Selection of a Minimal Set of Monitored Parameters for Automating Fault Diagnosis in Certain Cyclotron Devices
Full Text
PROCEEDINGS OF THE TOMSK POLYTECHNIC INSTITUTE,
AWARDED THE ORDER OF THE OCTOBER REVOLUTION
AND THE ORDER OF THE RED BANNER OF LABOR
Vol. 206 1973
SELECTION OF A MINIMAL SET OF MONITORED PARAMETERS FOR AUTOMATING FAULT DETECTION IN CERTAIN CYCLOTRON DEVICES
N. I. SABLIN
(Presented by the scientific seminar of the Automation and Computer Engineering Sector of the Research Institute of Nuclear Physics, Electronics, and Automation)
The problem of analyzing systems for the purpose of rationally constructing systems of automatic monitoring of operability and fault detection (or methods of the same purpose) is divided into 3 stages:
-
Determination of the minimum amount of information sufficient for drawing a conclusion about the operability of systems (monitoring the operability of systems).
-
Determination of the minimum amount of information sufficient for identifying the locations and causes of faults in the system (fault detection).
-
Optimization of test programs on the basis of the information obtained in the first two stages.
In works [1, 2], an analysis of cyclotron equipment was carried out with the aim of synthesizing an instrument for automatic monitoring of operability and fault detection. In the present work, the second stage of the above-mentioned problem is solved for certain cyclotron devices. For this purpose, in order to formalize the process, logical models of the devices under consideration were constructed, according to the method of V. V. Karibskii [3], on the basis of functional diagrams and the concept of functional dependence; these models make it possible to describe mathematically the properties of the devices being analyzed that are of interest to us. Then, on the basis of the logical models, the corresponding minimal sets of monitored parameters were determined.
High-Frequency Generator
The functional diagram of the high-frequency generator is shown in Fig. 1. The logical model of the generator, constructed on the basis of the functional diagram and the concept of functional dependence, is shown in Fig. 2.
In the logical model the following designations of blocks are adopted:
$Q_1 \div Q_5$ — respectively, the 1st, 2nd, 3rd, 4th, and 5th stages of amplification of high frequency;
$Q_6$ — the second stage of the driver amplifier;
$Q_7$ — the first stage of the driver amplifier;
$Q_8 \div Q_{10}$ — 2.5 kV and 1.25 kV rectifier;
$Q_{11}$ — the first stage of the master oscillator;
Fig. 1. Functional diagram of the high-frequency generator: I, II, III, IV, V—power stages of the high-frequency generator; 1—rectifier for the master oscillator and amplifier; 3—amplifier; 4—10/5 kV power rectifier; 5—2.5/25 kV rectifier; 6—400 V rectifier.
$Q_{12}$ — second stage of the master oscillator;
$Q_{13} \div Q_{15}$ — exciter rectifier;
$Q_{16}$ — selenium rectifier — 400 V;
$Q_{17}, Q_{18}$ — high-power rectifier 10.5 kV.
Fig. 2. Logical model of the high-frequency generator
The blocks of the logical model have external inputs
$z_{11}, z_{21}, z_3, z_{41}, z_{51}$ — voltage $3 \times 380$ V for the generator-tube filaments;
$z_{61}, z_{71}$ — filament voltage of the exciter-amplifier tubes;
$z_{81}, z_{91}, z_{10.1}, z_{17.1}, z_{18.1}$ — voltage $3 \times 10$ kV;
$z_{82}, z_{92}, z_{10.2}, z_{17.2}, z_{18.2}$ — voltage $3 \times 380$ V for the thyratron filaments and for obtaining the peak voltage on the thyratron grids, $\sim 350$ V;
$z_{83}, z_{93}, z_{10.3}, z_{17.3}, z_{18.3}$ — alternating voltage $3 \times 220$ V for obtaining a DC bias of 220 V on the thyratron grids;
$z_{13.1}, z_{14.1}, z_{15.1}$ — voltage $\sim 220$ V;
$z_{16.1}$ — voltage $\sim 380$ V.
