4TC00 Model-based systems engineering 2.8 Scalable solutions - reuse Functions 2.10 Stochastics

Transcription

1 4TC00 Model-based systems engineering 2.8 Scalable solutions - reuse Functions 2.10 Stochastics Bert van Beek (dr.ir. D.A. van Beek) Gem-Z d.a.v.beek@tue.nl 1 of 26

2 4TC00 Model-based systems engineering 2.8 Scalable solutions - reuse 2 Bert van Beek (dr.ir. D.A. van Beek) Gem-Z d.a.v.beek@tue.nl 2 of 26

3 Two producer system event int provide; automaton producer1: disc int nr = 0; location: edge provide!nr do nr := nr + 1; automaton producer2: disc int nr = 0; location: edge provide!nr do nr := nr + 1; 3 of 26

4 Equivalent system with definition and instantiation event int provide; automaton def Producer(): disc int nr = 0; location: edge provide!nr do nr := nr + 1; // Producer automaton definition producer1: Producer(); producer2: Producer(); // producer1 automaton instantiation // producer2 automaton instantiation 4 of 26

5 Two buffers in series Model two buffers in series: Output of first buffer is connected to input of second buffer. Capacities of the two buffers are 3 and 5, respectively. Buffers differ only in input connection, output connection and capacity. Therefore, use one automaton definition for the buffer, and two instantiations. Use parameters for the input, output, capacity. 5 of 26

6 Paramaterized automaton definition and instantiation event int buf1_in, buf1_buf2, buf2_out; automaton def Buffer(event int receive, s; alg int capacity): disc list int buf = []; location: edge receive? when size(buf) < capacity do buf := buf + [?]; edge s! buf[0] when size(buf) > 0 do buf := buf[1:]; buffer1: Buffer(buf1_in, buf1_buf2, 3); buffer2: Buffer(buf1_buf2, buf2_out, 5); Use alg for all non-event parameters 6 of 26

7 Equivalent model for the two buffers automaton buffer1: alg int capacity = 3; // create alg variable for alg parameter disc list int buf = []; location: edge buf1_in? when size(buf) < capacity do buf := buf + [?]; edge buf1_buf2! buf[0] when size(buf) > 0 do buf := buf[1:]; automaton buffer2: alg int capacity = 5; // create alg variable for alg parameter disc list int buf = []; location: edge buf1_buf2? when size(buf) < capacity do buf := buf + [?]; edge buf2_out! buf[0] when size(buf) > 0 do buf := buf[1:]; 7 of 26

8 Restricting event parameters automaton def Buffer(event int receive?, s!; alg int capacity): disc list int buf = []; location: receiving only sing only edge receive? when size(buf) < capacity do buf := buf + [?]; edge s! buf[0] when size(buf) > 0 do buf := buf[1:]; Event parameters can be postfixed with!,?, ~ to indicate:! usage of the event is restricted to sing.? usage of the event is restricted to receiving. ~ usage of the event is restricted to pure synchronization.!?,!~,?~ are also allowed and indicate that both indicated restricted usages are permitted.!?~ indicates no restriction and is the default interpretation if a restriction is not specified. 8 of 26

9 Groups group tank: cont V = 5; alg real Qi, Qo; equation V' = Qi - Qo; equation Qi = 1; equation Qo = sqrt(v); Use groups to provide additional hierarchical structure. Group definitions and group instantiations can be used just like automaton definitions and instantiations. 9 of 26

10 Imports - libraries - input variables See Sections 2.8.6, and in the CIF language tutorial. Input variables have already been discussed in the lecture on the car window system. 10 of 26

11 4TC00 Model-based systems engineering 2.9 Functions Bert van Beek (dr.ir. D.A. van Beek) Gem-Z of 26

12 User defined functions func real mean(list real vs): int length = size(vs); int index = 0; real sum = 0; while index < length: sum := sum + vs[index]; index := index + 1; type of returned value return sum / length; parameters declared by type followed by name internal variables declared by type followed by name // calculate the sum of the parameters // return the sum divided by the // number of parameters 12 of 26

