TRNSYS Based Model for Organic Rankine Cycle (ORC) to ...

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TRNSYS Based Model for Organic Rankine Cycle (ORC) to Produce 1kW Power

Abid Hussain1, Brian Fronk2 1National University of Sciences and Technology (NUST) Islamabad

2Oregon State University (OSU), Corvallis Oregon Abstract: Due to present energy crisis in Pakistan remote areas are completely deprived of electricity. A dynamic model of Organic Rankine Cycle is developed to determine optimized parameters to generate power using weather data for Lahore, Pakistan which can be further applicable to any remote area. Simulation is carried out in TRNSYS 17 a powerful tool for solar thermal power generation. Flat plate solar collector is utilized to heat glycol/water mixture (50:50) while n-pentane is used as working fluid. The results show that the maximum temperature obtained at the collector outlet is 90oC. The optimum working fluid flow rate is 600 kg/hr while the required inlet pressure for 1 kW power production is 5bar. Solar collector area is inversely related to cycle efficiency while turbine inlet pressure is directly related. Optimum collector area to produce required power is 16.6 m2 whereas overall cycle efficiency is 16%. The results of this simulation show that this process is feasible for Lahore, Pakistan. 1.0 Introduction Conventional Rankine Cycle uses water as working fluid while in Organic Rankine Cycle (ORC) water is replaced by a high molecular weight organic liquid. Purpose of replacing organic liquid with water is to recover heat from low temperature streams. Organic liquids have the ability to recover heat more efficiently because their evaporation occurs at lower temperature and pressure [1]. First commercial ORC power plant was built in 1970 [2]. ORC plants are mostly utilized to produce power by recovering heat from industrial waste streams, biomass and solar energy [3]. ORC require the same components as steam Rankine Cycle but since the temperature and pressures are not as high as in steam power plants, required equipment is not expensive and can be fabricated locally. Choice of working fluid is the most important step in designing an ORC. Characteristics of a good working fluid includes chemical and thermal stability, high latent heat of vaporization, isentropic or dry fluid, high density, high specific heat, low cost and ease of availability [1].

Pakistan is facing the worst energy crisis from last one decade. Pakistan’s electricity demand is around 2000 MW while it has a shortfall of 8000 MW [4]. In this situation when it is difficult to provide required power to major cities, remote areas are completely starved of electricity. The best way to provide electricity to these remote areas is through small scale renewable power plants. Organic Rankine Cycle (ORC) utilizing solar energy is the attractive choice because it generates electricity at low temperatures (100 to 250 oC) [5]. More than 60% of Pakistan’s electricity generation has been through fossil fuels which are not only non-renewable resources but also major contributors to global warming [2]. With the increasing energy demand and decreasing fossil fuels we need to increase our dependence on renewable resources. In order to establish small ORC power plants in remote areas we need to determine their feasibility. Simulating these plants for the required power output for a particular area is the best practice to determine the feasibility. In this study an ORC based TRNSYS model is developed to produce 1 kW of power which can be scaled up to any required output.

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2.0 Previous work: ORC is considered one of the best ways to utilize solar energy. A lot of work has already been done in this field. A comprehensive overview of different low temperature applications of ORC are analyzed by Bertrand F. T et al. [1]. Working fluid selection is the most critical parameter in ORC power plant. Huijuan et al. [6] have analyzed 35 fluids to determine their potential as working fluid in ORC power plant and their effect on cycle performances. Saleh et al. [7] studied the behavior of 31 fluids including alkanes, ethers and their fluorinated derivatives. Villarani et al [8] have worked on TRNSYS based model to predict production of 3 kW power at temperature of 150 oC from a prototype under construction in Italy. Musbaudene et al [9] have worked on simulation of ORC with R245fa as working fluid to produce 40kW of power from water heated at 80 to 95 oC. They identified the working and heating fluid flow rates as the critical parameters. Patnode [10] used Parabolic Trough Collectors to produce 354 MW of Power using TRNSYS simulation for steam Rankine cycle and ORC and validated data with experimental values. Wang et al. [11] worked on simulation of solar based ORC power plant and studied the performance change with respect to changing parameters and working fluids. Quoiline et al [12] have used a semi empirical model to compare the predicted parameters with the actual. Proposed model can be used to optimize the parameters by comparing different configurations and working fluids. Calise et al [13] studied the varying performance at temperatures from 120 to 300oC. It was found that n-pentane, n-butane and isobutene are the best working fluids for this temperature range.

