CN109164249B - Gasoline engine lubricating oil performance evaluation method based on vehicle-mounted diagnosis system - Google Patents

Gasoline engine lubricating oil performance evaluation method based on vehicle-mounted diagnosis system Download PDF

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CN109164249B
CN109164249B CN201811172027.3A CN201811172027A CN109164249B CN 109164249 B CN109164249 B CN 109164249B CN 201811172027 A CN201811172027 A CN 201811172027A CN 109164249 B CN109164249 B CN 109164249B
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李健
魏雷
段海涛
金永亮
贾丹
程冰雪
刘炼
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Wuhan Research Institute of Materials Protection
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Abstract

The invention discloses a gasoline engine lubricating oil performance evaluation method based on a vehicle-mounted diagnosis system, which comprises the steps of firstly, acquiring vehicle operation parameters corresponding to a plurality of different periods in the vehicle operation process through the vehicle-mounted diagnosis system, and acquiring engine lubricating oil samples at corresponding moments; then, detecting the physical and chemical properties, oxidation stability and lubricating oil component change of the collected engine lubricating oil sample to obtain lubricating oil performance parameters; then, carrying out data processing on the obtained vehicle operation parameters and the corresponding lubricating oil performance parameters, solving the comprehensive variation of the vehicle operation parameters and the comprehensive variation of the lubricating oil performance parameters, and establishing a theoretical model; and finally, the comprehensive variation of the performance parameters of the lubricating oil at the moment is calculated by monitoring the running parameters of the vehicle and calculating the comprehensive variation of the running parameters, and the calculated comprehensive variation is brought into the established theoretical model, so that the performance evaluation of the lubricating oil is realized. The invention can provide reference for manufacturers to develop an engine oil life evaluation system and an automobile user to evaluate an oil change period.

Description

Gasoline engine lubricating oil performance evaluation method based on vehicle-mounted diagnosis system
Technical Field
The invention belongs to the field of engine lubricating oil monitoring, relates to a gasoline engine lubricating oil performance evaluation method, and particularly relates to a gasoline engine lubricating oil performance evaluation method based on a vehicle-mounted diagnosis system.
Background
The engine oil plays important roles of reducing friction, preventing abrasion, carrying away heat, cleaning an engine and the like, and is an indispensable component for normal work of an engine of a fuel vehicle. The engine oil works under the conditions of high temperature and oxygen for a long time, and is inevitably subjected to oxidative degradation and performance reduction, so that the lubricating oil needs to be replaced before complete failure. Premature lubricant replacement results in increased vehicle maintenance costs and improper disposal of the spent lubricant can cause significant environmental pollution. And the untimely change of the lubricating oil can cause the excessive abrasion of the engine parts, cause huge loss and even produce catastrophic results, so the reasonable change of the engine oil has very important significance for saving the maintenance cost of vehicles, saving petroleum resources and reducing environmental pollution.
At present, two methods are mainly used for determining the oil change period of engine lubricating oil, one method is to perform laboratory performance detection analysis on the engine lubricating oil and determine the decay degree of the lubricating oil to judge whether the engine lubricating oil fails or not. Another method of determining the oil change period is to change based on the mileage recommended by the automobile manufacturer or 4S store. The oil change mileage and the oil change time recommended by manufacturers are generally determined according to the operation of an engine under extreme conditions, and are often conservative, common users under the extreme conditions are difficult to encounter, so that the oil change of many vehicle engines is too frequent, the vehicle operation states such as idling and frequent starting and stopping have great influence on the decay of the engine oil, and the decay degree of the performance of lubricating oil cannot be comprehensively reflected only through the vehicle operation mileage.
Some automobile manufacturers and learners try to monitor the state of the engine oil by using thermal, optical, electrical and other sensor technologies, but the method of monitoring the state of the engine oil by using the sensor is not widely used due to the limitations of expensive sensor, single function, complex design and installation and the like.
