Dynamics of project-driven systems A production model for repetitive processes in construction (VIVA)
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The document discusses a production model for repetitive processes in construction, focusing on the dynamics of project-driven systems. It emphasizes the importance of including transient states in modeling to enhance accuracy and provides methods for estimating productivity functions. Additionally, it highlights findings related to process variability and control methodologies while addressing limitations and future research directions.
Dynamics of project-driven systems A production model for repetitive processes in construction (VIVA)
- 1. Dynamics of project-driven systems A production model for repetitive processes in construction Ricardo Antunes The University of Auckland Department of Civil and Environmental Engineering August 1, 2017
- 2. Outline I - Research II - A Production Model for Construction: A Theoretical Framework III - Dynamics of production in Construction Productivity Function Estimation and Validation Quality of Fitness IV - Laws for production in project-driven processes in Construction V - Control VI - Conclusion Findings Limitations Future Research
- 3. Research Plan DoAct Check -setpoint error input output Figure 1: PDCA Control Loop
- 4. Construction System DesignFeasibility P1 P2 Pk-1 Pk Setpoint 1out 2in Start Construction project-driven production system Risk impact (disturbance) Risk Management Uncertainty End P = P 2out 3in P = P k-1out kin P = P Construction Feedback Figure 2: Construction system theoretical framework (Antunes et al., 2016; Antunes and Gonzalez, 2015)
- 5. Linear, time-invariant differential equation αn dn y(t) dtn + αn−1 dn−1 y(t) dtn−1 + . . . + α0y(t) = βm dm u(t) dtm + βm−1 dm−1 u(t) dum−1 + . . . + β0u(t) (1) in which all initial conditions are zero and where y(t) is the output, u(t) is the input, the αn’s and βm’s are the form of differential equation that represent the system, where n, m ∈ N0 , and α, β ∈ R.
- 6. Laplace Transform Taking the Laplace transform of both sides of Equation 1, L { αn dn y(t) dtn + αn−1 dn−1 y(t) dtn−1 + . . . + α0y(t) } = L { βm dm u(t) dtm + βm−1 dm−1 u(t) dum−1 + . . . + β0u(t) } , (2) results1 in (αnsn + αn−1sn−1 + . . . + α0)Y(s) = (βmsm + βm−1sm−1 + . . . + β0)U(s). (3) 1proof is shown in Section 6.6
- 7. Productivity Function In the s-domain23 , it is possible to isolate the output Y(s) and the input U(s) and express the equation as the ratio of them (Antunes et al., 2017). P(s) = Y(s) U(s) = (βmsm + βm−1sm−1 + . . . + β0) (αnsn + αn−1sn−1 + . . . + α0) (4) 2s is a variable in the frequency domain, s = σ + iω, where s ∈ C, σ, ω ∈ R 3the equivalent discrete from is shown in Section 4.3
- 8. Estimation and Validation u(t) Process P(t) y(t) Disturbance1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Est1 Validation 1 Estimation 2 Validation 2 Estimation 3 … Est1 Validation 1 Estimation 9 Estimation 9 … … Actualdepth(m) Figure 3: Estimation and Validation (Antunes, 2017; Antunes et al., 2015)
- 9. Quality of Fitness Unfitness(100%–NRMSE) Model quality for different sample sizes Data segment 1 Unfitness(100%-NRMSE) 2 3 4 5 6 7 8 9 0 20 40 60 80 Estimation Validation 9.50 11.01 7.91 6.09 6.41 12.51 13.30 17.39 15.12 15.51 11.16 9.74 16.25 14.78 15.03 13.05 8.44 12.43 11.57 11.71 11.18 11.69 23.85 22.18 22.47 13.04 11.69 23.85 22.18 22.47 18.56 11.31 48.88 46.87 47.21 72.64 9.65 45.87 44.21 44.49 0 7.20 43.79 42.38 42.62 Val unift Est unfit FPE Loss Fcn MSE Figure 4: Quality of fitness (Antunes et al., 2015)
- 10. Productivity Function vs Mean Figure 5: RSE comparison for A5 (?)
