T Lerher
email: tone.lerher@uni-mb.si

M Sraml

I Potrc

T Tollazzi

Travel time models for double-deep automated storage and retrieval systems

Keywords: WAREHOUSING SYSTEMS, AUTOMATED STORAGE, PROBABILITY Double-deep AS/RS, Travel time analysis, Mathematical modelling

Travel time models for double-deep automated storage and retrieval systems

Tone Lerher, Matjaz Sraml, Iztok Potrc, Tomaz Tollazzi

Introduction

Warehouses are an important aspect of economic activity. With regard to the rapid development of technology in the material handling equipment and the increase in the cost of labour, new approaches in designing warehouses have been developed. Modern warehousing systems can be generally classified as mechanized (conventional) or automated warehouses. A combination of labour and material handling equipment is utilized in mechanized systems to facilitate receiving, storage and shipping processes. Generally, the labour constitutes a high percentage of the overall cost in mechanized systems. On the contrary, automated warehouses attempt to minimize the labour element as much as possible by making the capital investment in equipment [START_REF] Gelders | Warehouse design optimization[END_REF].

An important part of automated warehouses is represented by automated storage and retrieval systems (AS/RS). The basic components of AS/RS are storage racks (SR), storage and retrieval machines (S/R machines), input/output (I/O) locations and accumulating conveyors. AS/RS offers the advantages of fewer material handlers, better material control (including security), and more efficient use of storage space. The disadvantage is that the capital and maintenance costs are high, and it is difficult to modify such a system once it is installed. As a result of this, the adoption of AS/RS must be economically and operationally justifiable, and its deployment must be carefully planned. Essentially, AS/RS are designed to achieve a high throughput capacity and to support accurate picking of transport unit loads (TUL). A modern warehouse using AS/RS combines the state-of-the-art "hardware" and information systems to achieve high-value added warehousing operations for a high variety of loads.

Various designs and configurations of the unit-load AS/RS have been made due to different requirements and operating conditions. Double-deep AS/RS essentially consist of two single-deep SR placed one behind the other, and so TUL are stored in the first or second storage lane of the SR. Each storage lane of the SR is independently accessible, and so any TUL can be stored in any storage lane at any level of the SR [START_REF] Bartholdi | Warehouse & Distribution Science[END_REF]. A typical double-deep AS/RS has the special design of the S/R machine, which moves the TUL to or from the first or second storage lane of the SR on the either side of the picking aisle. High lifting distances, high velocity in horizontal and vertical directions, precise handling and controlled movement are important features of the S/R machine. The S/R machine consists of a traveling structural frame, which is guided and supports a hoisted carriage on which the TUL is placed. The shuttle or load attachments on the hoisted carriage manipulate the TUL into and out of the SR position. Since TUL are stored in the first and second storage lane, a special design with double-deep load attachments, or with the satellite vehicle for heavier loads, is utilized. The advantage of the double-deep SR is that fewer aisles are needed, which results in a more efficient use of floor space. In general a 50 % aisle space saving is achieved in comparison with the single-deep SR.

Many producers of the warehouse equipment, such as Siemens Dematic, Stöcklin, Mias Maschinenbau München, etc., have begun to offer double-deep and deep lane AS/RS. The selection of single-or double-deep systems depends on the required throughput capacity and on the desired level of flexibility in the warehouse. The unit-load AS/RS have been the subject of many researchers over the past few years. [START_REF] Hausman | Optimal storage assignment in automatic warehousing systems[END_REF] and [START_REF] Graves | Storage retrieval interleaving in automatic warehousing systems[END_REF] have presented travel time models for unit-load AS/RS assuming that the SR is Square-In-Time (SIT). They have analyzed different storage strategies, e.g. randomized, turnover-based and class-based storage assignment rules. [START_REF] Gudehus | Principles of order picking: Operations in Distribution and Warehousing Systems[END_REF] has presented basic principles for the determination of cycle times according to unit-load AS/RS. With regard to other cycle time expressions, he has considered the impact of the acceleration and deceleration rate on travel times. [START_REF] Bozer | Travel-Time Models for Automated Storage and Retrieval Systems[END_REF] have presented analytical models for the calculation of single command cycle (SC) and dual command cycle (DC) for non SIT racks. Their models are based on randomized storage and retrieval with different I/O configurations of the input queue. [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF] and [START_REF] Vössner | Spielzeit Berechnung von Regalförderzeugen[END_REF] operating characteristics of the S/R machine for unit-load AS/RS and non SIT racks. While the majority of researchers have considered the unit-load single-deep AS/RS only, there is a lack of research for the unit-load double-deep AS/RS. Studies of double-deep AS/RS have been presented by authors [START_REF] Oser | Technology and throughput of double-deep multi-shuttle AS/RS[END_REF][START_REF] Oser | Expected cycle time in a class-based single-and double-deep storage system[END_REF] and [START_REF] Ritonja | Spielzeitberechnung von Bedienstrategien von Regalbediengäreten mit Mehrfach-Lastaufnahmemitteln[END_REF]. Their study is based on travel time models considering the multi-shuttle and class based storage system for mini-load AS/RS. Studies of multi-deep AS/RS have been presented by the following authors. [START_REF] Saygin | Travel-time models for flow-rack automated storage and retrieval systems[END_REF] have presented the travel-time models for the 3D flow-rack AS/RS. They have introduced the flow-rack, where TUL loaded by the S/R machine by one end of the rack, travels to another end of the rack to be retrieved. For the storage operation, the S/R machine operates in the same way as the S/R machine in the unit-load AS/RS. However, the retrieval operation for a particular TUL requires that the S/R machine removes all TUL stored in front of the requested TUL. The acceleration/deceleration effect on the travel time was not considered by the authors. De Koster at al. (2008) have presented an optimal storage rack design for the 3D compact AS/RS. They have introduced the combination of the S/R machine for TUL movement in the horizontal and vertical directions and the system of inbound and outbound conveyors (powered or non-powered) for the depth movement. They have analyzed the system performance and optimal dimension of the system for the random storage strategy in order to minimize the expected travel time of the S/R machine. In the continuation of their work, Yu and De Koster (2008a) have derived the expected single command cycle time under the full-turnover based storage policy. In order to implement the class-based policy, Yu and De Koster (2008b) have introduced the model for determining the optimal storage zone boundaries for the 3D compact AS/RS. For the determination of the zone boundaries, they have introduced the mixed-integer nonlinear model. The presented research is very useful and flexible tool when designing 3D compact AS/RS. According to the review of the multi-deep AS/RS the researchers used a different approach for analysing the system performance from the one that will be used in our paper.

According to the previous literature research, our paper presents the proposed analytical travel time models for unit-load double-deep AS/RS considering the real operating characteristics of the S/R machine. Since we are dealing with two storage lanes in the storage rack the blocking of the TUL during the retrieval process will be introduced. The proposed analytical travel time models are based on randomized storage and retrieval of TUL under the condition of rearrangement of blocking TUL during the retrieval process (the application of the FEM 9.851 guideline). The guideline FEM 9.851 is a commonly used procedure for calculating cycle times. The proposed analytical travel time models for unit-load double-deep AS/RS are also validated through discrete event simulations.

Statistical analysis of travel time

When developing the proposed analytical travel time models for double-deep AS/RS, the real operating characteristics of the S/R machine have been considered [START_REF] Lerher | Analytical travel time models for multi aisle automated storage and retrieval systems[END_REF]. We estimate that the analytical travel time models based on the assumption that the S/R machine travels with a uniform velocity only are too general. If we limit ourselves to using the uniform velocity only, the average travel time for a cycle becomes shorter and consequently the throughput capacities become larger, which is not in accordance with the practice. The above mentioned statement becomes even more evident by the short SR.

When developing the proposed analytical travel time models for double-deep AS/RS, the following assumptions were considered:

-The double-deep AS/RS is considered to be divided into picking aisles with double-deep SR on both sides of the aisle.

-The double-deep SR is considered to be a continuous rectangular pick face where the I/O location is located in the lower left-hand corner of the SR. -The S/R machine operates either on single or dual command cycle. The hoisted carriage has place for only one TUL. In principle TUL will be stored first in the second storage lane of the SR, which will minimize the number of rearrangements during the retrieval operation.

-The S/R machine is equipped with the load attachments and can serve in the first storage lane of the SR and in the second storage lane of the SR.

-The specification of the S/R machine (max. velocities in the horizontal and vertical directions and acceleration and deceleration rates) as well as the length and the height of the SR are known.

-The S/R machine and the hoisted carriage travel simultaneously in the horizontal and vertical directions in the aisle.

-The length and the height of the SR are long enough for the S/R machine to reach maximal velocity from the I/O location.

-The randomized storage assignment rule has been used. the bay depth, a w the aisle width.