As an important means for monitoring exhaust emission, an on-board diagnostic system (OBD) becomes a necessary system for vehicles to come into the market, and the application of the OBD can be further popularized along with further enhancement of environmental protection awareness. Besides monitoring exhaust emission, a sensor embedded in the vehicle-mounted diagnosis system can also acquire real-time vehicle running information and diagnose the running state of the vehicle. The method is not completely used for judging the state of the engine oil, but the vehicle-mounted diagnosis system is initiatively used for exploring the oil change period of the lubricating oil, so that a new idea is provided for the research of the oil change period of the vehicle lubricating oil. At present, a unified method for determining the oil change period is not available internationally, and the development of an accurate, reliable and high-feasibility engine lubricating oil performance evaluation method has important significance for promoting the quality-based replacement of lubricating oil.
Disclosure of Invention
The invention aims to realize a real-time, efficient and convenient method for evaluating the performance of engine lubricating oil, combine real-time running parameters such as running time of a vehicle engine, idle time of the engine, starting times of the engine, running mileage of the vehicle, service time of lubricating oil and the like monitored by a vehicle-mounted diagnosis system to represent the running working condition of the vehicle, simultaneously carry out analysis on physicochemical performance, oxidation stability and lubricating oil composition change of a lubricating oil laboratory, and combine a data processing method to establish a relation model between the comprehensive variation of the vehicle running parameters and the comprehensive variation of the lubricating oil performance parameters so as to realize the purpose of evaluating the decay degree of the lubricating oil performance through the real-time vehicle running parameters.
The technical scheme adopted by the invention is as follows: a gasoline engine lubricating oil performance evaluation method based on an on-board diagnosis system is characterized by comprising the following steps:
step 1: acquiring vehicle operation parameters corresponding to a plurality of different periods in the vehicle operation process through a vehicle-mounted diagnosis system, and acquiring an engine lubricating oil sample at a corresponding moment; the vehicle operation parameters comprise the service time of lubricating oil, the vehicle operation mileage, the engine operation time, the engine idle time and the engine starting times;
step 2: detecting the physical and chemical properties, oxidation stability and lubricating oil component change of the engine lubricating oil sample collected in the step 1 to obtain lubricating oil performance parameters; the performance parameters of the lubricating oil comprise a total acid value, an initial oxidation temperature, an oxidation value, a nitration value, a vulcanization value and a ZDTP value of the lubricating oil;
and step 3: performing data processing on the vehicle operation parameters obtained in the step 1 and the step 2 and the corresponding lubricating oil performance parameters, solving the comprehensive variation of the vehicle operation parameters and the comprehensive variation of the lubricating oil performance parameters, and establishing a theoretical model;
and 4, step 4: the comprehensive variation of the performance parameters of the lubricating oil at the moment is calculated by monitoring the running parameters of the vehicle and calculating the comprehensive variation of the running parameters, and the calculated comprehensive variation is brought into the established theoretical model, so that the performance evaluation of the lubricating oil is realized.
The invention has the beneficial effects that:
(1) according to the gasoline engine lubricating oil performance evaluation method based on the vehicle-mounted diagnosis system, the vehicle operation parameters and the corresponding lubricating oil performance parameters can be measured at 4-6 moments to establish a relation model between the vehicle operation parameters and the lubricating oil performance parameters, the model precision is high, and the lubricating oil performance evaluation through the vehicle operation parameters is realized.
(2) According to the gasoline engine lubricating oil performance evaluation method based on the vehicle-mounted diagnosis system, the sensor embedded in the vehicle-mounted diagnosis system is utilized, the sensor and the engine structure do not need to be additionally installed or modified, the real-time running parameters of the vehicle can be obtained by combining the intelligent mobile terminal, and reference can be provided for automobile manufacturers to develop an engine oil life evaluation system.
(3) The gasoline engine lubricating oil performance evaluation method based on the vehicle-mounted diagnosis system is combined with the low-cost vehicle-mounted diagnosis system box and the intelligent mobile terminal, and can provide guidance for determining the oil change period for most of vehicle networking users.
