COMPREHENSIVE ASSESSMENT OF TECHNICAL CONDITION OF VEHICLES DURING OPERATION BASED ON HARRINGTON’S DESIRABILITY FUNCTION

The essence


The object of research is the process of changing the technical condition of vehicles during their operation. The study solved the problem of comprehensive evaluation of change in the technical condition based on Harrington's desirability function. The essence of the results is as follows. A scale of desirability was built and a set of criteria for assessing the technical condition of vehicles was clarified. A general desirability index is proposed as a convolution of partial Harrington desirability functions. When solving the investigated problem, the characteristics and properties of the partial and generalized Harrington's desirability function and their graphical representation were taken into account. Using an example of the technical condition of the chassis and braking system of vehicles, a set of controlled parameters was formed. Based on the values of the controlled parameters, the regression equation of the partial Harrington desirability functions was obtained. The value of the weighting coefficients of each of the criteria was determined and the generalized desirability function was calculated. As a result of the study, it was established that if the generalized criterion of desirability is D < 0.37, then individual nodes, systems, and units of the vehicle are in a pre-accident condition, if 0.37 £ D £ 0.63 -in a satisfactory condition, and if D > 0.63 -in a good condition and cannot be the cause of a traffic accident. An applied aspect of the results is the implementation of the technique of comprehensive assessment of the technical condition of the vehicle. This causes an increase in the productivity of the expert (specialist), will shorten the period of the auto technical examination, and improve its quality. The results could be used by insurance companies and investigators, investigators and judges when considering traffic accidents Keywords: Harrington function and desirability criteria, technical condition, vehicle, control parameter
UDC 629.083DOI: 10.15587/1729-4061.2024.298567

Introduction
Operational reliability and efficiency of vehicles significantly depends on the quality of the technical condition of their components, systems, and units.According to the current regulatory framework, the technical condition of nodes, systems, and assemblies is characterized by a set of variable properties that are determined by structural, technological, and operational parameters.When determining the technical condition of vehicles, diagnostic parameters are used, which are combined with the specified parameters.Diagnostic parameters make up a set of diagnostic information.
It was found that the process of assessing both the general technical condition and the condition of individual nodes, systems, and units of the vehicle during operation is quite complex.It requires the use of universal and effective diagnostic strategies to take into account parameters that are diverse in their physical nature.
At the same time, the issue of identification and comprehensive assessment of the technical condition of nodes, systems, assemblies, and vehicles as a whole is very important.To solve it, it is possible to use a number of approaches and criteria that are built on the basis of the methods of applied mathematics.Methods that have intellectual elements deserve attention: fuzzy methods and sets; method of neural networks; method of genetic algorithms; multi-agent method, etc.In this area, the method of comprehensive assessment of the technical condition of vehicles, based on the Harington desirability functions, is promising.
Therefore, it is a relevant task to carry out studies on devising a methodology for comprehensive and objective assessment of the technical condition of vehicles based on Harrington's desirability function.