Travelling of the S/R machine in the storage rack

Travel times of the S/R machine to any randomly selected location in the SR are variable times. They depend on the kinematics properties of the S/R machine and the hoisted carriage, the length L and the height H of the S/R and the storage policy. The travel time t xy from the I/O location to any randomly selected location in the SR is the maximal value of t x or t y , where t x is the horizontal travel time and t y is the vertical travel time. According to the condition of uniform distribution of storage locations in the SR and to the condition of the x-and y-coordinates independence, the cumulative distribution functions F x (t) and F y (t) have been accomplished. The cumulative distributions functions F x (t) and F y (t) are distinguished according to the following condition: (i) S/R machine travelling/hoisted carriage movement for type I (the obtained peak velocity is less than v max ) (ii) S/R machine travelling/hoisted carriage movement for type II (the obtained peak velocity is equal to v max ) 2.1.1 Travelling of the S/R machine and movement of the hoisted carriage from the I/O point to a randomly selected location in the SR -S/R machine travelling in the horizontal direction [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF]

2 2 2 0 4 ( ) 2 x x x x x x x x x x x x a t v t L a F t v t v v L v t L a L a v a    ≤ ≤       =     - ≤ ≤ +       (1)
-Hoisted carriage movement in the vertical direction [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF]

a t v t H a F t v t v v v H t H a H a v a    ≤ ≤         =     - ≤ ≤ +         (2)
2.1.2 Travelling of the S/R machine and movement of the hoisted carriage from a storage location to a randomly selected retrieval location in the SR -S/R machine travelling in the horizontal direction [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF])

2 2 4 2 2 3 2 4 2 2 2 2 2 2 0 2 16 ( ) 2 2 2 2 x x x x x x x x x x x x x x x x x x a a v t t t L L a F t v v v v v v L v t t t L a L L a L a L a v a    - ≤ ≤       =       - + + - - ≤ ≤ +           (3)
-Hoisted carriage movement in the vertical direction [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF])

2 2 4 2 2 3 2 4 2 2 2 2 2 2 0 2 16 ( ) 2 2 2 2 y y y y y y y y y y y y y y y y y y a a v t t t H H a F t v v v v v v v H t t t H a H H a H a H a v a    - ≤ ≤         =       - + + - - ≤ ≤ +               (4)
The distribution functions F ik (t), where (i = 1 or 2) and (k = 1,…,6), depend on the relationships among the values of the following parameters: v x , v y , a x , a y , L, H. Therefore F ik (t) can be specified with theoretically six different cases:

F o r P e e r R e v i e w O n l y ( ) ( ) ( ) 0 ik x y F t F t F t for t T = ⋅ ≤ ≤ (5)
where:

-F 1k (t) stands for travelling of the S/R machine and movement of the hoisted carriage from the I/O point to a randomly selected location in the SR and -F 2k (t) stands for travelling of the S/R machine and movement of the hoisted carriage from a storage location to a randomly selected retrieval location in the SR.

The expected travel time E ik (t), corresponding to the k th condition is equal to the next expression:

( ) max.( , ) 0 (1 ( )) x y T T ik ik E t F t dt = - ∫ (6)
For a more detailed insight into the statistical analysis of travel time considering the real operating characteristics of the S/R machine, see the research of [START_REF] Vössner | Spielzeit Berechnung von Regalförderzeugen[END_REF], [START_REF] Hwang | Travel time models considering the operating characteristics of the storage and retrieval machine[END_REF], [START_REF] Lerher | Model for designing of Automated Storage and Retrieval Systems[END_REF] and [START_REF] Ritonja | Spielzeitberechnung von Bedienstrategien von Regalbediengäreten mit Mehrfach-Lastaufnahmemitteln[END_REF].

Analytical analysis of travel time in the double-deep AS/RS

In the case of double-deep AS/RS, the average travel time for dual command cycle is enlarged for the rearrangement of the blocking TUL to the nearest free storage location in the SR. When developing the proposed analytical travel time models for double-deep AS/RS, the assumptions presented in FEM 9.851 guideline, have been considered. The FEM 9.851 guideline introduces the condition that the rearrangement of the blocking TUL can occur during the storage and retrieval processes. According to the presented storage strategy the storage process in the first or in the second storage lane, the TUL will always be first stored in the second storage lane. When all storage locations in the second storage lane are full, the storage in the first storage lane begins. According to the latter, the possibility of the rearrangement of the blocking TUL is eliminated. On the contrary, in the case of retrieval process the access to the second storage lane might be blocked by the blocking TUL in the first storage lane (a special case of retrieval). The problem can be solved by rearranging the blocking TUL to the nearest free storage location in the SR by using the Euclidian distance.

The rearrangement of TUL is performed by the next sequence (see Fig. 1): picking up the blocking TUL from the first storage lane of the SR (single-depth); repositioning the S/R machine to the nearest free storage location; setting down the formerly blocking TUL in the first or the second storage lane of the SR (single-or double-depth); repositioning the S/R machine to the earlier retrieval location; picking up the TUL to retrieve from the second storage lane of the SR (double-depth).

Figure 1. The procedure of rearranging TUL.

The rearranging of blocking TUL to the nearest free storage location is influenced by: -Fill-grade factor α, which has an affect on the rearrangement distances and the number of rearrangements.

-Storage strategies.

The definition of the rearrangement distance

The average rearrangement distance and consequently the average travel time to the nearest free storage location in the SR, using the randomized storage assignment rule, is influenced by the fill-grade factor α. The average rearrangement distance increases by increasing the fill-grade factor α. The travel time for the rearrangement represents only a small part of the cycle time, therefore it is possible to use the approximation for all storage location in the SR. In the proposed analytical travel time models for the calculation of the average rearrangement distance, the FEM 9.851 guideline and the results of simulation modelling analysis [START_REF] Ritonja | Spielzeitberechnung von Bedienstrategien von Regalbediengäreten mit Mehrfach-Lastaufnahmemitteln[END_REF] have been used. The expected value of the rearrangement distances E x in the horizontal and E y in the vertical direction is equal to the next expressions:

( ) ( )

1 1 3 1 1 1 3 1 x x y y L E n H E n α α = ⋅ - = ⋅ - (7)
The fill-grade factor α is determined by the next relationship:

( )

TUL TUL stored x y total n n n α = ⋅ (8)

The influence of the fill-grade factor α on the rearrangement of the TUL

3.2.1

The introduction of the storage strategy with the fill-grade factor α [0, 0.5]

The storage strategy with the fill-grade factor α [0, 0.5] (see Fig. 2) takes into consideration that:

-the TUL will always be first stored in the second storage lane of the SR, -when all storage locations in the second storage lane of the SR are full (α > 0.5), the storage in the first storage lane of the SR begins, -the possibility of the rearrangement of the blocking TUL is eliminated during the storage and the retrieval processes.

For the second storage lane of the SR equals:

The probability that the storage location in double-deep AS/RS is occupied is equal to the next expression:

.

2 Occ P α = (9)
The probability that the storage location in double-deep AS/RS is empty is equal to the next expression:

1 2 Free P α = - (10)
For the first storage lane of the SR equals:

The probability that the storage location in double-deep AS/RS is occupied is equal to the next expression:

. 0

Occ P = (11)
The probability that the storage location in double-deep AS/RS is empty is equal to the next expression: According to the value of the fill-grade factor α, which can be in the range from [0, 0.5] two different cases of the storage and retrieval processes (see Fig. 3) can occur during the working cycle [START_REF] Ritonja | Spielzeitberechnung von Bedienstrategien von Regalbediengäreten mit Mehrfach-Lastaufnahmemitteln[END_REF].

Figure 3. The two different cases of the storage and retrieval processes.

-CASE 1 (the first and the second storage lanes of the SR are both free)

The probability P 1 that the storage locations in the first and in the second storage lane of the SR are empty is equal to the next expression:

1 1 2

Free Free

P P P α = ⋅ = - (13)
-CASE 2 (the first storage lane of the SR is empty, while the second storage lane of the SR is occupied)

The probability P 2 that the storage locations in the first storage lane of the SR are empty and occupied in the second storage lane of the SR is equal to the next expression: The storage strategy with the fill-grade factor α [0.5, 1] (see Fig. 4) takes into consideration that:

-because all storage locations in the second storage lane of the SR are full (α > 0.5), the storage in the first storage lane of the SR begins, -the possibility of the rearrangement of the blocking TUL is eliminated during the storage process, -because the second storage lane of the SR might be blocked by the blocking TUL in the first storage lane of the SR, the rearrangement of the blocking TUL to the nearest free storage location during the retrieval process is introduced.

For the second storage lane of the SR equals:

The probability that the storage location in double-deep AS/RS is occupied is equal to the next expression:

.