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FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a diagram showing the integrated variation ω of the established operating parameters established in embodiment 1 of the present inventioni-driving parametersAnd gammai-oil propertiesA relation model of the comprehensive variation of the performance parameters of the lubricating oil;
FIG. 3 is a diagram illustrating the synthetic variation ω of the established operating parameters established in embodiment 2 of the present inventioni-driving parametersAnd gammai-oil propertiesA relation model of the comprehensive variation of the performance parameters of the lubricating oil;
FIG. 4 is a graph showing the integrated variation ω of the established operating parameters established in embodiment 3 of the present inventioni-driving parametersAnd gammai-oil propertiesAnd (3) a relational model of comprehensive variable quantity of the performance parameters of the lubricating oil.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
Referring to fig. 1, the method for evaluating the performance of the gasoline engine lubricating oil based on the on-board diagnostic system provided by the invention comprises the following steps:
step 1: the method comprises the steps that an intelligent mobile terminal is combined with a vehicle-mounted diagnosis system to obtain vehicle running parameters corresponding to a plurality of different periods (4-6 different periods are adopted in the embodiment) in the vehicle running process, and an engine lubricating oil sample at the corresponding moment is collected; the vehicle operation parameters comprise the service time of lubricating oil, the vehicle operation mileage, the engine operation time, the engine idle time and the engine starting times;
step 2: detecting the physical and chemical properties, oxidation stability and lubricating oil component change of the engine lubricating oil sample collected in the step 1 to obtain lubricating oil performance parameters; the performance parameters of the lubricating oil comprise total acid value, initial oxidation temperature, oxidation value, nitration value, vulcanization value and ZDTP value of the lubricating oil;
and step 3: performing data processing on the vehicle operation parameters obtained in the step 1 and the step 2 and the corresponding lubricating oil performance parameters, solving the comprehensive variation of the vehicle operation parameters and the comprehensive variation of the lubricating oil performance parameters, and establishing a theoretical model;
the specific implementation comprises the following substeps:
step 3.1: preprocessing acquired vehicle running parameters corresponding to a plurality of different periods in the vehicle running process;
the data preprocessing is carried out by dividing each vehicle operation parameter by the initial value of the vehicle operation parameter respectively so as to eliminate the difference between each parameter unit and the magnitude order; obtaining the operation parameter x of the vehicle after the pretreatmenti(k) Where i is 0,1,2, … …, n is the value of the vehicle operating parameter at different time periods, xi(1)~xi(5) Respectively the service time of lubricating oil, the running mileage of a vehicle, the running time of an engine, the idling time of the engine and the starting times of the engine;
step 3.2: defining the vehicle operation parameter obtained by primary monitoring as a reference factor x0(k) And the other time data is used as a comparison factor xi (k) through a formula deltai(k)=|xi(k)-x0(k) L, calculating the variation of each parameter in different periods relative to the initial monitoring parameter, and using a formula
Figure BDA0001822744040000041
Calculating the comprehensive variation value omega of the vehicle operation parameters at different momentsi
Step 3.3: performing data preprocessing on the performance parameters of the lubricating oil at different moments;
the performance parameters of the lubricating oil are divided by the initial values of the performance parameters respectively to carry out data preprocessing so as to eliminate the difference between the unit and the magnitude of each parameter; the performance parameter of the pretreated lubricating oil is obtained to be yi(k) Wherein i is 0,1,2, … …, n is the value of the performance parameter of the lubricating oil in different periods, y isi(1)~yi(6) Respectively the total acid value, the initial oxidation temperature, the oxidation value, the nitration value, the vulcanization value and the ZDTP value of the lubricating oil;
step 3.4: defining the first measured lubricating oil performance parameter as a reference factor y0(k) And the other time data is used as a comparison factor yi(k) Is given by the formula Δ'i(k)=|yi(k)-y0(k) L, calculating the variation of each parameter in different periods relative to the initial monitoring parameter, and using a formula
Figure BDA0001822744040000042
Calculating the comprehensive variation value gamma of the performance parameters of the lubricating oil at different momentsi
Step 3.5: the comprehensive variation quantity omega of the vehicle running parameters and the lubricating oil performance parameters obtained in the step 3.2 and the step 3.4iAnd gammaiEstablishing a theoretical model;
and 4, step 4: the comprehensive variation of the performance parameters of the lubricating oil at the moment is calculated by monitoring the running parameters of the vehicle and calculating the comprehensive variation of the running parameters, and the comprehensive variation is brought into the established theoretical model (linear model), so that the performance evaluation of the lubricating oil is realized.
The working principle of the present invention will be further described in detail with reference to the accompanying drawings and application examples.
