RISK ANALYSIS BASED ON ACCELERATION MEASUREMENTS FLORIN POPENTIU VLADICESCU

Part of the risks associated with the functioning of a ballistic system are connected with the variation of the cinematic parameters that define its evolution on the trajectory. The upgrading of such a system, usually classified as safety critical item, imposes a thorough investigation of the hazardous entities and situations, introduced by the new subsystems, either in normal functioning or in a circumstance of critical failure. In order to determine the functional differences between the reference system “old” and the hybrid prototype “old-new”, tests, relevant measurements and comparative analysis are made. Based on the knowledge experimentally captured, the package of preliminary assertions, regarding the components of the risk vectors (<probability of occurrence, severity of effects/ consequences> in conformity with the definitions in [1], [2], or < probability of occurrence, severity of effects/ consequences, probability of detection> in conformity with the definition in [3]) is refined, the main elements being retained to support the decision for certification and procedure to the series production.

The methods to be described further on deals with the assessment of the effects/ consequences of the relative risks, implied by the constructive and functional modifications, brought about to a ballistic system by the modernization of some of its subsystems, within the conditions of acknowledgment and acceptance of the absolute risks that are associated with the reference system “old’. The analysis are focused both to determine the level of alteration of the trajectory on which the ballistic system moves, alteration that may have as a consequence the modification of the utilization envelopes, and to quantify the effects on the operator of the job station, which can be unacceptable from the point of view of human resistance. By using the accelerations measured during the tests with the reference system “old”, the hybrid system “old-new” in normal functioning, and the hybrid system “old-new” in critical failure, the cinematic parameters (acceleration gradients, velocities, displacements) are calculated; then are assessed the differences between the 2 systems, by regression in the first method and by a probabilistic technique in the second method. The comparative analysis is distributed both to the ballistic department and to the human engineering department. Their conclusions are used to decide the acceptance/ rejection and the modification (if necessary) of the risk vectors, on the effects/ consequences component. In Part I the 2 methods are described and in Part II some results of an analysis already performed are given.

Part I

2. Risk assessment methods

Notation

2.1 Method I

Step 1: Perform the tests, acquiring for each of them, the acceleration signal on the main direction of movement (or on any other direction of interest), then choose the records for which plausible functioning and normal running of the measuring instrumentation are get; be X_i(), iN, 1im, Y_j(), jN, 1jn, Z_k(), kN, 1kp, the sets of such values;

Step 2: Approximate the recorded signals by means of numerical filters of high selectivity, chosen in such a way so as not to erase the traces (frequency bands) that characterise the functional differences between the 2 system classes: “old” and “old-new”. In [4] are discussed some issues about the numerical filtering of acceleration signals. Apply the scale transformation on the 2 axis and establish the start-up moments and the analysis interval, obtaining the significant acceleration fragments (time): Xa_i(t), Ya_j(t), Za_k(t);

Step 3: Compute the acceleration gradients(time): Xg_i(t), Yg_j(t), Zg_k(t), velocities(time) Xv_i(t), Yv_j(t), Zv_k(t) and displacements(time) Xd_i(t), Yd_j(t), Zd_k(t);

Step 4: Built up the correlation coefficient matrixes:

MIN(Ra_ij, Ra_ik)Ca, MIN(Rg_ij, Rg_ik)Cg, MIN(Rv_ij, Rv_ik)Cv, MIN(Rs_ij, Rs_ik)Cs;

Step 6: Analyse, by direct graphic comparison or by tracing the regression line, the signals between which there are some unsatisfactory correlation’s, then determine the causes. In the second part, there is a presentation of the decision-making orientation for some of them.

Step 7: Decide on the acceptance/ rejection and on the modification of the risk vectors, on the effects/ consequence component.

