| Citation: | CAI Jing, CAI Kun-ye, HUANG Shi-jie. Early warning method for heavy landing of civil aircraft based on real-time monitoring parameters[J]. Journal of Traffic and Transportation Engineering, 2022, 22(2): 298-309. doi: 10.19818/j.cnki.1671-1637.2022.02.024
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According to statistics, aviation safety accidents during the approach and landing phases, which account for only 4% of civil aircraft operating time, account for 60% of overall safety accidents. Heavy landing is a typical dangerous accident that occurs during the landing phase of an aircraft, which can cause structural damage, passenger injury, and even personal injury. A stable approach along the approach path with the required configuration, attitude, speed, and power is a prerequisite for ensuring safe or normal landing during the approach. Once an unstable approach state occurs and cannot be recognized by the pilot, there is a high possibility of dangerous accidents such as heavy landing. The flight parameters record a large number of approach state related parameters, extracting unstable approach features from them and identifying unstable approach states in advance is an important way to prevent aircraft from landing again. At present, the conditions for a heavy landing are defined in the aircraft maintenance manual. However, to determine whether a heavy landing has occurred, it is necessary to wait for the aircraft to land and have the crew report or maintenance personnel retrieve data from the onboard Quick Access Recorder (QAR) for judgment. Therefore, it is difficult to achieve automatic alarm after a heavy landing occurs, especially in advance warning of possible heavy landings to remind pilots to take corrective measures in a timely manner.
At present, research on heavy landings both domestically and internationally mainly focuses on the prevention of heavy landings from the perspective of flight operations, intelligent diagnosis after heavy landings occur, and the risks caused by heavy landings. Guo Hongbing[1]Studied the influence of external factors of aircraft and pilot operation factors on heavy landing, and proposed methods to prevent heavy landing from occurring based on this; Chen Yangjian and others[2]Studied the impact of ground to air wind shear on heavy landing and corresponding preventive measures; Xu Guimei and others[3-5]Studied diagnostic methods for heavy landing; Cai Kunye and others[6]Researched the design method of customized messages for heavy landing and conducted a message based accident cause analysis; Forrest and others[7]A structural health monitoring system for landing gear has been developed, which uses advanced sensor technology to monitor and track fatigue damage of the landing gear. The system can detect the occurrence of heavy landing events, but cannot make advance predictions; Shao et al[8-9]A study was conducted on the division of high-risk operational areas for a type of QAR exceedance event during the landing phase; Longhai River[10]Correlation analysis was conducted using QAR data to establish the correlation between various variables and landing loads, and the correlation between environmental factors, human factors variables, and heavy landing was classified and explored; Zheng Lei and others[11-12]By using clustering methods to mine the flight operation patterns contained in QAR data, and analyzing the correlation between flight operation patterns and QAR monitoring indicator values, the risk levels of different flight operation patterns were quantified; Wang et al[13]A risk assessment model for hard landing events has been established to improve the risk management level of aircraft hard landing events.
At present, some research has also been conducted on heavy landing warning, Zheng Wei[14]According to the Implementation and Management of Flight Quality Assurance (FOQA) for Air Transport Carriers, based on historical data of vertical load exceeding events in QAR, an autoregressive moving average model is used to predict the number of exceeding events in the next three months. This method belongs to the statistical category and does not use real-time monitoring data in QAR to predict whether the aircraft is about to make a heavy landing; Midtfjord et al[15]Establish a predictive evaluation model based on meteorological data and runway information to assist pilots in making safe landing decisions for aircraft; Pan Weijun and others[16]Based on onboard flight information and airport monitoring information, a neural network is used to establish a prediction model for the approach and landing speed of the rear aircraft between aircraft groups; Jeong et al[17]A numerical model was established based on artificial neural networks to estimate the maximum strain of specific regions and aircraft landing loads using basic flight parameters; Tong et al[18-19]We studied the prediction methods of vertical acceleration and flight speed closely related to heavy landing. In the vertical acceleration prediction model, the following one second vertical acceleration is used as the prediction target. Due to the extremely rapid changes in flight altitude during the landing phase, a 1-second advance warning cannot provide pilots with sufficient operational time, making the model impractical; In addition, relying solely on vertical acceleration as the warning target for heavy landing is not comprehensive enough, and is less than the four main evaluation parameters considered in the aircraft maintenance manual for judging heavy landing. Chen Si and others[20-22]Taking the historical operational data of the fleet as an example, a heavy landing risk warning model is established using methods such as support vector machines. But this type of method essentially only classifies heavy landings and does not truly achieve early prediction.
