Development of a particle number and particle mass emissions inventory for an urban fleet : a study in South-East Queensland

Motor vehicles are a major source of gaseous and particulate matter pollution in urban areas, particularly of ultrafine sized particles (diameters < 0.1 µm). Exposure to particulate matter has been found to be associated with serious health effects, including respiratory and cardiovascular disease, and mortality. Particle emissions generated by motor vehicles span a very broad size range (from around 0.003-10 µm) and are measured as different subsets of particle mass concentrations or particle number count. However, there exist scientific challenges in analysing and interpreting the large data sets on motor vehicle emission factors, and no understanding is available of the application of different particle metrics as a basis for air quality regulation. To date a comprehensive inventory covering the broad size range of particles emitted by motor vehicles, and which includes particle number, does not exist anywhere in the world. This thesis covers research related to four important and interrelated aspects pertaining to particulate matter generated by motor vehicle fleets. These include the derivation of suitable particle emission factors for use in transport modelling and health impact assessments; quantification of motor vehicle particle emission inventories; investigation of the particle characteristic modality within particle size distributions as a potential for developing air quality regulation; and review and synthesis of current knowledge on ultrafine particles as it relates to motor vehicles; and the application of these aspects to the quantification, control and management of motor vehicle particle emissions. In order to quantify emissions in terms of a comprehensive inventory, which covers the full size range of particles emitted by motor vehicle fleets, it was necessary to derive a suitable set of particle emission factors for different vehicle and road type combinations for particle number, particle volume, PM1, PM2.5 and PM1 (mass concentration of particles with aerodynamic diameters < 1 µm, < 2.5 µm and < 10 µm respectively). The very large data set of emission factors analysed in this study were sourced from measurement studies conducted in developed countries, and hence the derived set of emission factors are suitable for preparing inventories in other urban regions of the developed world. These emission factors are particularly useful for regions with a lack of measurement data to derive emission factors, or where experimental data are available but are of insufficient scope. The comprehensive particle emissions inventory presented in this thesis is the first published inventory of tailpipe particle emissions prepared for a motor vehicle fleet, and included the quantification of particle emissions covering the full size range of particles emitted by vehicles, based on measurement data. The inventory quantified particle emissions measured in terms of particle number and different particle mass size fractions. It was developed for the urban South-East Queensland fleet in Australia, and included testing the particle emission implications of future scenarios for different passenger and freight travel demand. The thesis also presents evidence of the usefulness of examining modality within particle size distributions as a basis for developing air quality regulations; and finds evidence to support the relevance of introducing a new PM1 mass ambient air quality standard for the majority of environments worldwide. The study found that a combination of PM1 and PM10 standards are likely to be a more discerning and suitable set of ambient air quality standards for controlling particles emitted from combustion and mechanically-generated sources, such as motor vehicles, than the current mass standards of PM2.5 and PM10. The study also reviewed and synthesized existing knowledge on ultrafine particles, with a specific focus on those originating from motor vehicles. It found that motor vehicles are significant contributors to both air pollution and ultrafine particles in urban areas, and that a standardized measurement procedure is not currently available for ultrafine particles. The review found discrepancies exist between outcomes of instrumentation used to measure ultrafine particles; that few data is available on ultrafine particle chemistry and composition, long term monitoring; characterization of their spatial and temporal distribution in urban areas; and that no inventories for particle number are available for motor vehicle fleets. This knowledge is critical for epidemiological studies and exposure-response assessment. Conclusions from this review included the recommendation that ultrafine particles in populated urban areas be considered a likely target for future air quality regulation based on particle number, due to their potential impacts on the environment. The research in this PhD thesis successfully integrated the elements needed to quantify and manage motor vehicle fleet emissions, and its novelty relates to the combining of expertise from two distinctly separate disciplines - from aerosol science and transport modelling. The new knowledge and concepts developed in this PhD research provide never before available data and methods which can be used to develop comprehensive, size-resolved inventories of motor vehicle particle emissions, and air quality regulations to control particle emissions to protect the health and well-being of current and future generations.

