Homework sample 1 (assignments 1, 2, 4, 5)

Title:

Optimization of Fixed and Operating Costs in Groundwater Remediation Using Optimal Control and Genetic Algorithms

Engineering objective:

To establish an efficient algorithm capable of solving groundwater remediation problem that simultaneously considering fixed and time-varying operating costs.

Engineering Motivation:

Specific
To reduce the total cost of groundwater remediation by 20% over that associate with the solution of the optimal control algorithm.

General
To calculate the minimal total cost, consisting of fixed and time-varying operating costs, in groundwater remediation.

Personal Motivation:

To publish the research finding in a prestigious journal

Technical argument outline

1. (Engineering Phenomenon)

Is there an optimal control algorithm capable of simultaneously considering fixed costs and time-varying operating costs in groundwater remediation planning?

2. (Engineering Problem)

If there is not, is it difficult to obtain an optimal solution of groundwater remediation planning?

3. (Range + Consequence of Problem)

If an optimal solution can not be obtained, will this lead to expensive total costs and a defective remediation plan?

Based on the above fact, we should establish an efficient algorithm capable of solving groundwater remediation problem that simultaneously considering fixed and time-varying operating costs.

Can we reduce the total cost of groundwater remediation by 20% over that associate with the solution of the optimal control algorithm.

Can we calculate the minimal total cost, consisting of fixed and time-varying operating costs, in groundwater remediation?

Engineering needs

Effectiveness:

The proposed algorithm must be capable of solving groundwater remediation problem that simultaneously considering fixed and time-varying operating costs.

Technical Feasibility:

The proposed algorithm must resolve the difficulty of discrete nature of fixed cost and the requirement of large computational resources associate with time-varying operation.

Desirability:

The proposed algorithm can calculate the minimal total cost, consisting of fixed and time-varying operating costs, therefore the result is more practical in groundwater remediation planning.

Preferability:

Total cost of the groundwater remediation must be 20% less than that associate with the solution of the optimal control algorithm.

Problem statement

Owing to there is not an optimal control algorithm capable of simultaneously considering fixed costs and time-varying operating costs, it is difficult to obtain an optimal solution of groundwater remediation planning. Because of the discrete nature of fixed costs, it is difficult to consider by optimal control algorithm and owing to the requirement of computational resources, the genetic algorithm cannot obtain the optimal policy when the time-varying operating costs are considering. Consequently, the total cost will be too expensive and lead to a defective remediation plan. Therefore, an efficient algorithm, integrate optimal control and genetic algorithm, must be designed to calculate the minimal total cost, consisting of fixed and time-varying operating costs, in groundwater remediation.

Hypothesis statement

An efficient algorithm capable of solving groundwater remediation problem that simultaneously considering fixed and time-varying operating costs can be established. An important advantage of GAs is that it is easy to incorporate the fixed cost associated with groundwater remediation. Therefore, the discrete nature of fixed cost can be considered using Genetic Algorithms. The requirement of computation resources associated with time-varying operating cost can be treated using Optimal Control Algorithm. Hence, the Optimal Control Algorithm is embedded into the Genetic Algorithm. The proposed algorithm can reduce the total cost of groundwater remediation by 20% over that associate with the solution of the optimal control algorithm. Consequently, the minimal total cost, consisting of fixed and time-varying operating costs, can be calculated in groundwater remediation.

Abstract

Owing to there is not an optimal control algorithm capable of simultaneously considering fixed costs and time-varying operating costs, it is difficult to obtain an optimal solution of time-varying groundwater remediation planning. An important advantage of Genetic Algorithms is that it is easy to incorporate the fixed cost associated with well installation of groundwater remediation. Therefore, the discrete nature of fixed cost can be considered using Genetic Algorithms. The requirement of computation resources associated with time-varying operating cost can be treated using Optimal Control Algorithm. Hence, the Optimal Control Algorithm is embedded into the Genetic Algorithms. A case study is also presented to demonstrate the proposed algorithm's effectiveness. Simulation results indicate that the proposed algorithm can reduce the total cost of groundwater remediation by 20% over that associate with the solution of the optimal control algorithm only. Consequently, the minimal total cost, consisting of fixed and time-varying operating costs, can be calculated in groundwater remediation.