| 指示空速/kts | 地速/kts | 垂直加速度/g | 侧向加速度/g | 纵向加速度/g |
| 0.984 0 | ||||
| 0 | 0.984 0 | 0.003 9 | 0.007 8 | |
| 0 | 0.977 0 | |||
| 0.984 0 | 0.003 9 | 0.007 8 |
DownLoad:
CSV
Monitoring parameters with a sampling frequency below 1 Hz can be filled in using B-spline interpolation. Taking the roll rate with a sampling frequency of 0.5 Hz as an example for curve fitting, the data fitting effect is as followsFigure 1As shown. After using the B-spline interpolation method, the variation curve of the roll rate value becomes smoother.
For parameters with a sampling frequency higher than 1 Hz, downsampling is required. Taking the vertical acceleration with a sampling frequency of 8 Hz as an example, to avoid missing the peak value of the vertical acceleration during prediction, the maximum value per second is taken as the extraction value for that second. The downsampling extraction effect of the vertical acceleration value is as follows:Figure 2As shown. By downsampling and extracting monitoring parameters with high sampling frequencies, the complexity of subsequent model training can be greatly reduced.
Different QAR real-time monitoring parameters have different dimensions and are not comparable, resulting in significant numerical differences. In order to eliminate the influence of different dimensions of each parameter on the model prediction results, it is necessary to normalize the data. For the data sequence of a certain monitoring parameter, normalization is requiredSThe data normalization method used is
| ˆSi=si−smeansmax−smin | (1) |
Table 2Listed some normalized parameters.
| 磁航向 | 指示空速 | 校准空速 | 侧向加速度 | 纵向加速度 |
| 0.940 107 | 0.967 611 | 0.963 851 | 0.206 493 | 0.734 692 |
| 0.934 657 | 0.962 645 | 0.952 812 | 0.218 411 | 0.737 892 |
| 0.929 232 | 0.956 667 | 0.939 877 | 0.208 141 | 0.735 080 |
| 0.923 869 | 0.950 275 | 0.928 458 | 0.217 700 | 0.749 733 |
| 0.918 603 | 0.944 075 | 0.921 970 | 0.209 979 | 0.760 535 |
| … | … | … | … | … |
| 0.913 471 | 0.938 670 | 0.923 349 | 0.145 924 | 0.742 374 |
| 0.908 509 | 0.934 664 | 0.931 382 | 0.082 092 | 0.711 762 |
| 0.903 751 | 0.932 662 | 0.942 735 | 0.078 559 | 0.692 435 |
DownLoad:
CSV
Aiming at the time series characteristics of QAR data, an LSTM neural network is used to propose a civil aircraft heavy landing prediction model based on real-time monitoring parameters, achieving early warning of heavy landing.
RNN faces a problem that gradients rapidly decrease or explosively increase during the training process of the network. Therefore, the most effective sequence model in practical applications is gated RNN, where two typical networks are long short-term memory and gated recurrent units, which can effectively avoid gradient vanishing and explosion phenomena[25-26].
