Study on Influencing Factors and Estimation Model of the Water Supply and Drainage Structure Cost in Substation

. Tis paper made an in-depth analysis of the articulation between a substation’s design parameters and water supply and drainage structure quantities and costs, innovatively built a hierarchical structure model of infuencing factors of quantities, and eventually extracted the key parameters afecting quantities. Meanwhile, the infuence path of the price level change on the water supply and drainage structure costs was also analyzed in this paper. Te BP neural network model and linear regression model were employed to estimate the ontology engineering cost and the price diference due to preparation time, so as to realize the purpose of quickly estimating the cost of substation water supply and drainage structure by knowing a few key parameters. Trough calculation and stimulated analysis, the error of the model is controlled within ± 3%, which provides an efective tool for quickly estimating the cost of substation water supply and drainage structure. Terefore, this model has practical signifcance and application value.


Introduction
Te water supply and drainage structure are one of the important components of the substation project. How to quickly and reasonably make accurate predictions and estimates of its cost is an urgent problem for constructors, designers, builders, and other participant units. At present, there is still a lack of an explicit model about the relationships among design parameters, price levels, and the corresponding cost. To calculate the cost of the water supply and drainage structure, it is necessary to frst calculate the detailed quantities according to the design plan and then the cost personnel calculate the project cost based on the budget regulations [1] of the power industry. Tis conventional way to calculate the cost gains low efciency, though high quality is promised, and is not suitable for the business requirement of rapidly estimating the cost.
Te cost of the water supply and drainage structure in the substation is mainly composed of four aspects, which are quantity, price, fee, and quota, and the cost's infuencing factors can also be attributed to these four aspects, i.e., quantity, price, fee charging, and quota [2]. Within the year of the adopted samples, the project quotas are subject to the unifed version of the quotas, the fee charging is implemented according to the unifed budget-making regulations, and the quotas and fee charging standards are relatively fxed. Terefore, the infuencing factors for cost changes are mainly attributed to the quantities and the price level. Te dimensions of analysis are divided into two aspects: the main quantities, such as the quantities of frefghting, water supply, and drainage, and the water source, and the price level, such as the price of equipment, main materials, labour, and machinery. Tis paper specializes in the analysis of the impact of changes in major quantities and price levels on the cost of water supply and drainage structure to achieve a rapid and reasonable estimation of the cost.
In normal times and unexpected situations such as fre, the water supply and drainage structure are supposed to safely and reliably provide sufcient water based on the users' requirements for water quality and pressure. A thorough analysis of the design parameters that afect the quantities of the water supply and drainage structure in a substation can make the infuence of the complex design parameters on the quantities more concise, thus identifying a few key parameters that have a greater impact on the quantities. Te frefghting water consumption of the main transformer is related to its voltage level and external size. Main transformers with voltage levels of 220 kV and above should adopt a water spray fre extinguishing system. Fire-fghting water spray needs to cover the external surface of the main transformer. Te larger the surface area of the main transformer is, the more water the frefghters use. Main transformers with voltage levels of 110 kV and below are not equipped with a water spray fre extinguishing system, and there is no water consumption for their frefghting.

Analysis of the Factors
Te water consumption of the building's frefghting is directly connected with the building's fre hazard. Te higher the fre hazard is, the more water it uses. For substations of the same scale, when the main transformer and power distribution devices are laid out indoors (referred to as "whole-indoor layout"), the fre hazard of buildings is the highest and the water consumption for the building's frefghting is the largest; when the main transformer is laid out outdoors and GIS is laid out indoors (referred to as "semiindoor layout"), the water consumption for building's frefghting takes the second place; when the main transformer and power distribution devices are laid out outdoors (referred to as "outdoor layout"), the fre hazard of the building is the lowest and the water consumption for frefghting is the smallest [1].
Te amount of domestic water used in a substation is directly related to the number of personnel on duty. Te higher the voltage level is, the more personnel are on duty, and the higher the domestic water consumption is.
Te diameter of frefghting and water supply pipelines is positively related to water consumption; the length of pipelines is positively related to the foor area of the substation; the foor area of the substation is associated with the substation's prospective scale and layout; and the length of the frefghting pipeline of the main transformer is positively related to the current scale of the main transformer in this period.

Quantities of Water Source.
Te quantities of the water source are highly correlated with the substation's water consumption, geographical location, and geological conditions [3]. Te water yield of the water source should satisfy the need for production water supply in the substation.
According to the substation's groundwater condition and its distance from the location of municipal water, a comprehensive judgment is made to choose the plan of digging a deep well or introducing tap water from outside.