Abstract

In time-varying groundwater remediation problem, the lack of an optimal control algorithm to simultaneously consider fixed costs and time-varying operating costs makes it nearly impossible to obtain an optimal solution. This study presents a novel algorithm that integrates Genetic Algorithm (GA) and Constrained Differential Dynamic Programming (CDDP) to solve this time-varying groundwater remediation problem. GA can easily incorporate the fixed costs associated with the installation of a well. Therefore, this study elucidates the discrete nature of fixed costs by using GA. Using GA to solve for time-varying policies would dramatically increase the computational resources required. Hence, the CDDP is used to handle problems associated with time-varying operating costs. Consequently, the CDDP is embedded into the GA. A case study that incorporates fixed and time-varying operating costs is also presented to demonstrate the effectiveness of the proposed algorithm. Simulation results indicate that the proposed algorithm can reduce the total cost of time-varying groundwater remediation problem by 20% when using only CDDP. By doing so, the minimal total cost (consisting of fixed and time-varying operating costs) can be calculated.

Title:

Parameter Estimation of Muskingum model using the Artificial Neural Network

Engineering Objectives:

To increase the efficiency on the parameter estimation of Muskingum model using a novel scheme based on the Artificial Neural Network.

Engineering Motivations:

Specific
To reduce the complexity on the parameter estimation of Muskingum model by using an objective means of estimating the physical parameters.

General
To obtain the required physical parameters for Muskingum Model in hydraulic engineering.

Personal Motivation

To publish in a prestigious journal

Technical argument outline

1. (Engineering Phenomenon)

Is the Muskingum Model the most widely used method on flood routing for hydraulic engineering?

2. (Engineering Problem)

If it is, does it lack an objective means of estimating the physical parameters?

3. (Range + Consequence of Problem)

If so, will this lower the efficiency and accuracy of flood discharge calculations?

Based on the above fact, we should develop a novel methodology to increase the efficiency on the parameter estimation of Muskingum model using the Artificial Neural Network.

Can we reduce the complexity on the parameter Estimation of Muskingum model by using an objective means of estimating the physical parameters?

Can we obtain the required physical parameters for Muskingum Model in hydraulic engineering?

Engineering Need

Effectiveness

The proposed methodology must increase the efficiency on the parameter estimation of Muskingum model using a novel scheme based on the Artificial Neural Network.

Technical Feasibility

The proposed methodology can obtain the required physical parameters for Muskingum model without subjective selection.

Desirability

The proposed methodology must increase the efficiency and accuracy of flood discharge calculation on flood routing.

Affordability

The proposed methodology can obtain the required physical parameters for Muskingum model as well as using conventional method.

Preferability

The proposed methodology must provide an objective means of estimating the physical parameters because conventional method is a subjective means of estimating the physical parameters.

Problem statement

Although the Muskingum Model is the most widely used method on flood routing for hydraulic engineering, it lacks an objective means of estimating the physical parameters. Consequently, the efficiency and accuracy of flood routing will be decreased. A proposed methodology must therefore be developed to improve the disadvantages of Muskingum model on parameter estimation.

Hypothesis statement

A novel scheme, capable of increasing the efficiency on the parameter estimation of Muskingum model using the Artificial Neural Network, can be developed. The Input and output neurons of Artificial Neural Network are designed according to the Muskingum formula, . After completing the learning phase of the ANN model, the sensitivity analysis of the ANN model is implemented to obtain the required physical parameters for Muskingum model on flood routing. The proposed scheme can reduce the complexity on the parameter Estimation of Muskingum model by using an objective means of estimating the physical parameters. Therefore, the required physical parameters for Muskingum Model on flood routing are easy to be obtained by this novel scheme.

Abstract

The Muskingum Model is the most widely used method on flood routing for hydraulic engineering. However, this method uses a subjective means of estimating the physical parameters, possibly lowering the efficiency of flood discharge calculations. Therefore, this study presents a novel scheme capable of reducing the complexity associated with the Muskingum model in estimating the parameters by applying an Artificial Neural Network (ANN). The input and output neurons of ANN are designed according to the Muskingum formula. After completing the learning phase of the ANN model, sensitivity analysis is performed to obtain the required parameters for Muskingum model on flood routing. A case study is also presented to demonstrate the proposed scheme's effectiveness. Simulation results indicate that the proposed scheme can reduce the complexity of the Muskingum model when estimating the parameters. Consequently, the proposed scheme can easily estimate the required parameters for the Muskingum on flood routing in an objective manner.

Introduction

Among the many models used for flood routing, the Muskingum Method is the most widely used owing to its simplicity. The Muskingum flood routing model was developed by the U.S. Corps of Engineers for the Muskingum Conservancy District Flood-Control Project over six decades ago. (NOTE: You need to cite a reference for this sentence.) The following continuity and storage equations are the most commonly used form of the Muskingum model:

(1)

(2)

where St, It and Ot denote the simultaneous amounts of storage, inflow, outflow, respectively, at time t; K is storage-time constant for the river reach, which has a value reasonably close the flow travel time through the river reach; and X is a weighting factor usually varying between 0 and 0.5 for reservoir storage. Eq. (1) to (2) may be induced as(NOTE: can be rewritten as instead?)