3.0 Schematic:

Fig (1) Schematic of Solar thermal Organic Rankine Cycle (ORC) Power Plant

Fig (1) shows a schematic of solar thermal ORC which contains thermal and a power loop. Thermal loop contains a pump and a collector. The output of collector is connected to source side of evaporator which is common equipment for both loops used to transfer heat from heating fluid to the working fluid. In this study the heating fluid is glycol/water mixture (50:50) while n-pentane is used as working fluid because it is a dry fluid which has higher heat capacity than other refrigerants and does not condense at the impeller

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blades. The working fluid is pumped to the load side of evaporator where heat is transferred to this fluid and it drives the turbine after evaporation and passes through a regenerator to preheat the working fluid before it enters the evaporator. After regenerator the working fluid is condensed to liquid form before entering the feed pump.

TRNSYS is simulation software which is utilized to determine the behavior of transient systems. We can simulate processes related to solar, thermal and electrical energy. TRNSYS computation is very quick compared to other simulation software and it has a wide range of solar thermal equipment in its library including STEC library specifically for Rankine and Brayton cycles. Effect of changing key parameters like type and flow rate of working fluid, turbine inlet pressure, collector type and area can be determined easily. Weather data files for TRNSYS are readily available and once the model is developed it can be applied to obtain any required output. In this study weather data for Lahore, Pakistan is utilized to determine the optimized parameters for required output power.

Nomenclature A Heat Transfer Area, m2 P Hydraulic Power, kW a̋ Outside fin area, m2 Q Evaporator Heat Transfer, kJ/hr Cp Heat capacity, kJ/kg.K Qc Condenser Heat Transfer, kJ/hr G Gravitational acceleration, m2/s q Volumetric flow rate, m3/hr ΔH Enthalpy change, kJ/kg 𝛥𝛥𝛥𝛥 Log mean temperature difference, K H Enthalpy, kJ/kg UD Overall heat transfer coefficient, kJ/hr.K L Length of tube, m WT Work done by turbine, kJ/hr ṁ Mass flow rate, kg/hr ρ Density, m3/kg N No. of tubes Ƞ Efficiency

4.0 Equipment Description: 4.1 Pumps: For heating fluid glycol/water mixture is utilized the specific gravity of this mixture does not show any considerable change so it is assumed constant (1.077). The enthalpy changes across pumps are considered zero. Pumps used for ORC are controlled by forcing function. Inlet flow rate of heating fluid is 2000 kg/hr and for working fluid is 600 kg/hr while developed head for both is 1m. The required hydraulic power is determined by (Eq.1) P = q ρ g h / 3.6 x 106 (Eq.1) 4.2 Collector: Weather data for Lahore Pakistan is utilized in this simulation. Flat plate solar collectors being cheap and easily available are selected to absorb solar radiations. Flat plate solar collectors can provide temperature around 100oC. The required area is determined by simulating thermal loop and determining the collector outlet temperature for required generator output of 1 kW which turned out to be 16.6m2. 4.3 Evaporator: A shell and tube heat exchanger is utilized as evaporator. Overall heat transfer coefficient and heat capacities of fluids are assumed constant. The source side inlet temperature is 90oC while source side flow rate is 2000kg/hr. The load side inlet temperature is 47oC and flow rate is 600kg/hr. The overall heat transfer coefficient of heat exchanger is obtained using Eq.2

UD = 𝑄𝑄.𝐴𝐴𝛥𝛥𝛥𝛥

Eq.2

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Q and A determined by Eq.3 and 4 Q = ṁ.Cp.𝛥𝛥𝛥𝛥 Eq.3 A = N.L.a̋ Eq.4 while 𝛥𝛥𝛥𝛥 is determined by log mean temperature difference (LMTD) method. 4.4 Turbine: Since the pressure drop ratios for ORC systems are smaller [1] single stage turbines can be utilized. The input pressure to the turbine is kept constant at 5bar while the enthalpy change can be determined by Eq.5 ΔH = Cp ΔT Eq.5 Efficiency of the turbine is determined by Eq.6 Ƞ = WT / ṁ ΔH Eq.6

4.5 Regenerator: The condensed organic liquid from pump is allowed to transfer heat from output mass flow of turbine in order to preheat the liquid to reduce evaporator load. The source inlet temperature of regenerator is 70oC and load inlet temperature is 35oC. The regenerator raises the temperature of feed to 47oC. Since regenerator is a shell and tube heat exchanger, Eq.2 to 5 can be used to determine overall heat transfer coefficient. 4.6 Condenser: The working fluid changes its phase in condenser by giving up latent heat. A water cooled condenser is utilized to remove heat from working fluid. Heat transfer through condenser can be determined by Eq.7 Qc = ṁ.Cp.ΔT Eq.7

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5.0 TRNSYS Model:

Fig (2) TRNSYS model for Solar Thermal ORC

Table (1) Key Parameters for ORC simulation Heating Fluid Glycol/Water Mixture Working Fluid n-Pentane Heating Fluid Flow rate 2000 kg/hr Working Fluid Flow rate 600 kg/hr Collector Area 16.6 m2 Pressure at Turbine inlet 5 bar Output power 1 kW

