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Gross domestic product (GDP) is an important indicator to measure a country's economic development. If the future development trend of a country's GDP can be accurately predicted, it will have a positive effect on the formulation and implementation of the country's future economic development policies. In order to explore the future development trend of China's GDP, the purpose of this paper is to establish a new grey forecasting model with time power term to forecast GDP.

Firstly, the shortcomings of the traditional grey prediction model with time power term are found out through analysis, and then the generalized grey prediction model with time power term is established (abbreviated as PTGM (1,1, α) model). Secondly, the PTGM (1,1, α) model is improved by linear interpolation method, and the optimized PTGM (1,1, α) model is established (abbreviated as OPTGM (1,1, α) model), and the parameters of the OPTGM (1,1, α) model are solved by the quantum genetic algorithm. Thirdly, the advantage of the OPTGM (1,1, α) model over the traditional grey models is illustrated by two real cases. Finally the OPTGM (1,1, α) model is used to predict China's GDP from 2020 to 2029.

The OPTGM (1,1, α) model is more suitable for predicting China's GDP than other grey prediction models.

A new grey prediction model with time power term is proposed.

The optimal material microstructures in pure material design are no longer efficient or optimal when accounting macroscopic structure performance with specific boundary conditions. Therefore, it is important to provide a novel multiscale topology optimization framework to tailor the topology of structure and the material to achieve specific applications. In comparison with porous materials, composites consisting of two or more phase materials are more attractive and advantageous from the perspective of engineering application. This paper aims to provide a novel concurrent topological design of structures and microscopic materials for thermal conductivity involving multi-material topology optimization (material distribution) at the lower scale.

In this work, the effective thermal conductivity properties of microscopic three or more phase materials are obtained via homogenization theory, which serves as a bridge of the macrostructure and the periodic material microstructures. The optimization problem, including the topological design of macrostructures and inverse homogenization of microscopic materials, are solved by bi-directional evolutionary structure optimization method.

As a result, the presented framework shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid macrostructures and material microstructures are obtained in terms of optimal thermal conductive path, which verify the effectiveness of the proposed mutliscale topology optimization method. Numerical examples adequately consider effects of initial guesses of the representative unit cell and of the volume constraints of adopted base materials at the microscopic scale on the final design. The resultant structures at both the scales with clear and distinctive boundary between different phases, making the manufacturing straightforward.

This paper presents a novel multiscale concurrent topology optimization method for structures and the underlying multi-phase materials for thermal conductivity. The authors have carried out the concurrent multi-phase topology optimization for both 2D and 3D cases, which makes this work distinguished from existing references. In addition, some interesting and efficient multi-phase material microstructures and macrostructures have been obtained in terms of optimal thermal conductive path.

The purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.

This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.

An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.

The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.

A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Accurate prediction of port cargo throughput within Free Trade Zones (FTZs) can optimize resource allocation, reduce environmental pollution, enhance economic benefits and promote sustainable transportation development.

This paper introduces a novel self-adaptive grey multivariate prediction modeling framework (FARDCGM(1,N)) to forecast port cargo throughput in China, addressing the challenges posed by mutations and time lag characteristics of time series data. The model explores policy-driven mechanisms and autoregressive time lag terms, incorporating policy dummy variables to capture deviations in system development trends. The inclusion of autoregressive time lag terms enhances the model’s ability to describe the evolving system complexity. Additionally, the fractional-order accumulative generation operation effectively captures data features, while the Grey Wolf Optimization algorithm determines optimal nonlinear parameters, enhancing the model’s robustness.

Verification using port cargo throughput forecasts for FTZs in Shanghai, Guangdong and Zhejiang provinces demonstrates the FARDCGM(1,N) model’s remarkable accuracy and stability. This innovative model proves to be an excellent forecasting tool for systematically analyzing port cargo throughput under external interventions and time lag effects.