(3)

(4)

(5)

(6)

constrain : C0+C1+C2=1 (7)

According to eq. (4) to (7), if eq. (3) can be used, three parameters (C0,C1 and C2 ) have to conform. In practice, although △t represents the time step and is the given value, K,X are unknown parameters. The conventional procedure for determining the values of K, X by trial and error method. By assuming a value of X, the values of are computed and plotted against the corresponding value of S. The correct value of X corresponds to the plot for which the width of the loop is minimum or the plot approximates a straight line.

Despite the use of this trial and error method for several decades, it is time-consuming and prone to subjective interpretation. To improve the trial and error method, Yoon and Padmanabhan S. Mohan proposed the objective approach of genetic algorithm to estimate the parameters of Muskingum routing models. According to their results, the genetic algorithm approach is much more efficient in estimating the parameters of Muskingum routing models than the conventional estimation methods owing to its ability to prevent the subjective and computational time associated with the conventional estimation methods. On the other hand, Chang-Shian Chen, Ning-Been Wang proposed a modified Muskingum flood routing model to describe the real flood characteristics more effectively. Their model was developed based on mass conservation law so that the effects of the upstream tributaries and the distance from each gauging station of tributary to the downstream control point in a basin could be included. A genetic algorithm was also employed to obtain the parameters in the process.

Above discussion indicates that the genetic algorithm can estimate the parameters of the Muskingum flood routing model. Besides, similar to the genetic algorithm, Artificial neural network (ANN) is a new computing architecture in the area of artificial intelligence (AI) and, therefore, may be an another good scheme to estimate the parameters of Muskingum flood routing model; In this study, we estimate three parameters ( C0、C1、C2) which symbolize the interactive relation between input variables (、、) and output variable() according to eq(3). Based on above meaning a novel scheme (ANN and sensitivity study) is proposed. ANN can accurately represent an internally complex relation between input and output variables. In addition, sensitivity study is applied to the neural network model to extract information from the key input variables that might strongly affect the output variables. ANN and sensitivity study have been performed to obtain information needed as follows: Zhichao G. and Robert E. undertook a nuclear power plant performance study by using the neural network and sensitivity analysis. The thermal performance data obtained from TVA nuclear power plant indicated that the plant probably lost some Megawatts of electric power due to the variation of the heat rate. Analyzing the raw data recorded weekly during the plant operations was difficult because a nuclear power plant is an extremely complex system with thousands of parameters. The neural network was set up to function as the internal thermodynamic model of the plant so as to predict the heat rate. Then, a sensitivity study was performed on the neural network model to extract information from the key parameters that might strongly affect the thermal performance. Another illustration involved the application of ANNs to assess voltage stability. A.A. El-Keib and X.ma proposed a multi-layer feed-forward artificial neural network with error back-propagation learning to calculate the voltage stability margin (VSM). Based on the energy method, a direct mapping relation between system loading conditions and VSMs was set up via the ANN. A systematic method for selecting the ANN's input variable was also developed using sensitivity analysis. Sensitivity analysis was perform to elucidate the system's responsive behavior to load changes, so that more appropriate ANN architectures could be designed to assess voltage stability.

In light of above developments, this investigation presents a novel scheme based on ANN and sensitivity study to estimate the parameters(C0、C1、C2) of Muskingum linear function. The Input and output neurons of Artificial Neural Network are designed according to the Muskingum formula , input neurons are、、and output neuron is. After completing the learning phase of the ANN model, the sensitivity analysis of the ANN model is implemented to extract information from practical data to reveal the significance of input neurons. The values of parameters(C0、C1、C2) are then obtained from the significance of input neurons with the limitation of C0+C1+C2=1. Finally, the proposed method compared with trial and error method from K、X.

A case study presented herein demonstrates the proposed scheme’s effectiveness. Simulation results indicate that the proposed scheme can reduce the complexity on the parameter estimation of Muskingum model by using an objective means of estimating the physical parameters. Consequently, the proposed scheme can easily estimate the required parameters for Muskingum Model on flood routing.

