CN110097223B - Early warning method for damage of power transmission line under typhoon disaster - Google Patents

Abstract

The invention provides a method for early warning damage of a power transmission line under typhoon disasters. The method comprises the steps of collecting meteorological information, equipment operation information, micro-terrain information and real-time damage information to construct a training set; information quantization, default value processing and standardization processing are carried out on the information in the training set; establishing a power transmission line damage probability hybrid prediction model based on extreme value I type probability distribution, a random forest method and a Monte Carlo method, and calculating damage probability; and calculating risk indexes according to the damage probability, and performing emergency repair after the disaster. The prediction model has stronger adaptability and higher reliability, and can reasonably estimate the needed emergency repair resources from the macroscopic view.

Description

A kind of early warning method for transmission line damage under typhoon disaster

technical field

The invention belongs to the field of power system risk assessment, and in particular relates to an early warning method for damage to power transmission lines under typhoon disasters.

Background technique

With economic development, the power infrastructure of the power grid has been continuously improved, but natural disasters will pose serious threats to power grid equipment. Among them, the threat of typhoon disasters to the power grid is the most significant, especially in coastal areas, typhoon disasters have caused serious damage to power grid facilities. Accidents such as large-scale power outages have caused a great impact on economic development and people's production and life. Therefore, there is an urgent need to establish effective early warning means.

In the past, some methods of early warning of transmission line damage did not consider the influencing factors comprehensively, such as the micro-topographic factors that have been proved to have an important impact in engineering practice; although some methods considered more comprehensive factors, the calculation methods were more complex and not suitable for large-scale Simulation calculation; some methods only use the deterministic wind speed for calculation, and fail to consider the uncertainty of the predicted wind speed, so the applicability is not strong.

It can be seen that these methods in the past have shortcomings such as insufficient data analysis considerations, insufficient applicability, and low efficiency of causal algorithms in the early warning of transmission line damage. Therefore, there is an urgent need to study a damage early warning method with comprehensive considerations, strong adaptability and high computational efficiency.

SUMMARY OF THE INVENTION

In order to solve the problems of insufficient consideration factors, weak applicability and low algorithm efficiency in the existing transmission line damage early warning method, the present invention proposes a transmission line damage early warning method under typhoon disaster.

The technical scheme of the present invention is an early warning method for the damage of power transmission lines under a typhoon disaster, which specifically comprises the following steps:

Step 1: Collect meteorological information, equipment operation information, micro-terrain information, and real-time damage information to construct a training set;

Step 2: Perform information quantification, default value processing, and standardization processing on the information in the training set;

Step 3: Establish a hybrid prediction model of transmission line damage probability based on extreme value I-type probability distribution, random forest method, and Monte Carlo method, and calculate the damage probability;

Step 4: Calculate the risk index according to the probability of damage, and carry out emergency repair after the disaster.

Preferably, the meteorological information in step 1 includes that the maximum gust is V;

The equipment operation information in step 1 includes that the operation time is T and the design wind speed is V';

The micro-topography information described in step 1 includes that the altitude is H, the slope aspect is A, the slope is S, the slope position is P, the underlying surface type is U, and the surface roughness is R;

The real-time damage information described in step 1 includes that the damage status of the equipment is Y;

The information in the training set described in step 1 is:

The maximum gust is V(m/s), the equipment running time is T(year), the design wind speed is V′(m/s), the altitude is H(m), the slope aspect is A(°), and the slope is S(°). ), the slope position is P, the underlying surface type is U, the surface roughness is R(m), and the damage state is Y; each data in the training set is a vector of length 10 composed of the above variables.