1 Occ P = (15)
The probability that the storage location in double-deep AS/RS is empty is equal to the next expression:

0 Free P = (16)
For the first storage lane of the SR equals:

The probability that the storage location in double-deep AS/RS is occupied is equal to the next expression:

. 2 1

Occ P α = - (17)
The probability that the storage location in double-deep AS/RS is empty is equal to the next expression: According to the value of the fill-grade factor α, which can be in the range from 0.5 to 1, two different cases of the storage and retrieval processes (see Fig. 5) can occur during the working cycle [START_REF] Ritonja | Spielzeitberechnung von Bedienstrategien von Regalbediengäreten mit Mehrfach-Lastaufnahmemitteln[END_REF]. -CASE 2 (the first storage lane of the SR is empty, while the second storage lane of the SR is occupied)

The probability P 2 that the SR locations in the first storage lane of the SR are empty and occupied in the second storage lane of the SR is equal to the next expression:

2 .

2 2

Free Occ

P P P α = ⋅ = - (19)
-CASE 3 (the first and the second storage lanes of the SR are both occupied)

The probability P 3 that the SR locations in the first and in the second storage lanes of the SR are occupied is equal to the next expression: According to our assumption in chapter 3.2.1, the probability of rearrangement during the storage and the retrieval processes is equal to the following expression:

-The storage process

( ) 0 R storage P = ( 21
)
-The retrieval process

( ) 0 R retrieval P = (22)
Because of the assumption that the probability of the rearrangement during the storage and the retrieval processes is equal to zero, the probability P R of the rearrangement during the dual command cycle equals 0.

3.3.2

The fill-grade factor α [0.5, 1]

According to our assumption in chapter 3.2.2, the probability of rearrangement during the storage and the retrieval processes is equal to the following expression:

-The storage process

( ) 0 R storage P = ( 23
)
-The retrieval process During the retrieval process and the random or first come -first serve (FCFS) storage policy, the rearrangement of the blocking TUL (see Fig. 6) will occur. It must be emphasised that the randomized storage assignment rule in the case of an infinite number of runs is equal to the FCFS storage policy. The probability of the rearrangement during the retrieval process is expressed by the relationship of the probability for the blockade (Case 3) and the sum of all probabilities P i of the retrieval locations.

( )

3 ( ) 2 3 2 1 2 1 2 2 2 2 2 1 2 R retrival P P P P α α α α α - - = = = + - + - (24)
Because of the assumption that the probability of the rearrangement during the storage process is equal to zero, the probability of the rearrangement during the retrieval process is equal to the following expression:

Single storage operation

For a single storage operation (Fig. 7), the single command cycle consists of the time of picking up the TUL at the pickup/deliver (PD) station, travelling to the destination position and setting down the TUL in the second storage lane of the SR, returning empty to the start position and setting down the TUL at the PD station. The cycle time is increased by the necessary control time, which stands for the waiting time of processing programs, sensor signals and the time of stabilization of the S/R machine. The control time could be associated with the load handling time. Therefore it is not directly included in our proposed models.

Single retrieval operation

The time of the single retrieval operation is developed inversely due to the storage operation. Because of there is no rearrangement in the single command cycle the expected single command cycle time E(SC) in case of retrieval equals expression (26).

Dual command cycle (single storage and single retrieval in the cycle)

The dual command cycle (Fig. 8) involves both storage and retrieval operations simultaneously. The dual command cycle time consists of the time of picking up the TUL at the PD station, travelling to the destination position and setting down the TUL in the second storage lane of the SR, travelling empty to the retrieval ( ) ( ) ( )

1 1 2 , ,

Single command cycle (single storage or single retrieval in the cycle)

Single storage operation

For the single storage operation (Fig. 9), the single command cycle consists of the time of picking up the TUL at the PD station, travelling to the destination position and setting down the TUL in the first storage lane of the SR, returning empty to the start position and setting down the TUL at the PD station.

Single retrieval operation

For the single retrieval operation (Fig. 10), the single command cycle consists of the time of travelling empty to the destination position in the double-deep SR, retrieving the TUL from the first or the second storage lane of the SR, returning to the start position and setting down the TUL at the PD station. Because the TUL are stored in the first and in the second storage lanes, the access to the second storage lane might be blocked by the blocking TUL. When a blockade occurs, the S/R machine has to pick up the blocking TUL from the first storage lane and rearrange it to the nearest free position, which can be either in the first or in the second storage lane. Therefore, instead of the regular retrieval time, the additional time for the rearrangement is attached. The expected single command cycle time E(SC) equals the next expression: ). The probability P 1 , which stands for the condition that the TUL will be pickup/setdown from the first storage lane of the SR, is equal to:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 , 1 1 2 2 1 1 2 2 SC SC R 2 SC 2 2 2 2 i i PD p p R E E E E t E t P t P t E t P t P t α α + = + = + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅     (
( )

3 1 2 3 2 1 2 1 +2
2 2 2 2 1 2

P P P P α α α α α - - = = = - + - (30)
The probability P 2 , which stands for the condition that the TUL will be pickup/setdown from the second storage lane of the SR, is equal to:

( ) ( ) 3 2 2 2 3 2 3 2 2 2 1 1 +2 +2 2 2
2 2 1 2 2 2 2 1 2

P P P P P P P α α α α α α α - - = + = + = - + - - + - (31)
The expected single command cycle time E(SC) now equals:

( ) ( ) ( ) 1 , 1 2 1 2 2 1 1 SC 2 2 2 2 4 1 1 2 2 2 2 i i PD p p R E t E t t t E t t t α α α α α α α + -       = + ⋅ + ⋅ + ⋅               -       + ⋅ + ⋅ + ⋅                 (32)

Dual command cycle (single storage and single retrieval in the cycle)

The dual command cycle involves both storage and retrieval operations simultaneously (Fig. 11). The dual command cycle time consists of the time to pickup the TUL at the PD station, travel to the destination position and setdown the TUL in the first storage lane of the SR, travel empty to the retrieval position, retrieve the TUL from the first or the second storage lane of the SR, return to the start position and setdown the TUL at the PD station. During the retrieval process rearrangement can occur.

( ) ( ) ( ) ( ) 1 1 2 , 1 , 1 2 M 1 2 2 1 1 DC 2 2 2 2 4 1 1 2 2 2 2 i i i i PD p p p p R E t E t t E t t t E t t t α α α α α α α + + + -       = + ⋅ + + + ⋅ + ⋅               -       + ⋅ + ⋅ + ⋅                 (33) 1 2 , i i p p t + +
the travel time from the storage position p i+1 to the retrieval position p i+2 (sec.).

Simulation model of double-deep AS/RS

To facilitate the evaluation of the performance and comparison of the proposed analytical travel time models for double-deep AS/RS, the discrete event simulation has been employed. The simulation model of doubledeep AS/RS consists of a single picking aisle, double-deep SR between picking aisle, S/R machine, I/O location, accumulating conveyors and it has been built using computer software AutoMod (Applied Materials AutoMod 2008).

The simulation model begins with the process which marks all storage compartments in the SR according to the prescribed storage area. After creating the list of free storage locations, the first TUL, which is situated in the I/O location and lies in the lower left-hand corner of the picking aisle enter the simulation model. Further on, the TUL receives a sign which belongs to the i th SR location. The S/R machine picks up the TUL from the I/O location, loads it into the hoisted carriage, and transfers it simultaneously in the horizontal and vertical directions to the i th SR location. For the storage operation, the randomized storage policy has been used and the condition that TUL will be stored first in the second SR lane has been applied. In this case there are no rearrangements for storages, and the probability of rearrangement equals to zero. Next, the TUL that has been stored is put on the waiting list by a computer (computer data base), where it waits for the retrieval operation.

For the retrieval process the FCFS request selection rules have been used. After the storage operation in the i th SR location, the S/R machine travels to the retrieval location to the j th SR location. During the retrieval process the access to the second storage lane of the SR might be blocked by the blocking TUL in the first storage lane of the SR(a special case of retrieval). In this case the S/R machine rearranges the blocking TUL to the nearest free storage location in the SR, which is selected by the application of euclidean distance. Next, the S/R machine travels back to the retrieval position, loads TUL into the hoisted carriage and moves it simultaneously in the horizontal and vertical directions to the I/O location, where the TUL departs the system. The dual command cycle is therefore associated with the time for storage and retrieval of TUL and additional time necessary for the rearrangement of the blocked TUL. As a performance measure the average dual command cycle time and consequently the throughput capacity have been used. The throughput capacity represents the number of transactions (stores and retrievals) that the S/R machine can perform in a given time period in the double-deep AS/RS. The throughput capacity is inversely dependent on the average travel cycle time. Therefore the average throughput capacity for the SC and DC in the double-deep AS/RS is given as follows:

(

) [ ] ( ) = (DC) 1 (SC) 0,1 2 M r AT T r T r T r AT λ η + - = = ⋅ (34)
where AT is average travel time [sec.]; r is the proportion between SC and DC; T [h] is the analyzed time; η stands for the efficiency of the S/R machine. The double-deep AS/RS is part of the project of designing automated warehouse for a producer of starter batteries. Because of the customer's demand for the high volume utilization of the SR, the double-deep AS/RS has been proposed. The demanded SR capacity Q was estimated to 2800 pallet places and the throughput capacity λ to 60 single command cycles per hour. The estimation of Q and λ was developed according to the projection of previous production capacity and forecasting capacities in the future. The basic TUL is based on the euro type of palette, with the average height of 1400 mm. Because of the heavy weight of starter batteries, the TUL weighs around 2000 kg. The latter was a very important parameter in designing the AS/RS. Because of the limited layout for the warehouse building (relatively short length of the building), the designers agreed to take advantage of the height of the SR. Therefore, the appropriate construction of the SR with the special requirements for the upright frames and rack beams that are able to hold out the weight of eighteen levels in the height has been selected. Also each storage compartment was equipped with the special traverse beam under the supports on palette. The special S/R machine for heavier loads was selected. The S/R machine has special telescopic load attachments that can pickup or setdown the TUL in the single-or doubledeep storage lane.

