Identifica����o fuzzy-multimodelos para sistemas n��o lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

Seleção seq��encial de descritores por an��lise da sem��ntica para recupera����o de imagens baseada no conte��do

With the rapid growth of databases of various types (text, multimedia, etc..), There exist a need to propose methods for ordering, access and retrieve data in a simple and fast way. The images databases, in addition to these needs, require a representation of the images so that the semantic content characteristics are considered. Accordingly, several proposals such as the textual annotations based retrieval has been made. In the annotations approach, the recovery is based on the comparison between the textual description that a user can make of images and descriptions of the images stored in database. Among its drawbacks, it is noted that the textual description is very dependent on the observer, in addition to the computational effort required to describe all the images in database. Another approach is the content based image retrieval - CBIR, where each image is represented by low-level features such as: color, shape, texture, etc. In this sense, the results in the area of CBIR has been very promising. However, the representation of the images semantic by low-level features is an open problem. New algorithms for the extraction of features as well as new methods of indexing have been proposed in the literature. However, these algorithms become increasingly complex. So, doing an analysis, it is natural to ask whether there is a relationship between semantics and low-level features extracted in an image? and if there is a relationship, which descriptors better represent the semantic? which leads us to a new question: how to use descriptors to represent the content of the images?. The work presented in this thesis, proposes a method to analyze the relationship between low-level descriptors and semantics in an attempt to answer the questions before. Still, it was observed that there are three possibilities of indexing images: Using composed characteristic vectors, using parallel and independent index structures (for each descriptor or set of them) and using characteristic vectors sorted in sequential order. Thus, the first two forms have been widely studied and applied in literature, but there were no records of the third way has even been explored. So this thesis also proposes to index using a sequential structure of descriptors and also the order of these descriptors should be based on the relationship that exists between each descriptor and semantics of the users. Finally, the proposed index in this thesis revealed better than the traditional approachs and yet, was showed experimentally that the order in this sequence is important and there is a direct relationship between this order and the relationship of low-level descriptors with the semantics of the users

An��lise e s��ntese de antenas e superf��cies seletivas de frequ��ncia utilizando computa����o evolucion��ria e intelig��ncia de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Seleção de features guiada por aten����o visual em imagens com f��vea

Visual attention is a very important task in autonomous robotics, but, because of its complexity, the processing time required is significant. We propose an architecture for feature selection using foveated images that is guided by visual attention tasks and that reduces the processing time required to perform these tasks. Our system can be applied in bottom-up or top-down visual attention. The foveated model determines which scales are to be used on the feature extraction algorithm. The system is able to discard features that are not extremely necessary for the tasks, thus, reducing the processing time. If the fovea is correctly placed, then it is possible to reduce the processing time without compromising the quality of the tasks outputs. The distance of the fovea from the object is also analyzed. If the visual system loses the tracking in top-down attention, basic strategies of fovea placement can be applied. Experiments have shown that it is possible to reduce up to 60% the processing time with this approach. To validate the method, we tested it with the feature algorithm known as Speeded Up Robust Features (SURF), one of the most efficient approaches for feature extraction. With the proposed architecture, we can accomplish real time requirements of robotics vision, mainly to be applied in autonomous robotics

Algoritmos gen��ticos aplicados a um comit�� de LS-SVM em problemas de classifica����o

The pattern classification is one of the machine learning subareas that has the most outstanding. Among the various approaches to solve pattern classification problems, the Support Vector Machines (SVM) receive great emphasis, due to its ease of use and good generalization performance. The Least Squares formulation of SVM (LS-SVM) finds the solution by solving a set of linear equations instead of quadratic programming implemented in SVM. The LS-SVMs provide some free parameters that have to be correctly chosen to achieve satisfactory results in a given task. Despite the LS-SVMs having high performance, lots of tools have been developed to improve them, mainly the development of new classifying methods and the employment of ensembles, in other words, a combination of several classifiers. In this work, our proposal is to use an ensemble and a Genetic Algorithm (GA), search algorithm based on the evolution of species, to enhance the LSSVM classification. In the construction of this ensemble, we use a random selection of attributes of the original problem, which it splits the original problem into smaller ones where each classifier will act. So, we apply a genetic algorithm to find effective values of the LS-SVM parameters and also to find a weight vector, measuring the importance of each machine in the final classification. Finally, the final classification is obtained by a linear combination of the decision values of the LS-SVMs with the weight vector. We used several classification problems, taken as benchmarks to evaluate the performance of the algorithm and compared the results with other classifiers

