Realizing Smart Plants Through Smart Design. of Sensor Networks. University of Oklahoma. Miguel J. Bagajewicz * *

Transcription

1 Realizing Smart Plants Through Smart Design Probability Distribution of Estimators of Sensor Networks CV s * Miguel J. Bagajewicz University of Oklahoma MV s * *

2 SMART PLANTS 2 Smart Plants prevent problems, Predict whereas Today s Plants react to problems Prevent Pro-Act SINGULAR EVENTS Fires, explosions. Environmental emissions. Unplanned plant shutdowns. SUBOPTIMAL OPERATIONS Off-specification products Off-Target production rates. Excessive Energy Consumption Jimmy L. Humphrey, John Forgac(BP), Son Huynh (IBM), Robert Chirico (NIST) Annual AIChE Meeting

3 SMART PLANTS 3 Recent AIChE Journal Article

4 4 SMART PLANTS

5 5 SMART PLANTS

6 Distillation Separation of Ethyl Benzene - Styrene 6 Condenser Distillation Column Feed Reflux = 457,000 lb/hr Accumulator 134,000 lb/hr EB 54.0 wt. % Styrene 45.7% Reboiler Steam 75,000 lb/hr Distillate 74,000 lb/hr EB 97.0% Styrene 3.0% Bottoms 60,000 lb/hr EB 0.2% Styrene 99.1% Condensate Basis: 500 million lb/yr Styrene Steam Usage = 1.31 lb/lb Styrene Steam Cost = $4.6 million/yr

7 Smart Distillation Query 7 (made in USA, about 100 industrial & Academics) With Accurate Real Time Material and Heat Balances, we Could: 1. CONTINUOUSLY operate columns at TIGHTER product specifications. 2. Monitor, diagnose, and troubleshoot columns via broadband. 3. Constantly compare performance of similar columns to identify under performers.

8 Key Challenges 8 Is there really such a thing as accurate real time material and heat balances in plants? How do we handle the volumes of data that are created? Will the benefits outweigh the costs?

9 Recent NSF Workshops 9 Cyberinfrastructure in Chemical and Biological Process Systems: Impact and Directions (Sept, 2006) -Zero incident smart plant operations was identified as 1 of 3 major challenges. Smart plant technologies were identified as follows: The Smart Plant is composed of smart assets that not only provide their basic process function but provide proactive feedback on the economic, environment, health and safety performance of that asset in aggregation with the other assets and in the moment. Smart plants operate to tighter specifications and involve a much greater understanding of the processes, greater automation and decision support, expanded use of automation, data and data interpretation, and a new-generation workforce that is trained and oriented toward a knowledge and information mindshare.

10 Recent NSF Workshops 10 -Furthermore, the report identified sensor networks as a key component of smart plant technology. -The report states: The concepts of smart plants, zero incidents, and national supply chain etc. all depend on increasingly larger numbers of sensors and more extensive sensor networks. Additionally, the demands on sensor networks are increasingly multipurpose data communications, automated control systems, long and short term planning, predictive modeling, optimization, environment, health and safety management, etc. Sensor networks are the information supply workhorses for these industries. A more recent workshop NSF Roadmap (April 2008) was specifically devoted to Smart Plants Development Workshop on Zero-Incident, Zero-Emission Smart Manufacturing

11 Recent NSF Workshops 11 - A more recent workshop NSF Roadmap (April 2008) was specifically devoted to Smart Plants Development Workshop on Zero-Incident, Zero-Emission Smart Manufacturing Instrumentation Networks were identified as key elements for the goals.

12 Our Response to the Challenge 12 Instrumentation should be judiciously chosen to produce the exact data Precise enough Bias free To achieve this, instrument hardware redundancy is too expansive Software redudancy (through data reconciliation, multiple use of data, model based inferences, etc.) are needed. A method to determine the right amount of instrumentation needs to Take into account the economic value of information Needs to be able to determine the right trade-off between value and cost.