13 Function application alg real m = mean([1.5, 3.2, 7.9, 15.8]); automaton a: disc real x; location: edge do x := 2 * mean([0.4, 1.5, 6.8]); CIF user defined functions are just like mathematical functions: Function called with the same input variables always returns the same result. Functions have no side effects: they only return a value. Functions cannot use disc, cont, alg variables: must all be passed as parameters. 13 of 26

14 Function statements Assignment statement: identical to assignment on edge Return statement: see example If statement While statement: see example Break statement 14 of 26

15 If statement func int signum(real x): if x > 0: return 1; elif x < 0: return -1; else return 0; 15 of 26

16 Next slide break statement 16 of 26

17 // Get the first 'n' values from 'xs' that do not equal 'bad'. func list int first_n(list int xs; int n; int bad): int index = 0; int x; list int result = []; while index < size(xs): x := xs[index]; if x!= bad: result := result + [x]; if size(result) = n: break; // break: continue after of while statement index := index + 1; return result; // First 3 values that do not equal 2: 'y' is [1, 5, 3]. alg list int y = first_n([1, 2, 5, 3, 4, 1], 3, 2); 17 of 26

18 4TC00 Model-based systems engineering 2.10 Stochastics Bert van Beek (dr.ir. D.A. van Beek) Gem-Z of 26

19 Example tossing a coin automaton coin_toss: disc dist bool d = bernoulli(0.5); disc bool outcome; // stochastic distribution d location toss: edge do (outcome, d) := sample d goto result; // draw a sample location result: edge when outcome goto heads; edge when not outcome goto tails; // evaluate outcome of sample location heads: edge tau goto toss; location tails: edge tau goto toss; 19 of 26

20 Discrete distributions Discrete distributions draw a sample from a limited number of values Bernoulli distribution: boolean Uniform distribution: integer automaton A: disc dist bool d1 = bernoulli(0.5); disc dist int d2 = uniform(1,10); disc bool b; disc int n; location: edge do (b, d1) := sample d1, (n, d2) := sample d2; 20 of 26

21 Continuous distributions automaton pennies: disc dist real d = normal(2.46, ); disc real weight; // weight of a penny location: edge do (weight, d) := sample d; normal(μμ, σσ 2 ) μμ: average σσ: standard deviation σσ 2 : variance 21 of 26

22 Constant distribution automaton pennies: disc dist real d = constant(2.46); disc real weight; // weight of a penny location: edge do (weight, d) := sample d; A continuous or discrete distribution can be (temporarily) changed to a constant distribution. Purpose of using a constant distribution is that it allows easier model validation, for the specific case of deterministic (non-stochastic) behavior. 22 of 26

23 Pseudo-randomness Computers are not stochastic they use a pseudorandom number generator: an algorithm to generate a (deterministic) sequence of numbers that approximate the properties of sequences of random numbers. the sequence is completely defined by an initial value, called the seed. In CIF, sample d is a mathematical function: when called with the same argument, always gives same result. Result of the sample function is a tuple consisting of: 1. the next value of the sequence of random numbers, 2. the updated distribution, that keeps track of the next sample in the sequence. 23 of 26

24 Demo: sample is a mathematical function // GUI input: reset gives same sample sequence // GUI input: restart simulation gives different sample sequence. automaton coin_toss: disc dist int d = uniform(0, 100); disc dist int d0 = d; disc dist int e = uniform(0, 100); disc dist int e0 = e; disc int outcome_d, outcome_e; disc int outcome_d0, outcome_e0; // equal samples location: edge do (outcome_d, d ) := sample d, // update d (outcome_d0, d0) := sample d0, // update d0 (= d) (outcome_e, e ) := sample e, // update e outcome_e0 := (sample e0)[0]; // e0 unchanged => // sample unchanged 24 of 26

25 Seed When a stochastic simulation produces an unexpected error, repeating the simulation may not produce the same error. To ensure that repeated stochastic simulations behave exactly the same, an initial seed may be provided with option: --distributions-seed=value 25 of 26

26 Demo sample_seed.cif predefined initial seed from "lib:cif3" import *; cif3sim( "sample_seed.cif", "--stateviz=1", "--distributions-seed=5" ); // seed 5 produces 22, 87, 20 automaton coin_toss: disc dist int d = uniform(0, 100); disc int outcome; location: edge do (outcome, d) := sample d; 26 of 26