Fig (2) shows the ORC model developed in TRNSYS 17 software to determine the effect of varying collector area and temperature through the day on generated power. Weather data used in this simulation is for Lahore Pakistan. After successful simulation, this model can be applied to determine the required collector area, heating /working fluid types and flow rates for any remote weather conditions for required output power. In this model the weather data provide solar irradiation to a flat plate collector which is connected to a pump operated through a forcing function which activate the pump allowing the heating

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fluid to flow during day time and shut down at night. The heating fluid enters the source side of an evaporator and raises the temperature of working fluid on the load side. The load side working fluid flow is also controlled by a pump connected to forcing function.

6.0 Results and Discussions: 6.1 Model Outputs: Initially the simulations are carried out for a day (16th June) in summer (4008 to 4032) when the solar radiations are very strong.

Fig (3) Simulation result of Collector outlet temperature

Fig (3) shows how collector outlet temperature changes through a day in summer. The maximum temperature achieved during a day is 90oC.

Fig (4) shows how the working fluid temperature rises in a day. Since the boiling point of working fluid is 36oC this temperature is enough to provide required inlet enthalpy to the turbine. The average heat transfer in the evaporator section is 26000kJ/hr. Fig ( 5) shows the heat transfer in evaporator through the day.

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Fig (4) Simulation result of evaporator temperature

Fig ( 5) Simulation result of evaporator heat transfer

The maximum temperature and pressure at the inlet of turbine are 76oC and 5bar. The power generated by turbine is 1.68 kW. Fig (6) shows the power generated by turbine in a day.

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Fig (6) Simulation result of turbine power

The turbine is connected to an electric generator. Fig (7) shows the output electric power obtained during the day.

Fig (7) Simulation result of generator power

The maximum outlet temperature from turbine is around 69oC. A regenerator is utilized to recover heat from turbine outlet stream which preheats the working fluid to 47oC and decreases the evaporator load. Fig (8) shows the heat transfer in regenerator.

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Fig (8) Simulation result of heat transfer through regenerator

Fig (10) shows the power generated for a whole year. It can be seen that the power output varies throughout the year due to varying solar radiations.

Fig (10) Simulation result of electric power generated in a year

6.2 Effect of Area, Pressure and Working fluid Flow rate: Fig (11) shows the effect of collector area on power generated. It can be seen that as we increase the area increase in power is not as significant because of decreasing efficiency.

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Fig (11) Change in generator power with increasing collector area.

Fig (12) Change in generator power with increasing collector area.

Keeping the required solar collector area at 16.6 m2 and turbine inlet pressure at 5 bar, Fig (12) shows as we increase the working fluid flow rate average generator output power for a summer day increases and around 600 kg/hr the generator output power reaches 3658 kJ/hr (1.01 kW). Fig (13) shows the effect of turbine inlet pressure on the power output of generator. Increasing the pressure increases the power output.

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Fig (13) Change in generator power with increasing collector area.

The overall cycle efficiency of the ORC system can be calculated by Eq.8 Overall Efficiency = WT + (Pump work) / Q Eq.8 Fig (14, 15, 16) show how overall efficiency of the system is affected by increasing turbine inlet pressure, collector area and working fluid flow rate.

Fig (14) Change in Cycle Efficiency with respect to increasing turbine inlet pressure

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Fig (15) Effect of collector area on cycle efficiency of the ORC system

Fig (16) Effect of working fluid flow rate on cycle efficiency of the ORC system

Conclusion: TRNSYS based ORC power plant for remote application has been simulated successfully. The results suggest that required collector area to produce 1 kW power on average from solar thermal ORC power plant using weather data from Lahore Pakistan is 16.6 m2. The maximum temperature to which glycol/water mixture with a flow rate of 2000 kg/hr is heated by flat plate collector is 90oC. n-Pentane with a flow rate of 600 kg/hr is heated up to 77oC in the evaporator. The pressure at the turbine inlet is kept at 5bar. Maximum heat transfer obtained in evaporator is 34000kJ/hr. The maximum output power obtained from turbine is 1.68 kW with a generator power of 1.29 kW with efficiency of 76%. The average power obtained during a summer day is 1.01 kW. It has been observed that increasing the solar collector area decreases the cycle efficiency while turbine inlet pressure has inverse relation with cycle efficiency. Overall cycle efficiency obtained from this simulation is 16%.

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Future Recommendations: A control system can be applied in order to increase the flow rates of heating and working fluid in order to achieve required heat transfer in evaporator when solar radiation are not strong enough to produce required power. In order to provide power during night as well a storage system can be coupled with the system. Heat can be recovered from the stream exiting regenerator which can provide hot water for domestic purpose.