13 Nature of Data At the heart of the problem we have Random errors and Biased instruments: Measurement Data with random & gross errors y = x + + Gross errors Random errors can be assessed and tolerated Biased instruments SHOULD be identified and this requires DATA RECONCILIATION That is MODELS!!! 0 Time

14 Maximum Profit Formulation for Sensor Netwok Design Maximize { Profit (Targets) - Cost (SN) } s.t. Performance Metrics (SN) Targets Maximize { Profit (Targets) - Cost (SN) } s.t. Performance Metrics (SN) = Targets Maximize { Profit (SN) - Cost (SN) }

15 The Upgrade Problem Let SN 0 be an existing network, then an upgrade to network SN has a Value defined as: Value (SN) = Profit (SN) - Profit (SN 0 ) Then the upgrade SND problem is defined as: Maximize { Value (SN) - Cost (SN) }

16 Minimum Capital Cost Formulation (single objective perspective) Minimize Sensor Network Cost (SN) s.t. Performance Metrics (SN) > Performance Targets where SN is the candidate sensor network, and Targets must be selected by the plant engineer

17 Minimum Capital Cost Formulation (integrated perspective) Minimize Sensor Network Cost (SN) s.t. Accounting Metrics (SN) > Precision Targets Detection Metrics (SN) > Fault Targets Control Metrics (SN) > Control Targets Unfortunately, Targets still need to be selected. Still no quantification of upgrade benefits.

18 SND Perspectives Material Accounting/Parameter Estimation: Goal: Precise measurement/estimation of production rates. Impact: Inventory costs and amount of lost product. Control Systems: Goal: Reduce variations around set operating points. Impact: Product quality and throughput capabilities. Fault Diagnosis: Goal: Quickly and accurately identify equipment failures. Impact: Downtime losses and safety issues.

19 Integrated Maximum Profit Problem 3 Maximize { { V i (SN) } - Cost (SN) } i 1 where V i (SN) are the Value functions from the three perspectives i=1 Control Systems i=2 Material Accounting i=3 Fault Diagnosis

20 The Control System Perspective CV s Feasible Steady-State Operating Point Constraint Polytope of Feasible Operating Points * MV s

21 Real-Time Optimization CV s Optimal Steady-State Point MV s *

22 Impact of Disturbances and Dynamics Conservative Operating Point CV s * Dynamic Operating Region Optimal Steady-State Point MV s *

23 Minimally Backed-off Operating Point Selection Conservative Operating Point CV s Backed-off Point * Dynamic Operating Regions MV s * * Optimal Steady-State Point

24 Maximum Profit Sensor Selection (control system perspective) Dynamic Operating Regions for Different Sensor Networks Minimally Backed-off Points * * Optimal Steady-State Point * MV s

25 Motivating Example Assume the current network (SN 0 ) consists of 6 sensors located at CSTR Process (A B+C) C Ai, C A, T, V, F, P each having a precision of 2%.

26 CSTR Example Upgrade Data: New 1% precision sensors can replace 2% sensors. Replacement cost is $1000/yr (includes purchase, installation, maintenance and replacement costs). 1% sensor available for other locations ($1000/yr ) Profit Function ($/yr): p( C A, F, Fc, Fvg ) M an [ ( CAi CA) F 2Fc 3F 1 vg ]

27 Concentration of A (lb mol / ft 3 ) Reactor Volume (ft 3 ) Motivating Example (control system perspective) Reactor Temperature (deg F) Reactor Exit Flow Rate (ft 3 / hr) Existing Network: profit = $28,970/yr, cost = $ 0 /yr Upgrade 5 Sensors: profit = $37,060/yr, cost = $5,000/yr Optimal Upgrade: profit = $36,030/yr, cost = $2,000/yr

28 Jacket Flow Rate (ft 3 / hr) Vapor Exit Flow Rate (lb mol / hr) Motivating Example (control system perspective) Jacket Temperature (deg F) Reactor Pressure (lbf / ft 2 ) Existing Network: profit = $28,970/yr, cost = $ 0 /yr Upgrade 5 Sensors: profit = $37,060/yr, cost = $5,000/yr Optimal Upgrade: profit = $36,030/yr, cost = $2,000/yr

29 Motivating Example (control system perspective) No New Sensors Value ($/yr) Sensor Costs ($/yr) Value - Sensor Costs ($/yr) 1 C A, P 7,060 2,000 5,060 2 C A, T c, P 7,630 3,000 4,630 3 P 4,500 1,000 3,500 4 T, P 5,420 2,000 3,420 5 C A, T, T c, V, P 8,090 5,000 3,080 6 T, T c, V, P 6,150 4,000 2,140 7 none 0 0 0

30 The Material Accounting Perspective Production Process Production Flow Stream Measurements ˆm, ˆ Estimator where and mˆ ˆ is the estimated production rate of p is the precision of the estimator

31 Distribution of Estimates Consider production stream p. Assume the target production rate is m*. Let g(, ˆ p,m ) be the estimate distribution function for the existing network, and g(, ~ p,m) be for the new Probability Distribution for Existing Estimator m* m* -Δ m* +Δ Probability Distribution for New Estimator

32 Downside Expected Production Loss Given an distribution g, ˆ p, m( SN0) one can calculate the probability that target production is not met. This is quantified as the Downside Expected Production Loss: DEPL( ˆ p, m ) T * m ( m * ) g(, ˆ p, m ) d 0.2T ˆ p, m

33 The Economic Value of an Upgrade (material accounting perspective) If a new network SN replaces SN 0, which has a distribution g, ~, ( SN) p m then upgrade value is defined as: V ( SN) K K S S DEPL ˆ p, m ˆ ( SN ) DEPL ~ ( SN) ( SN p, m o o ) ~ p, m ( SN ) p, m where K s is the product value (or the cost of inventory) and is a constant.

