Research on Driving Conditions and Fuel Consumption of Improved K-means Clustering Algorithm

The data collected in this paper are the actual road driving conditions of a city light vehicle in September 2019 (sampling frequency is 1Hz), among which, the data information includes time, GPS speed measurement, longitude and latitude, instantaneous fuel consumption, etc. Using fitting interpolation method to interpolate and fit the disturbed discontinuous data, wavelet decomposition and reconstruction method to smooth the contaminated data [9] the original data was reduced from 194511 to 164039 by Matlab preprocessing

Based on the analysis of relevant data and related research, 12 characteristic parameters are defined to describe the kinematic segments [10]. In this paper, 12 characteristic parameters including segment duration/T, travel distance/S, average speed/V_a, average driving speed/V_d, idle time ratio/T_i, acceleration time ratio/T_a, deceleration time ratio/T_d, cruise time ratio/T_c, speed standard deviation/V_std, average acceleration/a_a, average standard deviation of acceleration/a_std, average deceleration/a_d etc.

The interval from the start of one idling speed to the beginning of the next idling speed is called the kinematic segment [11]. This paper uses Python to develop related programs, uses stack and loop traversal data for processing, and divides 2445 kinematics segments from 164039 preprocessed data.

The actual test species will have more or less interference, which often produces outliers or noises, which will affect the clustering effect. Here, we construct a residual point distance mean sum method to eliminate the influence of noise and outliers [15]. For the i point in the data, the sum of distances between each point and other points is S_i, and the sum of distances is H. When S_i > H, point i is regarded as an isolated point. Among them, the sample data is, the data dimension is, and the calculation is as follows: (2) Si=∑j−1n∑h−1d(xih−xjh)2 {S_i} = \sum\limits_{j - 1}^n {\sqrt {\sum\limits_{h - 1}^d {{{\left({{x_{ih}} - {x_{jh}}} \right)}^2}}}} (3) H=∑i−1nSin H = \sum\limits_{i - 1}^n {{{{S_i}} \over n}}

1) The maximum and minimum distance of the remaining data in the cluster and dataset is defined as: (4) Dmax=Max(d) {D_{\max}} = {\rm{Max}}\left(d \right)

Among them, d is a set consisting of the minimum value of the distance between each cluster and the remaining data in the data set.

2) d_k is the minimum value of the distance between each cluster and the remaining data in the data set, (5) dk=Min(∑k=1m(Xik−Xjk)2) {d_k} = {\rm{Min}}\left({\sum\limits_{k = 1}^m {{{\left({{X_{ik}} - {X_{jk}}} \right)}^2}}} \right)

Among them, X_i is the cluster center, X_j is the remaining data in the data set, and^m is the dimension of the data.

3) Determine whether to select the initial candidate center as the optimized candidate center. (6) Max(Min(D)t)>θ‖v1−v2‖ {\rm{Max}}\left({{\rm{Min}}{{\left({\rm{D}} \right)}_t}} \right) > \theta \left\| {{v_1} - {v_2}} \right\|

Among them, v₁, v₂ are the points that first become the candidate centers after optimization, θ is the parameter, which can be 0.5.

4) The criterion function of the K – means algorithm for clustering is the error sum of square criterion function. (7) Jc=∑i=1k∑p∈Ci(‖P−Mi‖)2 {J_c} = \sum\limits_{i = 1}^k {\sum\limits_{p \in {C_i}} {{{\left({\left\| {P - {M_i}} \right\|} \right)}^2}}}

Among them, M_i is the mean value of all data in class C_i, p is each data in class C_i, and J_c is the function of sample and cluster center.

ω= [ω₁, ω₂, ⋯, ω_n]^T ∈ R^n×d, The weight ω is introduced to distinguish the relationship between the sample data and the cluster center, (8) σdω(xj,ci)=∑m=1dωjm(xjm−cim)2 \sigma {d_\omega}\left({{x_j},{c_i}} \right) = \sqrt {\sum\limits_{m = 1}^d {{\omega _{jm}}{{\left({{x_{jm}} - {c_{im}}} \right)}^2}}} (9) ωjm=xjm1n∑j=1nxjm {\omega _{jm}} = {{{x_{jm}}} \over {{1 \over n}\sum\limits_{j = 1}^n {{x_{jm}}}}}

The initial new weight is as follows: (10) WiNew=Wi(1+Ainit−AiAinit) {{\rm{W}}_{{\rm{iNew}}}} = {{\rm{W}}_{\rm{i}}}\left({1 + {{{{\rm{A}}_{{\rm{init}}}} - {{\rm{A}}_{\rm{i}}}} \over {{{\rm{A}}_{{\rm{init}}}}}}} \right)

Among them, the clustering accuracy is (11) Ai=NcorN% {{\rm{A}}_{\rm{i}}} = {{{N_{cor}}} \over N}\%

Among them, ω_j = (ω_j1, ω_j2, ⋯, ω_jd)^T is d dimensional vector, x_jm is the m component of the j sample, 1n∑j=1nxjm {1 \over n}\sum\limits_{j = 1}^n {{x_{jm}}} the average of the sum of the m component of each data object in the sample data set. It can be seen that ω is a weight that can reflect the overall distribution characteristics of the sample Value [5].