Preferably, the process of quantizing the information in the training set described in step 2 is:

Since V, T, V', H, A, S, P, U, and R are all data formats, only the information Y in the training set is quantized, and the damaged state after quantization is represented by Y*;

The default value processing for the information in the training set described in step 2 is:

The default values of V, T, V', H, A, S, P, U and R are filled with the median respectively, and the processed variables are:

After the default value processing, the maximum gust is V _f , the equipment running time after the default value processing is T _f , the design wind speed after the default value processing is V _f ′, the altitude after the default value processing is H _f , and the default value processing The slope aspect is A _f , the default value of the slope after processing is S _f , the default value of the slope position after processing is P _f , the type of the underlying surface after the default value processing is U _f , and the surface roughness after the default value processing is R _f ;

The data standardization processing on the data after the default value processing described in step 2 is as follows:

Calculate V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f respectively according to the standardized variables, and the specific formula is:

X ^* = (xx _min )/(x _max -x _min )

In the formula, x is the value of V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f in the data after the default value processing, and x _min is the default value processing The minimum value among the post-data V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f , x _max is the default value of the post-processing data V _f , T _f , V The maximum value among _f ′, H _f , A _f , S _f , P _f , U _f , and R _f , X* is the variable after normalization, namely: the maximum gust after normalization is V*, and the running time of the equipment after normalization is T* , the design wind speed after standardization is V′*, the altitude after standardization is H*, the slope aspect after standardization is A*, the slope after standardization is S*, the slope position after standardization is P*, the type of underlying surface after standardization is U*, The surface roughness after normalization is R*;

Preferably, the process based on the extreme value type I probability distribution described in step 3 is as follows:

Parameter estimation is performed on the extreme value type I probability distribution. Assuming that V _f obeys the extreme value type I probability distribution, the calculation formula of the extreme value type I probability distribution function is:

In the formula, a is the scale parameter of the distribution; u is the location parameter of the distribution, and the calculation formula of the probability density distribution function is:

The scale parameter and the location parameter can be estimated using the method of moments estimation.

The first-order moment (mathematical expectation) is calculated as:

Among them: y≈0.57722, the second-order moment (variance) calculation formula is:

The calculation formula of the scale parameter a is thus obtained:

The calculation formula of the position parameter u is:

Then the probability of occurrence of the maximum wind speed x _P that occurs once in N years is the guarantee rate, and its calculation formula is:

P(x _p )=P(V _f >x _P )=1-P(V _f ≤x _p )=1-F(x _p )

In the formula, P(x _p ) is the probability of occurrence of the maximum wind speed once in N years;

Based on the extreme value type I probability distribution, the distribution of the wind field is simulated and predicted in units of wind speed points, and the accuracy of the wind speed point can reach 1km × 1km. It is assumed that the maximum gust V _f at each gust point at different times satisfies the extreme value type I probability distribution , use V _f to calculate a and u, fit an extreme value I-type distribution for each wind speed point, and realize the simulation of wind field distribution;

The process of random forest method described in step 3 is as follows:

The input to the random forest algorithm is:

V*, V′*, T*, H*, A*, S*, P*, U*, R*;

The output is:

The probability that the damaged state is Y*=1;

The specific process of the Monte Carlo method described in step 3 is as follows:

When determined based on the extreme value I-type probability distribution, the Monte Carlo method is used to randomly extract the wind speed, and in each random wind field, assuming that the wind speed of each wind speed point is relatively independent, the distribution of the entire wind field can be simplified as Gust distribution at a single wind speed point;

M times wind speeds are randomly generated according to uniform distribution at N wind speed points, and the jth wind speed at the ith wind speed point is defined as Vi _,j , where i=1,2,...,N is the sequence of wind speed points , j=1,2,...,M is a sequence of random samples, and at the same time, the probability of occurrence of each random wind speed P (V _f =V _i,j ) is calculated by using the fitted extreme value I-type probability distribution;

The calculated damage probability described in step 3 is:

In each random wind field, the RF method is used to calculate the damage probability f of the tower ( _xi |V _f =V _i,j ), where x _i is the eigenvector at the wind speed point i, and V _f is the wind speed of x _i component, according to the Monte Carlo method, the damage probability of the tower at this wind speed point is equivalent to the average value of the M prediction results, and the calculation formula of the damage probability of the tower at each wind speed point is:

In the formula: M is the total sampling times, and Vi _,j is the wind speed generated by the jth time at the wind speed point i;

Preferably, the steps of calculating the risk index described in step 4 are as follows:

The damage probability is set to 0.5 as the threshold value, P _i >0.5 means the tower is damaged, P _i <0.5 means the tower is not damaged, and the calculation formula of the average Num of equipment damage units is:

The formula for calculating the average repair time T _Re is:

The formula for calculating the average value C of the repair cost is:

The formula for calculating the average value L of manpower requirements is:

The calculation formula of the average value V of the demand for emergency repair vehicles is:

In the formula, t is the repair time per unit of equipment; c is the repair cost per unit; m is the manpower required per unit of equipment; v is the repair cost per unit; ) is the indicator function, which is defined as follows:

The post-disaster repairs described in Step 4 are:

After obtaining the damage probability Pi of each wind speed point, at the same time, the risk indicators Num, C, L, and _V can guide the disaster prevention and mitigation department to pre-allocate equipment, expenses, personnel, and vehicle resources, and release the power outage duration warning information according to the T _Re index. .