Literature review and problem statement
In work [1] it is stated that the assessment of the technical condition of vehicles during operation is related to the need to take into account a number of criteria with different values and dimensions.This circumstance includes the difficulty of combining a set of indicators, values, and criteria during their computer processing.The complexity of the concept of technical condition is reflected in work [2].This is also emphasized in paper [3].These studies also deal with partial parameters for assessing the technical condition of nodes, systems, and units of vehicles.At the same time, a comprehensive assessment of the technical condition is more objective.Specific partial indicators of the technical condition of elements of vehicles are indicated in work [4].These are resource-determining elements of nodes, systems, and assemblies of vehicles.Elements of the vehicle's exterior design are also taken into account.At the same time, as noted in [5], it is indicated that different parameters have different units of measurement: both qualitative and quantitative.It is not very convenient when processing them.It is desirable to operate with integrated parameters, criteria that are dimensionless.
On the other hand, in work [6], the generalization of parameters is given on the example of a binary combination.This applies to the condition of vehicle tires and the timing of wheel brakes.It follows from this that the assessment of the general condition of the vehicle is a multi-criteria task.Such a task is best solved with the help of special mathematical tools -methods of applied mathematics.This is proposed in work [7].Since there are many methods of applied mathematics, one should choose among them those that take into account the specificity of the diagnostic database of the technical condition of vehicles.We can agree with the results reported in [8] on that the methods of fuzzy set theory are most suitable for this.But these methods require careful analysis and adaptation to a comprehensive assessment of the technical condition of vehicles.From this point of view, the methods of constructing the desirability function, which are reflected in work [9], deserve attention.At the same time, there is a need for their comparative analysis and the choice of Harrington's desirability function.Results of the comparative analysis would make it possible to devise a method of objective comprehensive assessment of the technical condition of nodes, systems, assemblies, and the vehicle as a whole.
In this context, it is important to identify the causes of traffic accidents and the propensity of these technical conditions to the possibilities of their implementation.In work [10] it is stated that the vehicle is the most potentially dangerous means of transportation, on which the majority of all traffic accidents occur.This is also confirmed by the results of studies [11,12], which provide statistical data on traffic accidents and their severity.
The seriousness of this problem and related social, economic, and moral-psychological problems is emphasized in work [13].Of course, the problem of identification of traffic accidents needs an objective solution.It is directly related to an objective comprehensive assessment of the technical condition of nodes, systems, assemblies, and vehicles as a whole.As stated in paper [14], in this connection, establishing the true causes of traffic accidents and ensuring a high level of objectivity in the conclusions of forensic auto technical experts is a priority goal of every investigation.There is a need to establish the real causes of traffic accidents.In work [15] it is noted that the causes of traffic accidents should be sought in the unsatisfactory technical condition of vehicles.This work reports the results of research into the technical condition of vehicles, identified malfunctions of individual units, systems, and units that could cause traffic accidents.
These questions are the results of research work [16].A number of shortcomings of the current procedure for assessing the technical parameters of vehicles during forensic examination are indicated, which, according to the authors, is outdated.This is confirmed by the research results in work [17].Paper [18] points out the imperfection of methods for assessing the technical condition and ability of vehicles to cause traffic accidents.This especially applies to modern vehicles.At the same time, a high error is allowed when evaluating individual indicators of the technical condition of vehicles.In work [19] it is noted that existing methods do not provide for taking into account a number of operational factors that affect the effectiveness of diagnosis regarding the quality of the technical condition of vehicles.It is noted that it is impossible to influence the expert's final conclusion, as well as the dri ver's ability to prevent traffic accidents when driving a modern vehicle that has high energy intensity and speed.
All this gives reasons for the expediency of conducting a study on the justified use of Harrington's desirability function.The introduction of criteria for an objective comprehensive assessment of the technical condition of nodes, systems, and assemblies of vehicles and their belongings will make it possible to identify the objective conditions for the occurrence of traffic accidents.

The aim and objectives of the study
The purpose of this study is to identify the possibilities of using Harrington's desirability function for a comprehensive assessment of the technical condition of vehicles during operation.This will make it possible to carry out an objective auto-technical examination of the influence of the technical state of nodes, systems, and units of the vehicle on the occurrence of a traffic accident.
To achieve the goal, the following tasks were set: -to determine the relationship between the controlled parameters of the technical condition and partial desirability functions; -to determine the connection of the partial function of desirability with the regulatory controlled parameters of vehicles; -to construct partial and generalized desirability functions and give their graphical interpretation.