The blocks of the logical model have the following external inputs and the internal inputs of blocks associated with them:
$y_1 = x_{21}$ — output of the first generator stage;
$y_2 = x_{31}$ — output of the second generator stage;
$y_3 = x_{41}$ — output of the third generator stage;
$y_4 = x_{51}$ — output of the fourth generator stage;
$y_5$ — output of the fifth generator stage;
$y_6 = x_{11}$ — output of the exciter amplifier;
$y_7 = x_{62}$ — output of the first stage of the exciter amplifier;
$y_8 = x_{13} = x_{23} = x_{61} = x_{71}$ — DC voltage 600 V for supplying the screen grids of the generator tubes and the anodes of the amplifier tubes;
$y_9 = x_{12}$ — anode voltage 1.25 kV of the first generator stage;
$y_{10} = x_{22}$ — anode voltage 2.5 kV of the second generator stage;
$y_{11}=x_{12.1}$ — output of the first stage of the master oscillator;
$y_{12}=x_7$ — output of the second stage of the master oscillator;
$y_{13}=x_{11.1}=x_{12.4}$ — stabilized voltage of 250 V for supplying the anodes of the master-oscillator tubes;
$y_{14}=x_{11.2}=x_{12.2}$ — voltage of 12.6 V for the tube-filament circuit;
$y_{15}=x_{11.3}=x_{12.3}=x_{63}=x_{73}$ — dc voltage of 250 V for supplying the screen grids of the amplifier and oscillator;
$y_{16}=x_{14}=x_{24}=x_{33}=x_{43}$ — dc bias voltage of −400 V for the control grids of the oscillator;
$y_{17}=x_{32}$ — anode voltage of 5 kV for the third stage of the oscillator;
$y_{18}=x_{52}=x_{42}$ — voltage of 10 kV. Let us agree to denote inadmissible values of the input and output signals by zero, and admissible values by one.
To determine the minimal set of monitored generator parameters required for finding a single fault, we shall single out the set of mandatory monitored parameters and construct a fault table. The fault table (Table 1) was constructed on the basis of the following operating conditions for the blocks of the logical model:
\[ \begin{aligned} y_1 &= Q_1 z_{11} y_6 y_8 y_9 y_{16},\\ y_2 &= Q_2 z_{21} y_1 y_8 y_{10} y_{16},\\ y_3 &= Q_3 z_{31} y_2 y_{16} y_{17},\\ y_4 &= Q_4 z_{41} y_3 y_6 y_{18},\\ y_5 &= Q_5 z_{51} y_4 y_{16} y_{18},\\ y_6 &= Q_6 z_{61} y_7 y_8 y_{15},\\ y_7 &= Q_7 z_{71} y_8 y_{12} y_{15},\\ y_8 &= Q_8 z_{81} z_{82} z_{83},\\ y_9 &= Q_9 z_{91} z_{92} z_{93}, \end{aligned} \qquad \begin{aligned} y_{10} &= Q_{10} z_{10.1} z_{10.2} z_{10.3},\\ y_{11} &= Q_{11} y_{13} y_{14} y_{15},\\ y_{12} &= Q_{12} y_{11} y_{13} y_{14} y_{15},\\ y_{13} &= Q_{13} z_{13.1},\\ y_{14} &= Q_{14} z_{14.1},\\ y_{15} &= Q_{15} z_{15.1},\\ y_{16} &= Q_{16} z_{16.1},\\ y_{17} &= Q_{17} z_{17.1} z_{17.2} z_{17.3},\\ y_{18} &= Q_{18} z_{18.1} z_{18.2} z_{18.3}. \end{aligned} \]
Analysis of the logical model of the generator made it possible to single out the set
\[ \{y_1;\ y_2;\ y_3;\ y_4;\ y_5;\ y_6;\ y_7;\ y_9;\ y_{10};\ y_{11};\ y_{15};\ y_{17}\} \tag{1} \]
of mandatory monitored parameters (outputs), since the faults of the blocks corresponding to them are distinguishable only at the indicated outputs. To determine the other monitored parameters, we select in Table 1 the columns corresponding to the mandatory outputs. Comparing the rows (examining only the selected columns), we write out all pairs of symbols (numbers) of blocks whose faults are indistinguishable from one another at the mandatory outputs, and for each such pair we write down the logical sums of the symbols of the outputs at which they are distinguishable:
\[ \begin{gathered} Q_1 \text{ from } Q_{16}\quad y_{16},\\ Q_4 \text{ from } Q_{18}\quad y_{18},\\ Q_7 \text{ from } Q_8\quad y_8,\\ Q_{11} \text{ from } Q_{13}\quad y_{13},\\ Q_{13} \text{ from } Q_{14}\quad y_{13}\cup y_{14},\\ Q_{14} \text{ from } Q_{15}\quad y_{14}\cup y_{15}. \end{gathered} \]
Having formed the logical product that includes the sets of mandatory monitored parameters and the parameters of system (1), we...
