Deflection of a Viscoelastic Cantilever under a Uniform Surface Stress: Applications to Static-mode Microcantilever Sensors Undergoing Adsorption

The equation governing the curvature of a viscoelastic microcantilever beam loaded with a uniform surface stress is derived. The present model is applicable to static-mode microcantilever sensors made with a rigid polymer, such as SU-8. An analytical solution to the differential equation governing the curvature is given for a specific surface stress representing adsorption of analyte onto the viscoelastic beam’s surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoney’s equation to analyze stress-induced deflection of viscoelastic microcantilevers (in the present case due to surface analyte adsorption) can lead to poor predictions of the beam’s response. It is shown that using a viscoelastic substrate can greatly increase sensitivity (due to a lower modulus), but at the cost of a longer response time due to viscoelasticcreep in the microcantilever. In addition, the effects of a coating on the cantilever are considered. By defining effective moduli for the coated-beam case, the analytical solution for the uncoated case can still be used. It is found that, unlike the case of a silicon microcantilever, the stress in the coating due to bending of a polymer cantilever can be significant, especially for metalcoatings. The theoretical results presented here can also be used to extract time-domain viscoelasticproperties of the polymermaterial from beam response data

Generalized Model of Resonant Polymer-Coated Microcantilevers in Viscous Liquid Media

Expressions describing the resonant frequency and quality factor of a dynamically driven, polymer-coated microcantilever in a viscous liquid medium have been obtained. These generalized formulas are used to describe the effects the operational medium and the viscoelastic coating have on the device sensitivity when used in liquid-phase chemical sensing applications. Shifts in the resonant frequency are normally assumed proportional to the mass of sorbed analyte in the sensing layer. However, the expression for the frequency shift derived in this work indicates that the frequency shift is also dependent on changes in the sensing layer’s loss and storage moduli, changes in the moment of inertia, and changes in the medium of operation’s viscosity and density. Not accounting for these factors will lead to incorrect analyte concentration predictions. The derived expressions are shown to reduce to well-known formulas found in the literature for the case of an uncoated cantilever in a viscous liquid medium and the case of a coated cantilever in air or in a vacuum. The theoretical results presented are then compared to available chemical sensor data in aqueous and viscous solutions

Microscopic determination of boundary shear and sublayer turbulence characteristics in an open channel

The application of a method of velocity determination in an open channel using a microscope and camera to record the motion of small particles suspended in water is described. Velocity measurements were made in a series of thin planes orientated parallel to the channel bottom for the case of two-dimensional laminar and turbulent open channel flow. Velocity profiles near the boundary were plotted and boundary shear computed from the rate of shear thus determined. Turbulence intensity was computed and the distribution of particle velocities examined. It was concluded that the method yields boundary shear values + to within - 15 percent and that this uncertainty can be reduced significantly. The maximum error is caused by uncertainty in the location of: the focal plane and in the location of a particle within the focal plane. This difficulty causes an even greater error in computation of turbulence intensity. This error increases as the distance from the boundary decreases, creating a serious disadvantage of the method. Particle velocity distributions exhibit a positive third moment which is in qualitative agreement with previous measurements. The results indicate that further investigation of the application of the method to open channel turbulent flow is justified. It is planned to modify the method so that particle motion can be viewed in a plane orientated normal to the boundary. This will considerably reduce the primary errors described in this report and permit more accurate turbulence measurements very near the boundary.U.S. Department of the InteriorU.S. Geological SurveyOpe

Load and Electricity Rates Prediction for Building Wide Optimization Applications

The reduction of energy consumption, use of renewable energy, and preservation of natural resources are becoming increasingly important. Several applications in the energy efficiency field aim at minimizing energy consumption and/or cost. To achieve this, these applications employ optimization techniques that require future prediction of the performance and various loads of a facility, campus, building, or an energy plant, such as hot water, cold water, and/or electric load. The prediction horizon may be as short as few hours to ten days into the future, depending on the application at hand. Furthermore, for the purpose of minimizing electricity cost, it is as necessary to know, as accurately as possible, what the electricity rates are over a given horizon. Therefore, a method for predicting hot water, cold water, and electric loads and electricity rates over a given horizon into the future has been developed (Load will be used to refer to hot water, cold water, and electric loads and electricity rates without loss of generality). The method developed takes into consideration the several factors contributing to the load value. These factors include time of day, day of week, schedules (in-session or out-of-session for a university campus for example), and weather (temperature and humidity). The load predicted consists of a deterministic term and a stochastic term. The deterministic term is calculated using linear regression models, whose coefficients are determined offline. These models rely on the typical load value for a given time of day and day-type (days with similar load profiles) and weather forecast. The latter is obtained from the National Oceanic and Atmospheric Administration (NOAA) through their National Digital Forecast Database (NDFD) service. The stochastic term is determined using an Auto-Regressive (AR) model, whose coefficients are determined offline. The AR model calculates future prediction errors based on the current prediction error. The stochastic element of the predicted load gives the method developed its adaptive property, and thus increases the accuracy of the prediction by updating the forecast using current measurements of the load. Historical weather and load data are used for determining the coefficients of the regression models and the AR model offline. For a given set of training data, the method developed generates a set of regression models for each day-type. Day-types are determined by a day-typing algorithm which specifies days with similar load profiles based on cluster analysis techniques. Outside air enthalpy and a typical load profile constitute the predictors variables in each set of regression models. Each day-type is characterized by a different typical load profile which is generated using an optimal data fitting technique. The AR model coefficients are determined using the residuals obtained from different sets of regression models. Given the determined models, the current load measurement, and weather forecast, the future load values are calculated by selecting the appropriate regression model and summing the deterministic and stochastic terms.