Desidrata����o de polpas de frutas pelo m��todo foam-mat

This study aimed to investigate the foam mat drying process of pineapple and mango pulp, as well as to evaluate the final product quality. Initially, the selection of fruit and additives was conducted based on density and stability determinations of mango, seriguela, umbu and pineapple foams. After selecting pineapple and mango for further studies, the fruit pulps and fruit foams were characterized in regard to their physicochemical composition. The temperature (60oC or 70oC) and the foam thickness (4 and 11 mm) were evaluated in accordance to the obtained drying curves and after model adjustment. Mango and pineapple powders obtained at the best process conditions were characterized in regard to their physicochemical composition, solubility, reconstitution time. Yoghurts were prepared with the addition of pineapple and mango powders and they were evaluated for their sensory acceptance. Results show that the best drying rates were achieved by using 70o C and layers 4mm thick for both fruits. The Page model successfully fitted the drying experimental data and it can be used as a predictive model. Pineapple and mango powders showed acid pH, high soluble solids content, low water activity (approx. 0.25), lipids between 1.46% and 2.03%, protein around 2.00%, and ascorbic acid content of 17,73 mg/100g and 14.32 mg/100g, for mango and pineapple, respectively. It was observed higher ascorbic acid retention for pineapple and mango powders processed at 70o C, which would be explained by the lower drying time applied. The fruit powders exhibited high solubility and fast reconstitution in water. The sensory acceptance indexes for yoghurts with the addition of both fruit powders were higher than 70%, which reflect the satisfactory product acceptance

Estudo dos par��metros de extra����o de fenol de efluentes aquosos por um tensoativo n��o i��nico

Environmental sustainability has become one of the topics of greatest interest in industry, mainly due to effluent generation. Phenols are found in many industries effluents, these industries might be refineries, coal processing, pharmaceutical, plastics, paints and paper and pulp industries. Because phenolic compounds are toxic to humans and aquatic organisms, Federal Resolution CONAMA No. 430 of 13.05.2011 limits the maximum content of phenols, in 0.5 mg.L-1, for release in freshwater bodies. In the effluents treatment, the liquid-liquid extraction process is the most economical for the phenol recovery, because consumes little energy, but in most cases implements an organic solvent, and the use of it can cause some environmental problems due to the high toxicity of this compound. Because of this, exists a need for new methodologies, which aims to replace these solvents for biodegradable ones. Some literature studies demonstrate the feasibility of phenolic compounds removing from aqueous effluents, by biodegradable solvents. In this extraction kind called "Cloud Point Extraction" is used a nonionic surfactant as extracting agent of phenolic compounds. In order to optimize the phenol extraction process, this paper studies the mathematical modeling and optimization of extraction parameters and investigates the effect of the independent variables in the process. A 32 full factorial design has been done with operating temperature and surfactant concentration as independent variables and, parameters extraction: Volumetric fraction of coacervate phase, surfactant and residual concentration of phenol in dilute phase after separation phase and phenol extraction efficiency, as dependent variables. To achieve the objectives presented before, the work was carried out in five steps: (i) selection of some literature data, (ii) use of Box-Behnken model to find out mathematical models that describes the process of phenol extraction, (iii) Data analysis were performed using STATISTICA 7.0 and the analysis of variance was used to assess the model significance and prediction (iv) models optimization using the response surface method (v) Mathematical models validation using additional measures, from samples different from the ones used to construct the model. The results showed that the mathematical models found are able to calculate the effect of the surfactant concentration and the operating temperature in each extraction parameter studied, respecting the boundaries used. The models optimization allowed the achievement of consistent and applicable results in a simple and quick way leading to high efficiency in process operation.