- 11. Finding the steady-state Table 1: Processes percentage duration in steady-state (?) A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 B6 ¯p 0 0 0 0 4.66 0 0 0 0 0 0 a 0 0 0 0 6.36 2.54 0 0 0 0 2.12 yssv 0 4.66 6.78 0.85 0 8.05 2.97 1.27 2.97 0.85 1.69
- 12. Step Response Productivity Function model P(s) Input Output Step input u(t) t t0 1 Step response y(t) t yssv tst0 Figure 6: Transient analysis for unit step input
- 13. Transient and variability Table 2: Flow variability and percentile reaction time (Antunes et al., 2016) Case ts tt ts/tt Cpk Pp SD(d) rd CV 1 4.67 184 2.54% 0.2438 0.5354 95.22 3481.40 0.0273 4 13.11 210 6.24% 0.0144 0.0344 14.89 32.12 0.4634 5 1.23 18 6.86% 0.0110 0.0260 278.44 458.68 0.6070 3 1.82 8 22.71% 0.0108 0.0258 315.13 510.27 0.6176 2 55.85 20 279.26% 0.0085 0.0204 27.81 35.55 0.7824 cd = coefficient of variation of the departure times (cd, = SDd/rd, i.e., CV = SD(y)/¯y) Cpk = process capability index Pp = process performance rd = departure rate (output mean the output, i.e., ¯y) SD(d) = standard deviation of the time between departures (output), i.e., SD(y)) tp = total process time ts = transient (settling) time ts/tt = percentile reaction time tt = total process time
- 14. Isolated and Connected Processes 5 10 15 20 25 30 35 40 45 50 ts (days) 2 4 6 8 10 12 14 16 18 ¯CT(days) Settling time and average cycle time ¯CT(ts) linear fitting 5 10 15 20 25 30 1/ψt1 (days) 2 4 6 8 10 12 14 16 18 ¯CT(days) Theoretical cycle time and average cycle time ¯CT(1/ψt1) linear fitting Figure 7: Transient and ¯CT and Connected Processes
- 15. Proportional Integral Derivative Control (reactive) Controller D + System G Reference r(t) Output y(t) A typical feedback loop control Sensor H _ Error e(t) Measured output b(t) Input u(t) Figure 8: A typical feedback loop control
- 16. Productivity Function Predictive Control ! " # $%"% & $%'("%'( & ) & $* +,", & +,'(",'( & ) & +* Output y(k) Productivity Function } u(k) Manipulated Variables (MV) v(k) Manipulated Disturbances (MD) d(k) Unmeasured Input Disturbances (UD) + + y(k) { u(k) Manipulated Variables (MV) Input Disturbance Model wid(k) White Noise xid(k) yod(k) Unmeasured Output Disturbances Output Disturbance Model wod(k) White Noise +yn(k) Measured Noise Measurement Noise Model wn(k) White Noise + ym(k) Measured Outputs (MO) ^ Figure 9: Model Predictive Control
- 17. Controlling Isolated and Connected Processes 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.15 0.2 0.25 0.3 Mean Sample MPC1 MPC2 MPC3 PID Isolated processes 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 Standard deviation 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.005 0.01 0.015 0.02 Pp 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.15 0.2 0.25 0.3 Mean Sample MPC1 MPC2 MPC3 PID Connected processes 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 Standard deviation 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 Pp Figure 10: Controlling Isolated and Connected Processes
- 18. Findings 1. There is transient state in project-driven construction processes 2. This transient can be measured 3. Including the transient on the modeling yields in more accurate models 4. Only 5 samples are required to estimate a Productivity Function model. 5. An input/output correlation higher than 60% is required. 6. A qualify of fitness higher than steady-state approaches is enough 7. Higher the transient time, higher the variability 8. Higher the transient time, higher the average cycle time 9. Equation for capacity P(0) but perform at capacity is challenging 10. Predictive control rather than reactive control
- 19. Limitations 1. Exploratory stage 2. No case illustrating unsteady state 3. Requires an input and output data 4. Model accuracy cannot be evaluated until some data has been produced 5. Some concepts are unfamiliar to general construction managers 6. One transient curve to represent all
- 20. What next? • Productivity Function and Learning Curve models • Process’ variability using Bode-plots • Simulated Risk Impact: extreme shock, wavelets (?, Fig.4)… • Multi-input-multi-output modeling and case analyses • Nonlinear models (also to be compared with multi variable Learning Curve models)
- 21. Bibliography Antunes, R. Offshore rig, drilling well, Brazil 2013, v1, 2017. URL https://data.mendeley.com/datasets/xn88z63ghs/1. Antunes, R., González, V. A., Walsh, K., Gonzalez, V. A., and Walsh, K. Identification of repetitive processes at steady- and unsteady-state: Transfer function. In 23rd Annual Conference of the International Group for Lean Construction, pages 793–802, Perth, Australia, 2015. ISBN 9780987455796. doi: 10.13140/RG.2.1.4193.7364. URL http://iglc.net/papers/Details/1194http://www.iglc.net/papers/details/1194. Antunes, R., González, V., and Walsh, K. Quicker reaction, lower variability: The effect of transient time in flow variability of project-driven production. In 24th Annual Conference of the International Group for Lean Construction, pages sect.1 pp. 73–82, Boston, MA, 2016. URL http://iglc.net/papers/Details/1332. Antunes, R., González, V. A., Walsh, K., and Rojas, O. Dynamics of Project-Driven Production Systems in Construction: Productivity Function. Journal of Computing in Civil Engineering, 31(5):17, 2017. ISSN 0887-3801. doi: 10.1061/(ASCE)CP.1943-5487.0000703. URL http://ascelibrary.org/doi/10.1061/{%}28ASCE{%}29CP.1943-5487.0000703. Antunes, R. M. S. and Gonzalez, V. A production model for construction: A theoretical framework. In Building a Better New Zealand, pages 223–233, Porirua, New Zealand, 2015. Branz Ltd. ISBN 978-1-927258-42-2. URL http://www.buildingabetternewzealand.co.nz/cms{_}show{_}download.php?id=202.