According to the project constraints and customer demands, the following data for the analysis have been applied: L = 22 m, H = 30 m, n x = 20, n y = 18, b w = 1100 mm, b d = 1200 mm, a w = 1500 mm, the I/O location (x = -1000, y = 1000) mm, v x = 1.5 m/s, v y = 1 m/s, a x + = 0.5 m/s 2 , a y + = 0.5 m/s 2 , a x -= 0.5 m/s 2 , a y -= 0.5 m/s 2 , v t = 0.7 m/s, t PD = 3.43 sec., t 1 = 3.43 sec. and t 2 = 6.86 sec.

Analyses and evaluation of results

The modified dual command cycle times and throughput capacities for the selected double-deep AS/RS, which are presented in the following Tables 1, 2, 3 and 4, are given on the basis of the performed analyses. Analyses have been conducted for the chosen AS/RS mentioned before, under the condition of possible rearrangement of TUL during the retrieval process. In order to receive the best representative average travel time, the simulation results correspond to a large number of runs for every single variant (α = 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.95) of the double-deep AS/RS. According to the simulation results presented in Tables 1,2, 3 and 4, the performance comparison between the proposed analytical models has been analysed. Table 1. The modified dual command cycle time analysis for the proposed double-deep AS/RS.

According to the results in the Table 1, the proposed analytical travel time models for the double-deep AS/RS, demonstrate good performances with regard to the results of simulation analysis. According to the increased fill-grade factor α, an increasing trend of the modified dual command cycle time can be noticed for both proposed models and the simulation model. This relationship can be explained by the increasing length of the rearrangement distances, which causes the enlargement of the rearrangement time and consequently the cycle time. Because the throughput performance is inversely dependant on the cycle time, the decreasing trend of throughput capacities with regard to the increased fill-grade factor α, can be noticed.

In general, according to the difference between the proposed analytical travel time models and the simulation model, small deviations in the range of -2.82 % are noticed. The latter show that the proposed analytical travel time models demonstrate satisfactory deviations of modified dual command cycle time and throughput performances for the selected double-deep AS/RS.

Because AS/RS usually have the fill-grade factor α = 0.85, 0.90 and 0.95 the analyses in the Tables 2, 3 and 4 correspond to the selected double-deep AS/RS with the chosen α. According to the demanded SR capacity Q and throughput capacity λ, the calculated single command cycle times (single storage operation) and modified dual command cycle times (single storage and single retrieval operation) and the throughput performance of the selected double-deep AS/RS correspond to the desired 60 single command cycles per hour. The throughput performance of the single command cycle in the case of proposed analytical travel time models is λ(SC) = 69 TUL/hour, whereas is the throughput capacity of simulation model λ(SC) = 70 TUL/hour. The deviation in the throughput performance between the proposed analytical model and simulation model, for the selected double-deep AS/RS (α = 0.85, 0.90 and 0.95), is in the range of -1.43 %. According to the results of the modified dual command cycle and the throughput performance, the deviation between the proposed analytical model and simulation model becomes higher and is in the range of 2.35 % (α = 0.95), which is still satisfactory. It must be emphasised that the demanded throughput performance λ also can be increased by utilizing both the single and dual command cycles, which is expressed in the Tables 2, 3 and 4 with the factor r. For example if the factor r = 0.6 (α = 0.95), the throughput performance is increased from 69 (70) to 79 (78) TUL/hour. The maximal throughput performance is expressed with the factor r = 1, which means that only dual command cycles are utilized.

Due to the demanded rack capacity, two double-deep AS/RS were chosen, which give us the desired rack capacity Q = 2880 pallet places.

Conclusions

In this paper, the proposed analytical travel time models for the unit-load double-deep AS/RS are presented. In contrast to other researchers who have been occupied in their analytical travel time models with uniform velocities only, the real operating characteristics of the S/R machine and FEM 9.851 guideline have been used in the proposed analytical travel time models. In the proposed models it has been assumed that according to the single shuttle system (only one TUL could be placed on the hoisted carriage), the rearrangement during the storage process does not occur. On the contrary, in the case of retrieval process the access to the second SR lane might be blocked by the blocking TUL in the first storage lane. The problem can be solved by rearranging the blocking TUL to the nearest free storage location in the SR. Thus, considering the randomized storage assignment rule and the above mentioned conditions, the proposed analytical travel time models have been developed.

The cycle time and the performance capacity of the selected double-deep AS/RS have been examined in order to investigate the efficiency of the proposed models in comparison with the simulation model of doubledeep AS/RS. In general, according to the difference between the proposed analytical travel time models and the simulation model, small deviations in the range of -2.82 % are noticed. Therefore the proposed analytical travel time models demonstrate good performances for designing the double-deep AS/RS and could be a very useful tool for the professionals in practice.

Figure 2 .

 2 Figure 2. The layout of the double-deep SR with the fill-grade factor α [0, 0.5].

  The introduction of the storage strategy with the fill-grade factor α [0.5, 1]

Figure 4 .

 4 Figure 4. The layout of the double-deep SR with the fill-grade factor α [0.5, 1].

Figure 5 .

 5 Figure 5. The two different cases of the storage and retrieval processes.

  The probability of rearrangements during the storage and retrieval processes 3.3.1 The fill-grade factor α [0, 0.5]

Figure 6 .

 6 Figure 6. The rearrangement in the double-deep AS/RS

  Single command cycle (single storage or single retrieval in the cycle)

Figure 7 .

 7 Figure 7. The course of single storage operation when λ [0, 0.5].

  the TUL from the second storage lane, returning to the start position and setting down the TUL at the PD station.

Figure 8 .

 8 Figure 8. The course of dual command cycle when λ [0, 0.5].

Figure 9 .

 9 Figure 9. The course of single storage operation when λ [0.5, 1].

Figure 10 .

 10 Figure 10. The course of single retrieval operation with rearranging TUL when λ [0.5, 1].

PP

  from the start position p i to the destination (retrieval) position p i+1 (sec.), 1 the probability of retrieval in the first storage lane of the SR, 1 t the pickup/setdown time in the first storage lane of the SR (sec.), 2 the probability of retrieval in the second storage lane of the SR, 2 t the pickup/setdown time in the second storage lane of the SR (sec.), R t the travel time from retrieval position to rearrangement position R (sec.

Figure 11 .

 11 Figure 11. The course of modified dual command cycle when λ [0.5, 1].

Figure 1 .

 1 Figure 1. The procedure of rearranging TUL.

Figure 2 .

 2 Figure 2. The layout of the double-deep SR with the fill-grade factor α [0, 0.5].

Figure 3 .

 3 Figure 3. The two different cases of the storage and retrieval processes.

Figure 4 .

 4 Figure 4. The layout of the double-deep SR with the fill-grade factor α [0.5, 1].

Figure 5 .

 5 Figure 5. The two different cases of the storage and retrieval processes.

Figure 6 .Figure 7 .

 67 Figure 6. The rearrangement in the double-deep AS/RS

Figure 8 .

 8 Figure 8. The course of dual command cycle when λ [0, 0.5].

Figure 9 .Figure 10 .Figure 11 .

 91011 Figure 9. The course of single storage operation when λ [0.5, 1].

  have presented travel time models considering the

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y

Table 2 .

 2 Cycle time and capacity analyses of the proposed double-deep AS/RS with α = 0.85.

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y

Table 3 .

 3 Cycle time and capacity analyses of the proposed double-deep AS/RS with α = 0.90.

Table 4 .

 4 Cycle time and capacity analyses of the proposed double-deep AS/RS with α = 0.95.

Table 1 .

 1 The modified dual command cycle time analysis for the proposed double-deep AS/RS.

		Modified dual command cycle time	Throughput performance of DC M
	α	Analytical	(sec.) Percent	Simulation	Analytical	(TUL/hour) Percent	Simulation
		E(DC) M	error	T(DC) M	λ(DC) M	error	λ(DC) M
	0.55	51.69 * 71.27 **	1.16 ***	50.87 70.45	91	-1.09	92
	0.60	51.86 71.36	0.79	51.31 70.80	91	-1.09	92
	0.65	52.06 71.5	0.31	51.84 71.28	91	0.00	91
	0.70	52.26 71.69	-0.36	52.53 71.95	90	0.00	90
	0.75	52.50 71.94	-0.92	53.18 72.61	90	1.12	89
	0.80	52.79 72.26	-1.42	53.84 73.3	90	2.27	88
	0.85	53.14 72.66	-1.96	54.6 74.11	89	2.30	87
	0.90	53.64 73.21	-2.27	55.34 74.91	89	2.30	87
	0.95	54.52 74.16	-2.82	56.61 76.31	87	2.35	85

Table 2 .

