Determination of the actual turbocharging characteristics of diesel engines using support vector machines (SVM)

. The article proposes and justifies a method that allows solving the problem of determining the characteristics of turbocharging of diesel engines of agricultural tractors without the use of test benches. The proposed application of support vector machines (SVM) has a number of advantages over traditional methods for determining the characteristics of turbocharging of diesel engines under operating conditions of agricultural tractors and machines..


Introduction
To facilitate the solution of the problem of choosing the most effective mode of operation of the MTU, Rosinformagrotekh FSBSI has developed a telemetric system for increasing the energy efficiency of machine and tractor units "Personal Assistant for the Machine Operator".The solution to this problem is to find a point on the combined characteristics of the engine (Figure 1), at which the necessary power reserve is provided, but energy efficiency is increased [1].The main monitored parameter used to calculate the degree and potential for energy efficiency improvement of an operation is the motor power utilization factor (1) [2][3][4][5][6]. (1) -turbocharging pressure at maximum power developed by the engine along the regulatory section of the regulatory characteristic at the current position of the engine crankshaft speed regulator control, kPa; -turbocharging pressure during engine idling ( ) in the regulatory section of the regulatory characteristic at the current position of the engine crankshaft speed regulator control, kPa.In this case, the current values of the turbocharging pressure are determined during the monitoring process, and the values are determined from the empirical characteristics determined by the manufacturer (Figure 1).For this purpose, the system has created a database that includes technical characteristics of more than 300 models of tractors from various manufacturers.
The problem when using the characteristics declared by the manufacturer for the purpose of determining the current degree of engine power utilization according to formula (1), presented earlier, are:  Quite wide ( 5%) range of permissible deviations of values even under standard conditions. A significant difference (up to  15 %) in the values of static boost pressure depending on the location of the sensor installation (before or after the charge air cooler, straightness of the charge line section, shape and cross-sectional area, etc.). The difference between the actual characteristics and the declared ones due to the individual design features, technical condition of the engine and its systems, etc.  Error of the measuring sensor.
It would be possible to obtain a much better result by having an individual boost pressure characteristic over the entire range of load and speed conditions of the engine, but to obtain it requires testing on a dynamometer, which is not available to most users of agricultural tractors.
One of the most well-known and accessible methods for determining the power characteristics of engines without using a dynamometer test bench is the acceleration method, which is based on the d'Alembert principle.When measuring torque on the engine shaft, acceleration of the inertial mass makes it possible to obtain an external characteristic of the dependence of torque on the speed of rotation of the engine crankshaft, identical to that obtained when determining on a brake test bench.
Figure 2 shows the time course of acceleration of a freely rotating rotor with a moment of inertia of 152 kgm 2 .When the engine accelerator is moved from a position corresponding to a crankshaft speed of 1000 rpm to a position corresponding to a rotation speed of 2000 rpm.If the values of the crankshaft rotation speed measured at the moment of acceleration are placed on the abscissa axis of the coordinate plane, and the corresponding torque values are placed on the ordinate axis, then the external speed characteristic of the engine torque will be obtained, very closely repeating the characteristic obtained on the brake stand by the method of sequential loading (Figure 2).However, an attempt to obtain an external characteristic of gas turbine boost pressure in a similar way leads to different results (Figure 3).The figure shows that the boost pressure values (for convenience, they are presented in the form of relative units, where the maximum value is taken as 100%) obtained by the acceleration method, although they are in the range of possible ABCDE values limited by the engine characteristic, coincide with it only at points A (minimum no-load engine speed) and E (maximum no-load engine speed), i.e. at steady state points.For all other rotation speed values, the obtained boost values differ from the standard characteristic.This phenomenon is explained by the lack of a transparent connection between the turbocharger wheel, which has inertia, and the engine shaft (there is only a gas connection) and is commonly called "turbo lag".The purpose of this study was to develop a method that allows one to determine the actual turbocharging characteristics of a diesel engine without using a test bench.

