We offer an information technology for diagnosing technical systems by monitoring the values of their internal parameters and comparing with the maximum allowable values. Diagnosed parameters of the internal elements of the technical system are determined by the mathematical calculations based on the well-known mathematical model of the system and the measured values of its output characteristics. Optimization methods are used for calculating the values of the internal parameters of the system.
The reliability of any technical device is determined by the quality of its development,
is ensured in the manufacturing process and maintained during operation. The
impossibility of creating absolutely reliable products makes relevant the research,
development and applying of principles, ways, methods and means, which increase reliability
by timely detection and elimination of equipment failures. The main ways to prevent
the failure of technical systems include the effective monitoring and diagnosis of their
technical condition. Timely detection and elimination of defects increases the
probability of failure-free operation, and also reduces the cost of operating controlled
objects. The time spent on device diagnostics can be significantly reduced by
automation of the diagnosis and using rational diagnostic procedures. There are different
variants of the strategy of finding defects for both automated and non-automated
diagnostics [
Failures occurring in the system due to strong changes in the values of its internal parameters are easier to detect because they lead to significant changes in the output characteristics. At the same time, the drift of the parameters of the system elements, for example, in the course of its operation under the influence of ageing and external factors, leads to small variations in the output characteristics with a slow deterioration of the properties. In addition, it is not always the overrange of the parameter of the internal element of the system beyond the permissible limits that leads to an unacceptable deviation of the controlled output characteristic. However, this may change for the worse the modes of operation of the system elements, which after a certain period of time will lead to an even greater change in the parameters and, as a result, to a defect. Such deviations of the internal parameters of the system are called latent defects, and they, as a rule, require the development of special diagnostic methods, since they are not detected by traditional methods. Also, during the operation of the system, there is a need not only to respond on the fly to its failures, but also to monitor the status of parameters and modes of operation of its elements and analyze trends in their work. This will allow not only to anticipate failures, but also to issue recommendations for their prevention by assessing the approximation of monitored parameters to their maximum allowable values, which can also vary depending on the time of operation, the effect of temperature and other external factors.
These tasks can be effectively solved by automated determination of the values of parameters and modes of operation of system elements based on stimulating input actions and experimentally obtained output characteristics. 2
The mathematical model should allow to determine the values of the parameters of the internal elements of the system being diagnosed from its known (measured) output characteristics.
In practice, there is only access to a limited number of circuit nodes, to which stimulated signals can be sent and output characteristics can be recorded. In addition, the number of internal circuit parameters is much greater than the number of obtainable nodes. Therefore, to determine the values of the parameters of internal elements from the measured output characteristics it is proposed to apply the optimization method. In the optimization process, the values of internal parameters are optimized so as to maximally bring the calculated values of the output characteristics of the system under diagnosis to the measured values.
As a criterion for the correspondence of the calculated values of the output characteristics to the measured values, we use the criterion of the minimum of the rootmean-square error (1):
M N f q ji 1 j1 i1
Yji calc q
Yji meas q 2 min , where Yji calc (q), Yji meas (q) are respectively the calculated and measured value of the jth output characteristic at the i-th point, which depends on the vector of parameters of the elements of the scheme q; ji are weighting indices of measurement accuracy of the j-th characteristic at the i-th point, which are calculated ji
1 jicalc M N (1 jimeas ) j1 i1 where jimeas is the relative measurement error of the i-th sample on the j-th output characteristic. 3
To minimize the mean-square error function, an optimization method is used.
The methods used to solve optimization issues are rather numerous [
It is most expedient to use the Davidon-Fletcher-Powell method [
The search for the minimum of the objective function (1) begins at the starting point q0 (usually, the nominal values of the diagnosed parameters), and the initial matrix H0 is taken as the indentity one. The iterative procedure can be represented as follows: 1. At step i, there is a point qi and the symmetric matrix Hi is positive defined. 2. As direction of the search, to take a direction di = - Hi gi.
3. To find the function i, which minimizes the function f (qi+i di), to do a onedimensional search along the straight line qi +i di .
4. To calculate the increase in the parameters vi = i di . 5. To calculate the new values of the parameters qi+1 =qi + vi .
6. To calculate the new values of the objective function f (qi+1) and its gradient gi+1 for the values of the parameters qi+1. If the values of |gi+1| or |vi | small enough, complete the optimization, otherwise continue.
7. To calculate the increase in the gradient ui = gi+1 - gi . 8. To calculate the matrix Ai
A vi vi i where vi is the vector of increment of parameter values, viT is the transposed vector of increment of parameter values, ui is the vector of increment of the gradient of the objective function.
9. To calculate the matrix Bi = - Hi ui uiT Hi / (uiT Hi ui), where Hi is the matrix H at the i-th iteration, ui is the gradient increment vector, uiT is the transposed gradient increment vector.
10. To update the matrix H in the following way: Hi+1 = Hi+ Ai + Bi , where Hi+1 is the matrix H at the i+1-st iteration, Hi is the matrix H at the i-th iteration, Ai is the matrix A at the i-th iteration, Bi is the matrix B at the i-th iteration.