The present invention has the following advantages:

Comprehensive consideration of meteorological information, equipment operation information, micro-topography information, traffic information, vegetation information, real-time damage information, etc., the factors considered are relatively comprehensive;

Using extreme value I-type probability distribution and Monte Carlo method to simulate the random wind field many times, considering the uncertainty of the predicted wind field, the hybrid prediction model of transmission line damage probability has stronger adaptability than using the deterministic predicted wind speed. and higher credibility;

The damage probability prediction model based on random forest method has high computational efficiency, especially suitable for large-scale prediction;

The calculation of risk indicators is based on historical statistical data and a mixed prediction model of transmission line damage probability, which can reasonably estimate the required emergency repair resources from a macro perspective.

Description of drawings

Fig. 1: method flow chart of the present invention;

Figure 2: Prediction of damage by a hybrid prediction model of damage probability in a wind farm.

Detailed ways

In order to facilitate the understanding and implementation of the present invention by those skilled in the art, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are only used to illustrate and explain the present invention, but not to limit it. this invention.

Below in conjunction with Fig. 1 to Fig. 2, the specific embodiment of the present invention is introduced, including the following steps:

Step 1, collecting meteorological information, equipment operation information, micro-topographic information, and real-time damage information to construct a training set;

The meteorological information described in the step 1 includes that the maximum gust is V, and ArcGIS10.4.1 is used to carry out inverse distance weight interpolation processing to the maximum gust V in the meteorological information, and the relevant data is extracted to the coordinate point where the equipment is located.

The equipment operation information in step 1 includes that the operation time is T and the design wind speed is V';

The micro-topographic information in step 1 includes the altitude as H, the slope aspect as A, the slope as S, the slope position as P, the underlying surface type as U, and the surface roughness as R. Distance weight interpolation processing, and extract relevant data to the coordinate point where the device is located;

The real-time damage information described in the step 1 includes that the damage state of the equipment is Y, and is provided by the remote monitoring or inspection personnel of the electric power department, and the present embodiment uses 1 to represent the tower damage state, and 0 represents the tower undamaged state;

The information in the training set described in step 1 is:

The maximum gust is V(m/s), the equipment running time is T(year), the design wind speed is V′(m/s), the altitude is H(m), the slope aspect is A(°), and the slope is S(°). ), the slope position is P, the underlying surface type is U, the surface roughness is R(m), and the damage state is Y; each data in the training set is a vector of length 10 composed of the above variables.

Step 2, performing information quantification, default value processing, and standardization processing on the information in the training set;

The process of quantifying the information in the training set described in step 2 is as follows:

Since V, T, V', H, A, S, P, U, and R are all data formats, only the information Y in the training set is quantized, and the damaged state after quantization is represented by Y*;

The default value processing for the information in the training set described in step 2 is:

The default values of V, T, V', H, A, S, P, U and R are filled with the median respectively, and the processed variables are:

After the default value processing, the maximum gust is V _f , the equipment running time after the default value processing is T _f , the design wind speed after the default value processing is V _f ′, the altitude after the default value processing is H _f , and the default value processing The slope aspect is A _f , the default value of the slope after processing is S _f , the default value of the slope position after processing is P _f , the type of the underlying surface after the default value processing is U _f , and the surface roughness after the default value processing is R _f ;

The data standardization processing on the data after the default value processing described in step 2 is as follows:

Calculate V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f respectively according to the standardized variables, and the specific formula is:

X ^* = (xx _min )/(x _max -x _min )