Example 1:
urban working condition driving tests are carried out on a commercial mineral oil-1, 6 vehicle operation parameters in different periods are obtained by monitoring through a vehicle-mounted diagnosis system, corresponding lubricating oil performance parameters are obtained through laboratory analysis and are shown in table 1, and the vehicle operation parameters comprise lubricating oil Service Time (ST), vehicle operation Mileage (MIL), Engine Operation Time (EOT), engine Idle Time (ITE) and vehicle starting times (NBS). The relative consumption of the corresponding lubricating oil property package Total Acid Number (TAN), the initial Oxidation temperature (OOT), the Oxidation number (Oxidation), the Nitration number (Nitration), the vulcanization number (vulcanization) and the ZDTP additive was determined.
TABLE 1 mineral oil-1 vehicle operating parameters and lubricating oil performance parameters modeling data sheet
Figure BDA0001822744040000051
The obtained data columns of the vehicle operation parameters and the lubricating oil performance parameters are divided by the corresponding data values of 47 days respectively, unit and order difference among different parameters are eliminated, and the obtained preprocessed data values are shown in table 2.
TABLE 2 pretreated operating parameters and lubricating oil Performance parameter values
Figure BDA0001822744040000052
Defining initial value data as reference factor x0(vehicle operation parameter value corresponding to 47 days after test), and other period data as comparison factor xi(vehicle running parameter values corresponding to 76-200 days in the test) by a formula deltai(k)=|xi(k)-x0(k) Solving the variable quantity of the operation parameter relative to the initial value, and combining the variable quantity with a formula
Figure BDA0001822744040000053
Calculating the comprehensive variation value omega of the vehicle operation parameters at different momentsiSuch as x0(k)=[x0(1),x0(2),x0(3),x0(4),x0(5)]=[1.0000,1.0000,1.0000,1.0000,1.0000],x1(k)=[x1(1),x1(2),x1(3),x1(4),x1(5)]=[1.6170,1.8075,1.6943,1.6285,1.6463]Using the given formula Δi(k)=|xi(k)-x0(k) Can | (Δ 1) ═ 0.6170,0.8075,0.6943,0.6285,0.6463]In combination with the formula
Figure BDA0001822744040000061
Can obtain omega11.4875. By using the same method, the comprehensive variation omega of the operation parameters can be calculatedi-driving parameters=[1.4875,0.6967,0.5103,0.3969,0.3207]. By the same method, the comprehensive variation gamma of the performance parameters of the lubricating oil can be obtainedi-oil properties=[10.1925,4.8481,3.7639,3.1109,2.8722]Establishing comprehensive variation of operation parameters omegai-driving parametersAnd gammai-oil propertiesThe relation model of the comprehensive variation of the performance parameters of the lubricating oil is shown in fig. 2, the theoretical model is that y is 6.4220x +0.5887, wherein x is the comprehensive variation of the vehicle operation parameters, y is the comprehensive variation of the performance parameters of the lubricating oil, and the model R is20.999, indicating high model accuracy.
The vehicle running parameters and the lubricating oil performance parameters (table 3) obtained in the running test process of 230-410 days are taken as verification data to verify the accuracy of the established model, the errors of the obtained modulus theoretical calculation value and the laboratory detection analysis value are shown in table 4, and the error range of the theoretical calculation and the laboratory detection is-0.2470-0.1147, which indicates that the method has high prediction precision.
TABLE 3 vehicle operating parameters and lube oil Performance parameter verification data sheet
Figure BDA0001822744040000062
TABLE 4 lubricating oil performance parameter comprehensive variation theoretical calculation value and experimental detection value
Figure BDA0001822744040000063
Example 2:
an urban working condition running test is carried out on another commercially available mineral oil-2, the vehicle operation parameters and the lubricating oil performance parameters are shown in table 5, and a theoretical model is established by taking the vehicle operation data and the lubricating oil performance parameters of 19 days, 48 days, 79 days, 108 days and 137 days of lubricating oil service as modeling data and is shown in fig. 3. The theoretical model is y-7.1277 x +1.6753, wherein x is the comprehensive variation of the vehicle operation parameters, y is the comprehensive variation of the lubricating oil performance parameters, and the model R20.950, indicating high model accuracy. The prediction accuracy of the model is verified by using the 156-day service data of the lubricating oil, after 156 days of service of the lubricating oil, the comprehensive variation of the vehicle operation parameters is 0.1843, the comprehensive variation of the performance parameters of the lubricating oil detected in a laboratory is 2.8907, the comprehensive variation of the performance parameters of the lubricating oil calculated theoretically is 2.9889, the error between the calculated theoretical value and the detected value of the laboratory is 0.0982, and the model prediction accuracy is high.
