Automated Model Based Requirement Coverage Analysis Tool Chethan C U
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1 Automated Model Based Requirement Coverage Analysis Tool Chethan C U cchethan@moog.com chethan.cu@gmail.com 22 The MathWorks, Inc.
2 Outline DO 78B guidelines for Software Testing Functional Requirements Integrator Anti-wind up Analysis Functional Metric Characteristics Metric Definition Integrator, PersistenceOnOff Structural Coverage Analysis using Simulink Design verifier, Reactis Moog Functional Coverage Tool Mutation Testing 2
3 Introduction Software Verification for Aircraft Software is done as per "Software Considerations in Airborne Systems and Equipment Certification." RTCA/DO-78B, Washington, D.C The DO-78B Guidelines suggests to perform: Requirement Based Testing verify the correct functionality of the Software. Structural Coverage Analysis to determine which parts of the code was not exercised during the Requirement Based Testing. % Structural Coverage DOES NOT mean % Requirement Coverage. 3
4 Process Followed Requirements Test Cases Code Execute Manual Functional Reviews Structural Coverage Results Expected/Actual 4
5 Ambiguous Requirements Integrator function shall be implemented as per the algorithm below: During Initialization: out=ic prevo=ic previ=input During Normal Operation: out=prevo + DT*input if out>ul out=ul elseif out<ll out=ll Where DT is sample Time. Equivalent Code I if(initialized==) { out=ic; prevo=ic; previ=input; } else { out=prevo + DT*input; if (out>ul) out=ul; elseif(out<ll) out=ll; previ= input; prevo=out; } OR Equivalent Code- II if(initialized==) { out=ic; prevo=ic; previ=input; } else { out=prevo + DT*input; previ= input; prevo=out; if (out>ul) out=ul; elseif(out<ll) out=ll; } Improper Code!!! 5
6 Integrator Design Issues Limits the State K Ts z - Discrete - Time Integrator Signal Signal Builder Scope Limits the Output K Ts z - Discrete - Time Integrator Saturation 6
7 Mag Integrator coming out of Saturation Integrator Comparison 8 6 Inp Integ + Sat Anti Integ Time 7
8 Proper Functional Requirements The Integrator shall be implemented as per the equation: Output = Previous Output + DT*input Where, Previous Output is the output obtained at the previous execution frame and DT is the sample time. The output During the first frame of execution shall be equal to IC. If the Output is greater than UL then Output shall be made equal to UL If the Output is less than LL then the Output shall be made equal to LL When the Integrator Output has reached a limit, the output will be limited such that any Input sign change will be immediately reflected in the Output. 8
9 Coverage Metrics in Existence Structural Code Coverage Statement Coverage, Decision Coverage, Condition Coverage, Multiple Condition Coverage, Condition/Decision Coverage, Modified Condition/Decision Coverage Simulink block coverage Decision, Condition, MC/DC, Look-up Table, Signal Range Drawback These metrics do not talk about the functionality of the control system element 9
10 Characteristics of a Functional Metric The metric should be functionality based. The metric should be based on the input - output relation of the block under test. The metric should be independent of the platform being used. The metric should have an capability of test Case optimization.
11 Metric Definition We define a pair of cells for each functional requirements. The first cell of the pair is discrete (TRUE/FALSE) which tells if a particular functional requirement is exercised or not. The second cell defines a distance to coverage, a continuous metric which can be minimized to ensure coverage T/F Distance to coverage
12 Integrator Metric Defination Integrator Output 5 Distance from Max. value of output and the UL -5 Distance from Min value of output and the LL Time in secs 2
13 Integrator -- Metric Defination Time in secs 3
14 Integrator Metrics # Discrete Metric Continuous Metric Output of the Integrator has reached the UL abs(min(output-ul)) 2 Output of the Integrator has reached the LL 3 Output is non-zero and lesser than UL and greater than LL 4 Integrator comes out of saturation from UL 5 Integrator comes out of saturation from LL abs(min(output-ll)) abs(min(output(nonze ro)-(ul+ll)/2)) When Output == UL, Drive input towards values < When Output == LL, Drive input towards values > 4
15 Integrator -- Simulink Design Verifier Test Case Test Case 2 Test Case Time in secs % Structural Coverage 5
16 SDV Integrator Report #: Type Model Item Description Test Case Decision 2 Decision 3 Decision 4 Decision Discrete-Time Integrator Discrete-Time Integrator Discrete-Time Integrator Discrete-Time Integrator integration result <= lower limit F integration result <= lower limit T integration result >= upper limit F integration result >= upper limit T 3 2 6
17 Integrator -- Reactis 2 x 5 Test Case x 2 Test Case Time in secs 7
18 Reactis Integrator Report 8
19 Output Comparison for Structural Coverage Tests of Integrator x x Test Case Test Case 2 Test Case 3 Test Case 4 Test Case
20 Integrator Moog Functional Coverage Tool Metric Count Output>= UL 65 frames Output <= LL 4 frames Output is non-zero, Output<LL and >UL Coming out of saturation of UL 395 frames transition 5-5 Input Output UL LL Coming out of saturation of UL transition