| {f_t} = \sigma \left[ {{\mathit{\boldsymbol{W}}_{\rm{f}}}{{\left( {{h_{t - 1}}, {x_t}} \right)}^{\rm{T}}} + {b_{\rm{f}}}} \right] | (2) |
The input gate is
| {i_t} = \sigma \left[ {{\mathit{\boldsymbol{W}}_{\rm{i}}}{{\left( {{h_{t - 1}}, {x_t}} \right)}^{\rm{T}}} + {b_{\rm{i}}}} \right] | (3) |
| {C_t} = {f_t}{C_{t - 1}} + {i_t}\tanh \left[ {{\mathit{\boldsymbol{W}}_{\rm{c}}}{{\left( {{h_{t - 1}}, {x_t}} \right)}^{\rm{T}}} + {b_{\rm{c}}}} \right] | (4) |
| {o_t} = \sigma \left[ {{\mathit{\boldsymbol{W}}_{\rm{o}}}{{\left( {{h_{t - 1}}, {x_t}} \right)}^{\rm{T}}} + {b_{\rm{o}}}} \right] | (5) |
| {h_t} = {o_t}\tanh \left( {{C_t}} \right) | (6) |
| \gamma \left( {{X_0}, {X_j}} \right) = \frac{1}{n}\sum\limits_{k = 1}^n \gamma \left[ {{X_0}(k), {X_j}(k)} \right] | (7) |
| X_j^\prime = {X_j}/{X_0} = \left\{ {X_j^\prime (1), X_j^\prime (2), \cdots , X_j^\prime (n)} \right\} | (8) |
Step 2: Find thejThe parameter sequence and reference sequence arekThe absolute difference of pointsΔj(k）For
| {\Delta _j}(k) = \left| {X_j^\prime (k) - 1} \right| | (9) |
Step 3: Find the maximum difference between two levelsMThe minimum difference between two levelsmRemember
| \begin{array}{l} M = \mathop {\max }\limits_j \left\{ {\mathop {\max }\limits_k \left[ {{\Delta _j}(k)} \right]} \right\}\\ m = \mathop {\min }\limits_j \left\{ {\mathop {\min }\limits_k \left[ {{\Delta _j}(k)} \right]} \right\} \end{array} | (10) |
| {\gamma _{0j}}(k) = \frac{{m + \varepsilon M}}{{{\Delta _j}(k) + \varepsilon M}}\;\;\;{\kern 1pt} \varepsilon \in (0, 1) | (11) |
In the formula:εTo determine the resolution coefficient.
| {\gamma _{0j}} = \frac{1}{n}\sum\limits_{k = 1}^n {{\gamma _{0j}}} (k) | (12) |
When the correlation coefficient between two parameters is below 0.30, it indicates that the relationship between the two is extremely weak and can be ignored; When the correlation coefficient is between 0.30 and 0.50, there is a low correlation; When the correlation coefficient is between 0.50 and 0.80, it indicates a moderate correlation; When the correlation coefficient is between 0.80 and 0.95, it indicates a high degree of correlation; When the correlation coefficient reaches 0.95 or above, it indicates a significant correlation.Figure 4The darker the color, the higher the negative correlation, and the lighter the color, the higher the positive correlation. supportFigure 4The correlation coefficient between the two parameters is higher than 0.80, indicating that the parameters with colors that are too dark or too light are redundantly removed. Finally, 26 parameters are selected as input parameters for the prediction modelTable 3As shown.
| 编号 | 参数 | 编号 | 参数 | |
| A1 | 左副翼角度 | A29 | 侧向加速度 | |
| A3 | 飞行高度 | A30 | 纵向加速 | |
| A6 | 偏航角 | A31 | N11转速 | |
| A9 | 左升降舵角度 | A36 | 俯仰率 | |
| A11 | 踏板角度 | A37 | 垂直下降率 | |
| A13 | 左发燃油流量 | A43 | 横滚率 | |
| A15 | 襟翼位置 | A44 | 方向舵位置 | |
| A16 | 地速 | A46 | 同步角 | |
| A17 | 着陆质量 | A48 | 安定面位置 | |
| A18 | 磁航向 | A49 | 航迹角度 | |
| A23 | 风向 | A50 | 垂直加速度 | |
| A24 | 风速 | A51 | 偏高率 | |
| A26 | 指示空速 | A52 | 角度 |
DownLoad:
CSV
According to the aircraft maintenance manual, the situation of heavy landing exceeding the limit can be subdivided into various types. Taking a typical commercial aircraft model in service as an example, the following is given:Figure 5The heavy landing determination process shown subdivides the heavy landing.
(2) Overweight landing
(4) Hard landing
(5) Severe hard landing
Neural network sequence prediction modeling can be divided into the following four steps.
Step 1: Input data preprocessing. Process the data into a state that the model can accept.
The algorithm flow of the LSTM neural network model is shown inFigure 6The heavy landing prediction model based on LSTM consists of 4 layers, including 1 input layer, 2 LSTM neural layers with Dropout, and 1 output layer. The structure of the prediction model for heavy landing is as followsFigure 7As shown.
Step 1: Initialize the weights using the Xavier method.
