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good classifier prenciple



Classification is a process of dividing a particle-laden gas stream into two, ideally at a particular particle size, known as the cut size. An important industrial application of classifiers is to reduce overgrinding in a mill by separating the grinding zone output into fine and coarse fractions. Many types of classifier are available, which can be categorized according to their operating principles. A distinction must be made between gas cleaning equipment, in which the aim is the removal of all solids from the gas stream, and classifiers in which a partition of the particle size distribution is sought. Prasher (1987) identifies the following categories: a) screens, b) cross-flow systems, c) elutriation, d) inertia systems, e) centrifugal systems without moving parts, f) centrifugal systems with rotating walls, and g) mechanical rotor systems. A classification process may combine these alternative principles, sometimes within a single separator, to achieve a desired result.

These contain apertures which are uniformly-sized and spaced, and which may have circular, square or rectangular shapes. Particles which are smaller than the aperture in at least two dimensions pass through, and larger ones are retained on the surface. The screen is shaken or vibrated to assist motion of particles to the surface, and continuous screens are often tilted to further aid particle bed motion along the screen surface. Static (or low-frequency) screens or grizzlies have a different construction. They are comprised of parallel bars or rods with uniformly clear openings, often tapered from feed to discharge ends. The bars may lie horizontally above a bin, or be inclined to provide the feed to a crusher.

It is in principle possible to winnow out fines from a falling curtain of material of constant density by a cross-current of air. In practice, humidity of the air (and moisture on the particles) leads to blockage of the narrow ducts necessary to give a thin enough falling curtain for winnowing. It is possible to winnow thin flakes; Etkin et al. (1980) has successfully classified mica particles with an aspect ratio greater than 30.

Gravity counter-current classifiers (elutriators) have been reviewed by Wessel (1962). A simple example, the Gonnell (1928) classifier, consists of a long vertical cylindrical tube with a conical transition zone located at the bottom end. Air flows up the tube, carrying with it the finer particles. The disadvantage of this and many other gravity counter-current classifiers is the presence of a laminar velocity profile in the gas, a large cone angle leading to flow separation and eddy formation, settling out of fines due to the retarded velocities near the walls, and the noise of vibrators necessary to prevent particle adhesion to the walls. Their advantage lies in the good dispersion of powders achieved in the cylindrical section. In the zig-zag classifier, vortex formation leads to the acceleration of the main flow owing to a reduction of the effective tube cross-section. Fines follow the main gas stream and coarse particles travel to the wall, and fall back against the main gas flow. In this design, the sharpness of cut is low at each stage (zig-zag), but a required cut size is generally achievable even at high velocities.

In an inertial classifier, the particle-laden gas stream is turned through 180 by appropriate internal baffling. In order to reach the exit port, the gas passes through a further 180 to continue in the same direction it was travelling before it was diverted. The fines are able to follow, more or less, the same route as the gas. However, the momentum of coarser or denser particles prevents them from following the same trajectory and they fall into a collection zone after the first turn.

The capacities of these types of classifiers cover a wide range. Generally, higher-capacity machines have a poorer sharpness of cut. Typical high-capacity industrial units are the cone classifier (often built into some types of mills) and the cyclone. The feed is given a high tangential velocity and is introduced near to the top of the unit. The gas flows in a spiralling fashion towards the bottom end where it experiences a flow reversal and passes up as a central core. In the cone classifier, the central core of gas actually flows in a reverse spiral up the wall of a central feed. Under the influence of centrifugal force, coarse particles are thrown to the inner wall of the cone or cyclone. Particles less than the cut size are carried up the central vortex and are carried out of the unit by the bulk of the gas flow. The diameter and position of the vortex finder at the top of the unit are critical in the determination of a specified cut size. Further information on cyclones is given in the overview article on Gas-Solid Separation.

The Larox classifier is another high capacity system, shown in Figure1. The particles are dispersed by the feed falling across an inlet gas; the coarsest particles fall through the gas stream and into an outlet chute, and are thereby separated. Classification of the remainder occurs in a horizontal cyclone. There are three adjustable flights (A, B and C) to be positioned to give the best cut.