Conclusion

To increase the efficiency of estimating parameters of the Muskingum model, this investigation presents a novel scheme based on ANN. Sensitivity analysis is also performed to estimate the parameters (C0、C1、C2) of the Muskingum linear function. The input and output neurons of ANN are designed according to the Muskingum formula. After completing the learning phase of the ANN model, sensitivity analysis of the ANN model is performed to obtain the required parameters for Muskingum model on flood routing. The proposed approach is compared with the trial and error method using different criteria for the selected data. In terms of estimating the parameter values (C0、C1、C2), both approaches yield similar results. With respect to the accuracy of flood routing as assessed by the three indicators (CE,EQp,ETp) , the proposed approach performs better or at least comparable to the trial and error method. Although these methods accurately estimate the parameters, the trial and error method not only uses a subjective means of estimation owing to the requirement of an initial hypothesis of parameters but is also time consuming due to the lack of an objective selection criteria for the proper values of parameters. Consequently, the proposed scheme can reduce the complexity associated with estimating the parameters of the Muskingum model by using an objective rather than a subjective means of doing so. Therefore, the proposed scheme can easily estimate the required parameters for the Muskingum Model on flood routing.

Title:

Adaptive Algorithm to Control A Structure's Shape Using Laminated Sensors and Actuators.

Engineering Objective:

To design a control algorithm capable of controlling the structure's shape without relying on information of external loading.

Engineering Motivation:

To control the structure's shape within a desired accuracy without depending on information of external loading.

To upgrade a tool machine's precision, thereby increasing market competitiveness of exported products.

Personal Motivation:

To fulfill academic requirements for doctoral degree.

Technical argument outline:

Can control algorithms control a structure's shape for industrial application?

If such a control algorithm exists, does it lack necessary information regarding external loading?

If this information is inadequate, will the structure's shape fail to meet industrial specifications?

Based on the above fact, we should design a control algorithm capable of controlling the structure's shape without relying on information of external loading.

Can we control the structure's shape within a desired accuracy without depending on information of external loading?

Can we upgrade a tool machine's precision, thereby increasing market competitiveness of exported products?

Engineering Need

Effectiveness

The proposed control algorithm must control the structure's shape within a desired accuracy.

Technical feasibility

The proposed control algorithm can integrate sensors and actuators into the laminated beam structure without the necessity for external loading information.

Desirability

The proposed control algorithm must ensure that tool machine's precision increases the market competitiveness of exported products.

Affordability

The proposed control algorithm can withstand an external loading less than 100kg.

Preferability

The proposed control algorithm does not rely on external loading information that previous algorithms do.

Problem statement

Although control algorithms can control a structure's shape for industrial applications, they fail to meet industrial specifications owing to their reliance on information of external loading. Consequently, the structure's shape can not adhere to industrial specifications and, ultimately, inhibit the market competitiveness of exported products. A control algorithm must therefore be developed to control the structure's shape within a desired accuracy..

Hypothesis statement

A control algorithm, capable of controlling the structure's shape without relying on information of external loading, can be developed. Deflection can be performed using the fourier sine series accompanied with Stokes' transformation. Also, Fourier sine series solution can be compared with the exact solution with respect to deflect results. The proposed algorithm can control the structure's shape within a desired accuracy without depending on information of external loading. Consequently, a tool machine's precision can be enhanced, thereby increasing market competitiveness of exported products?

Abstract

Although control algorithms can control a structure's shape for industrial applications, they fail to meet industrial specifications owing to their reliance on information of external loading. Therefore, this study presents a novel control algorithm capable of controlling the structure's shape without relying on information of external loading. Deflection is performed using the fourier sine series accompanied with Stokes' transformation. Fourier sine series solution is compared with the exact solution with respect to deflect results. A case study is also presented to demonstrate the proposed algorithm's effectiveness. Simulation results indicate that the structure's shape can be controlled within a desired accuracy without depending on information of external loading. Consequently, a tool machine's precision can be upgraded, thereby enhancing the market competitiveness of exported products.

Homework sample 2 (assignments 1, 2, 4, 5)

Abstract
Although parabolic phenomenon in ink jet printing can be slightly controlled by possessing the printing only in the constant speed region, the print quality will be markedly inhibited owing to the velocity variation while printing action exceeds the constant speed portion. Therefore, this study presents a novel scheme capable of efficiently compensating the parabolic effect in ink jet firing. Physical observation of the printer system is analyzed in detail and then the parabolic influence is adequately compensated using a precise velocity estimator realized by neural networks. The design is also implemented by CPLD to demonstrate the proposed scheme's effectiveness. Experimental results indicate that the alignment accuracy can be compensated within 15μm. Consequently, the parabolic event can be eliminated, thereby enhancing the print quality and enlarging the printing area and reducing the volume size of a printer.