References:

[1] B. F. Tchanche, G. Lambrinos, A. Frangoudakis, and G. Papadakis, “Low-grade heat conversion into power using organic Rankine cycles - A review of various applications,” Renew. Sustain. Energy Rev., vol. 15, no. 8, pp. 3963–3979, 2011.

[2] S. Quoilin, M. Van Den Broek, S. Declaye, P. Dewallef, and V. Lemort, “Techno-economic survey of organic rankine cycle (ORC) systems,” Renew. Sustain. Energy Rev., vol. 22, pp. 168–186, 2013.

[3] Y. Dai, J. Wang, and L. Gao, “Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery,” Energy Convers. Manag., vol. 50, no. 3, pp. 576–582, 2009.

[4] A. Hussain, M. Rahman, and J. A. Memon, “Forecasting electricity consumption in Pakistan: The way forward,” Energy Policy, vol. 90, pp. 73–80, 2016.

[5] H. Xi, M. J. Li, Y. L. He, and W. Q. Tao, “A graphical criterion for working fluid selection and thermodynamic system comparison in waste heat recovery,” Appl. Therm. Eng., vol. 89, pp. 772–782, 2015.

[6] H. Chen, D. Y. Goswami, and E. K. Stefanakos, “A review of thermodynamic cycles and working fluids for the conversion of low-grade heat,” Renew. Sustain. Energy Rev., vol. 14, no. 9, pp. 3059–3067, 2010.

[7] B. Saleh, G. Koglbauer, M. Wendland, and J. Fischer, “Working fluids for low-temperature organic Rankine cycles,” Energy, vol. 32, no. 7, pp. 1210–1221, 2007.

[8] M. Villarini, E. Bocci, A. Di Carlo, D. Sbordone, M. C. Falvo, and L. Martirano, “Technical-economic analysis of an innovative small scale solar thermal - ORC cogenerative system,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 7972 LNCS, no. PART 2, pp. 271–287, 2013.

[9] M. O. Bamgbopa, “With R245Fa As Working Fluid,” pp. 1–8, 2012.

[10] A. Patnode, “Simulation and performance evaluation of parabolic trough solar power plants,” Univ. Wisconsin-Madison, vol. Master, pp. 5–271, 2006.

[11] M. Wang, J. Wang, Y. Zhao, P. Zhao, and Y. Dai, “Thermodynamic analysis and optimization of a solar-driven regenerative organic Rankine cycle (ORC) based on flat-plate solar collectors,” Appl. Therm. Eng., vol. 50, no. 1, pp. 816–825, 2013.

[12] S. Quoilin, V. Lemort, and J. Lebrun, “Experimental study and modeling of an Organic Rankine Cycle using scroll expander,” Appl. Energy, vol. 87, no. 4, pp. 1260–1268, 2010.

[13] Calise, “Design and Parametric Optimization of an Organic Rankine Cycle Powered By Solar Energy,” Am. J. Eng. Appl. Sci., vol. 6, no. 2, pp. 178–204, 2013.

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Summary of Primary Training Activities Completed

Presentations

There will be a Final Presentation on 30th November, 2016 about the research work I have completed while my stay at Oregon State University, United States.

Number of Courses

I have audited following courses during Fall 2016

ME 507 Design Seminar Series by OSU Design Engineering Lab (One hour) Basic Matlab for Env Sci (CE_640) by Dr. Hill (Two hours)

Number of Seminars and Workshops

1. Functional Lock-In and the Problem of Design Transformation and Engineering Global

Development: Using Emerging Markets Constraints to Drive the Innovation of Global

Technologies, A Special Joint Seminar by Dr. Andy Dong and Dr. Amos Winter

2. Turbulent Combustion Modeling for Large Eddy Simulation: Beyond Premixed vs. Non-

premixed Modes by Dr. Michael E. Mueller

3. Success as a Student Researcher, A Discussion of Best Practices, Topic 1: Developing a

Research Plan and Literature by Dr. Bryony DuPont, OSU Design Engineering Lab

4. Success as a Student Researcher, A Discussion of Best Practices, Topic 2:

Communicating Your Work by Dr. Bryony DuPont, OSU Design Engineering Lab

5. Symbiotic Systems for Energy, Water, and Food by Dr. Alexander H. Slocum,

Pappalardo Professor of Mechanical Engineering at MIT, a MacVicar Faculty Teaching

Fellow, and ASME Fellow

6. OSU Design Engineering Lab Faculty Panel by Dr. Bryony DuPont, Dr. Chris Hoyle, Dr.

Matt Campbell, and Dr. Onan Demirel, OSU Design Engineering Lab

7. Success as a Student Researcher, A Discussion of Best Practices, Topic 3: Writing by Dr.

Bryony DuPont, OSU Design Engineering Lab

8. Three Day Workshop on Energy Policy by Dr. Clark Miller, Arizona State University (ASU)

No. of Field Trips:

The only field trip was on 15th September, 2016

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Other Activities

Apart from the above mentioned activities, the following tasks were also completed.