The impact of anxiety on processing efficiency : implications for the attentional control theory

The Attentional Control Theory (ACT) proposes that high-anxious individuals maintain performance effectiveness (accuracy) at the expense of processing efficiency (response time), in particular, the two central executive functions of inhibition and shifting. In contrast, research has generally failed to consider the third executive function which relates to the function of updating. In the current study, seventy-five participants completed the Parametric Go/No-Go and n-back tasks, as well as the State-Trait Anxiety Inventory in order to explore the effects of anxiety on attention. Results indicated that anxiety lead to decay in processing efficiency, but not in performance effectiveness, across all three Central Executive functions (inhibition, set-shifting and updating). Interestingly, participants with high levels of trait anxiety also exhibited impaired performance effectiveness on the n-back task designed to measure the updating function. Findings are discussed in relation to developing a new model of ACT that also includes the role of preattentive processes and dual-task coordination when exploring the effects of anxiety on task performance.

University Student Depression Inventory (USDI) : confirmatory factor analysis and review of psychometric properties

Background: The 30-item USDI is a self-report measure that assesses depressive symptoms among university students. It consists of three correlated three factors: Lethargy, Cognitive-Emotional and Academic motivation. The current research used confirmatory factor analysis to asses construct validity and determine whether the original factor structure would be replicated in a different sample. Psychometric properties were also examined. Method: Participants were 1148 students (mean age 22.84 years, SD = 6.85) across all faculties from a large Australian metropolitan university. Students completed a questionnaire comprising of the USDI, the Depression Anxiety Stress Scale (DASS) and Life Satisfaction Scale (LSS). Results: The three correlated factor model was shown to be an acceptable fit to the data, indicating sound construct validity. Internal consistency of the scale was also demonstrated to be sound, with high Cronbach Alpha values. Temporal stability of the scale was also shown to be strong through test-retest analysis. Finally, concurrent and discriminant validity was examined with correlations between the USDI and DASS subscales as well as the LSS, with sound results contributing to further support the construct validity of the scale. Cut-off points were also developed to aid total score interpretation. Limitations: Response rates are unclear. In addition, the representativeness of the sample could be improved potentially through targeted recruitment (i.e. reviewing the online sample statistics during data collection, examining the representativeness trends and addressing particular faculties within the university that were underrepresented). Conclusions: The USDI provides a valid and reliable method of assessing depressive symptoms found among university students.

Case-control study on risk factors of esophageal cancer

Objective: To explore the influencing factors of esophageal cancer in the trunk basin of Dawen river , Shandong province. Methods: A case- control study was carried out: 195 living cases of diagnosed esophageal cancer and 195 controls were matched by age and sex and surveyed by a unified inventory. Results: T he following items could rises the risk of esophageal cancer : hard dry diet, smoke homemade cigarettes, alcohol consumption> 500 ml/ day, relatives with tumor in history ( OR = 51850, OR = 161 158, OR = 111 513, OR = 11 827, respectively ) . While drinking tea may have protective effect against esophageal cancer ( OR = 01 311). Conclusion: The high incidence of esophageal cancer in the area is relative not only to the environment and dietary factors, but also to the family history of esophageal cancer.

Examining the predictive value of combining the theory of planned behaviour and the volunteer functions inventory

The functions of the volunteer functions inventory were combined with the constructs of the theory of planned behaviour (i.e., attitudes, subjective norms, and perceived behavioural control) to establish whether a stronger, single explanatory model prevailed. Undertaken in the context of episodic, skilled volunteering by individuals who were retired or approaching retirement (N = 186), the research advances on prior studies which either examined the predictive capacity of each model independently or compared their explanatory value. Using hierarchical regression analysis, the functions of the volunteer functions inventory (when controlling for demographic variables) explained an additional 7.0% of variability in individuals’ willingness to volunteer over and above that accounted for by the theory of planned behaviour. Significant predictors in the final model included attitudes, subjective norms and perceived behavioural control from the theory of planned behaviour and the understanding function from the volunteer functions inventory. It is proposed that the items comprising the understanding function may represent a deeper psychological construct (e.g., self-actualisation) not accounted for by the theory of planned behaviour. The findings highlight the potential benefit of combining these two prominent models in terms of improving understanding of volunteerism and providing a single parsimonious model for raising rates of this important behaviour.