If A_final > A_init, accept the new weight and set A_init =A_final ; otherwise, keep the old weight unchanged.

According to the above working condition data, the improved K-means algorithm is used for processing. First, edge data and outliers are detected, and abnormal points are eliminated. As shown in Figure 4 below, cluster 1 is a normal clustered point. Cluster 2 is the outlier of edge data. As can be seen in Figure 5, the edge data is relatively distant from most normal points, and most of the edge data are outliers, which can be eliminated.

Figure 4.

Figure 5.

According to the above-mentioned improved principal component analysis, the contribution factor and the characteristic value with high correlation are used to draw the three-dimensional graph, as shown in Figure 6. In this paper, the average speed, driving distance and cruise time ratio are selected to represent each point of clustering.

Figure 6.

The improved K-Means clustering algorithm divides the kinematic segments into four categories, which are represented by cluster 1, cluster 2, cluster 3 and Cluster 4. It can be seen from Figure 7 that the first type is downtown area, where the vehicles start and stop frequently and the speed is low, and the average speed, cruise time ratio and driving distance are low; the second type is the living area, which is congested, with more start and stop times, and lower average speed, cruise time ratio and driving distance; the third type is suburban area, with smooth road conditions, less starting and stopping times, average speed, cruise time ratio and driving distance The fourth type is high-speed area, with smooth traffic, less start and stop times, high average speed, cruise time ratio and driving distance.

Figure 7.

According to the proportion of the total time of various time segments in the driving cycle of all data sets, the time taken by each driving cycle in the final construction cycle can be calculated [16]. This paper takes 1400s to construct vehicle driving cycle, as shown in Figure 8 below. The first type of low speed segment, the second type of medium speed segment, and the third type of medium high speed segment. The fourth type of high-speed video.

Figure 8.

From the speed and acceleration to verify the difference between the constructed driving cycle and the experimental data [11], this is a relatively standard verification method. Matlab software is used to calculate the speed acceleration joint distribution matrix of the vehicle driving cycle data, as shown in Figure 9.

Figure 9.

As can be seen from Figure 9 above, the joint velocity acceleration difference distribution of the experimental data and the improved clustering algorithm in this paper is within the ±1.2% range, and the calculated distribution difference value (SAFD_diff) is 1.05%, while the difference value (SAFD_diff) of the speed acceleration joint distribution between the experimental data and TKM is 0.97%. Therefore, the driving cycle constructed in this paper meets the driving characteristics of light vehicles, meets the development requirements of vehicle driving cycle construction, and has strong applicability.

This paper uses the working condition construction method of literature [17] and literature [18]. According to the data of this paper, the improved principal component algorithm of this paper is combined with the four algorithms respectively, and 20 experiments are performed, as shown in Figure 10. The results show that, In this paper, the improved K-means clustering algorithm can not only weaken the influence of noise points on the initial center, but also greatly shorten the clustering time based on the stable clustering effect.

Figure 10.

The results of programming using Matlab are shown in Table 2 above. The comparison of the four algorithms in terms of the number of error-clustering samples, average running time, average correct rate and SAFD_diff, the improved K-means algorithm in this paper performs better in clustering performance and time consumption. The average running time is 44.2% less than that of traditional K-means clustering.

As shown in figures 11 and 12, the instantaneous fuel consumption is large at low speed, medium and low speed, the torque fluctuation in the region is larger than that in the high speed region, the instantaneous fuel consumption rate in the high speed region is relatively stable, and the instantaneous fuel consumption rate in the low speed region and medium speed region is obviously increased. It can be observed in Figure 13 that the instantaneous fuel consumption increases briefly at low speed, and then the fluctuation trend is roughly consistent with the driving speed. As can be seen from Figure 14, the engine speed is mainly distributed in 1500–2500r / min under driving condition, and the opening of accelerator pedal is concentrated in 0.12–0.18, indicating that the driving condition is in medium high speed state.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

It can be observed from Figure 15 above that the instantaneous fuel consumption is mostly concentrated in the speed of 1000–1500r / min, and the percentage of torque is 10% – 30%, which indicates that this part is composed of high-speed, medium speed and low-speed driving conditions. There are a few relatively concentrated areas in the speed range of 1500–2500r / min. it can be observed that this part is the instantaneous fuel consumption generated under the condition of high engine speed and low torque percentage, which may be due to driving It is caused by the extreme operation of the driver.

Figure 15.