In the formula, x is the value of V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f in the data after the default value processing, and x _min is the default value processing The minimum value among the post-data V _f , T _f , V _f ′, H _f , A _f , S _f , P _f , U _f , and R _f , x _max is the default value of the post-processing data V _f , T _f , V The maximum value among _f ′, H _f , A _f , S _f , P _f , U _f , and R _f , X* is the variable after normalization, namely: the maximum gust after normalization is V*, and the running time of the equipment after normalization is T* , the design wind speed after standardization is V′*, the altitude after standardization is H*, the slope aspect after standardization is A*, the slope after standardization is S*, the slope position after standardization is P*, the type of underlying surface after standardization is U*, The surface roughness after normalization is R*;

Step 3, based on the extreme value I-type probability distribution, random forest method, and Monte Carlo method, establish a mixed prediction model of transmission line damage probability, and calculate the damage probability;

The process based on the extreme value type I probability distribution described in step 3 is as follows:

Parameter estimation is performed on the extreme value type I probability distribution. Assuming that V _f obeys the extreme value type I probability distribution, the calculation formula of the extreme value type I probability distribution function is:

In the formula, a is the scale parameter of the distribution; u is the location parameter of the distribution, and the calculation formula of the probability density distribution function is:

The scale parameter and the location parameter can be estimated using the method of moments estimation.

The first-order moment (mathematical expectation) is calculated as:

Among them: y≈0.57722, the second-order moment (variance) calculation formula is:

The calculation formula of the scale parameter a is thus obtained:

The calculation formula of the position parameter u is:

Then the probability of occurrence of the maximum wind speed x _P that occurs once in N years is the guarantee rate, and its calculation formula is:

P(x _p )=P(V _f >x _P )=1-P(V _f ≤x _p )=1-F(x _p )

In the formula, P(x _p ) is the probability of occurrence of the maximum wind speed once in N years;

Using the hourly forecast data 24 hours before the typhoon landed, matching the wind speed point for each tower based on the nearest geographical distance, and using each tower as a new wind speed point, the accuracy of the wind speed point can reach 1km × 1km. Based on the extreme value type I probability distribution, the distribution of the predicted wind field is simulated in units of wind speed points. Assuming that the maximum gust V _f at each gust point at different times satisfies the extreme value type I probability distribution, use V _f to calculate a and u, as Each wind speed point is fitted with an extreme value I-type distribution to realize the simulation of wind field distribution;

The process of random forest method described in step 3 is as follows:

The input to the random forest algorithm is:

V*, V′*, T*, H*, A*, S*, P*, U*, R*;

The output is:

The probability that the damaged state is Y*=1;

The specific process of the Monte Carlo method described in step 3 is as follows:

When determined based on the extreme value I-type probability distribution, the Monte Carlo method is used to randomly extract the wind speed, and in each random wind field, assuming that the wind speed of each wind speed point is relatively independent, the distribution of the entire wind field can be simplified as For the gust distribution at a single wind speed point, since the wind speed point has been matched to the coordinates of the tower, the damage probability at the wind speed point is actually the damage probability of the transmission line;

M times wind speeds are randomly generated according to uniform distribution at N wind speed points, and the jth wind speed at the ith wind speed point is defined as Vi _,j , where i=1,2,...,N is the sequence of wind speed points , j=1,2,...,M is the sequence of random samples, set N=83973, M=50, and use the fitted extreme value I-type probability distribution to calculate the probability P(V _f =V _i,j );

The calculated damage probability described in step 3 is:

In each random wind field, the RF method is used to calculate the damage probability f of the tower ( _xi |V _f =V _i,j ), where x _i is the eigenvector at the wind speed point i, and V _f is the wind speed of x _i component, according to the Monte Carlo method, the damage probability of the tower at this wind speed point is equivalent to the average value of the M prediction results, and the calculation formula of the damage probability of the tower at each wind speed point is:

In the formula: M is the total sampling times, V _i,j is the wind speed generated at the jth time at the wind speed point i. Use ArcGIS10.4.1 to visualize the results, and obtain the damage prediction of the mixed prediction model of damage probability under the predicted wind field shown in Figure 2.

Step 4: Calculate the risk index according to the probability of damage, and carry out emergency repair after the disaster.