Secagem de misturas de polpa de frutas tropicais em leito de jorro

Drying of fruit pulps in spouted beds of inert particles has been indicated as a viable technique to produce fruit powders. Most of the processes employed to produce dried fruit pulps and juices, such as Foam Mat, encapsulation by co-crystallization and spray drying utilize adjuvant and additives (such as thickeners, coating materials, emulsifiers, acidulants, flavors and dyes), which is not always desirable. The fruit pulp composition exerts an important effect on the fruit powder production using a spouted bed. In the study by Medeiros (2001) it was concluded that lipids, starch and pectin contents play an important role on the process performance, enhancing the powder production; however, the drying of fruit pulps containing high content of reducing sugars (glucose and fructose) is practically unviable. This work has the objective of expanding the studies on drying of fruit pulps in spouted bed with aid of adjuvant (lipids, starch and pectin) aiming to enhance the dryer performance without jeopardizing the sensorial quality of the product. The optimum composition obtained by Medeiros (2001) was the basis for preparing the mixtures of pulps. The mixture formulations included pulps of mango (Mangifera indica), umbu (Spondias tuberosa) and red mombin (Spondia purpurea) with addition of cornstarch, pectin and lipids. Different products were used as lipids source: olive and Brazil nut oils, coconut milk, heavy milk, powder of palm fat and palm olein. First of all, experiments were conducted to define the best formulation of the fruit pulps mixture. This definition was based on the drying performance obtained for each mixture and on the sensorial characteristics of the dry powder. The mixture formulations were submitted to drying at fixed operating conditions of drying and atomizing air flow rate, load of inert particles, temperature and flow rate of the mixture. The best results were obtained with the compositions having powder of palm fat and palm olein in terms of the drying performance and sensorial analysis. Physical and physicochemical characteristics were determined for the dry powders obtained from the mixtures formulations. Solubility and reconstitution time as well as the properties of the product after reconstitution were also evaluated. According to these analyses, the powder from the mixtures formulations presented similar characteristics and compatible quality to those produced in other types of dryers. Considering that the palm olein is produced in Brazil and that it has been used in the food industry substituting the palm fat powder, further studies on drying performance were conducted with the composition that included the palm olein. A complete factorial design of experiments 23, with three repetitions at the central point was conducted to evaluate the effects of the air temperature, feeding flow rate and intermittence time on the responses related to the process performance (powder collection efficiency, material retained in the bed and angle of repose of the inert particles after the process) and to the product quality (mean moisture content, loss of vitamin C and solubility). Powder production was uniform for the majority of the experiments and the higher efficiency with lower retention in the bed (59.2% and 1.8g, respectively) were obtained for the air temperature of 80��C, mixture feed rate of 5ml/min in intervals of 10 min. The statistical analysis of the results showed that the process variables had individual or combined significant influences on the powder collection efficiency, material retention in the bed, powder moisture content and loss of vitamin C. At the experimental ranges of this work, the angle of repose and solubility were not influenced by the operating variables. From the results of the experimental design, statistical models were obtained for the powder moisture content and loss of vitamin C

An��lise da adi����o de res��duo oriundo do tratamento de esgotos em massa cer��mica utilizada para fabrica����o de telhas

Sludge of Wastewater Treatment Plants (WTPs) disposal is a problem for any municipality, for this reason the amount of sludge production is now a key issue in selecting treatment methods. It is necessary to investigate new applications for this waste type, due to the restrictions imposed by the environmental organs. The raw materials used in the Red Ceramic, are generally very heterogeneous, for this reason, such materials can tolerate the presence of different types of wastes. In Rio Grande do Norte, the roof tiles production corresponds to 60,61% from the total of ceramic units produced. Due to the importance of the ceramic industry of roof tiles for the state, allied to the environmental problem of the sludge disposal, this work had for objective to verify the possibility of the incorporation of sewage sludge in ceramic body used for production of roof tiles. In the research, sludge originating from drying beds of WTP of the Central Campus from UFRN and clays originating from a ceramic industry from Goianinha/RN were used. The raw materials were characterized by techniques of: analysis of particles distribution by diffraction to laser; real density; consistence limits; chemical analysis by X-ray fluorescence; mineralogical analysis by X-ray diffraction; organic matter; and solids content. Five batches of roof tiles were manufactured in the approximate dosages of 2%, 4%, 6%, 8% and 10%. To evaluate the properties of each final product, tests of water absorption, impermeability, bending strength, leachability and solubility were accomplished. The roof tiles manufactured with sludge presented characteristics similar to the roof tiles without sludge in relation to the environmental risk. The results showed that it is possible to use approximately up to 4% of sludge in ceramic bodies for production of roof tiles. However, it is observed that the high amount of organic matter (71%) present in the sludge is shown as factor that limits the sludge incorporation in ceramic bodies, worsening the quality of the roof tiles. It is necessary the use of mixtures of different raw materials under point of view of the granulometry and of the other chemical and mineralogical properties for the obtaining of a satisfactory mass to the production of ceramic roof tiles