Materials and methods
The rapid progress and recent breakthroughs achieved in the field of machine learning are encouraging more and more scientific fields to use such computational data analysis.Machine learning (ML) algorithms will allow solving many problems in a wide variety of scientific fields, including medicine, materials science, natural sciences, as well as in everyday human life.Intelligent identification and classification of observed parameters, implemented in real time, can reduce the level of uncertainty when assessing the current state of a complex technical system.The use of machine intelligence for monitoring, in particular, makes it possible to implement self-learning (this possibility is determined by the ability to interpret observed data), makes it possible to select and implement exactly those test procedures that best correspond to the current state of the monitored system, and also allows you to dynamically configure control parameters systems [7][8][9][10].It is these opportunities that we tried to apply to solve the identified problem within the framework of the study.

Results
The ABCDE region (Fig. 1) is a set limited by the maximum and minimum values of linear functions of the form: (2) -coefficient characterizing the degree of unevenness of the regulator (1); coefficient characterizing the i-th position of the engine crankshaft speed regulator control.
Conventionally, the position of the regulator control corresponding to the coefficient b of the function (2) to which the section AB of the characteristic belongs can be taken as 0% (minimum speed of the engine crankshaft), and the position corresponding to the coefficient b of the function (2) to which the section DE of the characteristic belongs -for 100% (maximum engine speed).
Section AE of the characteristic is a set of paired values of boost pressure and engine crankshaft speed at idle (without load), so the experimental determination of these values is not difficult.To do this, the engine governor control must be moved to the position corresponding to the maximum rotation speed, the current values of boost pressure and engine speed (point E) must be recorded, and then, gradually changing the position of the governor control to a minimum, obtain a series of paired values that determine the AE section and the point A of the characteristics.
The results of this sequence of actions allow you to:  Determine the range of possible empirical values of the coefficients of functions (2). Using the obtained values of the engine crankshaft speed at point E and point D (the values at this point correspond to the rated engine crankshaft speed and are given in the technical documentation intended for the consumer), it becomes possible to determine the empirical value of the degree of unevenness of the regulator (1) and, accordingly, the coefficient k of functions (2).Thus, the procedure carried out allows us to determine the left and right boundaries of the actual characteristic, the entire set of linear functions (2) that define the characteristic, as well as the entire region of the minimum values of these functions that limit the characteristic (Figure 1) by the line AE.
Next, for the final formation of the actual characteristic, one should obtain the empirical BCD function that determines the maximum values of functions (2).When solving this problem, the following options for initial conditions should be considered:  Option 1.The BCD function is known for the entire range of possible функций (13), functions (13), but requires empirical confirmation (clarification). Option 2. A number of values of the BCD function are known for a finite number of values b i of functions (13), but require empirical confirmation (clarification). Option 3. BCD function is unknown.
The most likely option is Option 2, which involves a limited engine specification provided to the consumer.Most often in this case there is only one declared boost pressure value -at the rated engine speed (point D in Fig. 1).Predicted pressure value at point C (at this point the engine develops maximum torque, maximum fuel supply to the combustion chambers per cycle and, accordingly, the expected maximum value of turbocharging pressure).For industrial diesel engines used on agricultural tractors, the maximum torque zone is located in the engine crankshaft speed range of 1400-1600 rpm.The torque reserve value of most modern engines is 45-50%, and is usually given in the technical documentation.
The value of the third point (point B in Figure 1) for forming the characteristic can be taken equal to the obtained point A, or obtained experimentally.To do this, when the engine is running at minimum engine speed, you should engage the gear and, without disengaging the parking brake, release the clutch before the engine starts to run unstable.The maximum boost pressure recorded in this case will be the ordinate value of point B. The values obtained in this way allow us to form the basic BCD function, which requires empirical confirmation (clarification), i.e.Option 1 described above.
To obtain the basic BCD function in the case of complete absence of reference information (Option 3), you should refer to Figure 3.The figure shows that the acceleration mode of the inertial mass (the tractor itself acts as the inertial mass in production conditions) allows for a very high degree of convergence determine two points in the range of possible values (A and E) and obtain values close to the boost values at the nominal mode (point D).By approximating the measured data and these three values as reference values using the LOESS method, it is also possible to obtain the first basic boost characteristic (Figure 4).
The next stage of characteristic modeling is adaptation, by which, in this study, we will understand the process of evolution of the primary (basic characteristic) to the actual (true) one, during operational operation due to the emergence of new data.It is obvious that during engine operation in various modes, the boost pressure in the line will sooner or later take on all the values in the ABCDE region.
By monitoring engine speed and boost pressure and using support vector machines (SVM), it is possible to obtain a boost profile for a specific engine without using a test bench.
To solve the problem, the following classifying characteristics were selected:  Each obtained paired value of boost pressure and engine crankshaft speed belongs to the true characteristic. Each obtained paired value of boost pressure and engine crankshaft speed belongs to some function (2). When each new maximum of function (2) appears, the basic BCD function is recalculated. The maximum value of each function (2) cannot be considered conditionally true until the following conditions are met: a) a positive increment of successive values is obtained with a negative increment ; b) for each i-th position of the engine speed regulator control and two consecutive values the condition is satisfied: • The values of the functions forming the ABCDE region can be considered conditionally true only if they are obtained by approximating at least three conditionally true paired values that differ from each other in the parameter by no more than 50 rpm.The characteristics were refined using the method of virtual simulation of normal tractor operation in the OpenML environment.The analysis was carried out on a database in *.csv format, obtained by monitoring the operating parameters of the tractor in normal operating mode using the "Personal Assistant Operator" telemetry system.The registration frequency of the measured parameters was 5 Hz, the total number of records was approximately 1,100,000.At the same time, the algorithm monitored the appearance of boost pressure values that went beyond the scope of the region and calculated a new approximating function of the region's boundaries.The new function was tested and... if successful, it replaced the previous one and was accepted as the main one.The evolution of the model during the study period and the resulting performance are presented in Figure 4.