Equipment of Water Supply and Drainage Structure.
Equipment of the water supply and drainage engineering refers to pneumatic water supply installation, deep well fre pump set, submersible sewage pump, and other equipment related to water supply and drainage structure, which is generally set up according to the prospective scale of the whole substation and is positively related to the water consumption of the prospective scale of the whole station.

Water Pump House and Firefghting
Pool. Te water pump house and frefghting pool, designed according to the prospective scale of the whole substation, are positively related to the water consumption of the prospective scale of the whole substation. Te more amount of water it uses, the larger the building volume of the water pump house and the frefghting pool is, and the larger the quantities are.

Quantities of Drainage
System. Te drainage system is divided into the indoor drainage system, an in-station drainage system, and an outside-station drainage system.
Te length of in-station drainage pipes is positively related to the foor area of the substation. Te rain inlets are arranged on both sides of the road. After being collected by rain inlets, the rainwater is discharged to the rainwater inspection wells at the lowest part of the substation through drainage pipes and continues to be discharged to the outside of the substation. Te diameter of the drainage pipes is positively related to the drainage volume, which is positively correlated with the local hydrometeorological rainstorm intensity as well as the water consumption of the substation.
Te diameter of the sewage drainage pipes is positively related to water consumption. Oil-immersed electrical equipment is equipped with the accident oil pool and oil drainage pipeline. Te diameter of the oil drainage pipeline is positively related to the accidental oil discharge amount, and the length of the oil drainage pipeline is positively correlated with the scale of oil-immersed equipment, such as the main transformer, and their distance from the accident oil pool. Te indoor drainage system is positively related to the water consumption of the building, and its quantities are small. Te quantities of the outside-station drainage system are associated with the geographical location of the substation. Te farther the suitable drainage point is from the substation and the worse the construction conditions outside the station are, the larger the quantities are.

Hierarchical Structure Model of the Factors Infuencing the
Quantities. Te factors infuencing the quantities of a substation's water supply and drainage structure have an obvious hierarchy. According to the successive logical relationship between the design parameters and the forming process of quantities [4], the infuencing factors are summarized into four layers: the overall scale layer, the technical parameters layer, the cost structure layer, and the quantities layer. Each layer has a clear logical relationship and lucid functional route, as shown in Figure 1.
Except for the water source and outside-station drainage, which are related to the substation's geological conditions and geographical location, for the quantities of in-station water supply and drainage structure, only the diameter of the substation drainage pipeline is related to the hydrology and meteorology, and the other quantities are eventually determined by four design parameters, namely the voltage level, the prospective scale, the layout, and the current scale of the main transformer. Trough the statistics of the sample data of a province in the past fve years, these four design parameters can determine 98% of the quantities of water supply and drainage structures except for the water source and outside-station drainage [3].

Analysis of the Impact of Price Level on Project Cost
Te cost of the water supply and drainage structure in the substation is composed of the ontology engineering cost and the price diference due to preparation time. Te ontology engineering cost is afected by quantities determined by the design parameters; the price diference due to preparation time, based on the ontology engineering cost, is afected by the price level [5].

Price Level of Equipment.
Te total price of equipment for water supply and drainage structures is afected by changes in its price level. However, there are few types of equipment for water supply and drainage structures in substations, and the price level of equipment is relatively stable [6]. Terefore, the total price of the equipment is greatly afected by the quantities and less afected by the changes in the equipment's unit price.

Price Level of Materials.
Quantities of water supply and drainage structures can eventually be classifed into various types of construction materials. Te price level of materials directly afects the price diference due to preparation time in the project cost, and the material price diference is the main content of the price diference due to preparation time.    Mathematical Problems in Engineering price diference of labor's man-day, while in Shandong province, it is adjusted by 9.46% and included in the price diference of labor's man-day.

Price Level of Machinery's Unit Operation.
Te market price of the main machinery's unit operation for the construction project is regularly released by the China Electric Power Project Cost Administration, and the theoretical calculation method of the mechanical price diference is the same as the material price diferences.