• Completed Lab Safety and CITI Responsible Conduct of Research Online Training

• Learned about OSU library journal system

• Developed competency in literature review and bibliographic tools/packages through

OSU library and graduate school workshops

• Took six weeks MIME Toastmasters Club “Speech-craft” Training

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Cultural Exchange Highlights

This visit has been a perfect opportunity for me to learn about American Culture. The first cultural exchange activity was Apple Picking. We went to country side farm with my American friends from lab. The event was not only limited to apple picking but there was a whole fruit market where people were selling fresh fruit. There was live music which is pretty rare in Pakistan. We picked apples and pears from dozens of different types. Walked around the place, met local farmers and natives. There was an old lady giving out free apple pie, I tried it for the first time in my life and it was delicious. It was couple of weeks before Halloween so we could see pumpkins everywhere.

The second activity was on Halloween. We went to McNairy Dining Hall for Pumpkin painting and costume competition. We made couple of friends there who later took us to American Football game OSU vs. Washington State. We went to Hogwarts themed Memorial Union and Haunted House with some American friends. Learned a lot about how people celebrate Halloween. Learned to paint and carve the pumpkin.

The third cultural activity was an excursion to New Port. We saw some sea lions just at coast, went to light house beside the coast, learned about how people used to navigate and travel in the past. We went to underwater sea garden and Wax Museum at New Port and later that day visited Lincoln city Shopping Mall. We walked around that place and bought some clothes, shoes and had experience of how shopping at those malls are different from my country.

It’s fascinating how organized everything is in United States. People are organized in their lives, have a specific routine and rules. People tend to do enjoy their lives by keeping a good balance between work and life. Everyone is loyal to their work doesn’t matter the kind of work they are doing. Cleanliness is something they don’t compromise. All these things have really impressed me and I hope to go back and share all my experiences with my colleagues, friends and family.

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APPENDIX-A

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APPENDIX-B

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APPENDIX-C

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Audited Courses:

S.no Course Code

Name & Description By

1 CE-640 Basic Matlab for Envi Sci Introduction to basic programming and data analysis skills, writing optimized routines to analyze data sets utilizing matrix, algebra and vectorization of functions, basic graphics and visualization, hands on computer lab experience.

Dr. Hill

2 ME-507 Design Seminar Series Transformation and Global Technology in Design by Dr. Winter Symbiotic System for Energy, Water, and Food by Dr. Alexander H. Slocum

OSU Design Engineering

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APPENDIX-D

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Assignment1 Part 1 % plotting circle circumference and area versus radius r= [1 2 8 20]; C = 2*pi*r; A = pi*r.^2; subplot(121); plot(r,C); xlabel ('radius'); ylabel ('Circumference'); grid on; hold on; subplot(122); plot(r,A); xlabel ('radius'); ylabel ('Area'); grid on; hold on; Part 2 % Finding min, max, mean and standard dev from random numbers x=[0 1 2 3 4 5 6 8]; s1=rng; r1=randn(10,8); rng(s1); a1=1.50.*(r1)+0; m1=mean (a1(:)); sd1=std (a1(:)); % minimum stats y1=min(a1); subplot(221); plot(x, y1,'+'); hold on; title('minimum statistics'); % max stats z1=max (a1); subplot(222); plot(x,z1,'+'); hold on; title('maximum statistics'); % mean stats

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n1=mean (a1); subplot(223); plot(x,n1,'+'); hold on; title('mean statistics'); % standard deviation stats d1=std (a1); subplot(224); plot(x,d1,'+'); axis ([0 8 -5 5]); hold on; title('standards deviation statistics'); randn(10,8); s2=rng; r2=randn(10,8); rng(s2); a2=1.50.*(r2)+0; m2=mean (a2(:)); sd2=std (a2(:)); % minimum stats y2=min(a2); subplot(221); plot(x, y2,'*'); hold on; % maximum stats z2=max (a2); subplot(222); plot(x,z2,'+'); hold on; %mean stats n2=mean (a2); subplot(223); plot(x,n2,'+'); hold on; % standard deviation stats d2=std (a2); subplot(224); plot(x,d2,'+'); hold on; randn(10,8);