Sorption-induced Static Bending of Microcantilevers Coated with Viscoelastic Material

Absorption of a chemical analyte into a polymercoating results in an expansion governed by the concentration and type of analyte that has diffused into the bulk of the coating. When the coating is attached to a microcantilever, this expansion results in bending of the device. Assuming that absorption (i.e., diffusion across the surface barrier into the bulk of the coating) is Fickian, with a rate of absorption that is proportional to the difference between the absorbed concentration and the equilibrium concentration, and the coating is elastic, the bending response of the coated device should exhibit a first-order behavior. However, for polymercoatings, complex behaviors exhibiting an overshoot that slowly decays to the steady-state value have been observed. A theoretical model of absorption-induced static bending of a microcantilever coated with a viscoelastic material is presented, starting from the general stress/strain relationship for a viscoelastic material. The model accounts for viscoelasticstress relaxation and possible coating plasticization. Calculated responses show that the model is capable of reproducing the same transient behavior exhibited in the experimental data. The theory presented can also be used for extracting viscoelasticproperties of the coating from the measured bending data

Validation of the Victorian Gambling Screen

This report is a result of research commissioned by the Gambling Research Panel (GRP) to, firstly, identify current gambling patterns and perceptions and, secondly, evaluate the Victorian Gambling Screen. The first research requirement was addressed in the 2003 Victorian Longitudinal Community Attitudes Survey while this report, Validation of the Victorian Gambling Screen, addresses the second requirement.Funded by the Victorian Government through the Community Support Fun

2003 Victorian Longitudinal Community Attitudes Survey

This report is Project 3 of the Gambling Research Panel’s 2001–2002 Research Plan, and is the eighth in a series of community attitudes surveys. The survey was conducted by ACNielsen in April and May 2003 using an effective random sample of 8,479 Victorian residents, a significantly larger sample than previous Victorian gambling surveys, and the resultant data provided to the Australian National University research team for analysis in July 2003. Three groups were identified — non-gamblers, non-regular gamblers and regular gamblers — and interviewed about their gambling behaviour, and their attitudes to gambling and its impact on the community. The significant finding of this survey is that large numbers of Victorians continue to experience problems associated with their gambling. Therefore problem gambling remains an important issue for public policy

System Identification for Model Predictive Control of Building Region Temperature

Model predictive control (MPC) is a promising technology for energy cost optimization of buildings because it provides a natural framework for optimally controlling such systems by computing control actions that minimize the energy cost while meeting constraints. In our previous work, we developed a cascaded MPC framework capable of minimizing the energy cost of building zone temperature control applications. The outer loop MPC computes power set-points to minimize the energy cost while ensuring that the zone temperature is maintained within its comfort constraints. The inner loop MPC receives the power set-points from the outer loop MPC and manipulates the zone temperature set-point to ensure that the zone power consumption tracks the power set-points computed by the outer layer MPC. Since both MPCs require a predictive model, a modeling framework and system identification (SI) methodology must be developed that is capable of accurately predicting the energy usage and zone temperature for a diverse range of building zones. In this work, two grey-box models for the outer and inner loop MPCs are developed and parameterized. The model parameters are fit to input-output data for a particular zone application so that the resulting model accurately predicts the behavior of the zone. State and disturbance estimation, which is required by the MPCs, is performed via a Kalman filter with a steady-state Kalman gain. The model parameters and Kalman gains of each grey-box model are updated in a sequential fashion. The significant disturbances affecting the zone temperature (e.g., outside temperature and occupancy) may typically be considered as a slowly varying disturbance (with respect to the control time-scale). To prevent steady-state offset in the identified model caused by the slowly time-varying disturbance, a high-pass filter is applied to the input-output data to filter out the effect of the disturbance. The model parameters are subsequently computed from the filtered input-output data without the Kalman filter applied. The Kalman gain is also adjusted as the model parameters are updated to ensure stability of the resulting observer and for optimal estimation. After the model parameters are computed, the steady-state Kalman gain matrix is parameterized and the parameters are updated using the prediction error method with the unfiltered input-output data and the updated model parameters. The Kalman gain update methodology is advantageous because it avoids the need to estimate the noise statistics. Stability of the observer is verified after the parameters are updated. If the updated parameters result in an unstable observer, the update is rejected and the previous parameters are retained. Additionally, since a standard quadratic cost function that penalizes the squared prediction error is sensitive to data outliers in the prediction error method, a piecewise defined cost function is employed to reduce its sensitivity to outliers and to improve the robustness of the SI methodology. The cost function penalizes the squared prediction error when the error is within certain thresholds. When the error is outside the thresholds, the cost function evaluates to a constant. The SI algorithm is applied to a building zone to assess the approach