11. To increase i by one and to go back to step 2. 4
Functional capabilities and organization of software determine the basic requirements for the software system under development for automated diagnostics of the parameters of elements of technical systems.
The requirements to the functional capabilities of the complex can be formulated as follows.
The complex should allow: ─ to analyze the characteristics of the technical system at the design stage; ─ to obtain, according to the results of the analysis, the necessary test input effects and measurement points of the controlled output characteristics; ─ by measured output characteristics to determine the actual values of the parameters of the elements of the system; ─ automatically form the boundaries of the rejection tolerances for the parameters of the elements of the system, taking into account its lifetime, temperature and other external factors; ─ by comparing the actual values of the parameters of the elements with the maximum permissible values, give information about the causes of system malfunction to the element level.
The practical implementation of the functions of constructing a mathematical
model of the system being diagnosed and calculating its output characteristics can be
performed using the methods and algorithms described in [
To implement the functions of calculating the values of the internal parameters of the system from the known values of its output characteristics, the additional use of the diagnostic model of the system [12] is necessary, on the basis of the objective function (1).
From the point of view of software organization, the complex should meet the following requirements: tional capabilities; system being diagnosed; of diagnosing technical systems; elements. ─ have a block-modular structure that allows you to effectively complement the complex with other functional blocks and software patterns that extend its func─ to be able to function as part of an integrated CAD-system used in the design of the ─ be open to the emergence of new numerical analysis methods used in the operation of the complex in order to increase the efficiency of its application in the process ─ to incorporate a database of maximum permissible values of parameters of system 5
The structure of the developed software complex is shown in Figure 1 [13], where the dotted line outlines the software modules that are part of the CAD for designing the diagnosed system and are used by the developed software complex. The arrows in the diagram show the direction of data transfer between the modules.
Element parameqi+1 ters calculation module f, g, q no
Another important task of developing an automated diagnostics software complex is the development of an algorithm for its functioning. The algorithm of functioning of the complex is implemented by the managing program, which coordinates the interaction of program modules and ensures the implementation of certain procedures.
The algorithm of functioning of the complex, the block diagram of which is shown in Figure 2, is based on the method presented in Section 3, the requirements for the program complex and the structure of the complex presented above.
Block 1. The start of the algorithm of the software complex functioning.
Block 2. Introduction of the necessary source data: a basic diagram, technological tolerances on the parameters of elements, factor coefficients, maximum allowable modes of operation of elements, values of external factors, the parameter value of the calculation process cessation, the choice of diagnosable parameters and restrictions on them.
Block 3. Set of the input effects, measurement points and measurable values of the output characteristics.
Block 4. Formation of a mathematical model of the system being diagnosed with the data inserted.
Block 5. Calculation of output characteristics and functions of parametric sensitivity of output characteristics to changes in the values of the parameters of the elements.
Block 6. On the basis of the parametric sensitivity functions of the output characteristics, the formation of a test matrix with respect to the diagnosed parameters and the calculation of the rank of the matrix .
Block 7. Determination of the degree of the possibility of a solution with respect to the diagnosable parameters nq, where nq is the number of diagnosable parameters. If the condition of diagnosability 0 is fulfilled, then the weighting factors are calculated (block 8). If the condition 0 is not fulfilled, then additional input actions and control points of measurement are needed, that is, a return to the fulfilment of block 3.
Block 8. The calculation of the weighting coefficients of the objective function on the basis of the measurement accuracy of the corresponding output characteristics.
Block 9. The calculation of the objective function to determine diagnosable parameters.
Block 10. Calculation of the gradient of the objective function.
Block 11. Checking the completion of the process of optimizing the values of diagnosable parameters.
Block 12. The inclusion of additional controlled characteristics.
Block 13. Calculation of parameters and modes of operation of the elements of the system being diagnosed.
Block 14. Calculation of the maximum permissible values of the parameters of the elements, taking into account the temperature and time of operation.
Block 15. Comparison of the calculated values of parameters and modes of operation of the elements of the system being diagnosed with the maximum allowable values.
Start Input of the initial data Setting signals ment points
stimulation and
measureFormation of a mathematical model Calculation characteristics parametric functions of output
and sensitivity Calculation of the rank of the test matrix 0 yes
no Calculation of coefficients
weight Calculation of the objective function The calculation of the gradient of the objective function 10 11 13 14 15 16 17 no 12 Inclusion of additional controlled characteristics
Block 16. Interpretation of the results of calculations and diagnostics, that is, the derivation of the calculated values of the parameters and modes of operation of the elements and the results of their comparison with the maximum allowable values of the classification of the technical state of the system being diagnosed.
Block 17. The end of the algorithm of the software complex functioning.