The steps for calculating the risk indicator described in step 4 are as follows:

The damage probability is set to 0.5 as the threshold value, P _i >0.5 means the tower is damaged, P _i <0.5 means the tower is not damaged, and the calculation formula of the average Num of equipment damage units is:

The formula for calculating the average repair time T _Re is:

The formula for calculating the average value C of the repair cost is:

The formula for calculating the average value L of manpower requirements is:

The calculation formula of the average value V of the demand for emergency repair vehicles is:

In the formula, t is the repair time per unit of equipment; c is the repair cost per unit; m is the manpower required per unit of equipment; v is the repair cost per unit; ) is the indicator function, which is defined as follows:

The post-disaster repairs described in Step 4 are:

Statistics t=0.001124, m=1.21231, v=0.18320, c=0.28165. After obtaining the damage probability Pi of each wind speed point, at the same time, the risk indicators Num, C, L, and _V can guide the disaster prevention and mitigation department to pre-allocate equipment, expenses, personnel, and vehicle resources, and release the power outage duration warning information according to the T _Re index. , the risk index Num=40, T _Re =0.45, M=49, V=8, C=11.266 are obtained in this example.

It should be understood that the above description of the preferred embodiments is relatively detailed, and therefore should not be considered as a limitation on the scope of the patent protection of the present invention. In the case of the protection scope, substitutions or deformations can also be made, which all fall within the protection scope of the present invention, and the claimed protection scope of the present invention shall be subject to the appended claims.

Claims (3)

1. A method for early warning damage of a power transmission line under typhoon disasters is characterized by comprising the following steps:

step 1: acquiring meteorological information, equipment operation information, micro-terrain information and real-time damage information to construct a training set;

step 2: information quantization, default value processing and standardization processing are carried out on the information in the training set;

and step 3: establishing a power transmission line damage probability hybrid prediction model based on extreme value I type probability distribution, a random forest method and a Monte Carlo method, and calculating damage probability;

and 4, step 4: calculating a risk index according to the damage probability, and performing emergency repair after the disaster;

the process based on the extreme value type I probability distribution in step 3 is as follows:

parameter estimation of extreme I-type probability distribution, assuming V_fObeying the extreme value I type probability distribution, the extreme value I type probability distribution function calculation formula is as follows:

in the formula, a is a distributed scale parameter; u is a distributed position parameter, and the probability density distribution function calculation formula is as follows:

estimating the scale parameter and the position parameter by using a moment estimation method;

the first moment is calculated by the formula:

wherein: y ≈ 0.57722, and the second moment calculation formula is:

the calculation formula for the scale parameter a is thus:

the calculation formula of the position parameter u is as follows:

the N year-round maximum wind speed x_PThe probability of occurrence is the guarantee rate, and the calculation formula is as follows:

P(x_p)＝P(V_f＞x_P)＝1-P(V_f≤x_p)＝1-F(x_p)

in the formula, P (x)_p) The probability of the occurrence of the maximum wind speed in N years;

based on extreme value I type probability distribution, the distribution of the wind field is simulated and predicted by taking the wind speed points as a unit, the precision of the wind speed points can reach 1km multiplied by 1km, and the maximum gust V of each gust point at different time is assumed_fSatisfy extreme value type I probability distribution, using V_fCalculating a and u, fitting an extreme value I-shaped distribution for each wind speed point, and realizing wind field distribution simulation;

the process of the random forest method in the step 3 is as follows:

the input of the random forest algorithm is as follows:

V*、V′*、T*、H*、A*、S*、P*、U*、R*；

the output is:

probability that the damage state is Y ═ 1;

the specific process of the Monte Carlo method in the step 3 is as follows:

after the probability distribution is determined based on the extreme value I type, the wind speed is randomly extracted by a Monte Carlo method, and under each random wind field, the wind speed of each wind speed point is assumed to be relatively independent, so that the distribution of the whole wind field can be simplified into the gust distribution of a single wind speed point;

randomly generating M times of wind speed on N wind speed points according to uniform distribution, and defining the jth wind speed at the ith wind speed point as V_i,jWherein, I is1, 2, N is a sequence of wind speed points, j is1, 2, M is a sequence of random samples, and the probability P (V) of each random wind speed is calculated by using the fitted extreme value I-type probability distribution_f＝V_i,j)；