Table 1
| $Q \backslash y_i$ | $y_1$ | $y_2$ | $y_3$ | $y_4$ | $y_5$ | $y_6$ | $y_7$ | $y_8$ | $y_9$ | $y_{10}$ | $y_{11}$ | $y_{12}$ | $y_{13}$ | $y_{14}$ | $y_{15}$ | $y_{16}$ | $y_{17}$ | $y_{18}$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $Q_1$ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_2$ | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_3$ | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_4$ | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_5$ | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_6$ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_7$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_8$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_9$ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_{10}$ | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_{11}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_{12}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| $Q_{13}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| $Q_{14}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| $Q_{15}$ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
| $Q_{16}$ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
| $Q_{17}$ | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| $Q_{18}$ | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
Fig. 3. Functional diagram of the cyclotron vacuum system. FN—fore-vacuum pumps; DN—diffusion pumps; AD—asynchronous motors; D—direct-current motor.
Visible labels in the diagram: SP-11; control of the cyclotron control devices; SP-50; chamber “A”; gate valve; D; DN; FN; AD; water; 220 V; 110 V; \(3 \times 380\) V.
including the sum \((y_{13}\cup y_{14})\), we obtain the following minimal sets of monitored parameters.
\[ \begin{gathered} y_1y_2y_3y_4y_5y_6y_7y_9y_{10}y_{11}y_{12}y_{17}y_{16}y_{18}y_8y_{13}(y_{14}\cup y_{15})=\\ =y_1y_2y_3y_4y_5y_6y_7y_8y_9y_{10}y_{11}y_{12}y_{13}y_{14}y_{16}y_{17}y_{18}\cup\\ y_1y_2y_3y_4y_5y_6y_7y_8y_9y_{10}y_{11}y_{12}y_{13}y_{15}y_{16}y_{17}y_{18}. \end{gathered} \]
Of the two minimal sets of monitored parameters, equal in length and differing from one another by the parameters \(y_{14}\) and \(y_{15}\), we choose the set whose technical implementation is simpler. The simpler set from the standpoint of technical implementation proved to be the set containing the parameter \(y_{15}\) (voltage 250 V), since, when monitoring the parameter \(y_{14}\), it is necessary to use an additional rectifier device.
Vacuum System
The functional diagram of the cyclotron vacuum system is shown in Fig. 3. The logical model of the vacuum system is shown in Fig. 4.
