H∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ’s formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.

A stochastic analysis method of transient responses using harmonic wavelets, Part 1: Time-invariant structural systems

The transient response components have significant impacts on the stochastic response analysis of structural systems subjected to nonstationary stochastic excitations. However, available stochastic analysis methods focus on the steady-state response components. This paper proposes a novel stochastic analysis method of the transient responses for multi-degree-of-freedom (MDOF) structural systems subjected to nonstationary stochastic excitations based on periodic generalized harmonic wavelets (GHW). Firstly, the importance of transient response components on structural systems is discussed in detail. The equations of motion of the MDOF structural systems are established by using the periodic GHW with considering the rigid displacement components. The linear algebraic equations with respect to the wavelet coefficients of responses and excitations are established, respectively. Then the connection equations of wavelet coefficients in all scales are established to include the transient components in the responses. A stochastic analysis method of transient responses for structural systems is proposed based on the periodic GHW, and the time-varying power spectral density functions of the structural responses are obtained in a semi-analytical form. The proposed method is validated by two numerical examples, which illustrate the high efficiency and high accuracy of the novel method.

Stability Analysis of Semi-Markov Jump Stochastic Nonlinear Systems

This paper is concerned with the problem of exponential stability for semi-Markov jump stochastic nonlinear systems. It is well known that the semi-Markov chain is an extension of the Markov chain, whose sojourn time distribution depends on the current and next state, and is no longer limited to the exponential distribution. However, in existing works, the independence and the distribution function limitation are imposed on the sojourn time of semi-Markov jump systems. In this paper, by developing a new stochastic analysis method, the problem of exponential stability is investigated for semi- Markov jump stochastic nonlinear systems without additional constraints for the sojourn time. In addition, mode-dependent linear comparable relationships are assumed among Lyapunov like functions, which can effectively reduce the conservatism caused by mode-independent case. Two examples are presented to demonstrate the effectiveness of the proposed results.

Stochastic analysis and invariant subspace method for handling option pricing with numerical simulation

‎ In this paper option pricing is given via stochastic analysis and invariant subspace method. Finally numerical solutions is driven and shown via diagram. The considered model is one of the most well known non-linear time series model in which the switching mechanism is controlled by an unobservable state variable that follows a first-order Markov chain. Some analytical solutions for option pricing are given under our considered model. Then numerical solutions are presented via finite difference method.

Hesitant Fuzzy-Stochastic Data Envelopment Analysis (HF-SDEA) Model for Benchmarking

The Data Envelopment Analysis (DEA) method is a method commonly used in benchmarking. The Dynamic Data Envelopment Analysis (DDEA) method was proposed to improve the DEA method in the benchmarking process. The DDEA method proposed can determine the effectiveness of the Decision Making Unit (DMU). The disadvantage of the DDEA model is that it cannot handle problems that involve benchmarking for stochastic data. To improve the DDEA method, the Stochastic Data Envelopment Analysis (SDEA) method is proposed which can be used for benchmarking involving stochastic data. The SDEA method itself has weaknesses in dealing with noise and uncertainty problems that will appear in the assessment process. The purpose of the research conducted by the researcher was to use the Hesitant Fuzzy method in optimizing the SDEA method so that the Hesitant Fuzzy model - Stochastic Data Envelopment Analysis (HF-SDEA) could be carried out benchmarking process in a situation where the assessment contained many elements of uncertainty. The results of this study are benchmarking methods that can do benchmarking for stochastic data on conditions that contain elements of uncertainty.

Determinants of nonperforming loans after recapitalization in the Nigerian banking industry: Does efficiency matter?

We examine the intertemporal relationship between nonperforming loans, efficiency and bank recapitalization in the Nigerian banking industry between 2011 and 2018. Using system generalized method of moments (SGMM) and stochastic frontier analysis (SFA), we document the importance of bank efficiency for addressing escalating nonperforming loans in the industry after recapitalization policies and the channels pass‐through between efficiency and the nonperforming loans‐recapitalization nexus. Our results validate the roles of firm‐level and macroeconomic variables: bank size, efficiency, profitability, capitalization, economic growth, inflation, and money supply for addressing nonperforming loans. Also, efficiency passes through recapitalization and bank size to address nonperforming loans. We recommend prudential policies for managerial and profit efficiency and lend supports for CBN's new round of recapitalization policy to address escalating nonperforming loans in the industry.

Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations

In this paper, we propose a novel group decision making (GDM) method with probabilistic hesitant fuzzy preference relations (PHFPRs) based on the modified probability calculation method and data envelopment analysis (DEA) cross-efficiency. The primary advantage of the method is that it can reduce information loss and ensure the reliability of the decision-making result. A modified probability calculation method for hesitant fuzzy preference relations (HFPRs) is first proposed to obtain complete and normalized PHFPRs. Then, for the consistent additive preference relation (APR), we construct an output-oriented DEA model to derive the priority vector, in which each alternative is regarded as a decision-making unit (DMU). A DEA cross-efficiency model is further proposed to yield the priority vector, irrespective of whether the desired consistency level is achieved. Furthermore, a stochastic analysis method is developed to obtain the expected priority vector for any PHFPR, and a mathematical programming model is established to obtain the weight vector of decision makers based on group consensus. Finally, the procedure of the GDM method based on the modified probability calculation and the DEA cross-efficiency is designed. We also show the applicability and effectiveness of the proposed GDM method using illustrative examples.

Uncertainties of thermal boundaries and soil properties on permafrost table of frozen ground in Qinghai-Tibet Plateau

In the permafrost regions of the Qinghai-Tibet Plateau (QTP), the permafrost table has a significant effect on the stability of geotechnical engineering. The thermal boundaries and soil properties are the key factors affecting the permafrost table. Complex geological environments and human activities can lead to the uncertainties of thermal boundaries and soil properties. In this paper, an array of field experiments and Monte Carlo (MC) simulations of thermal boundaries and soil properties are carried out. The coefficient of variation (COV), scale of fluctuation (SOF), and autocorrelation distance (ACD) of uncertainties of thermal boundaries and soil properties are investigated. A stochastic analysis method of the probabilistic permafrost table is then proposed, and the statistical properties of permafrost table on the QTP are computed by self-compiled program. The proposed stochastic analysis method is verified with the calculated and measured temperature observations. According to the relationship between ACD and SOF for the five theoretical autocorrelation functions (ACFs), the effects of ACF, COV, and ACD of soil properties and the COV of thermal boundaries on the permafrost tables are analyzed. The results show that the effects of different ACFs of soil properties on the standard deviation (SD) of permafrost table depth are not obvious. The SD of permafrost table depth increases with time, and the larger the COVs of thermal boundaries and soil properties, the deeper the SD of permafrost table; the longer the ACD of soil properties, the shallower the SD of permafrost table. This study can provide a reference for the stability analysis of geotechnical engineering on the QTP considering the uncertainties of thermal boundaries and soil properties.

Оценки эффективности деятельности предприятий промышленной отрасли

Objective: To evaluate the efficiency of Russian industrial enterprises based on the stochastic method using financial indicators for 2017-2018. Method: the parametric SFA (Stochastic Frontier Analysis) method based on a stochastic model of the production function is used to assess the efficiency of enterprises. In order to achieve more accurate results, a modification of this method was performed. And also with the help of the developed modified SFA method, the bankruptcy of industrial enterprises of the Russian Federation was predicted on the basis of selected significant financial indicators. 35 bankrupt enterprises and 35 operating enterprises of the same industry were analyzed. Results: As a result of the work done using open sources, you can see how the efficiency of different enterprises in the same industry changes over several years. Conclusion: This study suggests the ability to use the Stochastic Frontier Analysis method and its modification on the studied data in the process of monitoring the dynamics of the efficiency of enterprises both bankrupt and operating. Such an assessment of efficiency can be recommended to other sectors of the economy.

Spatial-temporal characteristics of industrial land use efficiency in provincial China based on a stochastic frontier production function approach

Improving industrial land use efficiency is of great significance for sustainable industrial development. This paper measures the industrial land use efficiency (ILUE) in China, and explores its spatial-temporal characteristics and influencing factors by using a stochastic frontier analysis (SFA) method. A translog SFA model that characterizes the relationship between industrial land productivity and land input level is established to estimate the efficiency. The estimation results of the SFA model and related tests both show that the stochastic frontier method for ILUE measurement is suitable, and the contribution rate of technical inefficiency term to the mixed error reaches 66.9%. ILUE levels in China show an increasing trend from 2004 to 2017. The average efficiency in the east is the highest. ILUE in the west gradually surpassed that in the northeast in recent years. Reduction of the inter-group difference greatly contributed to the decrease in overall difference, but it is still the main source of overall difference. Results of the inefficiency function show that enterprise ownership structure produces negative impact on ILUE. The specialization of high-tech manufacturing industry, urbanization level and transportation condition have positive influence on ILUE, while the specialization of the chemical and rubber industry and the local financial pressure exert negative effects. Based on these, some policy recommendations for ILUE improvement are further proposed.