Step 2: Choose ReLU function for the LSTM layer activation function and softmax function for the fully connected layer activation function.
| L = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^N {{{\left( {{Y_{{\rm{p}}, i}} - {Y_{{\rm{r}}, i}}} \right)}^2}} } | (13) |
According to the analysis in Section 2.2, there are a total of 26 input parameters for the prediction model, and each parameter will have its own front endnThe data sequence of seconds is input as a variable into the prediction model, therefore, the model acceptsnA data sequence of x 26 in length. According to the analysis in Section 2.3, the predicted parameters of the model include four heavy landing evaluation parameters: landing mass, vertical acceleration, vertical descent rate, pitch rate, etc. The prediction model is based on the inputn26 data sequence, output 4 prediction parametersmThe data sequence within seconds, therefore, the model outputsmA 4x4 long data sequence. So, the prediction model relies on input historynA time series of seconds, with historical cases as training data input into the model. By calculating the loss function, backpropagation is used to adjust the weights of neural network nodes, making the predicted values closer to the true values and predicting the futuremThe variation of the second parameter. The final predicted parameters are used to make judgments on heavy landings and achieve the goal of early warning for heavy landings.
The prediction model achieves early warning of heavy landing events through multi-step prediction of four evaluation parameters for heavy landing. The training set interval and input-output step size of the model are two key factors. According to statistics, the final approach and landing phases of an aircraft generally take 120-180 seconds,Figure 8The changes of four evaluation parameters within 140 seconds at different flight altitudes were provided.
To verify the impact of interval selection in the training set on prediction accuracy, the input and output step sizes of the model were set to 16, which means that the model predicts the changes in re landing evaluation parameters for the next 16 seconds based on the data sequence of the past 16 seconds.Figure 9~11The model training sets were provided with training results selected from flight altitudes of 600, 400, and 200 ft to the end of landing.
| 飞行高度/ft | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 600 | 0.006 2 | 0.051 9 | 0.008 2 | 0.064 8 |
| 400 | 0.002 9 | 0.038 7 | 0.003 2 | 0.047 3 |
| 200 | 0.001 5 | 0.024 1 | 0.003 0 | 0.027 2 |
DownLoad:
CSV
| 输入步长 | 输出步长 | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 8 | 8 | 0.002 9 | 0.041 5 | 0.003 2 | 0.043 7 |
| 8 | 16 | 0.003 7 | 0.043 4 | 0.004 4 | 0.046 7 |
| 8 | 24 | 0.006 3 | 0.058 8 | 0.005 4 | 0.071 9 |
| 16 | 8 | 0.002 6 | 0.011 4 | 0.001 8 | 0.030 7 |
| 16 | 16 | 0.003 7 | 0.013 8 | 0.002 4 | 0.035 3 |
| 16 | 24 | 0.003 9 | 0.030 1 | 0.004 2 | 0.049 7 |
| 24 | 8 | 0.001 8 | 0.010 7 | 0.002 6 | 0.011 4 |
| 24 | 16 | 0.002 4 | 0.011 3 | 0.002 9 | 0.012 1 |
| 24 | 24 | 0.003 2 | 0.020 6 | 0.003 7 | 0.023 2 |
DownLoad:
CSV
according toTable 5Based on the training results, construct a heatmap by averaging the absolute error values of models from different groups, such asFigure 12As shown.
The number of input parameters for a model is not necessarily better, as some parameters can interfere with the model's prediction performance. Using the optimized prediction model determined in Section 3.2, the prediction performance of the model was compared with the original 52 parameters and the 26 parameters obtained after feature selection. The prediction performance is as follows:Table 6As shown.
| 输入参数数量 | 测试集损失值 | 测试集平均绝对误差 |
| 52 | 0.010 9 | 0.021 0 |
| 26 | 0.001 8 | 0.010 7 |
DownLoad:
CSV
The confusion matrix is a simple square matrix used to display the prediction results of a model, that is, to evaluate the prediction performance of the model using the number of true (TP), true negative (FN), false positive (FP), and false negative (FN). To verify the actual prediction performance of the model, 50 sets of segment data from a certain airline's recorded heavy landing events and segment data from normal landings were selected as inputs for the model, including 5 sets of segment data from heavy landing accidents. Due to the relatively low occurrence of heavy landing events by airlines, the segment data for heavy landing events is much less than that for normal segments. The model adopts an input and output step size of 8-24. Based on the obtained model prediction results, draw the following graph:Figure 13The confusion matrix shown.