Driven by distraction: Investigating the effects of anxiety on driving performance using the Attentional Control Theory

This study investigates the effects of trait anxiety on self-reported driving behaviours through its negative impacts on Central Executive functions. Following a self-report study that found trait anxiety to be significantly related to driving behaviours, the present study extended the predictions of Eysenck and Calvo’s Attentional Control Theory, proposing that anxiety affects driving behaviours, in particular driving lapses, through its impact across the Central Executive. Seventy-five Australian drivers participated in the study, completing the Parametric Go/No-Go and n-back tasks, as well as the State-Trait Anxiety Inventory and the Driving Behaviour Questionnaire. While both trait anxiety and processing efficiency of the Central Executive was found to significantly predict driving lapses, trait anxiety remained a strong predictor of driving lapses after processing efficiency was controlled for. It is concluded that while processing efficiency of the central Executive is a key determinant of driving lapses, another Central Executive function that is closer to the driving lapses in the trait anxiety – driving lapses relationship may be needed. Suggestions regarding how to improve future trait anxiety – driving behaviours research are discussed.

Quality Assessment of a Forest Inventory Based on Airborne Laser Scanning

In this study, a quality assessment method based on sampling of primary laser inventory units (microsegments) was analysed. The accuracy of a laser inventory carried out in Kuhmo was analysed as a case study. Field sample plots were measured on the sampled microsegments in the Kuhmo inventory area. Two main questions were considered. Did the ALS based inventory meet the accuracy requirements set for the provider and how should a reliable, cost-efficient and independent quality assessment be undertaken. The agreement between control measurement and ALS based inventory was analysed in four ways: 1) The root mean squared errors (RMSEs) and bias were calculated. 2) Scatter plots with 95% confidence intervals were plotted and the placing of identity lines was checked. 3) Bland-Altman plots were drawn so that the mean difference of attributes between the control method and ALS-method was calculated and plotted against average value of attributes. 4) The tolerance limits were defined and combined with Bland-Altman plots. The RMSE values were compared to a reference study from which the accuracy requirements had been set to the service provider. The accuracy requirements in Kuhmo were achieved, however comparison of RMSE values proved to be difficult. Field control measurements are costly and time-consuming, but they are considered to be robust. However, control measurements might include errors, which are difficult to take into account. Using the Bland-Altman plots none of the compared methods are considered to be completely exact, so this offers a fair way to interpret results of assessment. The tolerance limits to be set on order combined with Bland-Altman plots were suggested to be taken in practise. In addition, bias should be calculated for total area. Some other approaches for quality control were briefly examined. No method was found to fulfil all the required demands of statistical reliability, cost-efficiency, time efficiency, simplicity and speed of implementation. Some benefits and shortcomings of the studied methods were discussed.

Field measurement of beef pen manure methane and nitrous oxide reveals a surprise for inventory calculations