A robust ranking of maritime connectivity: revisiting UNCTAD’s liner shipping connectivity index (LSCI)

Maritime connectivity is becoming increasingly important due to its inextricable relation to maritime trade, especially in the global economy. This paper presents a robust framework to rank countries on their maritime connectivity. Typically, in most index creation models, the arithmetic mean is used to build a composite index. In this paper, we propose a more reliable ranking approach, by applying the method of stochastic multicriteria acceptability analysis (SMAA). In this, we take into account the variability in the weights assigned to the connectivity factors, thus producing a probabilistic ranking for each country (i.e., the probability to achieve a certain rank). UNCTAD’s ranking, based simply on the arithmetic mean, where all the weights are equal, becomes a special case of our approach. Our results show that China achieves the highest level of connectivity, followed by Singapore.

Can Existing Theories Explain China’s Outward Foreign Direct Investment in Belt and Road Countries

This study examines the extent to which existing foreign direct investment (FDI) theories apply to Chinese investment in the Belt and Road Initiative (BRI) countries. This is important because existing explanations of Chinese outward FDI (OFDI) generally make scant reference to these theories. By using OFDI data for BRI countries between 2003 and 2017, we tested hypothesizes applicable to existing theories by using both pooled ordinary least squares (PLOS) and stochastic frontier analysis (SFA) methods. The results show that a large part of the existing theories apply to Chinese OFDI. Chinese OFDI is likely to choose countries with big market size, abundant natural resources, cheap unskilled labor, stable politics, good infrastructure, high trade cost and high investment cost. These positive findings notwithstanding, they do not invalidate the alternative factors cited by commentators which have not been subject to direct testing, which may require the use of qualitative analytical approaches.

Stabilization of Aperiodic Sampled-Data Boolean Control Networks: A Delay Approach

In this article, a novel method for the global stochastic stability analysis of aperiodic sampled-data Boolean control networks (BCNs) is introduced. In our article, the sampling instants of aperiodic sampled-data control (ASDC) are uncertain and only the activation frequencies of the sampling interval are known. Using the semitensor product of matrices, a BCN under ASDC can be transformed into a Boolean network (BN) with stochastic delays. Specifically, the ASDC is represented as a delayed control. Here, the time-varying delay is a random variable generated by a Markov chain and its transition probability matrix can be obtained by the activation frequencies of the sampling interval. Notably, the value of the time-varying delay is less than the upper bound of the sampling interval and when its present value is given, there are only two possible values that can be taken at the next moment. Subsequently, by using the Lyapunov function and augmented method, a sufficient condition for the global stochastic stability of BCNs under ASDC is provided. In particular, the aforementioned results are applicable to the sampled-data control with constant sampling interval. Finally, a numerical example is presented to demonstrate our results.

Drivers and Policy Choices of Industrial Total-Factor Coal Productivity: Evidence From Eastern China

Identifying the critical factors of industrial total-factor coal productivity (TCP) and its promotion paths will help achieve the goals of regional energy conservation and pollution reduction. Based on the perspective of total-factor productivity, this paper integrates the methods of stochastic frontier analysis (SFA), Kaya identity, and STIRPAT model to systematically diagnose the temporal and spatial characteristics and the heterogeneous sources of the industrial TCP in 11 provinces of eastern China, and it proposes some differentiated regulatory policies for different provinces. The results show that the TCP is increasing year by year and tends to converge, which indicates that increasing TCP is more and more challenging. Further research shows that there are significant spatial differences in the impact of the economic development level (EDL), industrial economic structure (IES), energy consumption intensity (ECI), and energy consumption structure (ECS) on industrial TCP. As the original driving factors of technological progress, the impact of R&D investment intensity (RII) and R&D investment levels (RIL) on industrial TCP is relatively consistent in different regions. The former has a negative congestion effect on TCP due to the imbalance of R&D investment structure, while the latter has a positive effect on TCP. Therefore, the eastern region should increase R&D expenditure and optimize R&D expenditure structure as a general way to improve TCP in each region and adopt differentiated regulatory policies in economic development and energy utilization according to local conditions.