Spiral classifiers, such as the Alpine Mikroplex design for separation in the superfine region, were developed to partially overcome undesirable boundary layer effects associated with spinning fluids at stationary walls (Rumpf and Leschonski (1967)). Air is introduced tangentially at the periphery into a flat cylindrical space and moves along spiral flow lines into the center, from where it is drawn off. The fines follow the flow while the coarse particles spin round at the circumference; in some designs, this recirculating coarse stream is reclassified by passage of the incoming air through it. The coarse fraction leaves through a slit at the periphery (as in the Walther Classifier) or is removed using a screw extractor (as in the Alpine Mikroplex Classifier). The cut size theoretically has a stable circular trajectory in the classifying zone, but (in common with most other classifiers) separation is poorer with higher solids loadings.

To extend effective separation over a wider range of operating parameters, many classifiers are designed with a mechanical rotor built into them. The rotor has several effects: 1) large particles are deflected back into the classifier, thereby reducing the proportion of coarse particles in the fine product, 2) it aids recirculation of the air stream in some classifier types, and 3) the generation of a forced vortex keeps large particles at the periphery, but fines follow a helical trajectory to the center where they pass out with the exiting air.

naive bayes classifier explained

naive bayes classifier explained

Naive Bayes Classifier is a simple model that's usually used in classification problems. The math behind it is quite easy to understand and the underlying principles are quite intuitive. Yet this model performs surprisingly well on many cases and this model and its variations are used in many problems. So in this article we are going to explain the math and the logic behind the model and also implement a Naive Bayes Classifier in Python and Scikit-Learn.

This article is part of a mini-series of two about the Naive Bayes Classifier. This will cover the theory, maths and principles behing the classifier. If you are more interested in the implementation using Python and Scikit-Learn, please read the other article, Naive Bayes Classifier Tutorial in Python and Scikit-Learn.

Classification tasks in Machine Learning are responsible for mapping a series of inputs X = [x1, x2, ..., xn] to a series of probabilities Y = [y1, y2, ..., ym]. This means that given one particular set of observation X = (x1, x2, ..., xn), we need to find out what is the odd that Y is yi and in order to obtain a classification, we just need to choose the highest yi.

Yeah, I know, I also don't like these things explained this way. I know a formal explanation is necessary, but let's also try it in another way. Let's have this fictional table that we can use to predict if a city will experience a traffic jam.

So in a classification task, our goal would be to train a classifier model that can take information from the left(the weather outside, what kind of day it is and the time of the day) and can predict if the city will experience a traffic jam.

where y1 is the probability that there's no traffic jam and y2 is the probability that there is a traffic jam. We only need to choose the highest probability and we're done, we've obtained our prediction.

What we know from the probability theory is that if X1 and X2 are independent values(meaning that, for example, the fact that the weather is rainy and that today is a weekend day are totally independent, there's no conditional relation between them), then we can use this equation.

Now in our example, this assumption is true. There is absolutely no way that the fact that today is rainy is influenced by the fact that today is Saturday. But generally speaking, this assumption is not true in most of the cases. If we observe a large number of variables for a classification tasks, chances are that at least some of those variables are dependent(for example, education level and monthly income).

But the Naive Bayes Classifier is called naive just because it works based on this assumption. We consider all observed variables to be independent, because using the equation above helps us simplify the next steps.

So let's take a look back at our table to see what happens. Let's try to see what it is the probability of there being a traffic jam given the fact that the weather is clear, today is a workday and it's morning time(first line in our table).

You can see that this is already becoming a painful process. You might have doubts because the intuition behind this model looks very simple(although calculating so many probabilities may give you a headache) but it simply works very well and it's used in so many use cases. Let's see some of them.