In step 3, the damage probability is calculated as follows:

under each random wind field, the damage probability f (x) of the tower is calculated by using an RF method_i|V_f＝V_i,j) Wherein x is_iIs a feature vector at wind speed point i, V_fIs x_iAccording to the Monte Carlo method, the tower damage probability at the wind speed point is equivalent to the average value of the wind speeds of M times, and the calculation formula of the tower damage probability at each wind speed point is as follows:

in the formula: m is the number of wind speeds, V_i,jThe wind speed generated at the jth time at the wind speed point i;

the steps of calculating the risk indicator in step 4 are as follows:

setting the damage probability 0.5 as threshold value, P_i>0.5 consider the tower to be damaged, P_i<0.5 represents that the tower is not damaged, and the calculation formula of the average Num of the damaged unit number of the equipment is as follows:

mean value of repair time T_ReThe calculation formula is as follows:

the average value C of the repair cost is calculated according to the formula:

the average value L of the manpower demand is calculated by the formula:

the calculation formula of the average value V of the emergency repair vehicle requirement is as follows:

in the formula, t is the unit equipment repair duration; c is unit repair cost; m is the manpower needed by the unit equipment; v is the unit repair cost; all are obtained from historical statistical data; [. cndot. ] is an upward rounding function, and I (. cndot.) is an indicator function, defined as follows:

in the step 4, the post-disaster rush repair is carried out as follows:

obtaining the damage probability P of each wind speed point_iThen, the risk indexes Num, C, L and V can guide the disaster prevention and reduction department to pre-allocate equipment, cost, personnel and vehicle resources and according to T_ReAnd (4) releasing early warning information of power failure duration by indexes.

2. The method for early warning of damage to a power transmission line in a typhoon disaster according to claim 1, wherein the meteorological information in step 1 includes that the maximum gust is V;

in the step 1, the equipment operation information comprises operation time T and design wind speed V';

the microtopography information in the step 1 comprises an altitude H, a slope A, a slope S, a slope P, a bedding surface type U and a surface roughness R;

the real-time damage information in the step 1 comprises that the damage state of the equipment is Y;

in step 1, the information in the training set is:

the maximum gust is V, the equipment operation time is T, the design wind speed is V', the altitude is H, the slope direction is A, the slope is S, the slope position is P, the type of the underlying surface is U, the surface roughness is R and the damage state is Y; each piece of data in the training set is a length 10 vector made up of the variables described above.

3. The method for early warning of damage to a power transmission line in a typhoon disaster according to claim 1, wherein the step 2 of quantifying the information in the training set comprises the following steps:

because V, T, V' and H, A, S, P, U, R are in data format, only information Y in the training set is quantized, and the damage state after quantization is represented by Y;

in step 2, the default value processing of the information in the training set is as follows:

filling the default values of V, T, V' and H, A, S, P, U, R by using median respectively to obtain the processed variables as follows:

the maximum gust is V after the default value is processed_fThe running time of the equipment after default value processing is T_fThe design wind speed after the default value processing is V_f' after default value processing, the altitude is H_fThe slope direction after the default value processing is A_fThe gradient is S after the default value is processed_fAfter the default value is processed, the slope position is P_fThe type of the underlying surface is U after the default value processing_fThe surface roughness after default value processing is R_f；

The data after the default value processing is subjected to data standardization processing as follows:

respectively combine V with_f、T_f、V_f′、H_f、A_f、S_f、P_f、U_f、R_fAccording to the standardized variable calculation, the concrete formula is as follows:

X^*＝(x-x_min)/(x_max-x_min)

wherein x is V in the data processed by default value_f、T_f、V_f′、H_f、A_f、S_f、P_f、U_f、R_fValue of (1), x_minData V processed for default values_f、T_f、V_f′、H_f、A_f、S_f、P_f、U_f、R_fMinimum value of (1), x_maxData V processed for default values_f、T_f、V_f′、H_f、A_f、S_f、P_f、U_f、R_fX is the maximum value in the data normalization process: the method comprises the steps of standardizing a maximum gust V, standardizing equipment running time T, standardizing a designed wind speed V, standardizing an altitude H, standardizing a slope direction A, standardizing a slope S, standardizing a slope position P, standardizing a lower pad type U and standardizing a surface roughness R.

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