Figure 14~17The multi-step prediction effects of vertical descent rate, landing mass, pitch rate, and vertical acceleration in one of the heavy landing events were presented separately.
(2) By optimizing the flight altitude selection interval and input-output step size in the heavy landing prediction model, the model's prediction performance and accuracy have been improved. The warning can be advanced by 8 seconds, with a prediction accuracy of 98% and an average absolute error of only 0.0183. This provides sufficient time margin for pilots to take measures to avoid heavy landings.
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Figures(17) / Tables(6)
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He Zhu-qing, Sun Lin-yan. Model and algorithm of vehicle routing problem under dynamic traffic[J]. Journal of Traffic and Transportation Engineering, 2007, 7(1): 111-115.
| 指示空速/kts | 地速/kts | 垂直加速度/g | 侧向加速度/g | 纵向加速度/g |
| 0.984 0 | ||||
| 0 | 0.984 0 | 0.003 9 | 0.007 8 | |
| 0 | 0.977 0 | |||
| 0.984 0 | 0.003 9 | 0.007 8 |
DownLoad:
CSV
| 磁航向 | 指示空速 | 校准空速 | 侧向加速度 | 纵向加速度 |
| 0.940 107 | 0.967 611 | 0.963 851 | 0.206 493 | 0.734 692 |
| 0.934 657 | 0.962 645 | 0.952 812 | 0.218 411 | 0.737 892 |
| 0.929 232 | 0.956 667 | 0.939 877 | 0.208 141 | 0.735 080 |
| 0.923 869 | 0.950 275 | 0.928 458 | 0.217 700 | 0.749 733 |
| 0.918 603 | 0.944 075 | 0.921 970 | 0.209 979 | 0.760 535 |
| … | … | … | … | … |
| 0.913 471 | 0.938 670 | 0.923 349 | 0.145 924 | 0.742 374 |
| 0.908 509 | 0.934 664 | 0.931 382 | 0.082 092 | 0.711 762 |
| 0.903 751 | 0.932 662 | 0.942 735 | 0.078 559 | 0.692 435 |
DownLoad:
CSV
| 编号 | 参数 | 编号 | 参数 | |
| A1 | 左副翼角度 | A29 | 侧向加速度 | |
| A3 | 飞行高度 | A30 | 纵向加速 | |
| A6 | 偏航角 | A31 | N11转速 | |
| A9 | 左升降舵角度 | A36 | 俯仰率 | |
| A11 | 踏板角度 | A37 | 垂直下降率 | |
| A13 | 左发燃油流量 | A43 | 横滚率 | |
| A15 | 襟翼位置 | A44 | 方向舵位置 | |
| A16 | 地速 | A46 | 同步角 | |
| A17 | 着陆质量 | A48 | 安定面位置 | |
| A18 | 磁航向 | A49 | 航迹角度 | |
| A23 | 风向 | A50 | 垂直加速度 | |
| A24 | 风速 | A51 | 偏高率 | |
| A26 | 指示空速 | A52 | 角度 |
DownLoad:
CSV
| 飞行高度/ft | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 600 | 0.006 2 | 0.051 9 | 0.008 2 | 0.064 8 |
| 400 | 0.002 9 | 0.038 7 | 0.003 2 | 0.047 3 |
| 200 | 0.001 5 | 0.024 1 | 0.003 0 | 0.027 2 |
DownLoad:
CSV
| 输入步长 | 输出步长 | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 8 | 8 | 0.002 9 | 0.041 5 | 0.003 2 | 0.043 7 |
| 8 | 16 | 0.003 7 | 0.043 4 | 0.004 4 | 0.046 7 |