The study materials and methods
The object of our research is the technical condition of vehicles.Research hypothesis: one of the possible ways to assess the technical condition of vehicles, including auto technical examination of traffic accidents, is to use the generalized Harrington desirability function [9,10].It is assumed that the relationship between the controlled parameter and the corresponding partial desirability function is linear.At the same time, the lowest level of desirability corresponds to the maximum permissible value of the parameter, and the best value of the parameter corresponds to the largest value of desirability d.
The generalized desirability function is widely used in the process of conducting various kinds of experimental studies and processing their results.The basis of the construction of the generalized function is the idea of transforming the obtained values of the property indicators into a dimensionless scale of desirability.
The Harrington desirability function has the following advantages: -it is quantitative; -it is expressed by one number; -a given set of values of individual evaluation parameters corresponds to one value of the function; -it has a universal character, and therefore can be used in various areas; -it comprehensively characterizes the object, that is, it meets the requirements of completeness; -it provides a simple way to convert indicators using one graph for all criteria; -it is neutral when generalizing to the final result during construction; -only personal preferences affect the scale of desirability; -it is adequate, which should be understood as the equivalence of partial and generalized functions to the measured values of the optimization parameters in the sense that they can be used for all computational operations defined on the set of values of the optimization parameters.
The purpose of the scale of desirability is to establish the correspondence between the values of the criteria in the physical scales of the value of the corresponding criterion.The scale of desirability is arranged so that a better value of the criterion corresponds to a greater value of desirability.To convert the criterion values into a scale of desirability, the set of values of each criterion is divided into subsets, for which it is possible to say that the quality of the object on each of them is close to the assessment of good, satisfactory, or poor.It should be noted that there may be more gradations.Standard marks on the desirability scale are strictly mandatory.Based on the available experience, the following standard gradations can be recommended (Table 1).The construction of a scale of desirability, which establishes the relationship between the value of the criterion y and its corresponding value d, according to a partial function of desirability, is subjective and reflects the attitude of the researcher to individual criteria.
To construct a scale of desirability, it is convenient to use the method of quantitative assessments with an interval of values of desirability d from zero to one, although other va riants of the scale are possible.The value of the partial function d = 0 corresponds to the most unacceptable measured value of this parameter, and d = 1 to the best value of the parameter, at which its further improvement is either impossible or impractical.The critical point of transition to acceptable quality is the value . . 1 0 36788 0 37 Due to the fact that the values 0.00...0.20 and 0.20...0.37 are unacceptable according to the criterion of desirability, and the values 0.37...1.00are acceptable.
Desirability functions can be of one of three types: 1. Two-way dependences, which are used for indicators for which the deviation of the characteristic from its optimal level in any direction leads to a decrease in quality.
2. One-sided increasing dependences, which are used for those indicators for which their quality increases in the case of an increase in the characteristic, but up to the level of 100 %.
3. One-sided decreasing dependences, which are used for those indicators for which their quality increases in the event of a decrease in the sign, but up to the level of 100 %.
The simplest type of transformation is one in which there is an upper and (or) lower limit of criteria values, and these limits are uniform and do not allow for changes.
The partial function of desirability under one-sided restriction (Fig. 1) takes the form: Similarly, a partial desirability function can be obtained if the constraint of the criterion from above is given.If there is a bilateral restriction for this parameter (Fig. 2), then: For a two-sided restriction, the conversion of the measured criterion y into the scale d is performed using the expression: To determine the coded parameter y′, you can use the following analytical expression: The exponent n can be calculated by presetting some value of y with a corresponding desirability value, preferably between good and very good: For one-sided constraints of the form y £ y max or y > y min , another exponential dependence serves as a more convenient form of transformation of y into d: where d is a partial function of desirability, and ′ y is calculated by the formula: The coefficients b 0i and b 1i can be determined by setting the appropriate desirability values for two values of y, preferably in the interval 0.2 < d < 0.8.
where i is the number of analyzed parameters, α i are weighting factors that indicate the importance of partial criteria.
If at least one partial desirability d i = 0, then the generalized function D i = 0.This means that the investigated object is in an unsatisfactory (emergency) state.If all With the generalized desirability index D, all operations can be performed, as with any other system response, and can also be used for research and further optimization of the process.

1. Relation between the controlled parameters of the technical condition of vehicles and partial desirability functions
The types of controlled parameters of vehicles and the limits of their permissible values are given in Table 2.The basic values of the partial desirability functions and the values of the controlled parameters of the vehicle state are given in Table 3.
According to expression (6): Similarly, according to the data in Table 3, the coefficients b 0 and b 1 for other controlled parameters are determined and given in Table 4.