Autonomous Optimization and Control for Central Plants with Energy Storage

A model predictive control (MPC) framework is used to determine how to optimize the distribution of energy resources across a central energy facility including chillers, water heaters, and thermal energy storage; present the results to an operator; and execute the plan. The objective of this MPC framework is to minimize cost in real-time in response to both real-time energy prices and demand charges as well as allow the operator to appropriately interact with the system. Operators must be given the correct intersection points in order to build trust before they are willing to turn the tool over and put it into fully autonomous mode. Once in autonomous mode, operators need to be able to intervene and impute their knowledge of the facilities they are serving into the system without disengaging optimization. For example, an operator may be working on a central energy facility that serves a college campus on Friday night before a home football game. The optimization system is predicting the electrical load, but does not have knowledge of the football game. Rather than try to include every possible factor into the prediction of the loads, a daunting task, the optimization system empowers the operator to make human-in-the-loop decisions in these rare scenarios without exiting autonomous (auto) mode. Without this empowerment, the operator either takes the system out of auto mode or allows the system to make poor decisions. Both scenarios will result in an optimization system that has low “on time†and thus saves little money. A cascaded, model predictive control framework lends itself well to allowing an operator to intervene. The system presented is a four tiered approach to central plant optimization. The first tier is the prediction of the energy loads of the campus; i.e., the inputs to the optimization system. The predictions are made for a week in advance, giving the operator ample time to react to predictions they do not agree with and override the predictions if they feel it necessary. The predictions are inputs to the subplant-level optimization. The subplant-level optimization determines the optimal distribution of energy across major equipment classes (subplants and storage) for the prediction horizon and sends the current distribution to the equipment level optimization. The operators are able to use the subplant-level optimization for “advisory†only and enter their own load distribution into the equipment level optimization. This could be done if they feel that they need to be conservative with the charge of the tank. Finally, the equipment level optimization determines the devices to turn on and their setpoints in each subplant and sends those setpoints to the building automation system. These decisions can be overridden, but should be extremely rare as the system takes device availability, accumulated runtime, etc. as inputs. Building an optimization system that empowers the operator ensures that the campus owner realizes the full potential of his investment. Optimal plant control has shown over 10% savings, for large plants this can translate to savings of more than US $1 million per year

Model Predictive Control for Central Plant Optimization with Thermal Energy Storage

An optimization framework is used in order to determine how to distribute both hot and cold water loads across a central energy plant including heat pump chillers, conventional chillers, water heaters, and hot and cold water (thermal energy) storage. The objective of the optimization framework is to minimize cost in response to both real-time energy prices and demand charges. The linear programming framework used allows for the optimal solution to be found in real-time. Real-time optimization lead to two separate applications: A planning tool and a real-time optimization tool. In the planning tool the optimization is performed repeatedly with a sliding horizon accepting a subset of the optimized distribution trajectory horizon as each subsequent optimization problem is solved. This is the same strategy as model predictive control except that in the design and planning tool the optimization is working on a given set of loads, weather (e.g. TMY data), and real-time pricing data and does not need to predict these values. By choosing the varying lengths of the horizon (2 to 10 days) and size of the accepted subset (1 to 24 hours), the design and planning tool can be used to find the design year’s optimal distribution trajectory in less than 5 minutes for interactive plant design, or the design and planning tool can perform a high fidelity run in a few hours. The fast solution times also allow for the optimization framework to be used in real-time to optimize the load distribution of an operational central plant using a desktop computer or microcontroller in an onsite Enterprise controller. In the real-time optimization tool Model Predictive Control is used; estimation, prediction, and optimization are performed to find the optimal distribution of loads for duration of the horizon in the presence of disturbances. The first distribution trajectory in the horizon is then applied to the central energy plant and the estimation, prediction, and optimization is repeated in 15 minutes using new plant telemetry and forecasts. Prediction is performed using a deterministic plus stochastic model where the deterministic portion of the model is a simplified system representing the load of all buildings connected to the central energy plant and the stochastic model is used to respond to disturbances in the load. The deterministic system uses forecasted weather, time of day, and day type in order to determine a predicted load. The estimator uses past data to determine the current state of the stochastic model; the current state is then projected forward and added to the deterministic system’s projection. In simulation, the system has demonstrated more than 10% savings over other schedule based control trajectories even when the subplants are assumed to be running optimally in both cases (i.e., optimal chiller staging, etc.). For large plants this can mean savings of more than US $1 million per year