If you're like me, all of this theory is almost meaningless unless we see the classifier in action. So let's see it used on a real-world example. We'll use a Scikit-Learn implementation in Python and play with a dataset. This was quite a lenghty article, so to make it easier, I've split this subject into a mini-series of two articles. For the implementation in Python and Scikit-Learn, please read Naive Bayes Classifier Tutorial in Python and Scikit-Learn.

mechanical centrifugal air classifiers - chemical engineering | page 1

mechanical centrifugal air classifiers - chemical engineering | page 1

Mechanical centrifugal air classifiers are used extensively to process aggregates, ceramics, chemicals, foods, minerals, metals, plastics, flyash and other materials. They are normally employed when the particle size that you need to separate is too fine to screen. The air-classified product can be either the granular coarse discharge with very little fines and dust, or it can be the fines discharge with very little coarse material.

Air classifiers eliminate the blinding and breakage issues associated with screens. They work by balancing the physical principles of centrifugal force, drag force, collision and gravity to generate a high-precision method of classifying particles according to size and density. For dry materials of 100-mesh and smaller, air classification provides the most effective and efficient means for separating a product from the feed stream, for dedusting, or, when used in conjunction with grinding equipment, for increasing productivity.

Mechanical centrifugal air classifiers are masters of accuracy. They are a good choice when the separation curve or cutpoint is too fine for screens (200400 mesh or finer), when the capacity is too large for screens (up to 800 ton/h) and when easy adjustability is required to meet various product specifications.

One of the most significant advantages of a classifier is its dry process. For dedusting aggregates, dry processing eliminates the need for water or settling ponds, saving money and land, and benefiting the environment.

Air classifiers do not handle the more aggressive work that pulverizers do and they operate at much lower speeds, so the equipment is less susceptible to wear. With the addition of protective liners, air classifiers can be used to economically process even abrasive powders, such as silica, flyash and ceramics.

Air classifiers have the ability to separate powders as coarse as 80 mesh (180 m), and as fine as 23 m. The fineness of air-classified products is controlled by a precise balance among the quantity of rejector blades, the speed at which the rejector blades operate, the velocity of the airflow and the rate at which the material is fed. Even with fragile powders, air classifiers rarely fracture or degrade particles because they do not operate at pulverizer speeds and most of the feed never makes contact with the rotating parts.

Air classifiers can be used as a single sizing device in an open circuit where the feed is split into a fines discharge and a coarse discharge. This equipment can also be used in closed-circuit with mills. In this case, use of the air classifier maximizes the capacity of the mill and reduces the mills energy consumption because the mill does not have to serve as the sizing device (Figure 1).

While density does play a role in air-classifier separation, the internal air currents are mostly affected by the overall mass and weight of the particles in the feed. Lighter and smaller particles are removed by the airflow, while heavier and larger particles are not entrained in the airflow. If the lower-density material also has a finer particle size, then air classifiers can be very effective. However, large particles with low density can have a similar mass and weight as some small particles with high density. This can reduce the effectiveness of an air classifiers density separation.

Moisture effects are limited by surface moisture, rather than inherent moisture. Inherent moisture is naturally found inside particles of ores, minerals or stone sand after natural drying occurs in air. Inherent moisture does not hinder an air classifiers ability to remove fine powder or fine dust from coarse particles. For example, crushed coal is successfully air classified with inherent moisture as high as 10%.

Surface moisture, on the other hand, is found on the surface of ores, minerals or stone sand and comes from rainfall or from spraying water in an aggregate plant or quarry during dust suppression. Surface moisture is detrimental to the performance of air classifiers because the fine particles stick to the large particles and airflow is not enough to remove them. When surface moisture is very high, the water also centrifuges out and results in equipment clogging.

The performance of air classifiers in aggregate plants or quarries is limited by the surface moisture in the stone sand. The drier the rock is (12%), the more dust can be removed, often allowing air classifiers to replace water wash systems altogether. When higher surface moisture is present in stone sand (2.53.0%), the fines stick to the rock and larger air classifiers are required with more airflow than usual to be effective. When the surface moisture is very high (3.54.0% or more), the water centrifuges out and results in equipment clogging.