21 Persistence On/Off -- Algorithm Inputs: INP, Init, Pers_On, Pers_Off Output: OUT During Initialization: OUT = Init During normal operation: if (INP is TRUE and has remained TRUE for Pers_On frames) OUT = TRUE elseif (INP is FALSE and has remained FALSE for Pers_Off frames) OUT = FALSE Else OUT = Previous frame value of OUT 2
22 Persistence On/Off Design Variations INP OUT Signal PersistenceOnOff Pers_On =.5 sec Pers_Of f = sec Signal Builder Scope INP OUT INP OUT.9.8 PersistenceOn Pers_On =.5 sec Pers_Of f = sec PersistenceOff Pers_Of f = sec
23 Persistence On/Off Design Comparison 23
24 Persistence On + Persistence Off ~= Persistence OnOff 24
25 Metric Definition for Persistence OnOff 25
26 Persistence OnOff Metrics # Discrete Metric Continuous Metric IC is tested for TRUE value NA 2 IC is tested for FALSE value NA 3 Input has a TRUE pulse whose width is less than PersOn 4 Input has a TRUE pulse whose width is greater than PersOn 5 Input has a FALSE pulse whose width is less than PersOff 6 Input has a FALSE pulse whose width is greater than PersOff abs(person/2- min. TRUE pulse Width ) abs(person - max. TRUE pulse Width ) abs(persoff/2- min. FALSE pulse Width ) abs(person/2 - max. FALSE pulse Width ) 26
27 Persistence On/Off Simulink Design Verifier Test Case (IC =) Test Case 2 (IC = ).5 Input Input
28 SDV Persistence On/Off Report Summary Metric Decision (D) Coverage % (2/2) decision outcomes % Structural Coverage Condition (C) % (2/2) condition outcomes 28
29 Persistence On/Off -- Reactis Test Case Test Case
30 Reactis Persistence On/Off Report 3
31 Persistence On/Off Moog Functional Coverage Tool Metric IC tested for TRUE IC tested for FALSE Input has a TRUE pulse whose width is less than PersOn Input has a TRUE pulse whose width is greater than PersOn Input has a FALSE pulse whose width is lesser than PersOff Input has a FALSE pulse whose width is greater than PersOff Count Inp Out PersOn =.5 sec PersOff = sec 3
32 Moog Functional Coverage Review Tool 32
33 Model Under Test AnalogIn K Ts (z+) 2(z-) 2 AnalogIn2 5 Constant <= Relational Operator Discrete-Time Integrator UL=, LL=- AND AnalogOut -5 Constant2 >= Relational Operator Constant Switch u2 ~= 33
34 Functional Coverage Report Discrete-Time Integrator Dmetric Cmetric Number of samples Output is equal to UL and Input is greater than 58 Number of samples Output is equal to LL and Input is less than 62 Number of samples the Output is less than UL and greater than LL and is non-zero 28.3 Number of times the output comes out of saturation from UL 4 Number of times the output comes out of saturation from LL 2 AND Dmetric Cmetric Showing the effect of Input of AND on the Output N/A Showing the effect of Input2 of AND on the Output N/A Switch Dmetric Cmetric Number of frames the Input and Input3 are unequal and Input2 is TRUE Number of frames the Input and Input3 are unequal and Input2 is FALSE Relational Operator Dmetric Cmetric Number of frames the output is TRUE 38.6 Number of frames the output is FALSE Relational Operator Dmetric Cmetric Number of frames the output is TRUE Number of frames the output is FALSE
35 Metric Verification using Mutation Test case were designed to provide complete functional coverage as defined using the Moog Functional metrics. Simulink block Test Case Mutant Simulink Block + - Error 35
36 Different Mutants Logical Mutants (&,,~<,^) Arithmetic mutants (+,-,*,/) Data Mutants (add +/- error of.) Variable Mutants ( replace Variable with another Variable in the code) Manual Mutants -- Intern students from Colleges are making these for us. 36
37 Nand, Xor Mutant Analysis A B A &B ~(A&B) A XOR B These are the Test Cases that prove the MCDC of an AND gate 37
38 MCDC Analysis for Complex Combinational Logic Complex Combinational Logics with 6 inputs. Automated test cases to achieve MCDC. 65 mutants for each combinational logic. <All possible mutants>. Average Probability of killing a Mutant is 98 % 38
39 What are we working on now? Complete Qualified tool as per DO -78B guidelines. Automated Test Case generation using the Functional Metrics as assertions to be achieved. Defining System level functional metrics Integrate the functional metrics to Simulink Design verifier!!?? 39
40 Genetic Algorithm for test Case generation We are researching various Optimization tool for Test case optimization. GA has provided the initial results for an Integrator with limits. A sine signal whose Amplitude, Frequency and Bias are varied by the GA algorithm to achieve Zero Dmetrics 4
41 Test Case generation for Integrator using GA 4
42 Take Away % Structural code Coverage doesn t mean % functional coverage. Test, Test, Test!! Add Random tests.. Verify the quality of the tests using mutations. Follow process Like doing reviews.. few errors are easily found by reviews than tests There are no short cuts in testing.. Processes can be automated but cannot be removed. 42
43 Thank You LinkedIn : Chethan C U Next Generation Flight Controls Moog Provides a complete end to end solution in the development and V&V of the Lateral Control Electronics for Boeing Aircraft 43
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