In the logical model the following designations of blocks are adopted:
\(Q_1;\ Q_6;\ Q_{11};\ Q_{16};\ Q_{21};\ Q_{26}\) — fore-vacuum pumps;
\(Q_2;\ Q_7;\ Q_{12};\ Q_{17};\ Q_{22};\ Q_{27}\) — electric motors of the fore-vacuum pumps;
\(Q_3;\ Q_8;\ Q_{13};\ Q_{18};\ Q_{23}\) — vacuum gate valves;
\(Q_4;\ Q_9;\ Q_{14};\ Q_{19};\ Q_{24}\) — gate-valve drives;
\(Q_5;\ Q_{10};\ Q_{15};\ Q_{20};\ Q_{25}\) — diffusion pumps;
\(Q_{28}\) — chamber;
\(Q_{29}\) — ion guide;
\(Q_{30}\) — “D” chamber.
The blocks of the logical model have external outputs:
\(z_{5.1};\ z_{10.1};\ z_{15.1};\ z_{20.1};\ z_{25.1}\) — water for cooling the gate valves;
\(z_{5.2};\ z_{10.2};\ z_{15.2};\ z_{20.2};\ z_{25.2}\) — voltage for supplying the heaters of the diffusion pumps;
\(z_{4.1};\ z_{9.1};\ z_{14.1};\ z_{19.2};\ z_{24.1}\) — constant voltage 110 V;
\(z_{2.1};\ z_{7.1};\ z_{12.1};\ z_{17.1};\ z_{22.1};\ z_{27.1}\) — voltage \(3\times 380\) V.
The blocks of the logical model have the following external inputs and associated internal block inputs:
\(y_1=x_{28.2};\ y_6=x_{5.1};\ y_{11}=x_{10.1};\ y_{16}=x_{15.1};\ y_{21}=x_{20.1};\ y_{26}=x_{25.1}\) — proper operation of the fore-vacuum pumps (vacuum \(10^{-3}\) mm Hg);
\(y_2=x_{1.1};\ y_7=x_{6.1};\ y_{12}=x_{11.1};\ y_{17}=x_{16.1};\ y_{22}=x_{21.1};\ y_{27}=x_{26.1}\) — proper operation of the pump drives;
\(y_4=x_{3.1};\ y_9=x_{8.1};\ y_{14}=x_{13.1};\ y_{19}=x_{18.1};\ y_{24}=x_{23.1}\) — proper operation of the gate-valve drives;
\(y_5=x_{3.2};\ y_{10}=x_{8.2};\ y_{15}=x_{13.2};\ y_{20}=x_{18.2};\ y_{25}=x_{23.2}\) — proper operation of the diffusion pumps (vacuum \(10^{-5}\) mm Hg);
\(y_3=x_{28.1};\ y_8=x_{29.3};\ y_{13}=x_{29.2};\ y_{18}=x_{29.1};\ y_{23}=x_{30.1}\) — proper operation of the vacuum gate valves;
\(y_{28}=x_{29.1}\) — the chamber is in good working order with respect to vacuum;
\(y_{29}=x_{30.1}\) — the ion guide is in good working order with respect to vacuum;
\(y_{30}\) — chamber “D” is in good working order with respect to vacuum.
In view of the fact that faults of the blocks of the logical model of the vacuum system are distinguishable only at their outputs (since the output of each block is connected with only one block), all outputs (parameters) of the logical model of the vacuum system are mandatory for fault detection.
Fig. 4. Logical model of the cyclotron vacuum system.
Cooling System
A simplified functional diagram of the cooling system is presented in Fig. 5.
The logical model of the cooling system, constructed on the basis of the functional diagram and the concept of functional dependence, is presented in Fig. 6.
In the logical model the following designations of blocks are adopted:
\(Q_1\) — SP-44 electromagnet;
\(Q_2\) — air cooler;
\(Q_3\) — fan for cooling the SP-44 electromagnet;
\(Q_4; Q_{11}\) — centrifugal pumps;
\(Q_5\) — chamber with accelerator system;
\(Q_6\) — high-frequency generator;
\(Q_7\) — bending lenses;
\(Q_8\) — diffusion pumps;
\(Q_9\) — water-to-water cooler;
\(Q_{10}\) — drain tanks;
\(Q_{12}\) — distillers;
\(Q_{13}\) — anode resistors of the high-frequency generator;
\(Q_{14}\) — fan for cooling the anode resistors.