TABLE 5 mineral oil-2 running test vehicle operating parameter and lubricating oil performance parameter table
Figure BDA0001822744040000071
Example 3:
the two kinds of commercially available fully synthetic lubricating oils were subjected to city condition and city and high-speed mixed condition running tests, respectively, and the vehicle running parameters and the lubricating oil performance parameters are shown in table 6. The fully synthetic oil-1 runs under urban working condition, and a theoretical model is established by taking vehicle running data and lubricating oil performance parameters of lubricating oil which is in service for 23 days, 54 days, 83 days and 114 days as modeling data, as shown in figure 4. The theoretical model is y-12.6790 x +0.1610, wherein x is the comprehensive variation of the vehicle operation parameters, y is the comprehensive variation of the lubricating oil performance parameters, and the model R20.996, indicating high model fitting accuracy. The data of 143 days and 147 days of lubricating oil in service are used as verification data to verify the accuracy of the theoretical model, the comprehensive variation of the operating parameters of the crown blocks in 143 days and 147 days of lubricating oil in service are 0.2096 and 0.2038 respectively, the comprehensive variation of the performance parameters of lubricating oil detected in a laboratory is 3.0110 and 2.8164 respectively, the comprehensive variation of the performance parameters of lubricating oil calculated theoretically is 2.8185 and 2.7450 respectively, the errors of the calculated theoretical value and the detected value of the laboratory are-0.1925 and-0.0714 respectively, and the model prediction precision is high.
TABLE 6 running parameters and lubricating oil performance parameters of synthetic oil-1 and synthetic oil-2 running test vehicles
Figure BDA0001822744040000081
The fully synthetic oil-2 is a mixed operation vehicle condition of urban working conditions and high-speed working conditions, vehicle operation data and lubricating oil performance parameters of 25 days, 59 days, 93 days and 123 days of lubricating oil service are used as modeling data, and a theoretical model is established as shown in figure 4. The theoretical model is y-21.4551 x-0.2418, wherein x is the comprehensive variation of the vehicle operation parameters, y is the comprehensive variation of the lubricating oil performance parameters, and the model R20.998, indicating high model fitting accuracy. The method takes 154-day data of lubricating oil service as verification data to verify the accuracy of a theoretical model, the comprehensive variation of the operating parameters of a 154-day running vehicle of the lubricating oil service is 0.1579, the comprehensive variation of the performance parameters of the lubricating oil detected in a laboratory is 4.0351, the comprehensive variation of the performance parameters of the lubricating oil calculated in theory is 3.1460, the error between the theoretical calculation value and the detection value of the laboratory is 0.8891, and the model is modeledThe type prediction precision is high.