Avalia����o de bact��rias nitrificantes em filtros biol��gicos submersos aerados

This study investigates a new treatment system of wastewater by anaerobic and aerobic biological filters for nitrogen modification. The main objective of this study was evaluate, on a pilot scale, quantitatively and qualitatively the bacterian nitrifying community in a experimental sewage treatment system made by aerobics biological filters in series, in search of figure out the dynamic of nitrogen modification process. It was collected and laboratorial analysed microbiologically, regarding NMP of Nitrosomonas e Nitrobacter, and physical-chemically considering nitrogen sequence. We conclude that: the association in aerobic biological filters under nutrition controlled conditions and oxygen level allows the appearance of bacterian community responsible for the nitrogen modification; the method used, despite its limitations, provided the selection of autotrophic nitrifying microorganisms, allowing the identification of Nitrosomonas and Nitrobacter; the flow direction tested in the experimental unit did not affect the nitrifying bacterial community, certainly because they were kept drowned and did not occur flow speed that could breake the formed biomass; the nitrification process happened in aerated biological filters in all phases of the research, comproved by microbiological tests; in the third phase of the research the increase of the oxygen rate was significant for the nitrificant bacterian community in the aerate biological filters, allowing its growth, occurring relation between the efficiency of nitrification system and the quantity of organisms responsible for this process; the conduit used in aerated biological filters showed satisfactory performance support material to the nitrifying bacteria development

Mecanismos de controle do trabalho escolar em propostas de escrita narrativa em livros did��ticos de portugu��s (1974-2009)

This essay aims at investigating the writing proposals of Portuguese textbooks (LDP Livros Did��ticos de Portugu��s) for Middle School (EF Ensino Fundamental), from 6th to 9th grade, from the 70s to 2009. It aims to check, though the discourse reported in the Portuguese Textbook, the control directed to the practice of the teacher and the student to do in the teaching situations. Theoretically, we search for contributions that come from the Discourse Analysis of French filiation, so we can analyze the ideological constructions present in the discourse of the ―LDP‖ more specific lly the control directed to the te cher nd student the users of the book, in writing activities. It started from a corpus of 63 textbooks whereof the following steps were performed: a) mapping of the writing proposals contemplated in the ―LDP‖ of high school; b cutting in the selection of propos l ccording to the rese rch go ls intended (writing proposals of narrative texts). After mapping the writing proposals presented in the ―LDP‖ bout the criteri mentioned bove we re d the writing propos ls to ch rt the quantity of proposals of textual writing productions in each textbook (which usually follows a pattern : 12 chapters and, at the end, the writing proposal. Nevertheless, some books present 2 (two) or more writing proposals at the end of each chapter). We did a cutting in the corpus initi lly constituted 63 ―LDP‖ nd we selected 12 writing proposals of narrative texts presented in the ―LDPs‖ to present wh t we intend to n lyze. Then, we separated these proposals into two groups: 1) activities which present ―instruction guide‖ to be followed by the student; 2) writing activities that allow the student write with no need to follow a text pattern, i.e., which encourage authorship. By means of analyses, it was possible to demonstrate that, in the Basic School, generally, the writing practices concentrate, primarily, on copying activities, reproduction, rewriting and, in more advanced levels, in activities that which start from preset models, asking the students to produce text with similar themes, following the suggested structure. It is about ideals that are supposed to be followed and imitated by the students, depriving them to assume their authorship. In order to insert the student in the world of writing it s necess ry to go beyond the model of c nonic l texts pr ctice th t puts the students f r from the possibility to be ― uthors‖. In contr st to this tendency, we face, nowadays, proposals that prioritize the authorship, the creation of a style

Conectores sequenciadores e e a�� em contos e narrativas de experi��ncia pessoal escritos por alunos de ensino fundamental: uma abordagem sociofuncionalista

In this dissertation, based on two theoretical frameworks, American functionalism and variationist sociolinguistics, I take as subject the sequence connectors E and A��, which has the grammatical function of indicating retroactive-propeller sequenciation of information. I analyze the variable use of these connectors in texts written by students from two public schools in the city of Natal, RN, attending at the time of data collection (the year 2012), two distinct levels of basic education: the sixth and the ninth year. The students who contributed to this research wrote, as part of their activities in the classroom, texts of two narrative genres: narrative of personal experience (non-fictional) and short story (fictional). In addition, these students and their Portuguese teachers answered a test of linguistic attitude in which they gave their opinions regarding the appropriateness of the use of connectors E and A�� in contexts of speech and writing marked by distinct degrees of formality. The results obtained by means of quantitative analysis showed different tendencies of linguistic, social and stylistic distribution of connectors E and A�� in the narrative texts written by the students. I related these results to the action of two principles: the principle of persistence, linked to the process of change by grammaticalization, and the principle of stylistic markedness. Besides, I took into account the answers provided by students and teachers to the test of linguistic attitude for refine the interpretation of the results

Publicidade e moda: um estudo sobre a materialidade da m��dia e a produ����o de sentido na revista ffw>>mag!