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2. Method II

Step 1: Identical with the step 1, method I;

Step 2: Identical with the step 2, method I;

Step 3: Identical with the step 3, method I;

Step 4: Choose the variables that may characterise statistically the systems functioning within the interval selected for analysis, for example: the average values of accelerations, the average values of acceleration gradient, the maximum values of velocity, the total displacements: A_avgX, A_avgY, A_avgZ, G_avgX, G_avgY, G_avgZ , V_maxX, V_maxY, V_maxZ, S_DX, S_DY, S_DZ;

Step 5: Compute <_aX, _aX>, <_aY, _aY>, <_aZ, _aZ>, <_gX, _gX>, <_gY, _gY>, <_gZ, _gZ>, <_vX, _vX>, <_vY, _vY>, <_vZ, _vZ>, <_sX, _sX>, <_sY, _sY>, <_sZ, _sZ>;

Step 6: Compute P_A1(A_avgX-A_avgY>0), P_A2(A_avgX-A_avgZ>0), P_G1(G_avgX-G_avgY>0), P_G2(G_avgX-G_avgZ>0), P_V1(V_maxX-V_maxY>0), P_V2(V_maxX-V_maxZ>0), P_S1(S_DX-S_DY>0), P_S2(S_DX-S_DZ>0);

Step 7: Compare the obtained probabilities with the P_Amin, P_Amax, P_Gmin, P_Gmax, P_Vmin, P_Vmax, P_Smin, P_Smax values, established in the test plan or chosen after having performed the tests and the statistical computations:

P_Amin< P_A1(A_avgX-A_avgY>0)<P_Amax, P_Amin< P_A2(A_avgX-A_avgZ>0)<P_Amax

P_Gmin< P_G1(G_avgX-G_avgY>0)<P_Gmax, P_Gmin< P_G2(G_avgX-G_avgZ>0)<P_Gmax

P_Vmin< P_V1(V_maxX-V_maxY>0)<P_Vmax, P_Vmin< P_A2(V_maxX-V_maxZ>0)<P_Vmax

P_Smin< P_S1(S_DX-S_DY>0)<P_Smax, P_Smin< P_S2(S_DX-S_DZ>0)<P_Smax

Step 8: If there are any non- conformities, determine the causes. The second part details the decision-making orientation for some of them.

Step 9: Decide on the acceptance/ rejection and on the modification of the risk vectors, on the effects/ consequence axis.

Part II

3. Results

The 2 methods have been recently used to analyse the experimental results obtained during a safety-testing program. The reference “old” is a ballistic system powered by a cartridge with solid propellant. The “old-new” hybrid prototype has the mass and the centre of gravity slightly modified against the reference. Moreover, at a certain moment during the functioning, a quick-disconnect pin-socket connector is released. In these conditions, we can anticipate that, for the upgraded system, the level of accelerations is lesser over the whole period of functioning and, near to the moment of disconnection, there is a braking force, both for a normal functioning and for a critical failure of the connector.

These effects are visible on the acceleration diagrams, if we can assure the repeatability of the tests, from the point of view of the propulsion system functioning, and if mechanical interlocking or significant deterioration do not appear.

After tests performance, 7 records in the configuration m=1, n=5, p=1 have been validated for analysis. In Figures 1-4 are plotted (within the same system axis) the fragments: acceleration [g]/ time [ms], acceleration gradient [g/s]/ time [ms], velocity [m/s]/ time [ms], displacement [mm]/ time [ms], resulted from the application of steps 1-3, common for both methods.

Figure 1. Acceleration [g]/ Time [ms]

Figure 4. Displacement [mm]/ Time [ms]

Figure 3. Velocity [m/s]/ Time [ms]

3.1 Method I

Step 4: Built up the correlation coefficient matrixes:

Step 5: Compare the obtained correlation coefficients with the values specified in the test program: Ca=0.9, Cg=0.40, Cv=0.98, Cs=0.99.

Step 6: Analyse the diagrams between which there are some unsatisfactory correlation. We notice that these are Xa₁ and Ya₁ (correlation coefficient 0.68), Xa₁ and Za₁ (correlation coefficient 0.56); the bad correlation of the above signals determines the worse correlation of the acceleration gradient signals: Xg₁ and Yg₁ (correlation coefficient 0.03), Xg₁ and Zg₁ (correlation coefficient 0.00). We can easily notice that, in spite of these, the velocity signals and the total displacement signals are satisfactorily correlated. In Figures 5-6 graphical comparisons between Xa₁ and Ya₁ (by tracing the regression line, and by overlapping) are made. Xa₁ and Za_1.are plotted in figures 7-8 by the same techniques.