The blocks of the logical model have external inputs:
\(z_{21}; z_{12.1}\) — tap water;
\(z_{32}; z_{41}; z_{12.2}; z_{14.2}\) — voltage \(3 \times 380\) V;
\(z_{31}; z_{14.1}\) — air.
The blocks of the logical model have the following external and associated internal inputs of blocks:
\(y_1\) — temperature of the SP-44 electromagnet is normal;
\(y_2 = x_{11}\) — proper operation of the cooler (cooling air);
\(y_3 = x_{21}; y_{14} = x_{13.1}\) — fans are serviceable;
\(y_4 = x_{51} = x_{61} = x_{71} = x_{81}\) — centrifugal pumps are serviceable;
\(y_5 = x_{91}; y_6 = x_{92}; y_7 = x_{93}; y_8 = x_{94}\) — the corresponding blocks are cooled;
\(y_9 = x_{10.1}\) — the water-to-water cooler is serviceable;
\(y_{10} = x_{41}\) — drain tanks are serviceable;
\(y_{12} = x_{11.1}\) — distillers are serviceable;
\(y_{13}\) — temperature of the anode resistors is normal.
From the logical model it is evident that faults of all the blocks of the logical model are distinguishable only at their outputs; consequently, all outputs (parameters) of the blocks of the logical model of the cooling system are necessary for fault detection.
Compensation Devices
The functional diagram of the compensation devices is presented in Fig. 7. The logical model of the compensation devices is presented in Fig. 8.
In the logical model the following existing designations of blocks are introduced:
\(Q_1\) — modulator;
\(Q_2\) — alternating-current amplifier;
\(Q_3\) — phase-sensitive amplifier (demodulator);
\(Q_4\) — sinusoidal-oscillation generator;
\(Q_5 \div Q_7\) — power-supply units;
\(Q_8 \div Q_{10}\) — thyratron rectifier.
The blocks of the logical model have external inputs:
\(z_{11}\) — mismatch voltage;
Fig. 5. Simplified functional diagram of cyclotron cooling
Visible labels in the diagram:
- Water
- SP-44
- Water [[unclear: supply/line]]
- Fan
- Air
- Pumps
- Gate valve
- Control-and-signal tank
- Flowmeter
- Filters
- Vacuum pumps
- Water line for cooling
- Drain tank
- Pump
- Distiller
- Water [[unclear: “3-400?”]]
- [[unclear: “Ion”]] sorbers
- Fan
- Air
Fig. 6. Logical model of the cyclotron cooling system.
$z_{51};\ z_{61};\ z_{71}$ — 220 V voltage;
$z_{81};\ z_{91};\ z_{10.1}$ — thyratron filament voltage;
$z_{82};\ z_{92};\ z_{10.2}$ — 1000 V alternating voltage.
The blocks of the logical model have the following outputs and the internal inputs associated with them:
$y_1=x_{21}$ — transformed voltage;
$y_2=x_{31}$ — voltage from the output of the alternating-current amplifier;
Fig. 7. Functional diagram of the cyclotron compensating device.
PCU—phase-sensitive detector, VT-1000—thyratron rectifier for 1000 V
Fig. 8. Logical model of the compensating device
$y_3=x_{31}=x_{91}=x_{10.1}$ — voltage from the output of the phase-sensitive amplifier;
$y_4=x_{11}=x_{33}$ — sinusoidal generator voltage;
$y_5=x_{41}=x_{22}=x_{32}$ — lamp filament voltage = 6.3 V;
$y_6=x_{42}=x_{23}=x_{34}$ — anode supply voltage 300 V;
$y_7=x_{82}=x_{92}=x_{10.2}$ — thyratron bias voltage;
$y_8,\ y_9,\ y_{10}$ — output voltage of the thyratron rectifier.