 2 Cycle time and capacity analyses of the proposed double-deep AS/RS with α = 0.85.

			Cycle time			Throughput performance
			(sec.)				(TUL/hour)
		Analytical	Percent error	Simulation		Analytical	Percent error	Simulation
	E(SC)	47.19	(1.51) *	46.49	λ(SC)	69	(-1.43)	70
	E(DC) M	72.66	(-1.96)	74.11	λ(DC) M	89	(2.30)	87
	r		AT		r		λ(r)
	0.0	47.19	(1.51)	46.49	0.0	69	(-1.43)	70
	0.1	46.10	(1.22)	45.55	0.1	70	(-1.41)	71
	0.2	45.02	(0.93)	44.60	0.2	72	(-1.37)	73
	0.3	43.93	(0.62)	43.66	0.3	74	(0.00)	74
	0.4	42.85	(0.30)	42.72	0.4	76	(0.00)	76
	0.5	41.76	(-0.03)	41.77	0.5	78	(0.00)	78
	0.6	40.67	(-0.38)	40.83	0.6	80	(1.27)	79
	0.7	39.59	(-0.75)	39.89	0.7	82	(1.23)	81
	0.8	38.50	(-1.13)	38.94	0.8	84	(1.20)	83
	0.9	37.42	(-1.53)	38.00	0.9	87	(2.35)	85
	1.0	36.33	(-1.96)	37.06	1.0	89	(2.30)	87

Table 4 .

 4 Cycle time and capacity analyses of the proposed double-deep AS/RS with α = 0.95.

			Cycle time			Throughput performance
			(sec.)				(TUL/hour)
		Analytical	Percent error	Simulation		Analytical	Percent error	Simulation
	E(SC)	47.19	(1.51) *	46.49	λ(SC)	69	(-1.43)	70
	E(DC) M	74.16	(-2.82)	76.31	λ(DC) M	87	(2.35)	85
	r		AT		r		λ(r)
	0.0	47.19	(1.51)	46.49	0.0	69	(-1.43)	70
	0.1	46.18	(1.14)	45.66	0.1	70	(-1.41)	71
	0.2	45.17	(0.77)	44.82	0.2	72	(0.00)	72
	0.3	44.16	(0.38)	43.99	0.3	73	(-1.35)	74
	0.4	43.15	(-0.02)	43.16	0.4	75	(0.00)	75
	0.5	42.14	(-0.44)	42.32	0.5	77	(0.00)	77
	0.6	41.12	(-0.88)	41.49	0.6	79	(1.28)	78
	0.7	40.11	(-1.33)	40.66	0.7	81	(1.25)	80
	0.8	39.10	(-1.81)	39.82	0.8	83	(2.47)	81
	0.9	38.09	(-2.30)	38.99	0.9	85	(2.41)	83
	1.0	37.08	(-2.82)	38.16	1.0	87	(2.35)	85

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research

Acknowledgement

The authors of this paper would like to express a special thanks to all collaborators at the Faculty of Mechanical and Civil Engineering in Maribor and at the Institute of Logistic Systems in Graz and others colleagues who have in any way contributed to this manuscript.


Mohammad Al Yami

Roger I Grosvenor

Paul W Prickett

Al Yami

M Alyami

A microcontroller-based approach to monitoring pneumatic actuators

Keywords: FLEXIBLE ASSEMBLY, QUALITY Pneumatic actuator monitoring, pressure transient signal analysis, embedded microcontroller architecture, Digital Signal Controller (dsPIC)

This paper presents the development of a microcontroller-based process monitoring system that is capable of being embedded within high speed automated assembly systems. A generic architecture is presented to fully utilise the communication, data acquisition and signal processing attributes of a current generation microcontroller. The efficacy of this approach is illustrated by the development of an autonomous method in which the system acquires and analyses transient data related to the operation of a linear actuator. The performance of this system clearly identifies the potential of microcontroller based solutions as very powerful yet affordable real-time quality management tools.

The low costs associated with the implementation offer the prospect of affordable integrated quality management to a wide range of industries.

Recent advances in embedded microcontroller technology make it possible to consider that low cost solutions may be developed to monitor the operation of devices based upon the deployment of pneumatic actuators. This research has generated solutions that can support much needed quality management functions for applications, such as part transfer systems, where a number of pneumatic devices are operating continuously in confined spaces and hazardous conditions. This paper describes the current findings of this research activity and describes the approach taken to engineer such a system. Pneumatic linear actuators or cylinders are used in many manufacturing operations, including the automotive, manufacturing and food packaging industries. The main purpose of deploying such systems is to perform position control and enable parts handling, especially in robotic manipulators, end effectors and grippers. Such devices and systems often exhibit highly nonlinear characteristics mainly due to the compressibility of air and the variability of motion associated with the "stiction" which arises in cylinders. This makes achieving accurate dynamic position and stroke control difficult. These devices therefore tend to be limited to pre-set end position tasks. In these circumstances problems may arise due to part misalignment, incorrect workpiece selection, variability in air supply pressure and the obstruction of motion due to foreign objects.

The parameters that may be of interest when approaching the monitoring of such systems include the number and type of sensors needed, the nature of the computational resources required and the operating variables to be considered. Some work has been conducted into aspects of monitoring and controlling these devices, including research considering how the compressibility of air introduces a dead time (or delay) in the system's response that makes accurate control more challenging [Van Varseveld andBone 1997 andWang et.al 2004]. Air losses in cylinders and transmission lines have been shown to add more barriers to successful control [Messina et.al 2005].

These factors can make it difficult to achieve accurate position control without the use of added sensors. These sensors, and the controller needed to manage their operation, can be expensive.

The monitoring system outlined in this paper was developed based upon the data acquisition and processing capabilities of the current generation of microcontrollers. It was intended that the resulting system would be low cost, flexible and provide monitoring information for a range of applications and configurations. Advancements in microcontroller technology mean that current generation of devices can provide impressive levels of computational resources, as defined by processing power and computational speed, on a single device. The cost of such devices and their supporting circuitry typically vary between £50 and £300, depending upon the application being considered. This means that the development of a low cost distributed process monitoring system that offers real time diagnostic functionality can be considered. Previous experience indicates that investment in such a monitoring system will only be successful if it is reliable and can provide an acceptable cost-to-benefit ratio. In the case of the research described in this paper the attributes of the developed system, which include a plug-and-play capability, mean that it can provide a possible solution for a wide variety of monitoring applications.

Previous attempts have been reported based upon taking advantage of advances in low cost

computing resources to exploit the recent innovations in field bus systems, microprocessors and computing technologies [START_REF] Pu | Smart components-based servo pneumatic actuation systems[END_REF]. In this work the concept of intelligent component-based servo pneumatic actuation systems was advanced by designing templates for smart sensors, smart valves and smart actuators. It was proposed that limited intelligence can be embedded in such devices in order to provide information rather than raw data. These devices can then be integrated to form a smart pneumatic servo system capable of communication with the external world. process shutdowns resulting in the loss of production time and profits. The developed approach was signal-based, using parameters such as pressure and flow and employed an analysis methodology based upon wavelet decomposition. A pattern recognition technique was developed to diagnose unknown leakages and experiments were successfully carried out to test and verify the effectiveness of the proposed approach.

Another example of a fault detection and diagnostic system was developed for applications such as the mechanical systems operating pneumatic train doors commonly found in rapid transit systems [START_REF] Lehrasab | Industrial fault diagnosis: Pneumatic train door case study[END_REF]. These doors are often controlled by solenoid valves and faulty operation can be a significant source of delay in railway services. The research demonstrated how the health of the system can be determined using feature extraction methodologies. This included throw and activation time characteristics, spectral features of the door displacement profile as well as abstract features such as velocity profiles and pressure drop during the throw. Once a fault was indicated neural network models were utilised for diagnosis. The authors suggested the implementation of this approach in a distributed architecture and proposed that diagnostic results be integrated into the maintenance information system in order for a proactive maintenance regime to be produced.

Neural network enabled fault detection and identification was the basis of a system developed to manage actuator faults in a process control valve [START_REF] Karpenko | Diagnosis of process valve actuator faults using a multilayer neural network[END_REF]. A software package supplied by the valve manufacturer was used to communicate with onboard sensors and obtain its' position response under various operating conditions. Fault signatures associated with incorrect supply pressure, actuator vent blockage and diaphragm leakage were considered.