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s3=rng; r3=randn(10,8); rng(s3); a3=1.50.*(r3)+0; m3=mean (a3(:)); %by converting a3 10 rows 8 coloumn matrix to single coloumn sd3=std (a3(:)); % minimum stats y3=min(a3); subplot(221); plot(x, y3,'*'); hold on; % maximum stats z3=max (a3); subplot(222); plot(x,z3,'+'); hold on; % mean stats n3=mean (a3); subplot(223); plot(x,n3,'+'); hold on; % standard deviation stats d3=std (a3); subplot(224); plot(x,d3,'+'); hold on; randn(10,8); s4=rng; r4=randn(10,8); rng(s4); a4=1.50.*(r4)+0; m4=mean (a4(:)); sd4=std (a4(:)); % minimum stats y4=min(a4); subplot(221); plot(x, y4,'*'); hold on; % maximum stats z4=max (a4);

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subplot(222); plot(x,z4,'+'); hold on; % mean stats n4=mean (a4); subplot(223); plot(x,n4,'+'); hold on; % standard deviation stats d4=std (a4); subplot(224); plot(x,d4,'+'); hold on; randn(10,8); s5=rng; r5=randn(10,8); rng(s5); a5=1.50.*(r5)+0; m5=mean (a5(:)); sd5=std (a5(:)); % minimum stats y5=min(a5); subplot(221); plot(x, y5,'*'); axis([0 8 -5 5]); hold on; % maximum stats z5=max (a5); subplot(222); plot(x,z5,'+'); axis ([0 8 -5 5]); hold on; % mean stats n5=mean (a5); subplot(223); plot(x,n5,'+'); axis ([0 8 -5 5]); hold on; % standard deviation stats d5=std (a5);

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subplot(224); plot(x,d5,'+'); axis ([0 8 -5 5]); hold on; Assignment-3 Part 1 x=[1 3 5]; s1=rng; r1=randn(10,1,3); rng(s1); sqz=squeeze(r1); m1=min(sqz); m2=max(sqz); n1=mean(sqz); d1=std(sqz); plot(x,m1,'+'); hold on; plot(x,m2,'+'); hold on; plot(x,n1,'+'); hold on; plot(x,d1,'+'); hold on; axis ([0 8 -5 5]); Part 2 function y1=multGauss(g1) if isrow (g1) error('gaussian must be in matrix form') end amp=[1 1 1]; sigma=[3 3 3]; y1=gaussmf(g1,[sigma amp]); end function y2=multGauss2(g2) if isrow (g2) error('gaussian must be in matrix form') end amp=[1 1 1]; sigma=[3 3 3]; y2=gaussmf(g2,[sigma amp]);

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end clc; clear all; g1=[1 2 3; 4 5 6; 7 8 9] multGauss(g1) g2=[10 12 13; 14 15 16; 17 18 19] multGauss(g2) sum=multGauss(g1)+multGauss(g2) Part 3 function y=multGauss(x) for a=0:20 sigma=0.5; c=2; end y=0.1*(gaussmf(x,[sigma c])); plot(x,y) hold on for b=0:20 sigma1=1; c1=4; end y=0.5*(gaussmf(x,[sigma1 c1])); plot(x,y) hold on for c=0:20 sigma2=2; c2=6; end y=1*(gaussmf(x,[sigma1 c1])); plot(x,y) hold on for d=0:20 sigma3=3; c3=8; end y=2*(gaussmf(x,[sigma1 c1])); plot(x,y) hold on xlabel ('Domain Range'); ylabel ('Multi Gauss Output');

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end clc x=0:20; y=multGauss(x) Assignment-4 Part 1 clear all; clc; fid=fopen('students_earning_data.txt') fgetl(fid) fgetl(fid) fgetl(fid) [data]=textscan(fid, '%d32 %d8 %d8 %d8') fclose(fid); % Frank details Frank_ttl_1st_weekd_hrs = sum(data{2}(1:4,:)); Frank_ttl_2nd_weekd_hrs = sum(data{2}(7:11,:)); Frank_ttl_3rd_weekd_hrs = sum(data{2}(14:18,:)); Frank_ttl_4rth_weekd_hrs = sum(data{2}(21:25,:)); Frank_ttl_5th_weekd_hrs = sum(data{2}(28:30,:)); Frank_ttl_weekd_hrs = Frank_ttl_1st_weekd_hrs + Frank_ttl_2nd_weekd_hrs + Frank_ttl_3rd_weekd_hrs + Frank_ttl_4rth_weekd_hrs + Frank_ttl_5th_weekd_hrs Frank_eoweekd = 5*Frank_ttl_weekd_hrs Frank_ttl_1st_weeknd_hrs = sum(data{2}(5:6,:)); Frank_ttl_2nd_weeknd_hrs = sum(data{2}(12:13,:)); Frank_ttl_3rd_weeknd_hrs = sum(data{2}(19:20,:)); Frank_ttl_4rth_weeknd_hrs = sum(data{2}(26:27,:)); Frank_ttl_weeknd_hrs = Frank_ttl_1st_weeknd_hrs + Frank_ttl_2nd_weeknd_hrs + Frank_ttl_3rd_weeknd_hrs + Frank_ttl_4rth_weeknd_hrs Frank_eoweeknds = 5*Frank_ttl_weeknd_hrs % Anna details Anna_ttl_1st_weekd_hrs = sum(data{3}(1:4,:)); Anna_ttl_2nd_weekd_hrs = sum(data{3}(7:11,:)); Anna_ttl_3rd_weekd_hrs = sum(data{3}(14:18,:)); Anna_ttl_4rth_weekd_hrs = sum(data{3}(21:25,:)); Anna_ttl_5th_weekd_hrs = sum(data{3}(28:30,:)); Anna_ttl_weekd_hrs = Anna_ttl_1st_weekd_hrs + Anna_ttl_2nd_weekd_hrs + Anna_ttl_3rd_weekd_hrs +