A novel self-adaptive grey multivariate modeling framework, FARDCGM(1,N), is introduced for accurately predicting port cargo throughput, considering policy-driven impacts and autoregressive time-lag effects. The model incorporates the GWO algorithm for optimal parameter selection, enhancing adaptability to sudden changes. It explores the dual role of policy variables in influencing system trends and the impact of time lag on dynamic response rates, improving the model’s complexity handling.

The purpose of this study is to make a prediction of the R&D output of China from the perspective of R&D institutions and put forward a set of policy recommendations for further development of the science and technology in China.

In this paper, an improved discrete grey multivariable model is proposed, which takes both the interaction effects and the accumulative effects into account. As the current research on China's R&D activities is generally based on the perspective of universities or industrial enterprises above designated size while few studies put their focus on R&D institutions, this paper applies the proposed model to carry out an empirical analysis based on the data of China's R&D institutions from 2009 to 2019. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of the R&D output in China's R&D institutions is conducted into a future horizon from 2020 to 2023 by using the model.

The results indicate that China's R&D institutions have a good development trend and broad prospects, which is closely related to China's long-term investment in science and technology. Additionally, the R&D inputs of China possess obvious interaction effects and accumulative effects.

The paper considers the interaction effects and the accumulative effects of R&D inputs simultaneously and proposes an improved discrete grey multivariable model, which fills the gap in previous studies.

The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X², G², GM², and NM² in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart.

The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two‐sided control limits were obtained using percentile estimates of the empirical distribution of the averages of the demerit.

The demerit control chart of the weight set (1, 25, 50) shows a generally good performance, robust to direction of out‐of‐control, mostly outperforms the GM² and is recommended. The X², NM² are not recommended in view of inconsistency and bias. The performance of the demerit control chart of the weight set (1, 25, 50) does not dramatically change between both directions.

None of the multivariate control charts for counts presented in the literature deals with trinomial distribution representing the practical index of the quality of the production/process in which the classification of production outputs into three categories of “good”, “defective”, and “reworked” is common. The demerit‐based control chart presented here can be applied directly to this situation.

The research considers how to deal with the trinomial distribution with dip null hypothesis which no research study so far has presented. The study shows that the classical Pearson's X², Loglikelihood, modified Loglikelihood, and Neyman modified X² could fail to detect an “out‐of‐control”. This research provides an alternative control chart methodology based on demerit value with recommended weight set (1, 25, 50) for use in general.

In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm.

The presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy.

As a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself.

This paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance of the used algorithm. In addition, some new and interesting material microstructural topologies have been obtained to provide wider possible solutions to the material design.

The purpose of this paper is to introduce an evolutionary heuristic method for simultaneous optimization of topology and material property distribution of functionally graded (FG) structures under a prescribed loading condition.

The proposed procedure is inspired by heuristic nature of bi-directional evolutionary structural optimization (BESO) and genetic algorithm (GA). The optimization algorithm is developed in the context of minimum compliance (maximum stiffness) design problem. The problem is modeled by means of finite element method (FEM). The element-wise material volume fractions and elements’ status (i.e. existence or nonexistence in FE model) are introduced as design variables. After FE analysis, sensitivities are obtain and filtered according to BESO. Having determined sensitivities, by means of a heuristic scheme combined by GA, topology and material property distribution for the next cycle of optimization are determined by updating design variables.

The adopted method has been tested by means of several examples previously reported in literature. The comparison showed the superiority of the proposed method against its rival in terms of relative reduction in compliance, smoother material property distribution and computational cost.

The value of the described method lies in its simple (yet efficient) nature. In contrast with its only rival in literature which more relied on mathematical approach, proposed method uses a series of logic-based heuristic ideas to drive reasonable solutions but with far less computational cost.

Given that the use of Google Trends data is helpful to improve forecasting performance, this study aims to investigate whether the precision of forecast combination can benefit from the use of Google Trends Web search index along with the encompassing set.

Grey prediction models generate single-model forecasts, while Google Trends index serves as an explanatory variable for multivariate models. Then, three combination sets, including sets of univariate models (CUGM), all constituents (CAGM) and constituents that survive the forecast encompassing tests (CSET), are generated. Finally, commonly used combination methods combine the individual forecasts for each combination set.

The tourism volumes of four frequently searched-for cities in Taiwan are used to evaluate the accuracy of three combination sets. The encompassing tests show that multivariate grey models play a role to be reckoned with in forecast combinations. Furthermore, the empirical results indicate the usefulness of Google Trends index and encompassing tests for linear combination methods because linear combination methods coupled with CSET outperformed that coupled with CAGM and CUGM.

With Google Trends Web search index, the tourism sector may benefit from the use of linear combinations of constituents that survive encompassing tests to formulate business strategies for tourist destinations. A good forecasting practice by estimating ex ante forecasts post-COVID-19 can be further provided by scenario forecasting.

To improve the accuracy of combination forecasting, this research verifies the correlation between Google Trends index and combined forecasts in tourism along with encompassing tests.

過去的研究顯示 Google 搜尋趨勢資料有助於改善旅遊需求預測的準確度，本研究就此進一步探討 Google 搜尋趨勢網頁搜尋指標與涵蓋性檢定的使用對於組合預測準確度所造成的影響。

本研究以 Google 搜尋趨勢指標做為多變量灰色預測模式的解釋變數，並以單變量與多變量灰色模式產生各別預測值。在分別產生由所有的單變量模式 (CUGM)所有的模式 (CAGM), 以及經過涵蓋性檢定所留存下來之模式 (CSET) 所組成之集合後，就各別的組合集以常用的組合方法產生預測值。

以台灣的四個熱搜旅遊城市的旅遊人數進行三個組合集的預測準確度分析。涵蓋性檢定顯示多變量灰色模式在組合預測中扮演重要的角色，而結果亦呈現線性組合方法在 CSET優於在 CUGM 與 CAGM 的準確度，突顯搜尋趨勢指標與涵蓋性檢定對於線性組合方法的有用性。

藉由 Google 搜尋趨勢網頁搜尋指標與涵蓋性檢定，旅遊部門應可透過線性組合方法的預測規劃旅遊目的地的經營策略。新冠疫情下於各季的事前預測亦可結合情境預測具體呈現。

為提升組合預測在旅遊需求的預測準確度，本研究結合涵蓋性檢定以分析 Google 搜尋趨勢指標與組合預測準確度之間的關聯性。

旅遊需求,涵蓋性檢定,Google 搜尋趨勢,灰色預測,組合預測

研究型论文

Dado que el uso de los datos de Google Trends es útil para mejorar la precisión de las predicciones, este estudio examina si el uso del índice de búsqueda web de Google Trends combinado con la agregación de relevancia puede mejorar la precisión del predictor.

El modelo predictivo gris genera predicciones bajo un único modelo, mientras que el modelomultivariado utiliza el indicador Google Trends como variable explicativa. Se generaron tresensamblajes generales, incluido el Modelo armónico único (CUGM), los ensamblajes de todos loscomponentes (CAGM) y la prueba de presencia de componentes con predicción (CSET). Laspredicciones individuales encada grupo luego se combinan utilizando métodos de correlación deuso común.

Utilizando el número de turistas en las cuatro ciudades más investigadas de Taiwán, los tresgrupos combinados se clasificaron según su precisión. Las pruebas incluidas muestran que losmodelos multivariados en escala de grises son importantes para la predicción. Además, losresultados de las pruebas muestran que el índice de Google Trends y las pruebas que incluyenmétodos de suma lineal son útiles porque los métodos combinados con CSET funcionan majorque los métodos combinados con CSET. CAGM y VCUG.

La industria de viajes puede usar el índice de búsqueda web de Google Trends para desarrollarestrategias comerciales para atracciones basadas en un conjunto lineal de componentes.

Con el objetivo de mejorar la precisión de los pronósticos agregados, este estudio investiga larelación entre el índice de tendencias de Google y las expectativas generales de viaje junto con laevidencia global.

Demanda de viajes, Experiencia global, Tendencias de Google, Predicción gris

Trabajo de investigación