Experimental data was collected and neural networks trained, and tested. The authors claimed to be successful in the detection and identification of various magnitudes of the faults of interest.

The research outlined above supports the potential for developing low cost monitoring approaches that can be applied to pneumatically operated parts handling operations. However, most of the reported research solutions are not suited to such applications, either due to cost considerations or due to the time needed for diagnosis. This paper describes the development of a distributed process monitoring system which may be deployed to oversee operations based upon pneumatic actuators and illustrates its efficacy with an example application.

Monitoring System Architecture

The term "distributed system" is used here in to describe a system in which interconnected hardware or software components communicate and coordinate their actions. The main benefits of such systems include their robustness and reliability; since processing power is distributed the failure of a single element does not disable the entire system. Data can be maintained at different locations to further improve system reliability. Other attributes include functionality and scalability.

Since the system may incorporate various types of devices each element may be selected to optimise the function it is expected to perform. Additional task specific elements may be added as required. These attributes mean that the devices deployed in a distributed system can operate concurrently to undertake monitoring actions independently. Such actions must however be coordinated within suitably structured system architecture.

The Intelligent Process Monitoring and Management (IPMM) research group at Cardiff

School of Engineering has previously exploited the capabilities of the 8-bit microcontrollers in a range of monitoring applications; including the monitoring of machine tools [Amer et.al. 2006] and process plant [Ahsan et.al. 2006]. The advantages of such devices may be considered in terms of their low cost and ease of use. The limitations of such devices, most specifically measured in terms of their processing capabilities, may have previously restricted their application. However the current generation of microcontroller devices, such as those used in this research, has overcome such limitations. In particular the availability of the new more powerful microcontrollers and similar devices seems to offer an almost limitless potential in the engineering of product quality and process management and monitoring systems [Siddiqui et.al. 2007].

To support effective monitoring real-time information about the enactment of the process and the condition of selected machine components is needed. A fundamental aspect of the deployment of a monitoring system is data acquisition, which is normally enabled through the installation of various sensors and transducers. An industrial application may require a large number of such sensors. If this data is collected at a central location, communication infrastructure will have to be provided from every sensing element. This approach can lead to a complex communication network and result in a system that is hard to install and difficult to maintain.

Advances in wireless technologies have supported developments in this area, but the cost and data transmission limitations associated with such systems remains an important issue to consider. The handling of the data acquired from sensors in such applications tends to be very challenging. Data files can become very large and the communications infrastructure has to cope with the often continuous nature of much of the data. For example, the monitoring of a six station press line with a four stage part transfer system per station operating on a three second cycle, could result in some two million separate actuator motions per week. The effectiveness of the monitoring system may thus be compromised by the quantity of data to be acquired, processed and communicated. A modular, microcontroller-based, data acquisition and analysis system was therefore developed to provide a more applicable solution. The key aim in this system is the intelligent acquisition and analysis of data and the determination of any associated fault diagnosis at source, thus massively reducing data communication and storage requirements. the 16-bit dsPIC microcontrollers in the further development of this system. Their built-in digital signal processor and computational speed make them superior to the previous generations of microcontrollers, thereby promising considerable additional benefits to fault diagnosis.

Figure 1. IPMM Microcontroller based monitoring system architecture.

The Front End Node (FEN)

The key feature required in this approach was processing speed. The device selected for both the front-end node of the distributed process monitoring system had five (16-bit) timers; two of which can be paired to form a 32-bit timer if and when required. An input capture module, wellsuited for applications where the period or frequency measurement is required, is also available on In the developed approach any desired parameter can be connected to a suitably configured FEN. When processed the acquired digital data can be very quickly analysed using the same microcontroller to identify "pre-defined" known fault symptoms. If required the processed information can then be sent through the CAN bus to collaborating FENs. Signal acquisition and processing are thus performed in this layer of the monitoring system. It is important to state that data generated from each monitoring action will be analysed for possible faults and, if none are identified, the data is summarized and sent to a buffer. This retains data that can be interrogated should a fault condition occur, but, as more data is generated the previously analysed data which relates to normally enacted operations can be discarded.

Data Acquisition

The first step in the operation of the FENs is to acquire the required signals from different sensors and transducers. Various sensors are usually installed in the process or machine to perform such a task. In most cases the output measurement of a sensor requires signal conditioning to conform to the requirements of the data acquisition hardware. In the context of this research for example a typical pressure transducer output would be a 4-20 mA current signal. This signal had to be converted to voltage in the range 0 to 5 VDC as required by the dsPIC. The resulting signal then needs to be converted into digital format for processing using the ADC module embedded in the dsPIC. This employs the concept of successive approximation, which is the fastest and most commonly used technique in analogue to digital conversion. When using ADC some parameters have to be considered in order for a process monitoring and control system to be most effective and robust. Those of major importance include resolution; the available ADC converter has a 12-bit resolution, which provides 4096 levels of representation of the analogue signal. Another consideration is the sampling rate, which should be at least twice the maximum frequency content of the signal to avoid aliasing [START_REF] Smith | The Scientist and Engineer's Guide to Digital Signal Processing[END_REF]. For practical reasons, analogue signals are actually sampled at an even higher rate to account for the differences in performance between real-world ADC and the ideal one [START_REF] Huddleston | Intelligent Sensor Design Using the Microchip dsPIC[END_REF]. In this application the pressure signal was sampled at 2 KHz, which is five times the highest frequency content as empirically determined. Similar levels of capability were possible in the linearity, repeatability and range of the input signals.

The second types of signals that are of interest to monitoring systems are digital signals.

These can be acquired to provide information about discrete events in the process or machine such as the on/off state of a valve or a limit switch. Once these were interfaced with the microcontroller's timer modules it was possible to measure the time between discrete events.

The Connectivity node

The Connectivity node, which forms the second level in the distributed monitoring system architecture shown in Figure 1, has two functions. Firstly it is required to co-ordinate FEN activity in cases where the fault detection process proves to be challenging. Such co-ordination is critical under circumstances which require that information from various FENs be shared in order to reach a conclusive decision about the health of monitored parameters. For instance, if a node in a pneumatic system determines that the air pressure is too low, a message may be sent to notify other nodes in the system that may mistake the consequences of low pressure on the element they are monitoring as a fault. This can minimise the number of false alarms generated. In the deployed system possible faults and/or the associated data from various front-end-nodes can be combined and analysed. It's believed that eventually all remaining "known" fault conditions can be detected at this level.

The second function is to provide the communication link with the outside world. The adopted Ethernet based solution was implemented in a modular fashion following the TCP/IP protocol. It was thus designed to be independent of operating systems and to be capable of cooperative multitasking. This level is therefore used to provide a link between the FENs and a more powerful computer residing in level three of the system. Confirmed faults and associated operational information can be communicated to interested users and management functions embedded at level three for action and storage. In this way further analysis tools and expert-user knowledge can be deployed to identify the occurrence of "new" faults as they arise. Any new faults thus detected and diagnosed together with steps aimed at subsequent fault recognition may then be added to the list of known faults, and the developed detection process added to the capabilities of the FENs.

In practice the second level of the architecture shown in Figure 1 acts as a service level by providing and managing these communication tasks. Since the high performance microcontroller selected as the FEN module had the capacity to undertake these tasks it was determined that level two activities could be incorporated into the FENs. As such the FEN that first detects a possible fault condition assumes the role of the Connectivity node, and oversees all level two functions. All FENs can act in this way, providing a robustness and flexibility that takes full advantages of the capabilities of the deployed microcontroller devices. The resulting low-cost monitoring system has excellent capabilities in terms of signal acquisition and processing, a high level of integration, processing power, and communication facilities. Section three of this paper presents an example application of this system.

Level Three functions

Higher level management functions are undertaken at level three of the system. These functions may be undertaken locally or remotely. They will include the diagnosis of faults that require more advanced tools, and the continuing development of monitoring capabilities based upon the accrued data and information gathered from the deployed microcontrollers. It is important to note that any remote user, with the correct level of authority, may access any of these nodes directly. This supports the ability to monitor device operation in real time and provides access to all buffered data to support fault diagnosis. This facilitates the continuous improvement of the diagnostic ability of each node and of the overall system. In the application under consideration in this research the conditioned pressure transducer signal was connected to the ADC converter and sampled at a rate of 256 samples-per-second. The ADC was configured for one sample per interrupt, and its clock was derived from the system's oscillator. Data was transmitted as soon as a value becomes available. One of the microcontroller's digital outputs was used for the switch controlling the solenoid valve. An electronic switch was designed to control the operation of the valve. A 15V DC supply is used to power the solenoid valve. A simple control algorithm was implemented to perform this testing. LEDs on the expansion board were used to represent the status of the valve and to indicate faults to the operator whenever they occur. The output sample from the ADC was scaled for an on-board LCD screen. Using the built in UART2 communications module data was transmitted to a PC allowing Microsoft Excel to be used for initial data analysis to develop the monitoring system. The same link was subsequently used to evaluate the effectiveness of the monitoring system in determining the health of the process. In order to achieve the required speed of response it was determined to base the approach on transient events.