Discussion
It can be seen in (Figure 4) that the final model is almost identical to the characteristic obtained on the brake test bench and can be successfully used as a source of reference values for the compared parameters for calculating the most energy-efficient operating mode of a machine-tractor unit.
A diagram of how the quality of the model improves when new data is received during the operation of the tractor is presented in Figure 5.The figure shows that as new data is added, the accuracy of the characteristics of the gas turbine supercharging of the tractor increases, which confirms the hypothesis put forward.The figure also shows that the frequency of appearance of new data that changes the original model is a nonlinearly distributed value in time, which has a decreasing trend as the simulated values approach the actual ones.The analysis showed that the same type of load and speed modes of engine operation leads to an increase in the share of insignificant (not leading to a change in the basic model) new data.When the nature of the load and speed modes of engine operation changes (for example, when changing the type of work), the density of the appearance of new significant data (acceleration of model evolution) increases.

Conclusion
The study allowed us to draw the following conclusions:  The study showed that the developed algorithms make it possible to determine the actual characteristics of the turbocharging of a diesel engine without using a test bench. The developed algorithms can be used both to clarify a known characteristic and to determine a new one in the complete absence of initial data. Taking into account the specific operating modes of an agricultural tractor engine, the developed algorithms make it possible to begin the practical use of the model immediately after the calibration stage and determination of the acceleration characteristics. The study showed that the frequency of appearance of new data that changes the original model is a nonlinearly distributed value in time, and with the same type of load and speed modes of engine operation, it decreases as the simulated values approach the actual ones.When the nature of the load and speed modes of engine operation changes (for example, when the type of work changes), the density of the appearance of new data (acceleration of model evolution) may increase. The uneven appearance of new data allows us to consider the possibility of regulating the frequency of polling parameter values at various stages of the model's operation (primary calibration, intensive training, adequacy monitoring, etc.), which will reduce the requirements for hardware and computing resources.

Fig. 1 .
Fig. 1.Energy efficiency of diesel engine and characteristics of diesel engine turbocharging pressure.

Fig. 2 .
Fig. 2. Diagrams of acceleration of inertial mass attached to the engine crankshaft (torque measurement) and external speed characteristics of the engine torque obtained by the standard method and the acceleration method.

Fig. 3 .
Fig. 3. Diagrams of acceleration of inertial mass attached to the engine crankshaft (Turbocharger pressure measurement measurement) and external speed characteristics of the engine turbocharger pressure obtained by the standard method and the acceleration method.

Fig. 4 .
Fig. 4. Determination of the actual turbocharging characteristics of diesel engines using support vector machines (SVM).

Fig. 5 .
Fig. 5. Improving the quality of the model as new data is collected.