The proposal of this research is to analyze the convergence between fashion and communication shown on the materiality of the print media, and how the language from the supporter influences on the production of sense by the target market. Made real in the research corpus comprised of six ffw>>mag! magazines from the year 2011. The applied conceptual mechanism tries to investigate the production of sense from the physical attributes before interpreting the message s content, to do so, the Materiality of Communication is used, which offers an investigative apparatus of the media in its material shape, and those as influences in the communicative acts and processes. Methodologically, we adopt the Peircean Semiotics Theory, for its study focus on the analysis of the possible processes of production of sense. Through Semiotics we achieve the interpretative levels that allow us to clarify the questionings that come from the research s objectives, identifying and tracing the cognitive and intelligibility schemes bound to the media speeches of materiality. The analysis coordinated to the concepts and theories employed in this study point to a confirmation that the materiality of the reviewed media communicates to the readers in the same intensity as its content, provides a preview of the content and notifies the intentions of the publication. In the commercial way, characterizing the target audience it craves, and also in the conceptual way, demonstrating the ideas it wants to communicate. Where the convergence between communication and fashion unfolds as the materiality of the media by the choice of the materials and finishing options, and mainly by the selection and manipulation of technical images and colors from the cycles of fashion

O corpo no pensamento de Epicuro: limites e possibilidades

The theme that fits the perspective of this thesis comes from the interest of treating, in the Epicurean corpus, about the importance of the body and its manners of realization for understanding the thought of Epicurus of Samos. Based on the inferences contained in the texts that remained from Epicurus, we did an analysis of the aspects that characterize Epicurism as a thought that makes repeated references to the body as an instance of sensitivity. It was necessary, therefore, to discuss how the body is linked to the possibility of thought, and how the latter can be admitted as a body element. It is further understood that the atomistic physics converges to the idea that asserts natural phenomena as likely to be contained and explained by the observations that come from the senses which are manifested through the body. For this reason, it was also pertinent to reflect on the admission of the body as a key element for the interpretation of Epicurean thought, even under the constitution of language. The Epicurean construction about body image was also used for the interpretation and questioning of the dynamics that define the relationships between individuals, characterizing the koinon��a of the garden through the notion of corporeal unity. It was defined, therefore, that the characterization of the action field of individuals who lived in the Epicurean garden revolves around the use of logos, with the dialogues coming from the exercise of philosophy for therapeutic purposes, which were able to introduce a specific mode of political action marked by the absence of strange interests of the notion of phil��a

Rota����o diferencial em estrelas do tipo solar

Stellar differential rotation is an important key to understand hydromagnetic stellar dynamos, instabilities, and transport processes in stellar interiors as well as for a better treatment of tides in close binary and star-planet systems. The space-borne high-precision photometry with MOST, CoRoT, and Kepler has provided large and homogeneous datasets. This allows, for the first time, the study of differential rotation statistically robust samples covering almost all stages of stellar evolution. In this sense, we introduce a method to measure a lower limit to the amplitude of surface differential rotation from high-precision evenly sampled photometric time series such as those obtained by space-borne telescopes. It is designed for application to main-sequence late-type stars whose optical flux modulation is dominated by starspots. An autocorrelation of the time series is used to select stars that allow an accurate determination of spot rotation periods. A simple two-spot model is applied together with a Bayesian Information Criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty are obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov Chain (hereafter MCMC) approach. We apply our method to the Sun and eight other stars for which previous spot modelling has been performed to compare our results with previous ones. The selected stars are of spectral type F, G and K. Among the main results of this work, We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite to a successful measurement of differential rotation through spot modelling. For a proper MCMC analysis, it is necessary to take into account the strong correlations among different parameters that exists in spot modelling. For the planethosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation. We confirm that the Sun as a star in the optical passband is not suitable for a measurement of the differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison with more sophisticated procedures used until now in the study of stellar differential rotation