Air classifiers can be fed pneumatically and, in some cases, can be incorporated into a pneumatic conveying line. However, in a pneumatic feed process, particles enter the air classifier at a much higher velocity than gravity-fed particles. When these particles approach the classifier rejector blades at high velocities, they are more likely to pass through, which requires a higher rejecter speed to stop these oversize particles. Higher rejector speed can then result in higher wear and lower efficiency in fines-removal.

Internal-fan air classifiers recycle the air, and therefore, do not require airlocks, cyclones or baghouses to collect the separated fines. This design has a single shaft that controls three rotating elements the feed distributing plate, particle-sizing selector blades and circulating fan (Figure 2).

The feed distribution plate imposes centrifugal force on the feed particles, moving them into the classification zone. Coarse particles fall down into the inner cone and exit at the coarse discharge. The circulating fan creates an upward draft of air that carries finer particles away from the feed and through the selector blades. Properly sized fine particles pass through the internal fan still entrained in air. Fixed vanes recycle the air back into the classifier, while the properly sized fine particles drop out of the airflow and slide down the fines cone, where they exit.

External-fan air classifiers (Figure 3) require cyclones or baghouses to collect the separated fines. This design uses a variable-speed rotor with multiple, closely spaced rejector blades for ultra-fine and ultra-efficient applications. The feed distribution plate imposes centrifugal force on the feed particles, moving them into the classification zone. Coarse particles fall down into the inner cone and exit at the coarse discharge point. The external fan creates a draft of air that carries finer particles away from the feed and through the rotor. Properly sized fine particles, entrained in air, pass through the rotor and exit the air classifier. A cyclone or baghouse is required to recover the classified particles out of the airflow.

The most common methods of controlling particle size in mechanical centrifugal air classifiers are rejector speed, cage aperature size of rejector elements, airflow velocity and the ratio of feedrate to air.

Rejector speed controls the impact or collision force on the air-entrained particles as they attempt to exit the air classifier. Higher speed allows only the finest particles to pass through the rejector for collection. This increases the rejection of larger particles (Figure 4).

Airflow velocity generated by a fan controls the drag force on particles as they enter the classification zone. Higher airflow allows larger particles to be removed from the feed, while lower airflow allows only the finest particles to pass through the rejector cage for collection.

Rejector elements / cage-aperture controls impact the collision force on the air-entrained particles as they attempt to exit the air classifier. A greater quantity of rejector elements (blades or rods) makes the cage aperture smaller and allows only the finest particles to pass through the rejector for collection. This increases the rejection of larger particles.

Feedrate-to-air ratio controls the entrainment of particles in the airflow. A higher feedrate allows only the finest particles to pass through the rejector cage for collection. This increases the rejection of larger particles.

Cutpoint is simply the desired particle size that is intended to be classified. This value can be measured in millimeter mesh or micron size. Tolerance is the percentage of oversized or undersized particles allowed in the finished product. Yield is the percentage of production rate per unit of feedrate. Efficiency is the percentage of the desired particle-size fraction recovered as product from the total amount available in the feed.

Joseph Muscolino is product manager for air classifiers at Sturtevant Inc. (348 Circuit St., Hanover, MA 02339; Phone: 800-992-0209; Email: [email protected]; Web: www.sturtevantinc.com). Muscolino has 26 years of industrial experience with air classifiers and mills. He is a member of various professional societies, including the National Stone, Sand and Gravel Assn., and is the author of several technical articles and case histories. He received a B.S. in mechanical engineering from Northeastern University in 1981.

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machine learning - what is a classifier? - cross validated

machine learning - what is a classifier? - cross validated

Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

"An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category."

For example, in a churn model which predicts if a customer is at-risk of cancelling his/her subscription, the classifier may be a binary 0/1 flag variable in the historical analytical dataset, off of which the model was developed, which signals if the record has churned (1) or not churned (0).

As an example, a common dataset to test classifiers with is the iris dataset. The data that gets input to the classifier contains four measurements related to some flowers' physical dimensions. The job of the classifier then is to output the correct flower type for every input.

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