34 Motivating Example (material accounting perspective) No New Sensors Value ($/yr) Sensor Costs ($/yr) Value - Sensor Costs ($/yr) 1 C Ai F vg F All sensors ,000-12,644 In all cases the cost of adding sensors far exceeds the profit retuned in the form of Upgrade Value.

35 The Fault Perspective (Detection Formulation) Consider a set F of possible faults F={ f i }. Define a set A i (SN) as the set of sensors in SN that can observe fault f i. If A i (SN) is not empty then f i can be detected. Assume immediate correction occurs for detected faults. If all faults in F can be detected, then no production losses or safety incidents will be expected.

36 Diagnosis Formulation Define A ik (SN) as the set of sensors in SN that can resolve fault f i aginst f k. A ik (SN) is the symmetric difference between A i and A k : A ik A i A k A i A ik (SN) not empty for all k then f i can be diagnosed. If all faults in F can be diagnosed, then no production losses or safety incidents will be expected. A k

37 The Value of an Upgrade Let F u (SN) be the set of un-diagnosable (or undetectable) faults (from F) for a given configuration SN. The Expected Economic Loss due to F u (SN) is denoted: EEL ( F u (SN) ) If F u (SN) is empty then EEL ( F u (SN) ) = 0 The Value of an upgrade from SN 0 to SN is V(SN) = EEL ( F u (SN 0 ) ) - EEL ( F u (SN) )

38 Motivating Example (fault diagnosis perspective) No New Sensors Value ($/yr) Sensor Costs ($/yr) Value - Sensor Costs ($/yr) 1 T ci, T i 7,810 2,000 5,810 2 F c, T c, T i 7,810 3,000 4,810 3 T c, T ci 4,720 2,000 2,720 4 F c, T c 4,720 2,000 2,720

39 Integrated Perspective (CSTR Example) No New Sensors Value ($/yr) Sensor Costs ($/yr) Value - Sensor Costs ($/yr) 1 C A, P, T ci, T i 14,930 4,000 10,930 2 C A, P, F c, T c, T i 15,525 5,000 10,525 Case 1: union of best networks from individual perspectives. Case 2: union of second best networks. These are the best combinations given the tables presented. Exhaustive enumeration search is possible.

40 Computational method Tree search version one : the forward tree search Root node (no sensor) t = (0,0,0,..) t = (1,0,0,..) t = (0,1,0,..) t = (1,1,0,..) t = (1,0,1,..) Elements (cutsets or measurements ) are added one by one to nodes In a branch, always start with least costly node (branching criteria) Stop adding (stop going down the tree) when a feasible node is found or when the current node has a cost largest than the best found existing node

41 Computational method for cost-optimal SEN Tree search version two: the reverse tree search + Sensors are removed one by one out of the root node (which contains all sensors ) + Stop removing (stop going down the tree) when the node become infeasible t = (1,0,0,..) t = (1,1,0,..) Root node (all sensors) t = (0,1,0,..) t = (0,0,0,..) t = (1,0,1,..)

42 Methodology for Cost Optimal Cases Feasibility criteria for cost optimal nodes: Replaced by - precision threshold - residual precision threshold - Error detectability threshold - resilience threshold - accuracy threshold (maximum or stochastic).

43 Computational method for value-optimal SEN Tree search version one : the forward tree search Root node (no sensor) t = (0,0,0,..) t = (1,0,0,..) t = (1,1,0,..) t = (0,1,0,..) t = (1,0,1,..) Value is not guaranteed to be monotonically increasing with sensors, although the suspicion exist they are monotone in some order. We are working on techniques to capture good optimal solution. Genetic algorithms are also tried stand alone and hybrid with tree techniques.