Few data exist on direct greenhouse gas emissions from pen manure at beef feedlots. However, emission inventories attempt to account for these emissions. This study used a large chamber to isolate N2O and CH4 emissions from pen manure at two Australian commercial beef feedlots (stocking densities, 13-27 m(2) head) and related these emissions to a range of potential emission control factors, including masses and concentrations of volatile solids, NO3-, total N, NH4+, and organic C (OC), and additional factors such as total manure mass, cattle numbers, manure pack depth and density, temperature, and moisture content. Mean measured pen N2O emissions were 0.428 kg ha(-1) d(-1) (95% confidence interval [CI], 0.252-0.691) and 0.00405 kg ha(-1) d(-1) (95% CI, 0.00114-0.0110) for the northern and southern feedlots, respectively. Mean measured CH4 emission was 0.236 kg ha(-1) d(-1) (95% CI, 0.163-0.332) for the northern feedlot and 3.93 kg ha(-1) d(-1) (95% CI, 2.58-5.81) for the southern feedlot. Nitrous oxide emission increased with density, pH, temperature, and manure mass, whereas negative relationships were evident with moisture and OC. Strong relationships were not evident between N2O emission and masses or concentrations of NO3- or total N in the manure. This is significant because many standard inventory calculation protocols predict N2O emissions using the mass of N excreted by the animal.

Interim report on the progress of an inventory of artesian wells in Florida: leading to the enforcement of sections 370.051 - 370.54, Florida statues

One of the causes of lower artesian pressure, water waste and aquifer contamination is the misuse and insufficient care of artesian wells. In 1953, Senate Bill No. 57, entitled "An Act to Protect and Control the Artesian Waters of the State" (see Appendix) became a law. This law was passed through the efforts exerted by leading members of the Senate and the House of Representatives, who understood the need for a wise and controlled expenditure of our most valuable natural resource. The State Geologist and his authorized representatives were designated by this law to enforce this conservation measure; however, no financial provision was included for the 1953-55 biennium. The proposed program of the Florida Geological Survey for this biennium did not include the funds nor provide any full-time personnel for the enforcement of this statute. As a result, little actual work was accomplished during these two years, although much time was given to planning and discussion of the problem. Realizing that this program could provide additional basic data needed in the analysis of the water-supply problem, the State Geologist sought and was granted by the 1955 Legislature adequate funds with which to activate the first phase of the enforcement of Florida Statute No. 370.051-054. Enumerated below is a summary of the progress made on this investigation as outlined previously: 1. Data have been collected on 967 wildly flowing wells in 22 counties. 2. Chloride determinations have been run on 850 of the 967 wells. 3. Of the 967 wells, 554 have chlorides in excess of the 250 ppm, the upper limit assigned by the State Board of Health for public consumption. 4. Water escapes at the rate of 37, 762 gallons per minute from these 967 wells. This amounts to 54, 377, 280 gallons per day. The investigation is incomplete at this time; therefore, no final conclusions can be reached. However, from data already collected, the following recommendations are proposed: 1. That the present inventory of wildly flowing wells be completed for the entire State. 2. That the current inventory of wildly flowing wells be expanded at the conclusion of the present inventory to include all flowing wells. 3. That a complete statewide inventory program be established and conducted in cooperation with the Ground Water Branchof the U.S. Geological Survey. 4. That the enforcement functions as set down in Sections 370.051/.054, Florida Statutes, be separated from the program to collect water-resource data and that these functions be given to the Water Resources Department, if such is created (to be recommended by the Water Resources Study Commission in a water policy law presented to the 1957 Legislature). 5. That the research phase (well inventory) of the program remain under the direction of the Florida Geological Survey. (PDF contains 204 pages.)

Process control in agile supply chain network.

The work comprises a new theoretical development applied to aid decision making in an increasingly important commercial sector. Agile supply, where small volumes of high margin, short life cycle innovative products are offered, is increasingly carried out through a complex global supply chain network. We outline an equilibrium solution in such a supply chain network, which works through limited cooperation and coordination along edges (links) in the network. The links constitute the stochastic modelling entities rather than the nodes of the network. We utilise newly developed phase plane analysis to identify, model and predict characteristic behaviour in supply chain networks. The phase plane charts profile the flow of inventory and identify out of control conditions. They maintain quality within the network, as well as intelligently track the way the network evolves in conditions of changing variability. The methodology is essentially distribution free, relying as it does on the study of forecasting errors, and can be used to examine contractual details as well as strategic and game theoretical concepts between decision-making components (agents) of a network. We illustrate with typical data drawn from supply chain agile fashion products.