2. Relationship between partial desirability functions and normative controlled parameters of vehicles
As a result of the research, the dependences of partial desirability functions on the normative values of the controlled parameters of the vehicle were established: 1 68 0 087 In the presence of bilateral restrictions for the controlled parameters of the form y min £ y £ y max , the conversion of the values of the controlled parameters y into partial desirability d was performed according to expression (3).To determine the power of n, the following ratios are established: the maximum allowable value of the controlled parameter (y max , y min ) is given the value of the desirability function equal to 0.2, and the best value is 0.8 (Table 5).Indicators of power n for the controlled parameters у 4 and у 18 were determined according to expression (5), having previously determined the coefficient у′ based on expression (4).The power index for parameter у 4 was n = 0.922, and for parameter у 18 -n = 0.875.
As a result, the dependence of the partial desirability function on the normative values of the indicator of the air pressure in the tires of the vehicle will take the following form: Similarly, the dependence of the partial desirability function on the normative values of the tire adhesion coefficient with the surface was established: A fragment of the array of values of the controlled parameters of five M1 category vehicles, obtained as a result of undergoing technical maintenance and diagnostics, is given in Table 6.According to Table 6, it is possible to find the value of the controlled diagnostic parameters.They describe the working and malfunctioning states of vehicle components.

3. Partial and generalized desirability functions and their graphic interpretations
According to expressions (9) to (26), the values of the controlled diagnostic parameters are converted in partial desirability functions d (Table 7).Weighting coefficients α were calculated for each of the criteria, taking into account which the generalized desirability function D was calculated using formula (8).
Based on the derived partial desirability functions, plots of desirability criteria were constructed (Fig. 3).
It can be seen that the graphic display of Harrington's desirability function (Fig. 3) from the set of controlled parameters gives the intervals of their change in which the serviceable and faulty states of the vehicle elements are determined.We considered options with one-sided and two-sided restrictions.

Discussion of results of evaluating the technical condition of vehicles using the generalized Harrington desirability function
Controlled parameters of the chassis and braking system were used to devise a methodology for comprehensive assessment of the technical condition of vehicles during operation (Table 2).We transformed the corresponding values of the controlled parameters of the technical condition of vehicles into the values of the partial desirability functions; the generalized desirability parameter was evaluated (Tables 3, 4).It was found that the one-sided restriction is characteristic of the following controlled parameters: у 1 -у 3 , у 5 -у 17 .For one-sided restrictions to the controlled parameters of the form y £ y max , y ³ y min , the values of the controlled parameters y into partial desirability d were converted according to expression (6).To determine the coefficients b 0i and b 1i , which are included in expression (7), taking into account the linear dependence between y and d, the following relations were established: the maximum permissible value of the controlled parameter corresponds to the level of desirability, which is bad, equal to 0.2, and the best or very good is the highest -the desirability value is 0.8 (Table 3).The statistical database made it possible to obtain the dependence of partial desi rability functions on the normative values of the controlled parameters ( 9) to (26).The unknown coefficients b 0i and b 1i in the regression equation were determined by the method of least squares.
The values of the controlled diagnostic parameters of five vehicles are given in Tables 5-7.Analysis of our results (Table 7) for the fourth vehicle reveals that the value of the generalized Harrington desirability function D for this vehicle is 0.365.This value corresponds to the level of desirability «bad», which indicates the overall unsatisfactory technical condition of the vehicle.Partial desirability functions of the controlled parameters were analyzed to determine individual components and units of the vehicle that influenced the overall assessment of the vehicle's technical condition.
Table 7 clearly demonstrates that the values of d 2 , d 3 , d 6 , d 7 , d 9 and 22 correspond to the desirability level poorly.This means that the values of the controlled parameters: maximum effort; condition of steering rods; tire condition; braking time, front wheels; axial unevenness, rear wheels; anti-lock system -are outside the limits.The general technical condition of the vehicle, determined during forensic examination, indicates that malfunctions and the pre-accident condition of the above-mentioned units and assemblies could cause traffic accidents.
Thus, the use of the generalized desirability function D and its graphical interpretation for partial desirability functions (Fig. 3) allows for a comprehensive assessment of the technical condition of the vehicle.The above makes it possible to form an expert opinion on the influence of the technical condition of the components, systems, and units of the vehicle on the occurrence of traffic accidents [20][21][22][23][24][25]: -if D < 0.37, then individual components of the vehicle are in a pre-accident state.Malfunction of specific units of the vehicle causes traffic accidents involving a given vehicle; -if 0.37 £ D £ 0.63, then the components of the vehicle are in satisfactory condition and are unlikely to cause traffic accidents involving a given vehicle.At that time, it is necessary to pay attention to those units, systems, and assemblies of the vehicle, the partial diagnostic indicators of which are approaching an unsatisfactory state.Their detailed diagnosis can provide more information about their influence on the occurrence of traffic accidents.In addition, recommendations for unscheduled maintenance or replacement of parts may be given for these nodes, systems, and units.This minimizes the likelihood of future traffic accidents involving a given vehicle; -if D > 0.63, then the components, systems, and units of the vehicle are in good condition, which cannot be the cause of traffic accidents.
The limitations of our study are 0.37 £ D £ 0.63 and D > 0.63.They are acceptable for solving the problem of an integrated positive assessment of the technical condition and solving the issue of low probability of the vehicle causing a traffic accident.
The devised method of comprehensive assessment of the technical condition of vehicles requires further use of specific computer application packages.It is also necessary in the future to devise a methodology and algorithm for performing successive operations in a comprehensive and objective assessment of the technical condition of vehicles.