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Anna_ttl_4rth_weekd_hrs + Anna_ttl_5th_weekd_hrs Anna_eoweekd = 7.50*Anna_ttl_weekd_hrs Anna_ttl_1st_weeknd_hrs = sum(data{3}(5:6,:)); Anna_ttl_2nd_weeknd_hrs = sum(data{3}(12:13,:)); Anna_ttl_3rd_weeknd_hrs = sum(data{3}(19:20,:)); Anna_ttl_4rth_weeknd_hrs = sum(data{3}(26:27,:)); Anna_ttl_weeknd_hrs = Anna_ttl_1st_weeknd_hrs + Anna_ttl_2nd_weeknd_hrs + Anna_ttl_3rd_weeknd_hrs + Anna_ttl_4rth_weeknd_hrs Anna_eoweeknds = 7.50*Anna_ttl_weeknd_hrs % Rob details Rob_ttl_1st_weekd_hrs = sum(data{4}(1:4,:)); Rob_ttl_2nd_weekd_hrs = sum(data{4}(7:11,:)); Rob_ttl_3rd_weekd_hrs = sum(data{4}(14:18,:)); Rob_ttl_4rth_weekd_hrs = sum(data{4}(21:25,:)); Rob_ttl_5th_weekd_hrs = sum(data{4}(28:30,:)); Rob_ttl_weekd_hrs = Rob_ttl_1st_weekd_hrs + Rob_ttl_2nd_weekd_hrs + Rob_ttl_3rd_weekd_hrs + Rob_ttl_4rth_weekd_hrs + Rob_ttl_5th_weekd_hrs Rob_eoweekd = 15.0*Rob_ttl_weekd_hrs Rob_ttl_1st_weeknd_hrs = sum(data{4}(5:6,:)); Rob_ttl_2nd_weeknd_hrs = sum(data{4}(12:13,:)); Rob_ttl_3rd_weeknd_hrs = sum(data{4}(19:20,:)); Rob_ttl_4rth_weeknd_hrs = sum(data{4}(26:27,:)); Rob_ttl_weeknd_hrs = Rob_ttl_1st_weeknd_hrs + Rob_ttl_2nd_weeknd_hrs + Rob_ttl_3rd_weeknd_hrs + Rob_ttl_4rth_weeknd_hrs Rob_eoweeknds = 15.0*Rob_ttl_weeknd_hrs Part 2 clear all clc fid=fopen('students_earning_data.txt') fgetl(fid) fgetl(fid) fgetl(fid) [data]=textscan(fid, '%d32 %d16 %d16 %d16') fclose(fid); % for frank s=zeros(30,1); for i=1:30

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s(i,1)=s(i,1)+data{2}(i,:); sm = sum(s); i=[5]; switch i case [5] frank_weeknd_hr1 = data{2}(5,:); end i=[6]; switch i case [6] frank_weeknd_hr2 = data{2}(6,:); end i=[12]; switch i case [12] frank_weeknd_hr3 = data{2}(12,:); end i=[13]; switch i case [13] frank_weeknd_hr4 = data{2}(13,:); end i=[19]; switch i case [19] frank_weeknd_hr5 = data{2}(19,:); end i=[20]; switch i case [20] frank_weeknd_hr6 = data{2}(20,:); end i=[26]; switch i case [26] frank_weeknd_hr7 = data{2}(26,:); end i=[27]; switch i case [27]