The linear actuator used was a high speed precision device with a stroke of up to 100mm able to apply loads of up to 200 N. Precise adjustment of the mechanical end-position of the slide motion was possible. To facilitate the initial calibration tests this actuator was initially fitted with two plug-on proximity sensing units to indicate the defined actuator end-position. The sensors used on this rig operate with a supply voltage ranging from 8 to 30 VDC, with a maximum load current equal to 200 mA.

The operating pressures used for the testing ranged from 3 to 7 bar. The intention of this research was to produce a monitoring system that operates at any pressure within this range. This accommodates any possible set-up of the system and allows for localized changes in supply pressure in any potential implementation. The experimental procedure adopted in this work initially set the air supply pressure to a series of specific values. A set of test pieces of known dimensions were used to restrict movement to a known end position. The calibrated test piece was placed to limit the stroke and the end position was measured. At a given supply pressure, the time taken by the slide unit to reach an object was then measured. A relationship between the travel time and end of stroke was then realized. In this way, a time based monitoring system was developed. If the travel time at a specific supply pressure and intended end position does not match to a defined tolerance the pre-set value, assuming the same operating conditions, a faulty situation is indicated to the operator.

Signal Acquisition and Analysis.

To develop a robust and flexible monitoring solution, the system was evolved through three stages. Initially two limit-switches were used to monitor the home and end positions of the actuator. This provided details of stroke times and allowed the initialization of appropriate data acquisition and analysis tools. The next step removed one sensor and the pressure response at the inlet of the The data leading to the development of the technique capable of identifying the slide end position or the object size was initially acquired using the microcontroller. The output signal from the pressure transducer was converted into the correct format and the pressure samples were recorded and stored in an array. Data was then transmitted to a PC for analysis. This approach monitored only the pressure transient at the inlet to the actuator's cylinder. In this way, the cost of the monitoring system is reduced. In addition to monitoring actual actuator travel it was anticipated that the pressure signal measurements would also identify any faults arising during an operation.

Figure 3 illustrates the pressurization/actuation cycle for a test conducted at 5 bars with a 20mm test piece in position. It is typical of such tests and shows the effect of the response time of the solenoid valve, which causes a delay in actuation from the trigger point (Time "0" on the figure). Once the valve is triggered, it can be seen that air pressure takes some time to build up to provide sufficient force to overcome friction and push the slide piston from its home position. The transient overshoots before starting to settle during the slide motion; once it reaches the test piece resistance to motion is encountered leading to a decreasing oscillation in the pressure signal, which dies out with time. As soon as the valve receives the signal to close, air exits the cylinder to the atmosphere depending on the valve's response time and the pressure falls rapidly to zero. In order to simplify the monitoring task it was desirable that the sample peak of the pressure signal should be used to reference the effective start of the motion. It was observed from the calibration tests using the limit sensors that the sample peak always occurred a fixed time after the actual start of the motion. The actual elapsed time was found to vary in a linear fashion with test pressure. This behaviour effectively "fixed" the start point of the motion sensing procedure to the occurrence of the peak pressure signal.

The second point needed to establish travel time must clearly correspond to the instant at which motion ceases, defined in this work as the end position. For clarity in Figure 3 the high frequency component of the pressure signal has been smoothed using a moving average filter. A filtering process was also deployed on the raw signal to extract the dominant component information.

Careful investigation of responses for different end of stroke positions at each pressure identified that the squared rate of change could be used to identify the motion end point. Figure 3 again illustrates the procedure developed. The squared rate of change plot exhibits a clear peak corresponding to contact with the test piece. By establishing a threshold the designated "contact point" can easily be determined. Once again, through the initial calibration of this motion using end position sensors, good correlation was found between the established threshold point and the actual motion end point. The threshold value is shown in Figure 3 at 400 for a test at 5 bar This threshold was used except for pressures above 4 bar; the threshold below four bar was 250 to 300.

The microcontroller device deployed in this research was selected to provide the processing power and mathematical capability needed to identify both the start point and end point from the two samples and complete the analysis of travel times fast enough to facilitate effective process monitoring. This is a relatively simple procedure; the travel time is computed as the difference between contact time and home position time. In all tests the sampling rate used was 2 kHz. This procedure was applied for each supply pressure acting upon multiple objects.

Curve-fitting procedures were developed to obtain a surface capable of acting as a process model using a non-linear least squares technique to fit the actual data. Figure 4 shows the surface representing the resulting travel time measurements. The concept being developed in this research is to model this surface to allow predicted travel times to be generated for any combination of pressure and end position. Where, x is the end position in millimetres, y the applied pressure in bar, and z the travel time in milliseconds. The modelling procedure was found to converge after eight iterations at which point the parameters were estimated. The model was then exported to a more powerful mathematical modelling process to tune the parameters so that the best possible fit is achieved with a single set of parameters per surface. In the set up presented here the fitting parameters obtained were: A =-102.3, B = -0.53, C=-0.43 and D = 0.9.

The actual surface and the model were found to correlate well. Their computed correlation coefficient is 0.998, which signifies the goodness of the model performance. The model performs well in the estimation of travel time as compared to the time obtained from information extracted from the pressure transient.

Monitoring System Development

The system outlined above was applied to the monitoring of actuator operations running at rates of four cycles per second. The maximum motion tested was ±100mm, and it was found that the actuator end position could be determined with a precision of 1mm. Hundreds of cycle tests were undertaken for each of eight different end positions at a number of known pressures. In each case the end position was correctly assessed by the system before the actuator returned to the "start" position. It was thus established that the system had met an important requirement; that diagnosis of an error should be possible before the commencement of the next cycle. These tests established that the system was able to operate flexibly with different end positions, which reflects the needs of "pick and place" production systems.

In order to deploy the system within a production environment it is proposed that an operator will initially supervise a number of test cycles to calibrate the system to introduce a new product or set up and if required supervise the adjustment to the estimation parameters to suit the application in hand. To test this facility, actuator operations were undertaken at a series of "intermediate" pressures, i.e. 4.75 and 5.75 bar, for which no previous tests had been performed.

Since the performance surface for the actuator was embedded within the microcontroller it was possible for the system to match the anticipated performance with that measured to indicate satisfactory operations. This procedure was undertaken at level one of the deployed monitoring system. At this level the operator communicates directly with the dsPIC via simple controls.

Operator involvement was necessary in these initial tests to effectively establish the calibration of the new set-up by confirming that a correct operation had occurred. It was found that between ten and fifteen such cycles were sufficient to position the new set-up on the existing surface, following which unsupervised operation could continue. It should be noted that, once such an activity has been enacted, the results are added to the existing surface information and the activity does not have to be repeated. This is vital in a production environment, where several process variations may be normally present. Using this system each variation will be captured upon its first implementation and saved for future access. Similar actions were applied to the introduction of "new" end positions.

In many industrial settings the same operator can be required to oversee several elements of the process. Using this system it is possible that operator attention can be immediately drawn to any faults arising in the processes in real time so that prompt action can be taken, thus reducing operational cost and optimising performance. When needed to, for example following the installation of a new or replacement actuator, the operator can also interact with the system to redefine surface parameters and to manage the integration of the entire monitoring function based upon the collective expertise of each element retained within the system memory. This local control is represented by level two in the architecture, through which access may be gained to previously created performance surfaces stored within the management level PC. This ensures that the monitoring of any re-configured pneumatic systems can benefit from previously acquired performance surface information relating to the actuator hardware deployed. This facility is also important if more advanced fault detection and process management tools are to be deployed. The architecture facilitates the adoption of a "plug and play" facility, allowing the system to expand as required and supporting a flexible approach to process monitoring. This allows the surface models embedded within the devices to be continuously improved to accommodate different process setups, allow for different actuators etc. Fault diagnosis at this level can also help the development of improved process design, operation and management.

The research reported in this paper supports the deployment of a pressure based fault diagnosis system as a potential solution to monitoring the performance of any parts handling systems that are based upon linear pneumatic actuators. Initial tests have shown that the approach is both flexible and robust and can support reliable fault diagnosis. Most importantly the processing speed and power of the deployed microcontrollers means that this diagnosis can be accurately made in real time. In the tests outlined above diagnosis was achieved for cycle times of 0.25 seconds. In practice the microcontroller at the heart of this system operates at the micro-second level and can respond much faster than this if needs be. This suggests that the approach can accommodate the needs of many such implementations, potentially including high speed production processes. It also indicates that a single node may actually be used to monitor a number of linked actuator actions, with the individual performance surfaces being accessed as appropriate. Further investigations into the implications of these findings are ongoing but the expectation is that a single module will be capable of monitoring the operation of a complete transfer system containing multiple actuators.