Conclusions
1.The totality of the controlled parameters of the technical condition of the vehicle was determined using an example of the chassis and braking system parameters.The values of the partial Harrington desirability functions and the corresponding desirability value were found for the parameters change limits.If the equivalent braking distance changes from 0.1 m to 21.6 m, then the value of the partial desirability function decreases from 0.8 to 0.2.The desirability of the parameter at the lower limit corresponds to the «good» state, and at the upper limit -«bad».This makes it possible to establish a relationship between the values of the controlled parameters of the vehicle's technical condition and the values of the partial desirability function.
2. Based on the analysis of the database on the technical condition of the vehicle, the regression equation of the partial Harrington desirability functions from the normative controlled parameters was built.These equations are non-linear.They relate the controlled state parameters of the vehicles to the values of the partial desirability functions.Unknown regression coefficients are determined by the method of least squares.Based on these equations, it is determined that with the increase of the controlled parameters y 1 , y 2 , y 4 , y 8 -y 10 , y 12 , y 15 -y 18 , the value of the partial desirability function decreases.With the increase of controlled parameters y 3 , y 5 , y 6 , y 11 , y 13 , y 14 -increases.Regression equations make it possible to give a qualitative assessment of the technical condition of the vehicle based on normative parameters and values of partial desirability functions.
3. For the studied vehicles, the values of the controlled diagnostic parameters were converted into values of partial desirability functions.The values of partial desirability functions for all controlled parameters for each vehicle were determined by the calculated weighting coefficients.That made it possible to determine the value of the generalized desirability function D and evaluate the technical condition of the vehicle.The first and third vehicles are in good condition.The second and fifth vehicles are in satisfactory condition.The fourth vehicle is in poor condition.A graphical interpretation of the change in the desirability function

Fig. 1 .Fig. 2 .
Fig. 1.Partial desirability function under unilateral constraint equations that determines the coefficients b 01 and b 11 for the total angular gap y 1 takes the following form: of solving this system, we get b 01 = 1.72, b 11 = -0.22.

Table 1
Basic desirability scale marks

Table 3
Basic values of partial desirability functions and corresponding values of controlled vehicle state parameters

Table 4
The value of the coefficients b 0i and b 1і for the controlled parameters y i of the technical condition of vehicles

Table 5
Basic values of the desirability functions and the corresponding values of the controlled parameters of the technical condition of the vehicle

Table 6
Value of controlled diagnostic parameters of vehicles

Table 7
Partial and generalized desirability functions