Accounting for correlational structures in stochastic comparative life cycle assessments through copula modeling

The presence of correlations between input parameters in a life cycle assessment (LCA) is a well-known issue. On top of that, the univariate distribution of environmental indicators, in most cases, does not follow the Gaussian nor the lognormal distribution. In this article, we introduce the copula modeling to build joint multivariate sampling spaces, irrespective of the marginal distributions of the environmental indicators, for LCA uncertainty analyses. To exemplify the proposed method, we integrate the copula modeling to the stochastic multiattribute analysis (SMAA) method to perform the normalization and weighting steps in a comparative agricultural LCA. An attributional LCA was performed to compare the environmental impact of two tomato production systems (GH, greenhouse; OF, open field) with different intensification levels. To choose the best environmental performance system, we implemented the outranking procedure of the SMAA method but based on the true multivariate distribution of the environmental indicators. As required by the SMAA method, initially, we fitted skewed multivariate distributions among the environmental indicators but accounting for their correlation structure through the copula method. Afterwards, the standard SMAA procedure was followed, leading to the calculation of overall scores indicating the environmental performance of the systems under comparison. After individual LCAs were performed for each grower, the variability observed in the primary data was propagated to the environmental indicators. The marginal distributions of the environmental indicators showed a right skewed trend which were fitted to gamma, log-normal, or Weibull distributions as applicable. The application of the copula method for the environmental indicators of the GH and OF systems resulted in D-vine models consisting of 46 and 45 bivariate copulas requiring 47 parameters each, respectively. Sampling the multivariate space configured by the D-vine models and integrating it with the SMAA method indicated that the OF system is more likely to have a better environmental performance with a rank acceptability index (RAI) of 57.6% while the GH system yielded a lower RAI (42.4%). We applied a stochastic unbiased approach to compare the environmental performance of agricultural systems but recognizing the correlation structure of the indicators. The copula method introduced here can be applied to uncertainty or multicriteria decision analysis where correlation needs to be accounted for. Joining the copula and the SMAA methods to produce an unbiased preference indicator allows to evaluate scenarios in a realistic way, producing results that can easily be communicated.

Nonlinear stochastic dynamic analysis by evolutionary tail-equivalent linearization method

This study introduces the evolutionary tail-equivalent linearization method (ETELM) for nonlinear stochastic dynamic analysis. The method builds on the recently developed tail-equivalent linearization method (TELM) and it is designed for the class of evolutionary processes. The original TELM employs a tail-equivalent linear system (TELS) by equating the tail probability of a linear system response for a specified threshold to the first-order approximation of the tail probability of the nonlinear system response. For stationary problems, the TELS is time-independent and only one linear system needs to be defined for the specified threshold. However, for a transient input, the TELS is time dependent and an evolutionary tail-equivalent linear system (ETELS) must be defined to study the entire transient response. Algorithms are developed to determine a discrete-time ETELS based on a sequence of linearization points, and a continuous-time approximation based on Priestley’s evolutionary theory. The linearized evolutionary system is used to compute the response statistics of interest, including the first-passage probability, in first-order approximation. Numerical examples demonstrate the accuracy and limitations of the proposed method.

Stochastic Periodic Solution and Permanence of a Holling–Leslie Predator-Prey System with Impulsive Effects

Considering the environmental effects, a Holling–Leslie predator-prey system with impulsive and stochastic disturbance is proposed in this paper. Firstly, we prove that existence of periodic solution, the mean time boundness of variables is found by integral inequality, and we establish some sufficient conditions assuring the existencle of periodic Markovian process. Secondly, for periodic impulsive differential equation and system, it is different from previous research methods, by defining three restrictive conditions, we study the extinction and permanence in the mean of all species. Thirdly, by stochastic analysis method, we investigate the stochastic permanence of the system. Finally, some numerical simulations are given to illustrate the main results.

ℋ ∞ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61873002, 61703004, 61973199, 61573008, and 61973200).

We investigate the problem of ℋ ∞ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule, as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously. Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an ℋ ∞ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.