Network Structure's Construction and Selection.
Te construction of an estimation model of the water supply and drainage structure cost in the substation is based on the actual project data from the past three years, and its main infuencing factors [7] are explored. Each infuencing factor is taken as the input variable xi of the model. By establishing a nonlinear mathematical model between the model and the cost, the output variable y1, ontology engineering cost, is obtained. Te model is constructed by selecting the three-layer BP neural network as the predictive model. Te main factors afecting the ontology engineering cost can be obtained by analyzing the historical data, and then the number of inputlayer nodes is measured. Te main factors that have an impact on the cost of the substation's water supply and drainage structure are voltage level (x 1 ), prospective scale (x 2 ), the current scale of the main transformer (x 3 ), and layout (x 4 ). Terefore, the number of input-layer nodes is determined to be four. Te ontology engineering cost (y 1 ) is regarded as the output node, and its number of it is set to one. Usually, the number of nodes in the implicit layer between the input layer and the output layer is set as 10, 15, 20, and 25. According to the setting principles of nodes in the implicit layer of the BP neural network model, the more input and output units there are, the more hidden nodes exist. At the same time, the approximate process should be guaranteed to be complex and complete. Tere are many input units and nodes involved in this study, and their results are required to be normalized into one output unit after iterative prediction. Terefore, the number of nodes in the implicit layer is set to 25, which means the structure of the BP neural network model is 4-25-1. Te model structure is shown in Figure 2.

Data Processing and Algorithm
Training. Since the above-mentioned infuencing factors of ontology engineering cost are represented by text-structure data, they need to be preprocessed to be converted into algebraic form to participate in the input of the BP neural network. Te model chooses to process the data conversion of diferent infuencing factors' internal elements. Te specifc preprocessing principles are as follows: (i) Numbers 1, 2, and 3, respectively, represent the voltage levels of 110 kV, 220 kV, and 500 kV, and the weighted average of their proportion of the cost in the substation project is processed; (ii) Numbers 1-20, respectively, represent the combinations of the number of main transformer groups of the prospective scale and the circuit number of the high-voltage-side outgoing line. Te statistical data shows that the corresponding cost of the prospective scale of diferent combinations meets the law of normal distribution. (iii) Numbers 1, 2, and 3, respectively, represent the number of main transformer groups of the current construction scale, and the weighted average of the current scale of main transformers of diferent groups is processed. (iv) Numbers 1, 2, and 3, respectively, represent the layout modes, where the indoor mode is regarded as the base as a reference item, and the semi-indoor and outdoor modes are, respectively, determined by the scale factor.
Te model algorithm training is mainly divided into two processes: forward propagation and backward propagation. Between them, the forward propagation process is mainly used to calculate the fnal actual output after entering data and passing them through the input layer, implicit layer, and output layer, respectively. Te backward propagation process represents the deviation between the actual output and the desired output in the output layer and reversely adjusts the parameters of each layer according to the deviation value, which can fnally control the deviation within an acceptable range.
(1) Forward propagation process. In this model, the nodes of the input layer, implicit layer, and output layer are respectively set as n, d, and m, and the vector sets are expressed as  Figure 2: A network structure diagram of the model. y ∈ R m , y � y 1 . Te node calculation formulas and data transfer functions of the implicit layer and output layer are shown in the following equation: In the formulas of equations (1)-(3), W ij and b j are the weights and thresholds between the implicit layer and the input layer, respectively; W jk and b k are the weights and thresholds between the implicit layer and the output layer, respectively.
Te calculation function of the output nodes' error is shown in the following equation: In the formula (4), F k and t k are the actual output values and desired output values, respectively.
Te calculation function of total error is shown as follows: In the formula (5), p is the number of samples, and θ is the acceptable deviation.
(2) Backward propagation process. In order to better test the deviation between the actual output and the desired output, it is necessary to iterate the output weights and thresholds repeatedly and fnally obtain the correction results of both. Te deviation calculation formula and the calculation formula for the correction of weights and thresholds in each layer are shown as follows: In the formulas (6)- (9), n 0 is the number of iterations.

Algorithm Training and Deviation
Analysis. Based on the above models to train the data, the correction algorithm satisfes the gradient descent with the momentum algorithm, which can optimize the learning rate of the BP neural network. Referring to the relationship among the numbers of nodes in each layer, the maximum number of cycles of algorithm training is set to 20,000, the initial learning rate of training is set to 0.03, and the deviation value is set to 0.02. Te optimal learning rate is fnally obtained after 15,792 times. Figure 3 shows the curve of the algorithm training obtained by MATLAB simulation.
Te BP neural network is tested, and the estimation result of ontology engineering cost is obtained by denormalization of the 5 sets of predicted data. It can be seen from Table 1 that the deviation between the estimated value and the actual value is less than 8%, which is in line with the error range in the comparison and selection process in the decision-making stage. Terefore, the estimation model of ontology engineering cost of the substation's water supply and drainage structure based on the BP neural network is feasible (see Table 1).