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frank_weeknd_hr8 = data{2}(27,:); end end frank_eoweeknds = 5*(frank_weeknd_hr1+frank_weeknd_hr2+frank_weeknd_hr3+frank_weeknd_hr4+frank_weeknd_hr5+frank_week nd_hr6+frank_weeknd_hr7+frank_weeknd_hr8) frank_weekd_hrs1 = sm - data{2}(5,:); frank_weekd_hrs2 = frank_weekd_hrs1 - data{2}(6,:); frank_weekd_hrs3 = frank_weekd_hrs2 - data{2}(12,:); frank_weekd_hrs4 = frank_weekd_hrs3 - data{2}(13,:); frank_weekd_hrs5 = frank_weekd_hrs4 - data{2}(19,:); frank_weekd_hrs6 = frank_weekd_hrs5 - data{2}(20,:); frank_weekd_hrs7 = frank_weekd_hrs6 - data{2}(26,:); frank_weekd_hrs = frank_weekd_hrs7 - data{2}(27,:) frank_eoweekdays = 5*frank_weekd_hrs % for Anna s1=zeros(30,1); for j=1:30 s1(j,1)=s1(j,1)+data{3}(j,:); sm1 = sum(s1); j=[5]; switch j case [5] Anna_weeknd_hr1 = data{3}(5,:); end j=[6]; switch j case [6] Anna_weeknd_hr2 = data{3}(6,:); end j=[12]; switch j case [12] Anna_weeknd_hr3 = data{3}(12,:); end j=[13]; switch j case [13] Anna_weeknd_hr4 = data{3}(13,:);

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end j=[19]; switch j case [19] Anna_weeknd_hr5 = data{3}(19,:); end j=[20]; switch j case [20] Anna_weeknd_hr6 = data{3}(20,:); end j=[26]; switch j case [26] Anna_weeknd_hr7 = data{3}(26,:); end j=[27]; switch j case [27] Anna_weeknd_hr8 = data{3}(27,:); end end Anna_eoweeknds = 7.50*(Anna_weeknd_hr1+Anna_weeknd_hr2+Anna_weeknd_hr3+Anna_weeknd_hr4+Anna_weeknd_hr5+Anna_ weeknd_hr6+Anna_weeknd_hr7+Anna_weeknd_hr8) Anna_weekd_hrs1 = sm1 - data{3}(5,:); Anna_weekd_hrs2 = Anna_weekd_hrs1 - data{3}(6,:); Anna_weekd_hrs3 = Anna_weekd_hrs2 - data{3}(12,:); Anna_weekd_hrs4 = Anna_weekd_hrs3 - data{3}(13,:); Anna_weekd_hrs5 = Anna_weekd_hrs4 - data{3}(19,:); Anna_weekd_hrs6 = Anna_weekd_hrs5 - data{3}(20,:); Anna_weekd_hrs7 = Anna_weekd_hrs6 - data{3}(26,:); Anna_weekd_hrs = Anna_weekd_hrs7 - data{3}(27,:) Anna_eoweekdays = 7.50*Anna_weekd_hrs % for Rob s2=zeros(30,1); for k=1:30 s2(k,1)=s2(k,1)+data{4}(k,:); sm2 = sum(s2);

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k=[5]; switch k case [5] rob_weeknd_hr1 = data{4}(5,:); end k=[6]; switch k case [6] rob_weeknd_hr2 = data{4}(6,:); end k=[12]; switch k case [12] rob_weeknd_hr3 = data{4}(12,:); end k=[13]; switch k case [13] rob_weeknd_hr4 = data{4}(13,:); end k=[19]; switch k case [19] rob_weeknd_hr5 = data{4}(19,:); end k=[20]; switch k case [20] rob_weeknd_hr6 = data{4}(20,:); end k=[26]; switch k case [26] rob_weeknd_hr7 = data{4}(26,:); end k=[27]; switch k case [27] rob_weeknd_hr8 = data{4}(27,:); end

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end rob_eoweeknds = 15.0*(rob_weeknd_hr1+rob_weeknd_hr2+rob_weeknd_hr3+rob_weeknd_hr4+rob_weeknd_hr5+rob_weeknd_hr6+ rob_weeknd_hr7+rob_weeknd_hr8) rob_weekd_hrs1 = sm2 - data{4}(5,:); rob_weekd_hrs2 = rob_weekd_hrs1 - data{4}(6,:); rob_weekd_hrs3 = rob_weekd_hrs2 - data{4}(12,:); rob_weekd_hrs4 = rob_weekd_hrs3 - data{4}(13,:); rob_weekd_hrs5 = rob_weekd_hrs4 - data{4}(19,:); rob_weekd_hrs6 = rob_weekd_hrs5 - data{4}(20,:); rob_weekd_hrs7 = rob_weekd_hrs6 - data{4}(26,:); rob_weekd_hrs = rob_weekd_hrs7 - data{4}(27,:) rob_eoweekdays = 15.0*rob_weekd_hrs

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APPENDIX-E

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