One of the causes for the bad correlation is the delay (by 6 ms in the first case and 16 ms in the second case); by overlapping the moments when the signals reach the maximum value we can improve the correlation coefficients: 0.80 (Xa₁ and Ya₁) is 0.94 (Xa₁ and Za₁).

Another cause for the bad correlation of Xa₁ and Ya₁ signals is the temporary mechanical

interlocking (visible on Ya₁ diagrams), having no connection with the “new” subsystems functioning, which are integrated on the upgraded prototype.

In this situation we can choose one of the solutions: (a) Ya₁ is given up (automatically Yg₁, Yv₁, Ys₁ are given up) since there are satisfactory results for the other 4 tests of the same type; (b) the Ca criterion is given up (or is modified to include the value 0.80).

Figure 5. Acceleration [g]/ Acceleration [g] Figure 6. Acceleration [g]/ Time [ms]

Figure 7. Acceleration [g]/ Acceleration [g] Figure 8. Acceleration [g]/ Time [ms]

3.2 Method II

Step 4, 5: In Table 1 the chosen variables and the values <mean, standard deviation> are presented. The lack of information on X, Z variables makes this method hard to apply. However, we can go to step6.

(some of the probabilities will be 0 or 1).

Table 1.

Step 6: The computed probabilities are in conformity with Table 2.The data in Table 2 indicate that the “average values for acceleration”, “the maximum values of velocity” and the “total displacements” are greater for the reference system “old”. The results obtained for the “average values of acceleration gradient” are contradictory.

Step 7: Compare the computed probabilities with the values: P_Amin= P_Gmin = P_Vmin = P_Smin =0.5 si P_Amax= P_Gmax = P_Vmax = P_Smax=0.999.

Table 2.

Step 8: The probabilities that the differences between the X, Z variables be positive do not frame within the imposed limits. Because of the lack of information on X, Z dispersions, we can choose one of the solutions: (a) allocate standard deviation values for X, Z variables in a reasonable way, then recalculate the probabilities; (b) adopt some determinist acceptance criteria, the simplest being the framing of |A_avgX-A_avgZ|, |G_avgX-G_avgZ|, |V_maxX-V_maxZ|, |S_DX-S_DZ| between some limits.

Step 9: Both in case (a) and case (b) we can easily reach the acceptance decision and conclude that the hybrid system “old-new” does not introduce additional risks, so the risk vectors, on effects/ consequences component, does not change.

4. Conclusions

Both methods permit the investigation of the differences between the signals acquired during the tests with the reference system “old” and the signals acquired during the tests with the upgraded system “old-new”, the last being in normal functioning/ critical failure.

As the result of their application in the mentioned context, the conclusions are similar. Method II is mostly indicated if there is an apriori information on the distribution parameters of the variables, or if a great number of tests are performed.

Bibliography

[1] Birolini A., Quality and Reliability of Technical Systems, Theory-Practice-Management, Springer Verlag, 1997, 530 pp.

[2] Villemeur A., Reliability, Availability, Maintainability and Safety Assessment, vol. 1: Methods and Techniques, John Wiley & Sons, 1992, 357 pp.

[3] Kececioglu, D. Maintainability, Availability, and Operational Readiness Engineering Handbook, Volume I, 1/e, Prentice Hall Professional Technical Reference, 1995, 816 pp.

[4] Popentiu F., Radu M., Aircraft ejection systems- The acceleration variable (in Romanian), The annual Symposium of Reliability and Quality Engineering, Bucharest, Romania, 1992.

[5] Kales P., Reliability: For Technology, Engineering, and Management, 1/e, Prentice Hall Career & Technology , 1998, 392 pp.

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