Regression Model Construction of Price.
Tere are about 360 kinds of materials used in the water supply and drainage structure engineering, of which three types of materials, namely, concrete, steel, and pipe, account for about 85% of the total material cost. Concrete materials include concrete, medium sand, gravel, cement, bricks, etc.; steel materials include reinforcing bars, iron pieces, steel pipe, section steel, channel steel, angle steel, etc. [8]; pipe materials include reinforced concrete pipe and UPVC pipe of various pipe diameters, etc. Te concrete materials account for about 28% of the material cost, the steel materials account for about 49%, and the pipe materials account for about 8%.

Mathematical Problems in Engineering
By analyzing the material information prices from 2018 to 2022, there is a regression relationship among the prices of materials of the same kind. Te three types of materials are represented by the most used material, and other materials of the same kind establish a regression relationship with it. Concrete C30 is chosen as the representative of concrete materials, a round steel bar Φ12 is chosen as the representative of steel materials, and reinforced concrete pipe DN300 is chosen as the representative of pipe materials. Based on this, the calculation formula of the price diference due to preparation time y 2 is listed as follows: In the formula (10), p 1 i is the local current market price of the ith construction material, p 0 i is the budget price of the quota of the ith construction material, and q i is the quantity of the ith construction material.
In the formula (11), c i is the proportional coefcient of market price p 1 i and budget price of the quota p 0 i of each material; qi is the quantities of each material; p 0 i is the budget price of the quota of each material; m is the price diference coefcient of labor cost based on the ontology engineering cost; and n is the price diference coefcient of machinery one-shift cost based on the ontology engineering cost. q i can be obtained by decomposing the ontology engineering cost y 1 . Te price diference of construction machinery is generally smaller, less than 1%, and it is consistent with the changing trend of the unit price of machinery for one-shift installation. Terefore, m and n are implemented in accordance with the coefcients of labor cost and installation machinery cost of the documents issued by the China Electric Power Project Cost Administration.

Calculation of Regression Coefcient.
Te market prices of materials originate from the ofcial cost information websites that release the prices each month from 2017 to 2021, and a one-dimensional linear regression model of the prices among similar materials is constructed [9]. Because of the large variety of materials included, only representative material regression coefcients are listed in this paper.
Te calculation results of the regression coefcient of concrete materials' unit prices with the unit price of concrete C30 as the independent variable are shown in Table 2.
Te calculation results of the regression coefcient of steel materials' unit prices with the unit price of round steel bar Φ12 as the independent variable are shown in Table 3.
Te calculation results of the regression coefcient of the unit prices of pipe materials with the unit price of reinforced concrete pipe DN300 as the independent variable are shown in Table 4. It can be seen from the data in Table 4 that the simulation calculation results of the regression coefcient fuctuate greatly, which is due to the objective diferences in the infuence of materials and pipes' diameter on the simulation of the regression coefcient. Generally speaking, in the case of the same material, the larger the pipe's diameter is, the greater the regression coefcient is; in the case of a similar diameter of pipes, the regression coefcient of UPVC material is higher than that of reinforced concrete.

Simulation of Hydraulic Cost Estimation Model.
Te test of the regression model is based on the comparison and analysis of the actual data of substation projects from 110 kV to 500 kV in previous years, and the project features cover the construction scale of common substations, so as to verify the accuracy of the BP neural network, regression model, and project cost estimation results. Te simulation results of the substation water supply and drainage structure cost estimation model are shown in Table 5. After the induction and analysis of the existing data samples, the statistical mode is distributed under the voltage level of 200 kV, so more data of 220 kV are selected in the simulation link, and the experimental results can better test the prediction efect and accuracy of the model built in this study. Figure 4 shows the radar plot of the error between estimated values and actual values. From the relative error between the estimated values and actual values, it can be seen

Conclusion
By analyzing the infuence of design parameters on quantities in the substation project, this study has built a BP neural network model based on the four design parameters: the voltage level, the prospective scale, the current scale of the main transformer, and the layout, achieving a reasonable estimation of ontology engineering cost. An estimation model of price diference due to preparation time considering market price changes is also built, and the regression method is applied to measure the regression coefcient of the price of materials of the same kind, achieving a reasonable estimation of the price diference due to preparation time. Trough calculation and stimulated analysis, the model passes the test, and the error is controlled within ±3%.
Te cost estimation results are in line with the actual cost requirements, and this model solves the practical problem of rapidly estimating water supply and drainage structure costs for the participant units. On the basis of the cost model of the water supply and drainage structure, the next step of the study is to focus on the further exploration of the potential of design parameters in the rapid estimation of project cost, realizing more efcient practice and application of the cost model.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.