Somewhere between illusion of control and powerlessness : trying to situate the pathological gambler's locus of control

It has been suggested that pathological gamblers develop illusory perceptions of control regarding the outcome of the games and should express higher Internal and Chance locus of control. A sample of 48 outpatients diagnosed with pathological gambling disorder who participated in this ex post facto study, completed the Internality, Powerful Others, and Chance scale, the South Oaks Gambling Screen questionnaire, and the Beck Depression Inventory. Results for the locus of control measure were compared with a reference group. Pathological gamblers scored higher than the reference group on the Chance locus of control, which increased with the severity of cases. Moreover, Internal locus of control did show a curvilinear relationship with the severity of cases. Pathological gamblers have specific locus of control scores that vary in function of the severity, in a linear fashion or a non-linear fashion according to the scale. This effect might be caused by competition between "illusion of control" and the tendency to attribute adverse consequence of gambling to external causes.

Co-operative education and the development of self-esteem, an internal locus of control and work habits

This study compared approximately 50 grade 12 students studying In th~ co-operative education mode with approximately 50 grade 12 students studying in a traditional English course. Measures of self-esteem, locus of control and work habits were compared before and at the conclusion of one semester's involvement in the different programs. Using Coopersmith's Self-Esteem Inventory, the students who had chosen to study in the co-operative education mode scored significantly higher than the students in the traditional course. At the end of the semester, the co-operative education students' scores remained significantly higher than the English students'. Although the test showed no sjgnifi~ant changes in self-esteem. anecdotal reports indicated that co-operative education students had increased self-esteem over the semester. No significant differences in locus of control were observed between the two groups at any time. Significant differences in work habits were observed. While both groups had the same number of absences and the same marks before taking these courses, students who were involved in co-operative education had significantly fewer absences and significantly higher marks than the students studying in the traditional course. Anecdotal reports also indicated an improv~ment in work habits for students who had been involved in co-operative education. Recommendations of the study are for further research to determine more exactly how self-esteem and work habits develop in co-operative education students. Also. students. parents, teachers. and administrators need to be made aware of the success of this program.

Markov Process Modeling of A System Under WIPLOAD Control

This paper analyzes a proposed release controlmethodology, WIPLOAD Control (WIPLCtrl), using a transfer line case modeled by Markov process modeling methodology. The performance of WIPLCtrl is compared with that of CONWIP under 13 system configurations in terms of throughput, average inventory level, as well as average cycle time. As a supplement to the analytical model, a simulation model of the transfer line is used to observe the performance of the release control methodologies on the standard deviation of cycle time. From the analysis, we identify the system configurations in which the advantages of WIPLCtrl could be observed.

Implementación de buenas prácticas logísticas en el marco de seguridad industrial, almacenamiento y gestión del control de inventarios en la empresa Yokomotos

Con este trabajo se pretende generar una implementación de una mejora logística que agregue valor, aumente la eficiencia y mejore los procesos de almacenamiento y distribución, gestión del control de inventarios y seguridad industrial de la empresa YOKOMOTOS. Se realizó un estudio profundo de la situación y los problemas que tiene actualmente la empresa. Todo esto con el fin de dar resultados que diferencien a esta compañía en el mercado de los repuestos para motos, obteniendo mayor prestigio y reconocimiento a nivel latinoamericano. De igual forma se establecieron las posibles soluciones que permitieran mitigar estos problemas, mejorando los procesos en el área de almacenamiento, sistema de inventarios y seguridad industrial. Se realizaron diferentes pruebas piloto para analizar la viabilidad de nuestras soluciones, analizando espacios, tiempos y costos. Por último se implementó la mejor solución la cual se ajustó respondiendo a los requerimientos de la compañía, mejorando así los procesos de almacenamiento y distribución agregándole valor a su cadena.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.