Homework Example (assignment 6)

Introduction
Carbon nitride is a new theoretical design material with a ardness exceeding that of a diamond [1,2]. Nonetheless, as an example of a novel carbon-based covalently bonded network that could, like diamond, exhibit superior oxidation resistance, chemical inertness, wear resistance, thermal conductivity; and wide band gap property [3]. However, scientists have been unable to successfully synthesize this new material to ascertain whether or not it possesses a higher hardness than a diamond. Most investigations have only synthesized amorphous carbon nitride with a low nitrogen content (20~30%).

Over the last few years, it is found that the most research efforts on syntheses of carbon nitride have been already focused on developing different kinetic control approaches, such as laser ablation [4], DC magnetron sputtering [5], RF sputtering [6], ion beam deposition [7], ion implantation [8], plasma arc deposition [9], chemical vapor deposition [10], and UV assisted chemical synthesis [11]. However, in considerable cases only small crystallites embedded in an amorphous matrix have been observed. The crystallinity of these films is generally evidenced by the selected area electron diffraction patterns from nano-to micron-sized crystallites since the volume of the crystalline phases can be as low as less than 5% of the total volume in the deposited films [4]. An unambiguous characterization of this phase is thus difficult. The crystalline films with larger crystal sizes (several tens of microns) were reported by Chen, et al [12]; however, it is essentially a Si-C-N ternary system. Moreover, the most films produced so far have nitrogen concentrations from 20 to 30 at.%, which are much less than 57 at.% nitrogen required to form a homogenous stoichiometric C₃N₄ film. A high atomic N/C ratio of 1.39 was reported by Diani, et al [13]. However, their results show formation of amorphous films, which contain significant fraction of C≡N bonding and are readily decomposed at about 600oC,indicating a poor thermal stability. The presence of C≡N bonding precludes an extended carbon nitride solid, since the triply bonded nitrogen breaks the continuity of the network[14]. Therefore, be it crystalline or amorphous, synthesis of sp³-bonded carbon nitrides containing substantial amounts of nitrogen remains to be a challenging issue via kinetic control approaches.

Perhaps the most important point to be stressed is that the possibility to use different carbon and nitrogen sources via film deposition techniques. In the past, the most raw materials of carbon and nitrogen sources for synthesis of carbon nitrides are limited among methane, graphite, nitrogen gas and ammonia. Especially, in case of using N₂ as nitrogen source, because of the extremely high bond dissociation energy, 945 KJ/mol, of N₂, it provides little possibility of activated nitrogen atoms for incorporation with carbon leading to a lower nitrogen content in the common deposited films. Hence, the use of appropriately designed molecular or solid-state precursors and low enough synthesis temperatures to insure kinetic control of reaction products appears to be a promising direction for future efforts. The main challenge here is to develop appropriate carbonitro-precursors to cooperate with due kinetic control approaches. It is believed that the precursor with a high atomic N/C ratio and/or possessing similar ring structure as that in hypothetical B-C₃N₄ will be a good starting precursor for crystalline carbon nitride synthesis due to the possibility of providing abundant carbonitro-species and enhancing the nucleation and growth.

Therefore, in this work, a novel bio-molecular organic, 6-aminopurine (vitamin B4), is first proposed to be developed for synthesizing carbon nitride films. Other organics, such as azzadenine, has also been adopted and the effects of using different target materials is going to be published soon. As shown in Fig. 1, 6-aminopurine, which has a chemical formula of C₅N₅H₅, contains C-N single bonds and C=N double bonds and possesses a six-fold ring structure quite similar to that in the hypothetical B-C3N4 phase. Here, the six-fold ring structure is expected to be a main factor to enhance the nucleation and growth and to improve the crystallinity of carbon nitride. The high N/C ratio of 6-aminopurine is also anticipated to be beneficial to the formation of carbon nitride films by providing abundant carbonitro-species as intermediate states to effectively reduce the high activation energy barrier for the formation of carbon nitrides.

An optimum integration between carbon nitride precursors and synthetic techniques is emphatic to be the main issue in developing this superhard material. The choice of synthetic technique should accommodate this precursor's properties such as low melting temperature and electrical insulation. The ion beam sputtering technique provides a good energy controllability and flexibility of target shape and morphology. Optimization and control of ion beam deposition process required an improved knowledge of ion beam interaction with organic target and the evolution and dynamics of the ion beam induced plasma plume. Such carbonitro-organic targets do provide abundant specific chemical information than conventional separated carbon and nitrogen source to probe on the formation mechanisms of carbon nitride during ion beam sputtering [15]. A detailed understanding of the formation mechanisms is very important for effective synthesis of superhard carbon nitrides. Moreover, a transformation between bio-organic derived from the metabolism of creatures and superhard materials is also intriguing from both science and engineering application point of view. To our knowledge, this is the first attempt to adopt bio-molecular compounds for carbon nitride synthesis.