  An analytical fault detection and diagnosis strategy for pneumatic systems was introduced[START_REF] Li | Analytical fault detection and diagnosis (FDD) for pneumatic systems in robotics and manufacturing automation[END_REF] with the intention of preventing the failure of devices that can cause plant or

  Another important objective of this research was to develop and deploy data processing techniques capable of monitoring the operation of a particular machine function or activity, whilst keeping the number of added electronic components and sensors to a minimum. The hardware architecture developed in previous IPMM research is shown in Figure1. It was decided to deploy

  this chip. The microcontroller offers several I/O ports supporting multiple serial and parallel communication protocols. In this research communication between the nodes was supported by the adoption of a Controller Area Network (CAN) infrastructure which is employed in many areas of industrial automation. The CPU of this device has a 16-bit (data) modified Harvard architecture. It provides 144Kbytes of program memory, 4Kbytes of data EEPROM memory. It's possible to execute all instructions in a single cycle. The architecture supports program loop constructs through the use of DO and REPEAT instructions, yielding no program overhead. The CPU supports various flexibleaddressing modes to meet compiler needs; for most instructions the devices have the capability to perform a data (or a program) memory read, a data memory write and a working register (data) read in a single instruction cycle. The essential feature of the acquisition process supporting this development is that analogue signals have to be converted into a more convenient format so that they can be analysed in a meaningful and efficient manner as near to their source as is practical. This is achieved by means of the on board 12-bit (16 channel) analogue-to-digital converter.

  The test rig designed and constructed to research the development of this monitoring method is shown in Figure2. The Air Preparation unit (A) conditions the air by trapping moisture, removing impurities and adding lubrication. It also contained a regulator to maintain the supply pressure at a constant level. The Solenoid Valve (B) was chosen due to its high flow capacity, response speed, low power consumption and long life expectancy. The Pressure Transducer (C) measures the line pressure of the air supplied from the Air Receiver (D). The pressurised air is supplied to the Actuator (E), through the Solenoid Valve. The monitoring functions are integrated into the development board (F).

Figure 2 .

 2 Figure 2. Linear Actuator Test Rig.

  and analysed. The patterns associated with the operation of the actuator were then used to provide potential performance indicators. Finally, the pressure transient signal alone was monitored.

Figure 3 .

 3 Figure 3. Travel time computation at 5 bar using a 20mm test piece.

Figure 4 .

 4 Figure 4. The generated surface relating travel time, end position & pressure.

  A., Amer W., Ahsan Q., Grosvenor R.I. and Prickett P.W. 2007. Multi-band infinite impulse response filtering using microcontrollers for e-Monitoring applications. Microprocessors and Microsystems, 31, 370-380. Van Varseveld,R.B and Bone, G.M. 1997. Accurate Position Control of a Pneumatic Actuator Using on/off Solenoid Valves. IEEE/ASME Transactions on Mechatronics, 2(3),195-204. Wang, J., Wang, J. D, Daw, N. and Wu, Q.H. 2004. Identification of Pneumatic Cylinder Friction Parameters using Genetic Algorithm. IEEE/ASME Transaction on Mechatronics, 9(1),100-107.ACKNOWLEDGEMENT:M. Alyami is a PhD student sponsored by the Royal Commission of Jubail, Saudi Arabia.

FormattedFigure 1 .

 1 Figure 1. IPMM Microcontroller based monitoring system architecture.

Figure 2 .

 2 Figure 2. Linear Actuator Test Rig.

Figure 3 .

 3 Figure 3. Travel time computation at 5 bar using a 20mm test piece.

Figure 4 .

 4 Figure 4. The generated surface relating travel time, end position & pressure.

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research


Henrik Ka

Lars Alfredsson

Maria Feychting

Anders Ahlbom

Don't split your data

Keywords: False positive, Bayes, Genome wide association

False positive findings are a common problem in whole genome association studies. In this commentary we show that nothing is gained by randomly splitting a data sample to two equal sized subsets, where the first data subset is used for explorative purposes and the other sub set is used to confirm the findings in the first subset. We compare the random splitting procedure to using the full data sample for analysis, by using a Bayesian perspective with consideration taken to prior probability of a false positive finding.

Results from one study should be replicated in other studies independent from the original study. This is generally accepted wisdom and serves as a safeguard towards various types of bias but also towards false positive findings and has been discussed earlier [START_REF] Thomas | The problem of multiple inference in studies designed to generate hypothesis[END_REF]. In this article we focus on the question of whether a study should be randomly divided into two different smaller studies (splitting procedure) of which the second is used to test whether positive results from the first can be replicated.

The splitting procedure is used in genome wide association studies in which recent advances in molecular technology has made it possible to test hundreds of thousands single nucleotide polymorphisms (snps) in one single case control study [START_REF] Satagopan | Two-stage designs for gene-disease association studies[END_REF]. The absence of a priori information about the functioning of most of the tested gene variants makes the proportion of false positive results very high. The splitting procedure is used in genome wide association studies as a method to avoid reporting false positive results, and is sometimes misconceived as being a replication. For more information regarding split procedure please see Duncan et al. [START_REF] Thomas | Methodological issues in multistage genome-wide association studies[END_REF].

We show here that one does not gain anything from dividing a data set into two subsets, but that one actually loses.

The risk of false positive result depends on the level of statistical significance, the statistical power and, seen from a Bayesian perspective, the a priori probability of the hypothesis [START_REF] Wacholder | Assessing the probability that a positive report is false: an approach for molecular epidemiology studies[END_REF]. The random splitting procedure does reduce the risk of false positive result but the reason is simply that the test criterion becomes stricter. With two tests to pass instead of one, the effective significance level for the ''sequence'' of the two tests is reduced to (0.05) 2 = 0.0025 if 5% is used as significance level in each test. One can, of course, achieve the same thing by applying the 0.25% significance level directly on the full sample, and this would be preferable because the statistical power would be higher, compared to the split procedure. This is because the decision to continue to the second step in the split procedure is determined by the result of a test that only uses half of the data and, thus, has compromised power.

In the example in the Fig. 1 the power is 87% for a test on one half of the full sample using a = 0.05. Using the split procedure the power for two independent sequential tests is therefore (0.87) 2 = 0.76. A test on the full sample with a = 0.0025 has a power of 0.87 which is better than the 0.76 for the split procedure.

When analyzing false positive probabilities it is useful to invoke the Bayesian perspective and to consider the probability that a positive result is false (e.g., that an observed association between gene and disease is due to H. Ka ¨llberg (&) Á L. Alfredsson Á M. Feychting Á A. Ahlbom Institute of Environmental Medicine, Karolinska Institutet, Box 210, 171 77 Stockholm, Sweden e-mail: henrik.kallberg@ki.se chance). This is a Bayesian probability because it requires a priori probabilities for the alternative hypotheses. In the Fig. 1, false positive probabilities are plotted for various prior probabilities. It is apparent that the split procedure (dotted line) always performs worse than the procedure using the full sample (full line). For an a ´priori probability of 0.1%, the probability that a positive result is false, based on previous settings, is 74% for the full sample and 77% for the split procedure.

So far, we have discussed the apparent issue of loss of power and increase of false positive findings when splitting the sample in an attempt to minimize the risk of false positive results. There are, however, other issues that also are important here. One is the risk of false negative results and whether the need of replication put unnecessary hard constrains on new findings. There is a possibility that new and important findings are not published because the results have not been replicated, for instance, if there are no similar data available. This situation often occurs in the context of testing for gene-environment interaction, since few materials comprise information on both genes and environment.

As for replication purposes in terms of scientific validation of new findings there are at present no argument for using the random splitting procedure as a convenient way to replicate new discoveries.

The random splitting is in fact an unnecessary procedure which does not provide any protection against systematic biases such as confounding or selection bias. If there is a difference between the randomly splitted sub samples, it only shows that the randomisation procedure did not work properly. Random splitting of already collected data does not function as a safeguard against systematic biases in the same way as the randomisation procedure takes care of systematic biases in an experimental study or in the same way as new data from a different research group does.

In summary, when the split approach is compared to an analysis of the total sample and when compared for the same level of statistical significance the total sample approach gives a higher statistical power and as a consequence a lower probability that a statistically significant result is false. So the, perhaps intuitively appealing, notion that splitting the sample and use one half for generation of hypotheses and the other for replication appears to have no advantages over the alternative of performing the analyses on the total sample. Indeed, the splitting procedure performs worse and should not be thought of as an alternative to using ''true'' replication from independent studies carried out by independent investigators, populations and by using alternative methods.

Fig. 1

 1 Fig.1Probability of false positive results (y-axis) plotted against prior probabilities (H) for the alternative hypothesis when using split procedure (intermittent line) or using the full sample (full line a = 0.25%, dotted line a = 5%). False positive probability (FPP) was calculated by using: FPP = a(1 -H)/[a(1 -H) ? (1 -b) H] based on 1,000 cases and 1,000 controls, and a = 0.25 and tested against an OR = 1.5

Eur J Epidemiol (2010) 25:283-284 DOI 10.1007/s10654-010-9447-3