From the logical model of the compensating device, let us select the set of obligatorily monitored parameters. These parameters are the following outputs of the logical blocks:
$\{y_1;\ y_2;\ y_8;\ y_9;\ y_{10}\}$.
The remaining outputs of the minimal set of monitored parameters will be determined from the fault table (Table 2) of the compensation device. The fault table was constructed on the basis of the following equations for the operability of the units:
\[ \begin{aligned} y_1 &= Q_1 z_{11} y_4, &\qquad y_6 &= Q_6 z_{61},\\ y_2 &= Q_2 y_1 y_5 y_6, & y_7 &= Q_7 z_{71},\\ y_3 &= Q_3 y_2 y_4 y_5 y_6, & y_8 &= Q_8 z_{81} z_{82} y_3 y_7,\\ y_4 &= Q_4 y_5 y_6, & y_9 &= Q_9 z_{91} z_{92} y_3 y_7,\\ y_5 &= Q_5 z_{51}, & y_{10} &= Q_{10} z_{10,1} z_{10,2} y_3 y_7. \end{aligned} \]
Table 2
| \(Q_i \backslash y_i\) | \(y_1\) | \(y_2\) | \(y_3\) | \(y_4\) | \(y_5\) | \(y_6\) | \(y_7\) | \(y_8\) | \(y_9\) | \(y_{10}\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(Q_1\) | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| \(Q_2\) | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| \(Q_3\) | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| \(Q_4\) | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
| \(Q_5\) | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
| \(Q_6\) | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| \(Q_7\) | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| \(Q_8\) | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
| \(Q_9\) | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| \(Q_{10}\) | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
Let us mark in the table the columns corresponding to the mandatory outputs. Comparing the rows (considering only the marked columns), we shall write out all pairs of symbols (numbers) of units whose faults are distinguishable from one another at the mandatory outputs, and for each such pair we shall write the logical sums of the output symbols at which they are distinguishable:
\[ \begin{aligned} &Q_1 \text{ from } Q_4:\ y_4,\\ &Q_1 \text{ from } Q_5:\ y_4 \cup y_5,\\ &Q_1 \text{ from } Q_6:\ y_4 \cup y_6,\\ &Q_3 \text{ from } Q_7:\ y_3 \cup y_7,\\ &Q_4 \text{ from } Q_5:\ y_5,\\ &Q_5 \text{ from } Q_6:\ y_5 \cup y_6. \end{aligned} \]
From the sums written down it is clear that the outputs of the fourth, fifth, and sixth units are mandatory. Therefore the second \(y_4 \cup y_5\) and third \(y_4 \cup y_6\) sums may be excluded from further consideration.
Then all faults will differ from one another on the following sets of outputs:
\[ y_1 y_2 y_8 y_9 y_{10} y_4 y_5 y_6 (y_3 \cup y_7) = \]
\[ = y_1 y_2 y_3 y_4 y_5 y_6 y_8 y_9 y_{10} \cup y_1 y_2 y_4 y_5 y_6 y_7 y_8 y_9 y_{10}. \]
Both sets of parameters are the same in length; however, the parameter \(y_7\) (the bias voltage of the thyristo-
new). Therefore it is necessary to settle on the following minimal set:
\[ y_1;\ y_2;\ y_4;\ y_5;\ y_6;\ y_7;\ y_8;\ y_9;\ y_{10}. \]
REFERENCES
-
N. I. Sablin. A logical model of a cyclotron for analyzing accelerator equipment for purposes of automatic operability monitoring and fault detection. Publ. TPI, vol. 193, TSU Press, 1972.
-
N. I. Sablin. Synthesis of an instrument for automatic operability monitoring and automatic fault detection for the cyclotron of the Research Institute of Nuclear Physics, Electronics, and Automation at TPI. Publ. TPI, vol. 193, TSU Press, 1972.
-
V. V. Kariosky. Analysis of systems for operability monitoring and fault diagnosis. Avtomatika i telemekhanika, XXVI, 2, 1965.