On the basis of a driving test, a theoretical model is established by using the comprehensive variation of the running parameters of the test vehicle and the comprehensive variation of the performance of the test lubricating oil, and the relation between the running parameters of the vehicle and the performance decay of the lubricating oil in the test process is represented. The modeling method can be used for predicting the performance degradation degree of the engine oil by combining vehicle running parameters acquired by a vehicle-mounted diagnosis system, and provides reference for reasonable replacement of the oil replacement period of the lubricating oil. The method for monitoring the oil state of the engine by adopting the vehicle-mounted diagnosis system does not need to modify vehicles or increase sensors, and lays a good foundation for the popularization of the method. The vehicle-mounted diagnosis system can realize that a vehicle owner can acquire real-time running information of the vehicle at any time and any place by combining with a mobile phone application program, and the running state of the lubricating oil is calculated by the given method, so that the real-time monitoring of the state of the lubricating oil can be realized.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (4)

1. A gasoline engine lubricating oil performance evaluation method based on an on-board diagnosis system is characterized by comprising the following steps:
step 1: acquiring vehicle operation parameters corresponding to a plurality of different periods in the vehicle operation process through a vehicle-mounted diagnosis system, and acquiring an engine lubricating oil sample at a corresponding moment; the vehicle operation parameters comprise the service time of lubricating oil, the vehicle operation mileage, the engine operation time, the engine idle time and the engine starting times;
step 2: detecting the physical and chemical properties, oxidation stability and lubricating oil component change of the engine lubricating oil sample collected in the step 1 to obtain lubricating oil performance parameters; the performance parameters of the lubricating oil comprise a total acid value, an initial oxidation temperature, an oxidation value, a nitration value, a vulcanization value and a ZDTP value of the lubricating oil;
and step 3: performing data processing on the vehicle operation parameters obtained in the step 1 and the step 2 and the corresponding lubricating oil performance parameters, solving the comprehensive variation of the vehicle operation parameters and the comprehensive variation of the lubricating oil performance parameters, and establishing a theoretical model;
and 4, step 4: the comprehensive variation of the performance parameters of the lubricating oil at the moment is calculated by monitoring the running parameters of the vehicle and calculating the comprehensive variation of the running parameters, and the calculated comprehensive variation is brought into the established theoretical model, so that the performance evaluation of the lubricating oil is realized.
2. The gasoline engine lubricating oil performance evaluation method based on the on-vehicle diagnosis system according to claim 1, characterized in that: in the step 1, an intelligent mobile terminal is adopted to combine with a vehicle-mounted diagnosis system to obtain vehicle operation parameters.
3. The gasoline engine lubricating oil performance evaluation method based on the on-vehicle diagnosis system according to claim 1, characterized in that: the specific implementation of the step 3 comprises the following substeps:
step 3.1: preprocessing acquired vehicle running parameters corresponding to a plurality of different periods in the vehicle running process;
the data preprocessing is carried out by dividing each vehicle operation parameter by the initial value of the vehicle operation parameter respectively so as to eliminate the difference between each parameter unit and the magnitude order; obtaining the operation parameter x of the vehicle after the pretreatmenti(k) Where i is 0,1,2, … …, n is the value of the vehicle operating parameter at different time periods, xi(1)~xi(5) Respectively the service time of lubricating oil, the running mileage of a vehicle, the running time of an engine, the idling time of the engine and the starting times of the engine;
step 3.2: defining the vehicle operation parameter obtained by primary monitoring as a reference factor x0(k) The data at other time is used as a comparison factor xi(k) By the formula Δi(k)=|xi(k)-x0(k) L, calculating the variation of each parameter in different periods relative to the initial monitoring parameter, and using a formula
Figure FDA0003051199290000011
Calculating the comprehensive variation value omega of the vehicle operation parameters at different momentsi
Step 3.3: performing data preprocessing on the performance parameters of the lubricating oil at different moments;
the performance parameters of the lubricating oil are divided by the initial values of the performance parameters respectively to carry out data preprocessing so as to eliminate the difference between the unit and the magnitude of each parameter; the performance parameter of the pretreated lubricating oil is obtained to be yi(k) Wherein i is 0,1,2, … …, K is the value of the performance parameter of the lubricating oil in different periods, y isi(1)~yi(6) Respectively the total acid value, the initial oxidation temperature, the oxidation value, the nitration value, the vulcanization value and the ZDTP value of the lubricating oil;
step 3.4: defining the first measured lubricating oil performance parameter as a reference factor y0(k) And the other time data is used as a comparison factor yi(k) Is given by the formula Δ'i(k)=|yi(k)-y0(k) L, calculating the variation of each parameter in different periods relative to the initial monitoring parameter, and using a formula
Figure FDA0003051199290000021
Calculating the comprehensive variation value gamma of the performance parameters of the lubricating oil at different momentsi
Step 3.5: the comprehensive variation quantity omega of the vehicle running parameters and the lubricating oil performance parameters obtained in the step 3.2 and the step 3.4iAnd gammaiAnd establishing a theoretical model.
4. The gasoline engine lubricating oil performance evaluation method based on the on-vehicle diagnosis system according to any one of claims 1 to 3, characterized in that: and 3, establishing a theoretical model which is a linear model.
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