If according to the results of diagnosing any one or several internal parameters of the system go beyond their maximum permissible limits, the presence of a defect is ascertained. If any internal parameter of the system has not reached its maximum permissible value, but is close to it, we can speak of a possible defect in the near future. In this case, it is necessary to predict the behavior of the parameter [14] in order to take action in advance without allowing the parameter to go beyond the tolerances. 6
To test and confirm the practical application of the developed diagnostic method, we conduct the experimental studies of simple technical systems representing basic analog electrical circuits.
The passive RC low-pass filter was taken as the simplest test case [12]. Its basic electrical circuit diagram is shown in Figure 3.
The electrical parameters of the device are the resistance of resistors R1, R2 and the capacitance of capacitor C. Their nominal values:
C1 = 100 pF, R1 = 10 k, R2 = 10 k.
To ensure the diagnosability of the filter, it is necessary to select input influences and output characteristics sufficient for unambiguous determination of the parameters of the filter elements. Such a linear frequency-dependent device is advisable to diagnose in the frequency domain. If the stimulating signal is the input harmonic voltage V1, and the output controlled characteristic is V2, then in accordance with section 5 the test diagnostic matrix will have a rank of 1. Thus, when monitoring the voltage V2, it is impossible to ensure the diagnosability of three circuit parameters. In this case, the scheme can be diagnosed only with a single fault. If the input action is voltage V1, and the output controlled characteristic is alternating current I, then the test matrix will also have a rank equal to 1. If the output controlled characteristics are current I and voltage V2, then the rank of the resulting matrix is three, and the scheme will be diagnosed over all parameters. Therefore, the amplitude-frequency dependences of the output voltage V2 and the input current I are used as output characteristics. The test input is a harmonic voltage with amplitude of 1V and a frequency of 0, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz.
First, using CAD MAES-P [12] according to the specified scheme, parameter values and test input effects, the selected output characteristics were calculated. Then, using the diagnostic program, these parameters were used to calculate the values of the parameters of the elements, which were compared with their previously specified values. Thus, verification of the accuracy of identification of parameter values was carried out on the calculated output characteristics, which were taken as measured and corresponded to the values of the parameters of the elements, both within tolerances and beyond their limits [13]. The results of the calculation of the parameters of the filter elements are shown in Table 1.
From Table 1 it can be seen that in all cases, the parameters of the elements are uniquely identified with an error not exceeding 0.01%.
Maximum permissible values Lower Upper
Thus, the accuracy of diagnosing the parameters of the elements is almost determined by the accuracy of the measuring devices.
For more complex schemes, the error in diagnosing, in addition to the accuracy of measuring devices, also depends on the accuracy of mathematical models of the systems being diagnosed. 7
Thus, in the course of automated diagnostics, the problem inverse to the system design problem is solved — the values of the internal parameters of its mathematical model are calculated from the known (measured) output characteristics of the system.
For a successful diagnosis, the main condition is the presence of an adequate (fairly accurate) mathematical model of the system being diagnosed because the higher the accuracy of the system model, the higher the accuracy of diagnosis. Therefore, it will be most effective to diagnose a system using CAD-systems that are used during its design.
At the same time, it makes no difference to which particular area the diagnosed system belongs. It can be of any nature, provided it has a sufficiently accurate mathematical model and the possibility to apply test stimuli and measure the output characteristics necessary for a successful diagnosis.
So, as it is not possible to determine the values of all the internal parameters of its model by the usually available small set of output characteristics of the system, the key point in the diagnosis is to find and select those input test influences and control points for measuring the output characteristics that would uniquely determine the values of all internal parameters of the system being diagnosed. That is, they would ensure the single-extremes of the objective function (1), at least in a certain range of possible values of the internal parameters (usually 2-3 times exceeding the allowable spread of the parameter values according to the system specification).
To speed up this procedure and increase its efficiency, it is advisable to use methods based on neural networks and artificial intelligence [15, 16]. At the same time, the constantly increasing processing power of modern computers allows increasing the complexity of diagnosable systems (and their mathematical models) and approaching the solution of real practical problems. 12. Kasian, M., Kasian, K.: Diagnostic mathematical model of radio-electronic devices. In: 14th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering TCSET2018 - Proceedings, Slavske, 20-24 February 2018, pp. 123-127 (2018) 13. Kasyan, K., Kasyan, N.: Diagnosing of radio-electronic equipment with the help of traditional CAD systems. In: International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science, TCSET2006 Proceedings, Slavske, 28 February - 4 March 2006, pp. 585-587 (2006) 14. Kasian, K., Kasian, M.:. Elementwise Diagnosing of Technical Systems with High Reliability Requirements. In: XIII International Conference Modern problems of radio engineering, telecommunications, and computer science TCSET2016 - Proceedings, Slavske, 23-26 February 2016, pp.558-561 (2016) 15. Kruse, R., Borgelt, C., Klawonn, F. et. al.: Computational intelligence: a methodological introduction. Springer-Verlag, London (2013) 16. Ruan, D. (ed.): Intelligent hybrid systems: fuzzy logic, neural networks, and genetic algorithms. Springer, Berlin (2012)