44 Madron example Computational method for cost-optimal SEN Sensor precision of 2.5% (for all sensors) is used

45 Computational method for cost-optimal SEN Precision of 2.5 % is required for all streams except S1, S3, S9, S13, S17, S21 (totally 24-6 = 18 key variables). Residual precision of 5% is also required for stream S6, S14 Solutions : S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S13, S14, S15, S18,,S20, S21, S22, S23, S24 (20 measurements in the optimal solution). Cost is 272. Forward tree search : computation time more than 1 hour and a half Reverse tree search : Total computational time: 48 seconds Computational time for reverse tree search procedure only : 22 seconds Number of nodes explored : 778

46 Computational method for value-optimal SEN

47 Computational method for value-optimal SEN Key variables Ks values Probability of failure (all sensors) Mean of pdf of bias (all sensors) STD of pdf of bias (all sensors)

48 Computational method for value-optimal SEN Optimal solution Active cutsets : 1, 2, 3, 4, 5, 6, 7, 11, 51 Active streams : 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 18, 20, 23, 24 Objective value :

49 Computational method for value-optimal SEN Active cutsets : 1, 2, 3, 4, 5, 6 Active streams : 1, 2, 3, 9, 12, 13, 14, 20 Objective value : Adding cutset : 11 Adding streams : 4, 8, 10 Objective value : Adding cutset: 51 Adding streams : 6, 7, 16, 18, 23 Objective value : Stop here Non monotonic Adding cutsets (streams) Adding cutset : 7 Adding active streams : 24 Objective value :

50 Computational method for value-optimal SEN Active cutsets : 1, 2, 3, 4, 5, 6 Active streams : 1, 2, 3, 9, 12, 13, 14, 20 Objective value : Adding cutset : 51 Adding streams : 4, 6, 7, 10, 16, 18, 23 Objective value : Adding cutset: 11 Adding streams : 8 Objective value : Adding cutset : 7 Adding active streams : 24 Objective value : Monotonic Adding cutsets (streams) DEFL+COST IS MINIMIZED Max(DEFL 0 -DEFL- COST) < == > Min(DEFL+COST)

51 Crude Distillation Unit (CDU) U U U1 U2 U4 U5 U3 8 U U7 U8 13 U9 15 U13 34 U Streams 19 Units U U U16 37 UNITS 44 U3/U9- HEN U5- DESALTING UNIT U6- CRUDE VESSEL U10- PREFRACTIONATION TOWER U11/U14- CONDENSER U12/U17- FURNACE U13- ATMOSPHERIC TOWER U15/U16- ATMOSPHERIC PRODUCT DRYER U18- VACUUM TOWER U18 42 U U19 49 Blue streams indicate key variables 52

52 Results Precision of 5% in the flow was required in streams S17, S18, S31, S33, S35, S37, S43, S44, S45, S46, S47, S48, S50, S51 and S52. Also a residual precision of 25% was required in the same flowrates Minimum Cost. {S15, S16, S17, S18, S19, S29, S31, S32, S33, S35, S37, S42, S43, S44, S45, S46, S47, S48, S49, S50, S51, S52} or {S15, S16, S17, S18, S19, S29, S31, S32, S33, S35, S36, S42, S43, S44, S45, S46, S47, S48, S49, S50, S51, S52}

53 The Tennessee Eastman Plant Example The Tennessee Eastman Process

54 The Tennessee Eastman Plant Example 47 variables are considered as candidates for measurements: the flowrate and component compositions in the streams 6, 7, 8, 9, 10, 11 and the temperature and pressure in the reactor and separator. Sensor precision of 2% is used for all variables

55 The TE process example Case study TE1 Low Spec. TE2 Moderate Spec. TE3 High Spec. Number of key variables Requirement Observability Observability Observability Precision Thresholds 2% 2% 1.5% Number of sensors in optimal solution

56 Results for the TE process example Case Study Decomposed Equations method (9 subgraphs) Computation time No. of nodes explored TE1 Low Spec 6 key var. 2 min 40 seconds TE2 Moderate Spec 17 key var. TE3 High Spec 39 key var. >14 hours >10 hours (Suboptimal solution found in one second) 11,628 >0.52 millions >0.5 millions All Variables method Computation time 9 hr, 8 min > 3 days (45 days estimated) Not attempted No. of nodes explored 1,867,295 > 6 millions Inverted Variables method All Computation time No. of nodes explored Not used Not used 4 minutes 16 seconds 1726

57 Conclusions Smart Plants are more Profitable but they need Precise and Bias-Free Data Redundant measurements of the same variable ( hardware redundancy ) is too expensive Software redundancy is much less costly but needs process models. New profit formulation was developed Easier to interpret and sell the benefits of SND. Removes the need to select target performance. Aids in developing an integrated formulation. Integrated formulation investigated. Does provide synergism between the 3 perspectives. Computational questions remain and will require much more than an enumerative scheme.