| 8 | 24 | 0.006 3 | 0.058 8 | 0.005 4 | 0.071 9 |
| 16 | 8 | 0.002 6 | 0.011 4 | 0.001 8 | 0.030 7 |
| 16 | 16 | 0.003 7 | 0.013 8 | 0.002 4 | 0.035 3 |
| 16 | 24 | 0.003 9 | 0.030 1 | 0.004 2 | 0.049 7 |
| 24 | 8 | 0.001 8 | 0.010 7 | 0.002 6 | 0.011 4 |
| 24 | 16 | 0.002 4 | 0.011 3 | 0.002 9 | 0.012 1 |
| 24 | 24 | 0.003 2 | 0.020 6 | 0.003 7 | 0.023 2 |
DownLoad:
CSV
| 输入参数数量 | 测试集损失值 | 测试集平均绝对误差 |
| 52 | 0.010 9 | 0.021 0 |
| 26 | 0.001 8 | 0.010 7 |
DownLoad:
CSV
| 指示空速/kts | 地速/kts | 垂直加速度/g | 侧向加速度/g | 纵向加速度/g |
| 0.984 0 | ||||
| 0 | 0.984 0 | 0.003 9 | 0.007 8 | |
| 0 | 0.977 0 | |||
| 0.984 0 | 0.003 9 | 0.007 8 |
| 磁航向 | 指示空速 | 校准空速 | 侧向加速度 | 纵向加速度 |
| 0.940 107 | 0.967 611 | 0.963 851 | 0.206 493 | 0.734 692 |
| 0.934 657 | 0.962 645 | 0.952 812 | 0.218 411 | 0.737 892 |
| 0.929 232 | 0.956 667 | 0.939 877 | 0.208 141 | 0.735 080 |
| 0.923 869 | 0.950 275 | 0.928 458 | 0.217 700 | 0.749 733 |
| 0.918 603 | 0.944 075 | 0.921 970 | 0.209 979 | 0.760 535 |
| … | … | … | … | … |
| 0.913 471 | 0.938 670 | 0.923 349 | 0.145 924 | 0.742 374 |
| 0.908 509 | 0.934 664 | 0.931 382 | 0.082 092 | 0.711 762 |
| 0.903 751 | 0.932 662 | 0.942 735 | 0.078 559 | 0.692 435 |
| 编号 | 参数 | 编号 | 参数 | |
| A1 | 左副翼角度 | A29 | 侧向加速度 | |
| A3 | 飞行高度 | A30 | 纵向加速 | |
| A6 | 偏航角 | A31 | N11转速 | |
| A9 | 左升降舵角度 | A36 | 俯仰率 | |
| A11 | 踏板角度 | A37 | 垂直下降率 | |
| A13 | 左发燃油流量 | A43 | 横滚率 | |
| A15 | 襟翼位置 | A44 | 方向舵位置 | |
| A16 | 地速 | A46 | 同步角 | |
| A17 | 着陆质量 | A48 | 安定面位置 | |
| A18 | 磁航向 | A49 | 航迹角度 | |
| A23 | 风向 | A50 | 垂直加速度 | |
| A24 | 风速 | A51 | 偏高率 | |
| A26 | 指示空速 | A52 | 角度 |
| 飞行高度/ft | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 600 | 0.006 2 | 0.051 9 | 0.008 2 | 0.064 8 |
| 400 | 0.002 9 | 0.038 7 | 0.003 2 | 0.047 3 |
| 200 | 0.001 5 | 0.024 1 | 0.003 0 | 0.027 2 |
| 输入步长 | 输出步长 | 训练集损失值 | 训练集平均绝对误差 | 测试集损失值 | 测试集平均绝对误差 |
| 8 | 8 | 0.002 9 | 0.041 5 | 0.003 2 | 0.043 7 |
| 8 | 16 | 0.003 7 | 0.043 4 | 0.004 4 | 0.046 7 |
| 8 | 24 | 0.006 3 | 0.058 8 | 0.005 4 | 0.071 9 |
| 16 | 8 | 0.002 6 | 0.011 4 | 0.001 8 | 0.030 7 |
| 16 | 16 | 0.003 7 | 0.013 8 | 0.002 4 | 0.035 3 |
| 16 | 24 | 0.003 9 | 0.030 1 | 0.004 2 | 0.049 7 |
| 24 | 8 | 0.001 8 | 0.010 7 | 0.002 6 | 0.011 4 |
| 24 | 16 | 0.002 4 | 0.011 3 | 0.002 9 | 0.012 1 |
| 24 | 24 | 0.003 2 | 0.020 6 | 0.003 7 | 0.023 2 |
| 输入参数数量 | 测试集损失值 | 测试集平均绝对误差 |
| 52 | 0.010 9 | 0.021 0 |
| 26 | 0.001 8 | 0.010 7 |
DownLoad:
DownLoad:
