# A Perfect Decomposition Model for Analyzing Transportation Energy Consumption in China
## 1 Introduction  
Transportation has become one of the fastest growing energy consumption industries worldwide. Quantitative assessment of various factors affecting energy consumption is essential not only for a better understanding of past behaviors of transportation energy consumption, but also for estimating energy requirements of alternative industrialization strategies. To study the related issues of energy consumption in the transportation system, we should first clarify the composition of the transportation system. The national transportation system divides into the domestic inter-city transportation system composed of railway, highway, waterway, civil aviation, and pipeline, and the urban transportation system formed by urban road and rail transportation. Therefore, waterway transportation does not include ocean transportation. According to the nature of transportation tasks, road transportation can divide into operational transportation completed by operating vehicles, and non-operational transportation completed by non-operating vehicles. According to the different railway transportation systems undertaken, railway transportation can be divided into passenger and freight transportation completed by the national and local railway transportation systems with or without a network, and urban passenger transportation completed by the urban rail transit system. The inter-city transportation system, composed of five modes of transportation, undertakes the road transportation of operational and non-operational vehicles, the same as the transportation tasks of railway, waterway, civil aviation, and pipeline, defined as complex transportation. The transportation system is composed of the domestic inter-city transportation system, and the intra-city transportation system is a total transportation system. To facilitate the analysis and calculation andthe availability of data, the scope of the transportation system studied is the operational transportation system, which includes five modes of transportation (highway, railway, waterway, aviation, and pipeline). Decomposition methodology is an effective method dealing with energy consumption-related issues analysis. Studies can be traced back to the early 1980s. Laspeyres index decomposition was first proposed to analyze the influence factors of industrial energy consumption [1]. Many researchers subsequently applied this method to decompose the energy consumption change [2; 3; 4]. However, an important factor, called residual known as the sum of all the interactions of the main effects, was usually ignored, which caused large estimation errors. [PERSON] et al. is likely to be the first to analyze energy consumption problems using Divisia index decomposition [5; 6; 7]. The same decomposition methods were also directly applied in [PERSON] et al. [8; 9] and [PERSON] [10], where the residual was not resolved. Though [PERSON] [11; 12; 13] proposed a complete decomposition model, which disposed the residual according to the principle of \"common creation, equal distribution\", the error will become bigger when the time span of analysis is enlarged. Among Divisia index decomposition methods, two methods are widely applied: arithmetic mean Divisia index method (AMDI) [14] and logarithmic mean Divisia index decomposition method (LMDI) [15]. In the formulae of AMDI, logarithmic terms were introduced, which might lead to computational problems when zero values appear in the data set (i.e., denominator is zero). A framework for additive and multiplicative decomposition [16; 17] was extended based on the two general parametric Divisia index methods, i.e., additive and multiplicative decompositions [14]. The LMDI was proposed with the continuous development of the Divisia Decomposition [18; 19]. It is reasonable to replace arithmetic mean weight function by logarithmic mean weight function, because the latter can decompose the residual completely without generating unexplained residual. [PERSON].